Rotation speed determination method, apparatus, device, and storage medium

Abstract

This application relates to a method, apparatus, device, and storage medium for determining rotational speed, and pertains to the field of signal processing technology. The method applies a local cost constraint based on spectral intensity only at a first time point, thus ensuring frequency accuracy at key time points. For second time points other than the first time point, there are no trajectory shape constraints. The target frequency at the second time point is determined entirely through free optimization based on the time-frequency energy ridge. This avoids trajectory jumps caused by noise when unconstrained, and preserves the true nonlinear rotational speed characteristics through time-frequency energy ridge optimization, thereby improving the accuracy of rotational speed determination.

Description

Technical Field

[0001] This application relates to the field of signal processing technology, and in particular to a method, apparatus, device and storage medium for determining rotational speed. Background Technology

[0002] In fault diagnosis of rotating machinery (such as helicopter spindles, aircraft engines, and electric vehicle motors), order analysis is a core technology. Order analysis presupposes the accurate acquisition of the instantaneous rotational speed of the rotating machinery. However, in many practical scenarios, it is impossible to install physical speed sensors (such as tachometers), and the speed must be determined from vibration or acoustic signals through algorithms (i.e., order analysis without a tachometer).

[0003] In related technologies, to prevent noise interference when determining rotational speed, algorithms typically assume that the speed change is smooth and linear. When the user provides prior points, a tubular constraint based on linear interpolation is usually constructed. However, under highly nonlinear conditions such as helicopter run-up, the rotational speed curve may exhibit exponential or higher-order polynomial changes. In this case, the tubular constraint based on linear interpolation will forcibly limit the instantaneous rotational speed to the linear region, causing the actual nonlinear data to fall outside the constraint range, thus leading to inaccurate determined rotational speed. Summary of the Invention

[0004] This application provides a method, apparatus, device, and storage medium for determining rotational speed. The technical solution of this application is as follows.

[0005] According to one aspect of an embodiment of this application, a method for determining rotational speed is provided, the method comprising: The vibration signal of the rotating machinery is obtained from a time-frequency diagram and a constraint frequency at multiple first time points. The time-frequency diagram includes the spectral intensity of the vibration signal at multiple frequencies at multiple time points, and the multiple time points include the multiple first time points. For each first time point, based on the constraint frequency at the first time point and the spectral intensity of the plurality of frequencies at the first time point, the local cost of the plurality of frequencies at the first time point is determined. The local cost of each frequency is used to measure the degree of matching between the frequency and the time-frequency energy ridge of the time-frequency map. For each second time point, based on the spectral intensity of the plurality of frequencies at the second time point, the local cost of the plurality of frequencies at the second time point is determined, wherein the second time point is a time point other than the first time point among the plurality of time points; Based on the local costs of the multiple frequencies at the multiple time points, the target frequencies of the multiple time points are determined respectively, and the target frequency of each time point refers to the frequency selected by the time-frequency energy ridge at the time point. The rotational speed of the rotating machinery at each time point is determined based on the target frequency at that time point.

[0006] In some embodiments, determining the local cost of each of the plurality of frequencies at the first time point, based on the constraint frequency at the first time point and the spectral intensity of the plurality of frequencies at the first time point, includes: For each first time point, based on the spectral intensity and data function of the plurality of frequencies at the first time point, a first sub-cost of the plurality of frequencies at the first time point is determined, wherein the data function is used to constrain the target frequency at the first time point to the vicinity of the frequency with a large spectral intensity. Based on the constraint frequency at the first time point, the plurality of frequencies and the trap function, the second sub-cost of the plurality of frequencies at the first time point is determined respectively, and the trap function is used to constrain the target frequency at the first time point to be near the constraint frequency at the first time point. For each frequency, the local cost of the frequency at the first time point is determined based on the first sub-cost and the second sub-cost of the frequency at the first time point.

[0007] In some embodiments, the trap function includes a trap strength coefficient, the trap strength coefficient being used to constrain the degree of influence of the second sub-cost on the local cost, and the method further includes: For each time point, the potential depression intensity coefficient for that time point is determined based on at least one of the signal-to-noise ratio, local spectral peak contrast, and noise floor estimate of the time-frequency plot at that time point. The local spectral peak contrast is used to indicate the prominence of the peak with the largest spectral intensity at that time point in the time-frequency plot, and the noise floor estimate is used to indicate the overall level of background noise at that time point in the time-frequency plot.

[0008] In some embodiments, for each first time point, if the difference between the frequency with the largest spectral intensity at the first time point in the time-frequency diagram and the constraint frequency is less than a difference threshold, the trap function is a quadratic function; If the difference between the frequency with the largest spectral intensity at the first time point in the time-frequency graph and the constraint frequency is not less than the difference threshold, the trap function is a linear function.

[0009] In some embodiments, determining the target frequency for each of the plurality of time points based on the local costs of the plurality of frequencies at the plurality of time points includes: Based on the local costs of the multiple frequencies at the multiple time points, the minimum cumulative cost of the multiple frequencies at the multiple time points is determined. The minimum cumulative cost of each frequency at each time point is used to measure the degree of matching between the path corresponding to the frequency and the time-frequency energy ridge. The path refers to the frequency path from the first time point of the time-frequency graph to the time point, with the frequency at the time point as the endpoint. The target frequency for each of the multiple time points is determined based on the minimum cumulative cost of the multiple frequencies at the multiple time points.

[0010] In some embodiments, determining the minimum cumulative cost of the plurality of frequencies at the plurality of time points based on the local costs of the plurality of frequencies at the plurality of time points includes: For each time point, based on the minimum cumulative cost of the plurality of frequencies at the previous time point, the transfer cost of each frequency at the time point relative to the plurality of frequencies at the previous time point is determined. The transfer cost of each frequency at the time point relative to the plurality of frequencies at the previous time point refers to the cost of frequency jump when transferring from the plurality of frequencies at the previous time point to the frequency at the time point. The minimum cumulative cost of the plurality of frequencies at the first time point of the time-frequency diagram is the local cost of the plurality of frequencies at the first time point. For each frequency at each time point, the minimum value of the transfer costs of the frequency relative to the plurality of frequencies is determined as the minimum transfer cost of the frequency at that time point. Based on the minimum transfer cost of the frequency at that time point and the local cost, the minimum cumulative cost of the frequency at that time point is determined.

[0011] In some embodiments, determining the transfer cost of each frequency at the time point relative to the plurality of frequencies at the previous time point, based on the minimum cumulative cost of the plurality of frequencies at the previous time point, includes: For each frequency at the time point, a smoothing cost is determined between the frequency and multiple frequencies at the previous time point based on a smoothing function, wherein the smoothing function is used to constrain the smoothness of the time-frequency energy ridge. Based on the minimum cumulative cost of the plurality of frequencies at the previous time point and the smoothing cost between the frequencies and the plurality of frequencies, the transfer cost of the frequency at the time point relative to the plurality of frequencies at the previous time point is determined.

[0012] In some embodiments, the smoothing function includes a smoothing coefficient, the smoothing coefficient being used to constrain the degree of influence of the smoothing cost on the transition cost; the method further includes: The smoothing coefficient is determined based on the degree of interference from the interfering factors in the time-frequency graph.

[0013] In some embodiments, the target frequency at the last time point among the plurality of time points is the frequency corresponding to the minimum value among the plurality of minimum cumulative costs of the plurality of frequencies at the last time point, and determining the target frequency for each of the plurality of time points based on the minimum cumulative costs of the plurality of frequencies at the plurality of time points includes: Starting from the target frequency at the last time point, the transfer frequency corresponding to the target frequency at each time point is determined as the target frequency of the previous time point. The transfer frequency refers to the frequency corresponding to the minimum transfer cost from multiple frequencies at the previous time point to the target frequency at the current time point.

[0014] In some embodiments, the plurality of first time points includes the first time point and the last time point among the plurality of time points.

[0015] According to another aspect of the embodiments of this application, a speed determining device is provided, the device comprising: The acquisition module is used to acquire the time-frequency diagram of the vibration signal of the rotating machinery and the constraint frequencies at multiple first time points. The time-frequency diagram includes the spectral intensity of the vibration signal at multiple frequencies at multiple time points, and the multiple time points include the multiple first time points. The determination module is used to determine the local cost of the plurality of frequencies at the first time point for each first time point, based on the constraint frequency at the first time point and the spectral intensity of the plurality of frequencies at the first time point respectively. The local cost of each frequency is used to measure the degree of matching between the frequency and the time-frequency energy ridge of the time-frequency diagram. The determining module is further configured to, for each second time point, determine the local cost of the plurality of frequencies at the second time point based on the spectral intensity of the plurality of frequencies at the second time point, wherein the second time point is a time point other than the first time point among the plurality of time points; The determining module is further configured to determine the target frequency of each of the multiple time points based on the local cost of the multiple frequencies at the multiple time points respectively, wherein the target frequency of each time point refers to the frequency selected by the time-frequency energy ridge at the time point; The determining module is also used to determine the rotational speed of the rotating machinery at each time point based on the target frequency at each time point.

[0016] In some embodiments, the determining module is configured to: For each first time point, based on the spectral intensity and data function of the plurality of frequencies at the first time point, a first sub-cost of the plurality of frequencies at the first time point is determined, wherein the data function is used to constrain the target frequency at the first time point to the vicinity of the frequency with a large spectral intensity. Based on the constraint frequency at the first time point, the plurality of frequencies and the trap function, the second sub-cost of the plurality of frequencies at the first time point is determined respectively, and the trap function is used to constrain the target frequency at the first time point to be near the constraint frequency at the first time point. For each frequency, the local cost of the frequency at the first time point is determined based on the first sub-cost and the second sub-cost of the frequency at the first time point.

[0017] In some embodiments, the potential trap function includes a potential trap strength coefficient, which is used to constrain the degree of influence of the second sub-cost on the local cost, and the determining module is further configured to: For each time point, the potential depression intensity coefficient for that time point is determined based on at least one of the signal-to-noise ratio, local spectral peak contrast, and noise floor estimate of the time-frequency plot at that time point. The local spectral peak contrast is used to indicate the prominence of the peak with the largest spectral intensity at that time point in the time-frequency plot, and the noise floor estimate is used to indicate the overall level of background noise at that time point in the time-frequency plot.

[0018] In some embodiments, for each first time point, if the difference between the frequency with the largest spectral intensity at the first time point in the time-frequency diagram and the constraint frequency is less than a difference threshold, the trap function is a quadratic function; If the difference between the frequency with the largest spectral intensity at the first time point in the time-frequency graph and the constraint frequency is not less than the difference threshold, the trap function is a linear function.

[0019] In some embodiments, the determining module is configured to: Based on the local costs of the multiple frequencies at the multiple time points, the minimum cumulative cost of the multiple frequencies at the multiple time points is determined. The minimum cumulative cost of each frequency at each time point is used to measure the degree of matching between the path corresponding to the frequency and the time-frequency energy ridge. The path refers to the frequency path from the first time point of the time-frequency graph to the time point, with the frequency at the time point as the endpoint. The target frequency for each of the multiple time points is determined based on the minimum cumulative cost of the multiple frequencies at the multiple time points.

[0020] In some embodiments, the determining module is configured to: For each time point, based on the minimum cumulative cost of the plurality of frequencies at the previous time point, the transfer cost of each frequency at the time point relative to the plurality of frequencies at the previous time point is determined. The transfer cost of each frequency at the time point relative to the plurality of frequencies at the previous time point refers to the cost of frequency jump when transferring from the plurality of frequencies at the previous time point to the frequency at the time point. The minimum cumulative cost of the plurality of frequencies at the first time point of the time-frequency diagram is the local cost of the plurality of frequencies at the first time point. For each frequency at each time point, the minimum value of the transfer costs of the frequency relative to the plurality of frequencies is determined as the minimum transfer cost of the frequency at that time point. Based on the minimum transfer cost of the frequency at that time point and the local cost, the minimum cumulative cost of the frequency at that time point is determined.

[0021] In some embodiments, the determining module is configured to: For each frequency at the time point, a smoothing cost is determined between the frequency and multiple frequencies at the previous time point based on a smoothing function, wherein the smoothing function is used to constrain the smoothness of the time-frequency energy ridge. Based on the minimum cumulative cost of the plurality of frequencies at the previous time point and the smoothing cost between the frequencies and the plurality of frequencies, the transfer cost of the frequency at the time point relative to the plurality of frequencies at the previous time point is determined.

[0022] In some embodiments, the smoothing function includes a smoothing coefficient, which is used to constrain the degree to which the smoothing cost affects the transition cost; the determining module is further configured to: The smoothing coefficient is determined based on the degree of interference from the interfering factors in the time-frequency graph.

[0023] In some embodiments, the target frequency of the last time point among the plurality of time points is the frequency corresponding to the minimum value among the plurality of minimum cumulative costs at the last time point, and the determining module is configured to: Starting from the target frequency at the last time point, the transfer frequency corresponding to the target frequency at each time point is determined as the target frequency of the previous time point. The transfer frequency refers to the frequency corresponding to the minimum transfer cost from multiple frequencies at the previous time point to the target frequency at the current time point.

[0024] In some embodiments, the plurality of first time points includes the first time point and the last time point among the plurality of time points.

[0025] According to another aspect of the embodiments of this application, a computer device is provided, the computer device comprising: processor; Memory used to store the processor's executable instructions; The processor is configured to execute the instructions to implement the above-described speed determination method.

[0026] According to another aspect of the embodiments of this application, a computer-readable storage medium is provided, which, when the instructions in the computer-readable storage medium are executed by a processor of a computer device, enables the computer device to perform the above-described speed determination method.

[0027] According to another aspect of the embodiments of this application, a computer program product is provided, the computer program product including a computer program, which, when executed by a processor, implements the above-described speed determination method.

[0028] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application.

[0029] This application provides a method for determining rotational speed. This method applies a local cost constraint based on spectral intensity only at the first time point, thus ensuring the frequency accuracy at the key time point. There are no trajectory shape constraints for the second time point other than the first time point. The target frequency at the second time point is determined entirely by free optimization based on the time-frequency energy ridge. This avoids trajectory jumps caused by noise when there are no constraints, and retains the true nonlinear rotational speed characteristics through optimization of the time-frequency energy ridge, thereby improving the accuracy of rotational speed determination. Attached Figure Description

[0030] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application, and do not constitute an undue limitation of this application.

[0031] Figure 1 This is a schematic diagram illustrating an implementation environment according to an exemplary embodiment.

[0032] Figure 2 This is a flowchart illustrating a method for determining rotational speed according to an exemplary embodiment.

[0033] Figure 3 This is a flowchart illustrating a method for determining rotational speed according to an exemplary embodiment.

[0034] Figure 4 This is a flowchart illustrating a method for determining a time-frequency amplitude matrix according to an exemplary embodiment.

[0035] Figure 5 This is a flowchart illustrating a method for determining a time-frequency amplitude matrix according to an exemplary embodiment.

[0036] Figure 6 This is a flowchart illustrating a method for determining a time-frequency amplitude matrix according to an exemplary embodiment.

[0037] Figure 7 This is a flowchart illustrating a method for determining a time-frequency amplitude matrix according to an exemplary embodiment.

[0038] Figure 8 This is a flowchart illustrating a frequency correction method according to an exemplary embodiment.

[0039] Figure 9 This is a flowchart illustrating a frequency correction method according to an exemplary embodiment.

[0040] Figure 10 This is a block diagram illustrating a speed determining device according to an exemplary embodiment.

[0041] Figure 11 This is a schematic diagram of the structure of a terminal according to an exemplary embodiment.

[0042] Figure 12 This is a schematic diagram of the structure of a server according to an exemplary embodiment. Detailed Implementation

[0043] To enable those skilled in the art to better understand the technical solutions of this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.

[0044] It should be noted that the terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0045] It should be noted that all information (including but not limited to user device information, user personal information, etc.), data (including but not limited to data used for analysis, stored data, displayed data, etc.), and signals involved in this application have been authorized by the user or fully authorized by all parties, and the collection, use, and processing of related data must comply with the relevant laws, regulations, and standards of the relevant countries and regions. For example, the vibration signals involved in this application were obtained with full authorization.

[0046] The rotational speed determination method provided in this application can be executed by a computer device, which can be at least one of a terminal and a server. The following is a schematic diagram illustrating the implementation environment of the rotational speed determination method provided in this application. See also... Figure 1 , Figure 1 This is a schematic diagram of an implementation environment provided in an embodiment of this application. The implementation environment includes: terminal 101 and server 102.

[0047] In some embodiments, terminal 101 may run a client application with a target application, which provides the function of determining the instantaneous rotational speed of rotating machinery in real time or offline based on vibration sound signals. This application embodiment does not limit the implementation form of the target application; for example, it may be an application that requires downloading and installation, a mini-program that does not require installation, a web application, etc.

[0048] In this embodiment, terminal 101 can be installed at one or more monitoring locations on rotating machinery to acquire vibration signals from the rotating machinery. Server 102 provides background services for the target application. After acquiring the vibration signals from the rotating machinery, terminal 101 transmits the vibration signals to server 102. Server processes the vibration signals into a time-frequency graph, and then determines the frequency of each time point on the time-frequency energy ridge based on the time-frequency graph, and sends the frequency to terminal 101 for output.

[0049] In other embodiments, the terminal 101 itself may also acquire the vibration signal of the rotating machinery and process the vibration signal into a time-frequency diagram, and then determine the frequency of each time point on the time-frequency energy ridge based on the time-frequency diagram.

[0050] Terminal 101 can be a computer device such as a vibration sensor with signal processing and output display functions, a mobile phone, a tablet computer, a multimedia playback device, a PC (Personal Computer), a wearable device, a VR (Virtual Reality) device, an AR (Augmented Reality) device, or a MR (Mixed Reality) device. Server 102 can be a standalone physical server, a server cluster consisting of multiple physical servers, or a distributed file system. It can also be a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN (Content Delivery Network), and big data and artificial intelligence platforms. Server 102 and terminal 101 are directly or indirectly connected via wired or wireless communication.

[0051] Figure 2This is a flowchart illustrating a method for determining rotational speed according to an exemplary embodiment, such as... Figure 2 As shown, the method is performed by a computer device and includes at least one of the following steps.

[0052] 201. Obtain the time-frequency diagram of the vibration signal of the rotating machinery and the constraint frequencies at multiple first time points. The time-frequency diagram includes the spectral intensity of the vibration signal at multiple frequencies at multiple time points, and the multiple time points include multiple first time points.

[0053] Rotating machinery can be mechanical equipment with rotating parts, such as helicopter spindles, aircraft engines, electric vehicle motors, steam turbines, and compressors. Rotating machinery works by rotating motion and generates vibration signals during operation. Vibration signals are often used for condition monitoring and fault diagnosis of rotating machinery.

[0054] In this time-frequency graph, the horizontal axis represents time, and the vertical axis represents vibration amplitude. The vibration signal can be acquired by a vibration sensor installed on the rotating machinery. The horizontal axis of the time-frequency graph represents time, and the vertical axis represents frequency; the color intensity of each coordinate point represents the spectral intensity. Optionally, a short-time Fourier transform (STFT) can be performed on the vibration signal to obtain the time-frequency graph.

[0055] Optionally, a short-time Fourier transform is performed on the vibration signal to obtain the time-frequency amplitude matrix, and then a time-frequency diagram is obtained based on the time-frequency amplitude matrix. The multiple columns of the time-frequency amplitude matrix correspond to multiple time points, and the multiple rows correspond to multiple frequencies. Therefore, one element in the time-frequency amplitude matrix represents the time-frequency distribution amplitude of the vibration signal at a specific frequency at a given time point. The square of the absolute value of the time-frequency distribution amplitude is also known as the spectral intensity. It should be noted that multiple frequencies at different time points are the same, meaning that each frequency corresponds to a spectral intensity at each time point.

[0056] Each initial time point and its constrained frequency constitute a priori point, also known as an anchor point, used to constrain the target frequency at key time points. The number and specific timing of multiple priori points can be set as needed and are not specifically limited here.

[0057] It should be noted that in the short-time Fourier transform, the continuous vibration signal is divided into multiple frames for processing. Its time domain is continuous time, measured in seconds. After framing, the time dimension is discretized into frame indices. Therefore, the time axis of the time-frequency diagram is composed of discrete frame numbers; that is, each time point on the horizontal axis corresponds to a frame number, and thus a fixed-length time interval, used to characterize the time-frequency energy distribution of the vibration signal within that time period. The time interval between adjacent frames is determined by the frame shift (Hop Size). Based on the frame shift, continuous absolute time can be mapped to discrete frame numbers; that is, the frame number is the ratio of absolute time to the frame shift. When the absolute time of a priori points is not precisely aligned with the discrete frame number, the constraint frequencies of the priori points need to be mapped to the corresponding frames. This can be achieved using nearest neighbor mapping or linear interpolation weighted mapping. When using nearest neighbor mapping, the constraint frequencies of the priori points are directly assigned to the frame with the closest time. When using linear interpolation weighted mapping, the weights are calculated based on the absolute time of the prior point and the time distance between two adjacent frames, and the constraint effect of the prior point is smoothly distributed to the two adjacent frames, so that the constraint effect of the prior point is continuously transitioned in the time dimension.

[0058] 202. For each first time point, based on the constraint frequency at the first time point and the spectral intensity of multiple frequencies at the first time point, determine the local cost of multiple frequencies at the first time point. The local cost of each frequency is used to measure the degree of matching between the frequency and the time-frequency energy ridge of the time-frequency map.

[0059] Among them, the Constraint frequency at each time point Based on prior points rotational speed get, Indicates a point in time. This represents the rotational speed corresponding to the fundamental frequency. There is a corresponding relationship between the constraint frequency and the rotational speed, as shown in the formula: , Indicates the constraint frequency. Indicates the harmonic order to be tracked, when The fundamental frequency of the corresponding axis is the constraint frequency, which is also the constraint frequency corresponding to the fundamental frequency. In this embodiment, only the fundamental frequency is used. Taking this as an example, the harmonic order can also be other values, such as... Then the corresponding axis's 2nd harmonic, Then the k-th harmonic of the corresponding axis.

[0060] The time-frequency energy ridge refers to the frequency path formed by the highest energy frequency at each time point on the time-frequency graph. It is the optimal trajectory reflecting the change of the fundamental frequency vibration component of rotating machinery over time, and it corresponds to the bright fringe with the most concentrated and continuous energy on the time-frequency graph. Due to the fixed correspondence between frequency and rotational speed mentioned above, the time-frequency energy ridge also corresponds to the actual instantaneous rotational speed trajectory of machinery in the physical world.

[0061] It should be noted that while time-frequency energy ridges are clear and accurate in ideal clean data, they are not accurate due to interference from noise, weak energy segments, and multi-peak ambiguity. Therefore, constraints and costs must be introduced to combat these interferences in order to extract accurate time-frequency energy ridges. Accordingly, the time-frequency energy ridges mentioned in this application refer to the accurate time-frequency energy ridges to be extracted, not the original time-frequency energy ridges.

[0062] Local cost is used to measure the degree of matching between a frequency and the time-frequency energy ridge line of the time-frequency plot; in other words, local cost is a quantified value used to measure the degree of matching. Local cost is negatively correlated with the degree of matching; that is, the smaller the local cost, the greater the degree of matching. The target frequency at each time point on the time-frequency energy ridge line is the frequency to be determined, and the local cost of each frequency at each time point is used to measure the degree of matching between that frequency and the frequency of the time-frequency energy ridge line at that time point. Accordingly, the smaller the local cost of any frequency at that time point, the greater the probability that the time-frequency energy ridge line selects that frequency as the target frequency at that time point.

[0063] In this embodiment, by constraining the frequency, when the time-frequency energy ridge line is inaccurate due to data ambiguity or multiple peaks in the time-frequency graph, the constrained frequency tells the algorithm that the true rotational speed at this time point is near the constrained frequency, thus preventing the rotational speed from being skewed by noise and harmonics. Furthermore, by applying a local potential well through the constrained frequency only at the first time point among multiple time points, the time points between the first time points can freely fit the time-frequency energy ridge line, preserving the reliability of the constraint while avoiding the rigidity of the linear assumption.

[0064] 203. For each second time point, based on the spectral intensity of multiple frequencies at the second time point, determine the local cost of multiple frequencies at the second time point. The second time point is a time point other than the first time point among multiple time points.

[0065] The multiple time points include a first time point with a given constraint frequency and a second time point without a given constraint frequency. The number of first time points can be set as needed. Optionally, the number of first time points is less than a preset threshold, that is, the number of first time points is relatively small.

[0066] 204. Based on the local costs of multiple frequencies at multiple time points, determine the target frequencies for each of the multiple time points. The target frequency for each time point refers to the frequency selected by the time-frequency energy ridge at that time point.

[0067] In this embodiment, the frequency path formed by the target frequencies at multiple time points is also the time-frequency energy ridge on the time-frequency diagram, that is, the target frequency at each time point is the instantaneous frequency at that time point. Due to the fixed correspondence between frequency and rotational speed, the target frequency at each time point is also the instantaneous rotational speed of the rotating machinery at that time point.

[0068] 205. Determine the rotational speed of the rotating machinery at each time point based on the target frequency at that time point.

[0069] There is a corresponding relationship between frequency and rotational speed, as shown in step 202. Therefore, based on this correspondence and the target frequency, the rotational speed can be obtained.

[0070] It should be noted that the method provided in this application embodiment can be applied to offline analysis scenarios of rotating machinery rotation speed, as well as real-time analysis scenarios of rotating machinery rotation speed. For example, real-time analysis can be achieved by estimating a sliding time window / fixed time delay window.

[0071] This application provides a method for determining rotational speed. This method applies a local cost constraint based on spectral intensity only at the first time point, thus ensuring the frequency accuracy at the key time point. There are no trajectory shape constraints for the second time point other than the first time point. The target frequency at the second time point is determined entirely by free optimization based on the time-frequency energy ridge. This avoids trajectory jumps caused by noise when there are no constraints, and retains the true nonlinear rotational speed characteristics through optimization of the time-frequency energy ridge, thereby improving the accuracy of rotational speed determination.

[0072] The above Figure 2 The diagram shown is merely the basic flow of this application. The following section, based on a specific implementation method, further elaborates on the solution provided in this application. See also... Figure 3 , Figure 3 This is a flowchart illustrating a rotational speed determination method according to an exemplary embodiment, the method being performed by a computer device, the method comprising at least one of the following steps.

[0073] 301. Obtain the time-frequency diagram of the vibration signal of the rotating machinery and the constraint frequencies of multiple first time points. The time-frequency diagram includes the spectral intensity of the vibration signal at multiple frequencies at multiple time points, and the multiple time points include multiple first time points.

[0074] In this embodiment, step 301 is the same as step 201, and will not be described again here.

[0075] 302. For each first time point, based on the constraint frequency at the first time point and the spectral intensity of multiple frequencies at the first time point, determine the local cost of multiple frequencies at the first time point. The local cost of each frequency is used to measure the degree of matching between the frequency and the time-frequency energy ridge of the time-frequency map.

[0076] In some embodiments, the process of determining the local cost of multiple frequencies at each first time point based on the constraint frequency at the first time point and the spectral intensities of multiple frequencies at the first time point includes the following implementation: for each first time point, determining the first sub-cost of multiple frequencies at the first time point based on the spectral intensities of multiple frequencies at the first time point and a data function, wherein the data function is used to constrain the target frequency at the first time point to a frequency with a large spectral intensity; determining the second sub-cost of multiple frequencies at the first time point based on the constraint frequency at the first time point, multiple frequencies, and a potential trap function, wherein the potential trap function is used to constrain the target frequency at the first time point to a frequency near the constraint frequency at the first time point; and determining the local cost of each frequency at the first time point based on the first sub-cost and the second sub-cost of that frequency at the first time point.

[0077] Optionally, the process of determining the local cost of the frequency at the first time point based on the first sub-cost and the second sub-cost at the first time point includes the following implementation methods: determining the sum of the first sub-cost and the second sub-cost as the local cost; or, performing a weighted summation of the first sub-cost and the second sub-cost to obtain the local cost, wherein the weights of the first sub-cost and the second sub-cost can be set as needed.

[0078] For example, local cost can be expressed by the following formula (1): (1); in, Indicates a point in time. To represent frequency, then Represents frequency At the point of time Local cost, Represents frequency At the point of time The first cost, Represents frequency At the point of time The second sub-cost, for the second time point, is... .

[0079] In this embodiment, the first sub-cost is constructed based on spectral intensity, which restricts the target frequency to high-energy frequencies, ensuring that the frequency selection closely matches the true physical characteristics of the vibration signal and avoiding deviations caused by purely prior constraints that deviate from actual data. The second sub-cost is determined based on the constraint frequency of the prior point, which confines the target frequency to the vicinity of the constraint frequency. This helps to combat problems such as spectral peak blurring and multi-peak ambiguity caused by noise, harmonics, and other interference, preventing the frequency corresponding to the prior point from deviating. Combining the first and second sub-costs ensures that the local cost of the prior point neither blindly follows spurious spectral peaks caused by noise interference nor forcibly adheres to the prior point while ignoring real data, thus guaranteeing the accuracy of the determined target frequency.

[0080] In the data function, the first sub-cost is negatively correlated with the spectral intensity; that is, the greater the spectral intensity, the greater the first sub-cost. The data function can be set as needed, as shown in the following formula (2): (2); in, Indicates the cost of the first sub-sub. Indicates a point in time A frequency, Represents frequency At the point of time The time-frequency distribution amplitude, Represents frequency At the point of time Spectral intensity.

[0081] The trap function can be set as needed. Optionally, the trap function includes a trap strength coefficient, which is used to constrain the degree of influence of the second sub-cost on the local cost. The trap strength coefficient is positively correlated with the degree of influence, that is, the larger the trap strength coefficient, the greater the degree of influence of the second sub-cost on the local cost. The trap function is shown in the following formula (3): (3); in, Indicates the first The first point in time Indicates the first A frequency at a first point in time. Represents frequency At the point of time The second cost, Indicates a point in time The constraint frequency, This indicates the frequency resolution of the time-frequency plot, used to normalize the frequency deviation. This represents the potential depression strength coefficient, which is generally set to be sufficiently large (e.g., ), to ensure the path is at the point in time It is forcibly captured near the prior point, overcoming local noise and interference at that location.

[0082] In some embodiments, for each time point, the potential depression intensity coefficient at that time point is determined based on at least one of the signal-to-noise ratio of the time-frequency plot at that time point, the local spectral peak contrast, and the noise floor estimate. The local spectral peak contrast is used to indicate the prominence of the peak with the largest spectral intensity at that time point in the time-frequency plot, and the noise floor estimate is used to indicate the overall level of background noise in the time-frequency plot.

[0083] The local peak contrast is the ratio of the maximum spectral intensity to the second-largest spectral intensity at that time point. A higher local peak contrast indicates a more prominent main peak and a clearer signal; a lower local peak contrast indicates stronger multi-peak interference and makes the rotational speed peak more difficult to distinguish. The noise floor estimate is the statistical average or median of the spectral intensity of the remaining frequencies at the same time point in the time-frequency graph, after excluding several significant spectral peaks with high spectral intensity at that time point. It characterizes the overall level of background noise at the current time point.

[0084] Optionally, the potential well strength coefficient is positively correlated with the signal-to-noise ratio (SNR), meaning that the higher the SNR, the larger the potential well strength coefficient. This makes frequencies near the prior point more reliable, thus more forcefully pulling the path towards the prior point. The potential well strength coefficient is also positively correlated with the local spectral peak contrast, meaning that the greater the local spectral peak contrast, the larger the potential well strength coefficient. This makes the spectral peak of the target frequency more prominent relative to the background, making it more suitable for strong constraints. Conversely, low local spectral peak contrast reduces the potential well strength coefficient to avoid locking the path at unreliable frequencies. The potential well strength coefficient is negatively correlated with the noise floor estimate, meaning that the greater the noise floor estimate, the smaller the potential well strength coefficient. This results in greater noise, making the prior point more likely to be inaccurate or contaminated by interfering peaks. Consequently, the constraint effect of the local potential well should be weaker, allowing the global path to rely more on the path's continuity and smoothness.

[0085] In this embodiment, the potential well intensity coefficient is adaptively adjusted based on time-frequency quality indicators such as signal-to-noise ratio, local spectral peak contrast, and noise floor estimation. This achieves a dynamic balance between prior point constraints and time-frequency energy ridges. In other words, when interference is severe, the constraints based on prior points are strengthened to prevent path deviation, while when the signal is clear, the constraints of prior points are weakened to adapt to strong nonlinear speed changes. This improves the robustness of instantaneous speed extraction and reduces the dependence on dense prior points.

[0086] There are various types of trap functions, and different function forms can be used depending on the actual noise distribution in different scenarios. Traps functions can be parabolic, Gaussian, quadratic, linear, etc.

[0087] For example, the potential trap function of a parabolic shape is shown in the following formula (4): (4); in, Indicates the cost of the second sub-sub. Indicates the potential depression strength coefficient. Indicates the current frequency. The constraint frequency is represented. The parabolic trap function is the basic form of the trap function, which is computationally efficient and suitable for scenarios with good signal-to-noise ratio.

[0088] For example, the Gaussian trap function is shown in the following formula (5): (5); in, Indicates the cost of the second sub-sub. Indicates the potential depression strength coefficient. Indicates the current frequency. Indicates the constraint frequency. This represents the noise variance. A Gaussian trap function creates a deep trap at the prior point, resulting in a strong constraint. As the frequency deviates further from the constraint frequency at the prior point, the trap strength rapidly decays and approaches zero, avoiding unnecessary global strain on paths far from the prior point. Therefore, this trap function is suitable for scenarios where it is undesirable for the prior point to have an excessively strong or far-reaching impact on the entire path.

[0089] In some embodiments, the trap function can also be a piecewise robust function, which can include the following implementation: for each first time point, if the difference between the frequency with the largest spectral intensity at the first time point in the time-frequency graph and the constraint frequency is less than the difference threshold, the trap function is a quadratic function; if the difference between the frequency with the largest spectral intensity at the first time point in the time-frequency graph and the constraint frequency is not less than the difference threshold, the trap function is a linear function.

[0090] The quadratic and linear potential trap functions can be set as needed and are not specifically limited here. For example, the quadratic function can be a parabolic function and the linear function can be a straight line function.

[0091] The frequency with the highest spectral intensity is The constraint frequency is Taking an example as an illustration, then When using a quadratic trap function, When using a linear trap function, The threshold value represents the segmented threshold in this piecewise robust trap function, used to distinguish whether the frequency with the highest spectral intensity is close to or far from the prior point. This scheme effectively reduces the error of the prior point input by the user, such as mitigating the negative impact of slight deviations in the prior point on path planning and preventing path collapse caused by outlier prior points. This scheme is applicable to various scenarios, such as when manually annotating prior points is inaccurate or has recognition errors, leading to potentially off-target or outlier points, but the guiding role of the prior point is still desired. Another example is when there is high noise or interference peaks near the prior point, causing the frequency with the highest local spectral intensity to not necessarily be the target frequency. Yet another example is when it is desirable to both bring the path back near the prior point and prevent a single incorrect prior point from causing a global path error.

[0092] In this embodiment, the quadratic trap function penalizes small deviations gently and precisely. The closer the frequency is to the constraint frequency, the faster the cost decreases, accurately constraining the target frequency to near the constraint frequency while allowing for minor deviations, such as natural fluctuations in the spectral peak. Furthermore, the quadratic trap function does not force the frequency to be exactly equal to the constraint frequency, thus preserving the fit with the true spectral peak and preventing the path from deviating from the time-frequency energy ridge due to small errors in prior point labeling. In contrast, the linear trap function provides linearly controllable penalty for large deviations, avoiding the exponential increase in cost caused by excessive deviations in the quadratic trap function. This balances the constraint strength with path flexibility, resulting in greater robustness.

[0093] In some embodiments, given prior points may be abnormal. Optionally, prior points that exceed the time range of the time-frequency diagram can be directly ignored, while prior points that deviate significantly from the local spectral peaks can be controlled by weight reduction, which means reducing the potential trap strength coefficient.

[0094] In some embodiments, the multiple first time points include the first time point and the last time point among multiple time points. By setting the signal start point and the signal end point as prior points, dual constraints can be provided for dynamic path optimization. The prior of the start point is used to determine the initial frequency reference to ensure the stability of the initial segment of the path, while the prior of the end point is used to constrain the frequency at the end of the path to avoid drift at the tail of the signal due to energy reduction. Thus, the constraints at the start and end together form a closed frequency search interval, making the speed extraction result more robust and accurate.

[0095] Furthermore, since this embodiment requires only a small number of prior points to accurately track rotational speed curves of arbitrary shapes, such as exponential growth and S-shaped curves, it exhibits extremely strong nonlinear adaptability. Users do not need to manually mark dense prior points to indicate the shape of the constraint path, reducing labor costs and improving efficiency. Moreover, in a set of nonlinear acceleration signal examples, this method can still stably obtain rotational speed curves even with only sparse prior points, and the average error remains at a low level. Clearly, this method can extract accurate rotational speeds using only sparse prior points.

[0096] 303. For each second time point, based on the spectral intensity of multiple frequencies at the second time point, determine the local cost of multiple frequencies at the second time point. The second time point is a time point other than the first time point among the multiple time points.

[0097] In this embodiment of the application, since there is no frequency constraint at the second time point, optionally, the process of determining the local cost of multiple frequencies at the second time point based on the spectral intensity of multiple frequencies at the second time point includes the following steps: determining the first sub-cost of multiple frequencies at the second time point based on the spectral intensity and data function of multiple frequencies at the second time point, and determining the first sub-cost of each frequency at the second time point as the local cost of that frequency at the second time point. The data function and the first sub-cost mentioned here are described in the relevant section of step 302, and will not be repeated here.

[0098] 304. Based on the local costs of multiple frequencies at multiple time points, determine the minimum cumulative cost of multiple frequencies at multiple time points. The minimum cumulative cost of each frequency at each time point is used to measure the degree of matching between the path corresponding to that frequency and the time-frequency energy ridge. The path refers to the frequency path from the first time point of the time-frequency map to that time point, with the frequency at that time point as the endpoint.

[0099] The frequency path consists of multiple frequencies; that is, from the first time point to the current time point, one frequency is taken at each time point, and the path is formed by these frequencies. It should be noted that the multiple frequencies corresponding to different time points are the same, that is, each frequency has a minimum cumulative cost at each time point.

[0100] In some embodiments, the process of determining the minimum cumulative cost of multiple frequencies at multiple time points based on the local costs of multiple frequencies at multiple time points includes the following implementation: For each time point, based on the minimum cumulative cost of multiple frequencies at the previous time point, the transfer cost of each frequency at that time point relative to the multiple frequencies at the previous time point is determined. The transfer cost of each frequency at each time point relative to the multiple frequencies at the previous time point refers to the cost generated by the frequency jump when transferring from the multiple frequencies at the previous time point to the frequency at that time point. The minimum cumulative cost of multiple frequencies at the first time point of the time-frequency diagram is the local cost of multiple frequencies at the first time point. For each frequency at each time point, the minimum value among the transfer costs of that frequency relative to the multiple frequencies is determined as the minimum transfer cost of that frequency at that time point. Based on the minimum transfer cost and the local cost of that frequency at that time point, the minimum cumulative cost of that frequency at that time point is determined.

[0101] Optionally, the process of determining the minimum cumulative cost of a frequency at a given time point based on the minimum transfer cost and local cost of that frequency at that time point includes the following implementation methods: determining the sum of the minimum transfer cost and local cost of that frequency at that time point as the minimum cumulative cost of that frequency at that time point; or, performing a weighted summation of the minimum transfer cost and local cost of that frequency at that time point to obtain the minimum cumulative cost of that frequency at that time point. The weights of the minimum transfer cost and local cost can be set as needed.

[0102] In this embodiment, for ease of description, the time point is referred to as... ,frequency The corresponding minimum cumulative cost is defined as Local cost is defined as... The local cost is shown in formula (1).

[0103] For the first time point, since there is no minimum cumulative cost from the previous time point, the local cost of each frequency at the first time point is determined as the minimum cumulative cost of that frequency at the first time point, which can be expressed as: , Indicates the number of multiple frequencies. It can be any of multiple frequencies.

[0104] In this embodiment, for the current frequency, the transition cost between it and all frequencies at the previous time point is first calculated. Then, the minimum transition cost is taken, and combined with the current local cost, the globally optimal cumulative cost from the starting point to the current frequency is obtained. This ensures that each step selects the historically optimal path, guaranteeing that the final path is the path with the minimum cost globally, rather than a fragmented path pieced together from local optima. Furthermore, by recursively calculating the minimum cumulative cost point by time point and taking only the minimum transition cost at each time point, this embodiment only requires calculating the frequency transitions at adjacent time points, thus reducing computational complexity.

[0105] In some embodiments, the process of determining the transfer cost of each frequency at a given time point relative to the multiple frequencies at the previous time point based on the minimum cumulative cost of the multiple frequencies at the previous time point includes the following implementation: for each frequency at that time point, determining the smoothing cost between the frequency and the multiple frequencies at the previous time point based on a smoothing function, wherein the smoothing function is used to constrain the smoothness of the time-frequency energy ridge; and determining the transfer cost of the frequency at that time point relative to the multiple frequencies at the previous time point based on the minimum cumulative cost of the multiple frequencies at the previous time point and the smoothing cost between the frequency and the multiple frequencies.

[0106] In this embodiment, a smoothing cost is introduced into the transfer cost. The core function of the smoothing cost is to penalize frequency jumps. The larger the jump amplitude, the higher the smoothing cost and the higher the transfer cost. This conforms to the physical law that the rotational speed in rotating machinery is continuously changing, and avoids meaningless instantaneous jumps in the target frequency. Therefore, even if the frequency with the lowest local cost deviates from the time-frequency energy ridge line due to noise at a certain time point, the smoothing function will reject this jump through the high transfer cost, thereby forcing the path back to the smooth trend of the time-frequency energy ridge line, ensuring the accuracy of the determined target frequency.

[0107] The smoothing function can be set as needed, as shown in the following formula (6): (6); in, Indicates the smoothing cost. Represents the smoothing coefficient. Indicates a point in time frequency, Indicates a point in time The frequency.

[0108] In some embodiments, the process of determining the transfer cost of a frequency at a given time point relative to the multiple frequencies at the previous time point based on the minimum cumulative cost of the multiple frequencies at the previous time point and the smoothing cost between the frequency and the multiple frequencies can include the following implementation: for each frequency at the given time point, the sum or weighted sum of the transfer cost of the frequency relative to each frequency at the previous time point and the smoothing cost between the two frequencies is determined as the transfer cost of the frequency relative to each frequency at the previous time point.

[0109] The transfer cost can be expressed as: , Indicates the current time point The frequency k, Indicates the previous time point frequency , This represents the smoothing cost between two frequencies. Represents frequency At the previous point in time The minimum cumulative cost. The minimum transfer cost can be expressed as: .

[0110] For example, for the frequency k at the current time point, the minimum cumulative costs of multiple frequencies j1, j2, and j3 at the previous time point are D1, D2, and D3, respectively, and the smoothing costs between frequency k and multiple frequencies j1, j2, and j3 are B1, B2, and B3, respectively. Then, the transfer cost of frequency k relative to frequency j1 at the previous time point is the sum of D1 and B1, C1; the transfer cost of frequency k relative to frequency j2 at the previous time point is the sum of D2 and B2, C2; and the transfer cost of frequency k relative to frequency j3 at the previous time point is the sum of D3 and B3, C3.

[0111] Accordingly, the minimum value among C1, C2 and C3 is determined as the minimum transfer cost of frequency k at the current time point.

[0112] Alternatively, the minimum cumulative cost for each frequency at each time point can be expressed by the following formula (7): (7); in, Represents frequency At the point of time The minimum cumulative cost, Represents frequency At the point of time Local cost, Represents frequency At the point of time The minimum transfer cost.

[0113] In some embodiments, the smoothing function includes a smoothing coefficient, which is used to constrain the effect of the smoothing cost on the transfer cost, i.e., to suppress abrupt changes in the path; the smoothing coefficient can also be determined based on the degree of interference from interfering factors in the time-frequency plot. Interfering factors include, but are not limited to, at least one of all interfering factors that can blur the time-frequency energy ridge, cause multiple peaks to coexist, and make it difficult to identify in a single frame, such as one or more of background noise, harmonics, sidelobes, frequency crossings, and weak energy segments.

[0114] The degree of interference is a quantified value. For example, if the interfering factor is background noise, the degree of interference can be determined based on the signal-to-noise ratio (SNR). The higher the SNR, the lower the degree of interference.

[0115] The smoothing coefficient is related to the degree of disturbance; that is, the greater the disturbance, the larger the smoothing coefficient. Thus, the smoothing coefficient of the smoothing function can be dynamically adjusted. For strongly noisy conditions, the smoothing coefficient can be increased to strengthen the smoothing constraint and prevent the path from frequently jumping between noise peaks. For strongly nonlinear conditions, such as helicopter startup, the smoothing coefficient can be reduced to decrease the jump penalty and allow the path to quickly follow the nonlinear time-frequency energy ridge.

[0116] In some embodiments, the smoothing coefficient of the smoothing function and the trap strength coefficient of the trap function can be jointly adjusted to balance the smoothing cost and the second sub-cost. A large trap strength coefficient ensures that the time-frequency energy ridge passes through the prior point; while a large smoothing coefficient results in a stronger transfer penalty and a smoother path. Therefore, when the time-frequency energy ridge passes through the prior point but the path jitter is large, the smoothing coefficient is increased or the trap strength coefficient is decreased; when the path is very smooth but does not pass through the prior point, the trap strength coefficient is increased or the smoothing coefficient is decreased. For strong interference scenarios, a moderate trap strength coefficient and a large smoothing coefficient are typically used. This locks the correct path near the prior point while preventing noise constraints at non-prior points from causing target frequency jumps. Through this interplay, the prior point ensures the path does not deviate from the prior range, and the smoothing function ensures the path does not jump between prior points, ultimately resulting in a path with accurate key elements and stable intermediate paths.

[0117] 305. Based on the minimum cumulative cost of multiple frequencies at multiple time points, determine the target frequency for each of the multiple time points.

[0118] In some embodiments, the target frequency of the last time point among multiple time points is the frequency corresponding to the minimum value among multiple minimum cumulative costs of multiple frequencies at the last time point. The process of determining the target frequency of each of the multiple time points based on the minimum cumulative costs of multiple frequencies at multiple time points includes the following implementation: taking the target frequency of the last time point as the starting point, the transfer frequency corresponding to the target frequency of each time point is determined as the target frequency of the previous time point. The transfer frequency refers to the frequency corresponding to the minimum transfer cost from multiple frequencies at the previous time point to the target frequency of this time point.

[0119] In some embodiments, for each frequency at each time point, when determining its minimum transfer cost, the frequency at the previous time point corresponding to that minimum transfer cost is also recorded, that is, the transfer frequency of each frequency is recorded, such as through a matrix. Record, , = That is, to indicate a point in time. frequency The transfer frequency is .

[0120] Wherein, the target frequency at the last time point is the frequency corresponding to the minimum value among multiple minimum cumulative costs at the last time point, which can be expressed as: , Indicates the first The target frequency at each time point This represents the frequency corresponding to the minimum value among multiple minimum cumulative costs at the last time point.

[0121] In this embodiment, the globally optimal frequency at the last time point is first determined, which is the frequency corresponding to the minimum cumulative cost. This establishes the optimal frequency at the endpoint. Then, the process is reversed from the endpoint, and at each step, the optimal frequency of the previous frame that leads to the current optimal frequency is found, which is the frequency corresponding to the minimum transition cost. The resulting path is the globally optimal path from the starting point to the endpoint, rather than a patchwork trajectory of locally optimal values ​​frame by frame. Furthermore, during the backtracking process, the target frequency at each time point strictly corresponds to the frequency of the minimum transition cost at the previous time point. The transition cost already includes the jump penalty cost of the smoothing function. Thus, the trajectory obtained through backtracking is a globally optimal continuous path under smoothing constraints, avoiding the problem of excessive jumps in target frequency between adjacent time points. This aligns with the physical law of continuous changes in the rotational speed of rotating machinery, ensuring the accuracy of the determined target frequency.

[0122] In this embodiment of the application, the process of determining the target frequency of each time point based on the local cost of multiple frequencies at multiple time points is achieved through the above steps 304-305. It should be noted that this implementation method is only an optional implementation method for implementing the process. The process can also be implemented in other ways, such as directly determining the frequency corresponding to the minimum local cost at each time point as the target frequency.

[0123] In this embodiment, if only the frequency with the minimum local cost is selected at each time point, relying solely on the time-frequency matching information of the current time point may lead to path jumps between different spectral peaks due to noise, harmonic sidelobes, or frequency crossover interference. However, in this embodiment, global optimization is achieved through minimum cumulative cost. Since the total cost of each step is composed of the local cost at the current time point and the minimum cumulative cost at previous time points, dynamic programming searches for the solution with the minimum total cost in the entire path space, thereby obtaining the time-frequency energy ridge corresponding to the continuous, stable, and globally optimal instantaneous rotational speed trajectory.

[0124] 306. Determine the rotational speed of the rotating machinery at each time point based on the target frequency at that time point.

[0125] There is a corresponding relationship between frequency and rotational speed, and this relationship corresponds to the formula in step 202. Similarly, in step 202, the frequency can be obtained from the rotational speed using this formula. In this step, the rotational speed can be obtained from the frequency by reverse calculation using the same formula. It should be noted that step 202 and the harmonic order in this step... Maintain consistency.

[0126] It should be noted that for any possible path on the time-frequency graph Its basic cost function Defined as the weighted sum of the data terms and the smoothing terms, the basic cost function can be expressed as the following formula (8): (8); in, This represents the total number of times at multiple points in time. Represents a data item. This indicates the smoothing term.

[0127] The basic cost function is a comprehensive evaluation index used to measure the quality of each path on the time-frequency graph. The basic cost function consists of a data term and a smoothing term. For the data term, the greater the spectral intensity and the smaller the negative logarithm, the lower the cost. Therefore, the data term forces the path to choose the time-frequency energy ridge line with the strongest energy in the time-frequency graph. The smoothing term measures the drastic change in frequency between adjacent time points; the larger the jump amplitude, the larger the square penalty and the higher the total cost. Therefore, the smoothing term is used to ensure the continuity and smoothness of speed changes, conforming to the physical operating laws of rotating machinery. However, when determining the time-frequency energy ridge line using this basic cost function, under complex operating conditions such as strong interference, weak energy, and strong nonlinearity, it lacks prior constraints and adaptive capabilities, resulting in insufficient robustness and accuracy, leading to inaccurate determined time-frequency energy ridge lines.

[0128] In this embodiment, to determine the accurate time-frequency energy ridge, a priori points are introduced for guidance. Specifically, a sparse potential well term (i.e., a trap function) is superimposed on the basic cost function, resulting in an adjusted total cost function. It can be expressed as the following formula (9): (9); in, Represents the potential trap function. This represents the total number of multiple frequencies. Indicates a point in time. Indicates a point in time frequency, Represents frequency At the point of time The local trap, also known as the second subcost.

[0129] By adjusting the basic cost function in this way, the algorithm applies strong constraints only at the prior points, while the path is entirely driven by the basic cost function in the vast area between the prior points. This allows the path to freely follow the nonlinear time-frequency energy ridges (high-energy bands) of the signal without being bound by the linear pipelines in traditional algorithms, and reduces the dependence on the number of dense prior points.

[0130] This application provides a method for determining rotational speed. This method applies a local cost constraint based on spectral intensity only at the first time point, thus ensuring the frequency accuracy at the key time point. There are no trajectory shape constraints for the second time point other than the first time point. The target frequency at the second time point is determined entirely by free optimization based on the time-frequency energy ridge. This avoids trajectory jumps caused by noise when there are no constraints, and retains the true nonlinear rotational speed characteristics through optimization of the time-frequency energy ridge, thereby improving the accuracy of rotational speed determination.

[0131] Figure 4This is a flowchart illustrating a method for determining a time-frequency amplitude matrix according to an exemplary embodiment. See also: Figure 4 This method is performed by a computer device and includes the following steps: 401. Determine the vibration signal of the rotating machinery and at least two prior points of the vibration signal, each prior point representing a time point and a frequency.

[0132] In this embodiment, to determine the time-frequency amplitude matrix of the vibration signal, the computer device first determines the vibration signal and at least two prior points of the vibration signal. Additionally, the computer device can also acquire other relevant parameters of the vibration signal, such as the sampling frequency.

[0133] Optionally, the user manually inputs at least two sets of data on a computer device, and the computer device determines at least two prior points based on these two sets of data. Each set of data includes a time point and a frequency, where the frequency refers to the target frequency to be reached at that time point. Each set of data can then serve as a prior point. Alternatively, each set of data includes a time point and a rotational speed. By converting the rotational speed to a frequency, at least two prior points corresponding to the at least two sets of data can be determined.

[0134] In this embodiment, prior points are used as prior inputs to infer a more suitable target window length and time-frequency resolution, thereby generating a clearer time-frequency map. It should be noted that the prior points used in this embodiment are the same as those described above. Figure 2-3 The prior points used in the embodiments can be the same or different prior points, and no specific limitation is made here.

[0135] In some embodiments, the computer device may filter out aberrant prior points that are outside the time range from at least two prior points in order to avoid invalid prior points affecting the process of determining the target window length.

[0136] 402. Determine the average rate of change of frequency between at least two prior points.

[0137] At least two prior points not only provide location information, but their rate of frequency change also directly reflects the rate of rotational speed change of the vibration signal. Therefore, the computer equipment determines the average rate of frequency change between at least two prior points. The average rate of frequency change describes how quickly the frequency changes over time. Taking two prior points as an example, the ratio between the frequency difference and the time difference between these two prior points is the rate of frequency change between them.

[0138] When the computer equipment has determined more than two prior points, the ratio between the frequency difference and the time difference between each pair of adjacent prior points is determined as the frequency change rate between the two adjacent prior points, thereby obtaining multiple frequency change rates. Then, the average value of the multiple frequency change rates is determined to obtain the average frequency change rate between the at least two prior points.

[0139] That is, at least two prior points are: And the number of prior points is n, where n is an integer greater than 2. The average frequency change rate between at least two prior points is determined using the following formula (10): (10); in, This represents the average rate of change of frequency. This represents the frequency of the i-th prior point. This represents the frequency of the (i+1)th prior point. This represents the time point of the i-th prior point. This represents the time point of the (i+1)th prior point. This represents the average value, where i is an integer greater than 0 and less than n.

[0140] 403. The target window length is determined based on the average frequency change rate. The target window length is negatively correlated with the absolute value of the average frequency change rate.

[0141] The window length of an STFT represents the number of signal sampling points required to perform one STFT operation, and it determines both the frequency resolution and the time resolution. A longer window length results in higher frequency resolution and lower time resolution, making it more suitable for stationary signals. Conversely, a shorter window length results in lower frequency resolution and higher time resolution, making it more suitable for transient, non-stationary signals.

[0142] However, using a fixed window length, such as 1 second, cannot simultaneously handle the complex conditions of "rapid acceleration" and "steady-state operation." For example, if the window length is too long, when the signal frequency changes rapidly, the energy in the time-frequency graph will be stretched, resulting in "energy smearing." Or, due to frequency discreteness, the true frequency may not be located in the frequency grid points but may be assigned to adjacent grid points, causing a "pick-up fence effect" in the time-frequency graph. Moreover, since the path search process after determining the time-frequency amplitude matrix is ​​highly dependent on the energy concentration of the time-frequency graph, if the window length is inappropriate and the time-frequency graph exhibits "energy smearing" or "pick-up fence effect," the cost function of the subsequent path search algorithm will become invalid, resulting in "lockout" or "jump."

[0143] Therefore, in this embodiment of the application, the optimal target window length is adaptively determined based on the average frequency change rate of at least two prior points of the vibration signal, rather than being limited to using a fixed window length, and without blindly trying and failing.

[0144] Among them, the target window length is negatively correlated with the absolute value of the average frequency change rate; that is, the absolute value of the average frequency change rate... The larger the value, the longer the target window will be. The shorter the length, the more automatically it can prevent "energy smearing" from appearing on the time-frequency graph, and the absolute value of the average frequency change rate... The smaller the value, the longer the target window is. The longer the length, the higher the frequency resolution will be automatically.

[0145] 404. Using the target window length, perform a short-time Fourier transform on the vibration signal to obtain the time-frequency amplitude matrix of the vibration signal.

[0146] The time-frequency amplitude matrix consists of multiple rows and columns. Each column corresponds to a time point, and each row corresponds to a frequency. Each element in the time-frequency amplitude matrix represents the time-frequency distribution amplitude of the vibration signal at the corresponding frequency at the corresponding time point. It should be noted that different time points correspond to the same multiple frequencies, and each frequency corresponds to an amplitude at each time point.

[0147] This application provides a method for adaptively determining the window length based on prior guidance. It uses at least two prior points of the vibration signal as these points and determines a target window length negatively correlated with the absolute value of the average frequency change rate based on the average frequency change rate between these two points. This approach balances complex operating conditions where rapid acceleration and steady-state operation coexist, allowing the time-frequency amplitude matrix to automatically present a more suitable time-frequency resolution under different conditions. Specifically, it ensures that when the absolute value of the average frequency change rate is large, the target window length is shorter, automatically preventing "energy smearing" in the time-frequency graph; conversely, when the absolute value of the average frequency change rate is small, the target window length is longer, automatically improving frequency resolution. Furthermore, this application is no longer limited to using a fixed window length for STFT of rotating machinery vibration signals, improving flexibility and eliminating the need for multiple trials of different window lengths, avoiding blind trial and error and reducing unnecessary processing load.

[0148] Figure 5 This is a flowchart illustrating another method for determining the time-frequency amplitude matrix according to an exemplary embodiment, see [link to flowchart]. Figure 5 This method, executed by a computer device, provides a more detailed explanation of the process for determining the time-frequency amplitude matrix. The method includes the following steps: 501. Determine the vibration signal of the rotating machinery and at least two prior points of the vibration signal, each prior point representing a time point and a frequency.

[0149] 502. Determine the average rate of change of frequency between at least two prior points.

[0150] Steps 501-502 are the same as steps 401-402, and will not be repeated here.

[0151] 503. The target window length is determined based on the average frequency change rate. The target window length is negatively correlated with the square root of the absolute value of the average frequency change rate.

[0152] In some embodiments, using non-stationary signal processing theory, assuming the window function is a Gaussian window (i.e., when using a Gaussian window for STFT), the theoretically optimal window length is determined. The computer device then determines the target window length based on the average frequency change rate. The target window length is negatively correlated with the square root of the absolute value of the average frequency change rate, ensuring that the absolute value of the average frequency change rate is... The larger the value, the longer the target window will be. The shorter the length, the more automatically it can prevent the "energy smearing" phenomenon from appearing on the time-frequency graph, and the absolute value of the average frequency change rate... The smaller the value, the longer the target window is. The longer the window, the better the frequency resolution. Furthermore, considering that a larger frequency change rate necessitates a shorter window length, it cannot be simply shortened linearly according to a reciprocal relationship. Instead, a more "gentle" shortening method is used. Therefore, the target window length is set to be negatively correlated with the square root of the absolute value of the average frequency change rate, rather than negatively correlated with the absolute value of the average frequency change rate itself. This allows for the suppression of "energy smearing" without excessively sacrificing frequency resolution, resulting in a more stable vibration signal and less sensitivity to noise.

[0153] In some embodiments, the target window length can be expressed in the form of "number of sampling points" or "time length," with different units. The time length is equal to the quotient of the number of sampling points and the sampling frequency.

[0154] In some embodiments, the process of determining the target window length may include any of the following methods: 1. Determine the ratio between the first preset coefficient and the absolute value of the average frequency change rate, and determine the square root of this ratio as the target window length.

[0155] That is, the target window length is expressed in the form of "time length" and is determined by the following formula (11): (11); in, The target window length is expressed in the form of "time duration". This represents the first preset coefficient. This is a constant related to the window function, and its value can be 1 or 2, etc. This represents the average rate of change of frequency.

[0156] 2. Determine the ratio between the first preset coefficient and the absolute value of the average frequency change rate, and determine the target window length by multiplying the square root of this ratio by the sampling frequency of the vibration signal.

[0157] That is, the target window length is expressed in the form of "number of sampling points", and the target window length is determined by the following formula (12): (12); in, The target window length is expressed in the form of "number of sampling points". Indicates the sampling frequency of the vibration signal. This represents the first preset coefficient. This is a constant related to the window function, and its value can be 1 or 2, etc. This represents the average rate of change of frequency.

[0158] 504. Determine the target overlap rate that matches the target window length. The target overlap rate is negatively correlated with the target window length.

[0159] When performing STFT on a vibration signal, it is necessary to determine not only the window length but also the overlap rate. The overlap rate represents the ratio between the number of sampling points reused between two adjacent windows and the window length. The overlap rate affects the continuity of frequency changes over time. The higher the overlap rate, the smoother and more continuous the time-frequency plot; the lower the overlap rate, the worse the continuity of the time-frequency plot.

[0160] The overlap rate matching the target window length is determined based on the target window length. The target overlap rate is negatively correlated with the target window length. Then, the target window length and the target overlap rate are used to perform STFT on the vibration signal to obtain the time-frequency amplitude matrix of the vibration signal. This allows for the use of a higher target overlap rate for STFT when the target window length is short, thereby increasing the sampling density of the time axis. Conversely, a lower target overlap rate is used for STFT when the target window length is long, in order to reduce redundancy and the amount of processing required for the STFT process.

[0161] For example, the computer device sets a first overlap rate and a second overlap rate, where the first overlap rate is greater than the second overlap rate. The first overlap rate can be 87.5% or other values, and the second overlap rate can be 60% or other values, etc. The first overlap rate is a high overlap rate, suitable for cases with a short target window length, while the second overlap rate is a normal or low overlap rate, suitable for cases with a long target window length. Therefore, determining a target overlap rate that matches the target window length, where the target overlap rate is negatively correlated with the target window length, includes: determining the first overlap rate as the target overlap rate when the target window length is less than a window length threshold; or, determining the second overlap rate as the target overlap rate when the target window length is not less than a window length threshold.

[0162] The example above uses two overlap rates as an example. The computer device can automatically switch between the two overlap rates based on the relationship between the target window length and the window length threshold. In other examples, the computer device can also establish a mapping relationship between the target window length and the overlap rate, and determine the target overlap rate that matches the target window length based on this mapping relationship.

[0163] For example, if the mapping relationship is continuous, the computer device determines the mapping function between the target window length and the overlap rate. Using this mapping function, the target window length is calculated to obtain the target overlap rate matching the target window length. Alternatively, if the mapping relationship is discrete, it includes multiple window length intervals and the corresponding overlap rate for each interval, with more than two window length intervals. After determining the target window length, the computer device identifies the window length interval to which the target window length belongs from the multiple intervals and determines the overlap rate corresponding to that interval as the target overlap rate.

[0164] 505. Using the target window length and target overlap rate, perform a short-time Fourier transform on the vibration signal to obtain the time-frequency amplitude matrix of the vibration signal.

[0165] This application provides a method for adaptively determining the window length based on prior guidance. It uses at least two prior points of the vibration signal as these points and determines a target window length negatively correlated with the square root of the absolute value of the average frequency change rate based on the average frequency change rate between these two points. This approach balances complex operating conditions where rapid acceleration and steady-state operation coexist, allowing the time-frequency amplitude matrix to automatically present a more suitable time-frequency resolution under different conditions. Specifically, it ensures that when the absolute value of the average frequency change rate is large, the target window length is shorter, automatically preventing "energy smearing" in the time-frequency graph; conversely, when the absolute value of the average frequency change rate is small, the target window length is longer, automatically improving frequency resolution. Furthermore, this application is no longer limited to using a fixed window length for STFT of rotating machinery vibration signals, improving flexibility and eliminating the need for multiple trials of different window lengths, avoiding blind trial and error and reducing unnecessary processing load.

[0166] In addition, based on the determined target window length, the target overlap rate matching the target window length is adaptively determined. When the target window length is short, a higher target overlap rate is automatically adopted to increase the sampling density of the time axis to compensate for the information loss caused by the decrease in frequency resolution. When the target window length is long, a lower target overlap rate is automatically adopted to reduce redundancy and thus reduce the processing load of the STFT process.

[0167] Figure 6 This is a flowchart illustrating another method for determining the time-frequency amplitude matrix according to an exemplary embodiment, see [link to flowchart]. Figure 6This method, executed by a computer device, describes the process of determining the time-frequency amplitude matrix without knowing prior points. The method includes the following steps: 601. Without determining the a priori point of the vibration signal of the rotating machinery, determine the vibration signal and the total duration, maximum duration and minimum duration of the vibration signal.

[0168] The above Figure 4 and Figure 5 The illustrated embodiment assumes that the computer device has determined at least two prior points of the vibration signal. In another scenario, the computer device does not have prior points of the vibration signal. In this case, the computer device determines the time-frequency amplitude matrix of the vibration signal according to a fallback strategy.

[0169] The computer equipment acquires the total, maximum, and minimum durations of vibration signals. The total duration is used as a proxy variable for "operating condition dynamics," and a heuristic mapping function automatically adapts to the target window length, ensuring robustness in blind testing modes without predetermined prior points. The maximum duration is the upper limit of the window length; using the maximum duration as a constraint prevents excessively long target windows, which could lead to severe energy smearing in the transient phase and easy loss of lock-up during rapid speed changes. The minimum duration is the lower limit of the window length; using the minimum duration as a constraint prevents excessively short target windows, which could result in poor frequency resolution, overly coarse spectrograms, noise sensitivity, or computational instability.

[0170] 602. Determine the quotient between the total duration and the second preset coefficient to obtain the recommended duration. The second preset coefficient is greater than 1.

[0171] The second preset coefficient can be an empirical scaling factor, which maps the total duration of the vibration signal to a reference order of magnitude of a recommended duration. The second preset coefficient can also represent the number of time-scale units into which the entire vibration signal is to be divided.

[0172] 603. Based on the recommended duration, maximum duration, and minimum duration, select a target window length so that the target window length is no greater than the maximum duration and no less than the minimum duration.

[0173] In some embodiments, if the recommendation duration is no greater than the maximum duration and no less than the minimum duration, the recommendation duration is determined as the target window length. Alternatively, if the recommendation duration is greater than the maximum duration, the recommendation duration has exceeded the upper limit of the window length, and the maximum duration is determined as the target window length. Alternatively, if the recommendation duration is less than the minimum duration, the recommendation duration has fallen below the lower limit of the window length, and the minimum duration is determined as the target window length.

[0174] In some embodiments, the target window length can be expressed in the form of "number of sampling points" or "time length," with different units. The time length is equal to the quotient of the number of sampling points and the sampling frequency.

[0175] In some embodiments, the target window length is expressed in the form of "time length". The computer device determines the maximum value between the recommended duration and the minimum duration as the first duration, and the minimum value between the maximum duration and the first duration as the target window length. That is, the target window length is determined using the following formula (13): (13); in, Indicates the length of the target window. Indicates the total duration of the vibration signal. Indicates the maximum duration. Indicates the minimum duration. This represents the second preset coefficient. Indicates the maximum value. This represents the minimum value. Indicates the first duration.

[0176] In other embodiments, the target window length is expressed in the form of "number of sampling points". The computer device determines the first duration as the maximum value between the recommended duration and the minimum duration, and determines the target window length as the product of the maximum duration and the minimum value between the first duration and the sampling frequency of the vibration signal. That is, the target window length is determined using the following formula (14): (14); in, Indicates the length of the target window. Indicates the sampling frequency of the vibration signal. Indicates the total duration of the vibration signal. Indicates the maximum duration. Indicates the minimum duration. This represents the second preset coefficient. Indicates the maximum value. This represents the minimum value. Indicates the first duration.

[0177] In this embodiment, vibration signals with shorter total durations are considered to imply high dynamics, so a smaller target window length is used; while vibration signals with longer total durations are considered to imply steady state, so a longer target window length is used.

[0178] 604. The computer equipment uses the target window length to perform a short-time Fourier transform on the vibration signal to obtain the time-frequency amplitude matrix of the vibration signal.

[0179] Step 604 is similar to steps 404 and 504-505, and will not be repeated here.

[0180] This application provides a scheme for obtaining the target window length based on the total duration of the vibration signal without prior knowledge. A smaller target window length is used for vibration signals with shorter total durations, and a larger target window length is used for vibration signals with longer total durations. This achieves robust mapping based on the global dynamic characteristics of the vibration signal, automatically adapting to the target window length and ensuring robustness in blind testing mode. Furthermore, constraining the target window length with maximum and minimum durations prevents excessively long target windows, which could lead to severe energy smearing in the transient segment and easy loss of lock-up during rapid speed changes. It also prevents excessively short target windows, which could result in poor frequency resolution, overly coarse spectrograms, noise sensitivity, or computational instability.

[0181] It should be noted that this application provides two schemes: whether at least two prior points of the vibration signal are determined or not, a suitable target window length can be determined, and then STFT is performed on the vibration signal based on the target window length. Figure 4 and Figure 5 The proposed scheme can be called a "high-precision scheme". Considering that the target window length can be expressed in the form of "number of sampling points" or "time length", the computer equipment can determine the same target window length in both schemes to ensure that the processing flow after determining the target window length is universal.

[0182] For example, if computer equipment uniformly uses the form of "number of sampling points" to represent the target window length, then before performing STFT, it is usually necessary to multiply the time length by the sampling frequency, convert it into the number of sampling points, and configure the STFT parameters according to the number of sampling points.

[0183] Based on the above embodiments, in one possible implementation, after the computer device determines the target window length, it uses the target window length to perform a short-time Fourier transform on the vibration signal to obtain the time-frequency amplitude matrix of the vibration signal; then, it performs a monotonic transform on the time-frequency amplitude matrix to obtain the observation cost matrix; based on the observation cost matrix, it performs a path search in the time-frequency amplitude matrix to obtain a frequency ridge, the frequency ridge including a frequency corresponding to each time point in the vibration signal.

[0184] The observation cost matrix comprises multiple rows and columns, with each column corresponding to a time point and each row corresponding to a frequency. The size of the observation cost matrix is ​​equal to that of the time-frequency amplitude matrix, and each element in the matrix represents the observation cost of the vibration signal at the corresponding frequency within the corresponding time period. The frequency ridge refers to a frequency path that varies with time and forms a fixed multiple with the rotational speed; it corresponds to the time-frequency energy ridge on the time-frequency graph. The observation cost indicates the probability that the current time-frequency point belongs to a frequency ridge. The smaller the observation cost, the more likely the current time-frequency point is to be a point on the frequency ridge; the larger the observation cost, the less likely the current point is to be a point on the frequency ridge.

[0185] In some embodiments, a monotonic transformation is performed on the time-frequency amplitude matrix to obtain the observation cost matrix, including: The observation cost matrix is ​​obtained by monotonically transforming the time-frequency amplitude matrix using the following formula (15): Formula (15); in, Represents the observation cost matrix. This represents the time-frequency amplitude matrix.

[0186] Since the optimal target window length was determined in the aforementioned embodiments, ensuring that the time-frequency amplitude matrix was generated at the optimal time-frequency resolution, the highest quality time-frequency map and observation cost topography were constructed at the adaptive resolution. These can be used as key inputs to the dynamic programming algorithm used in the subsequent rotational speed trajectory search process, thereby improving the search success rate and stability. In the time-frequency map, the energy of the time-frequency energy ridge is the most concentrated and the width is the narrowest. The time-frequency energy ridge refers to the frequency path formed by the highest energy frequency at each time point in the time-frequency map corresponding to the time-frequency amplitude matrix. It represents the optimal trajectory reflecting the change of the fundamental frequency vibration component of the rotating machinery over time. It corresponds to the brightest and most continuous bright fringe in the time-frequency map, and the time-frequency energy ridge corresponds to the actual instantaneous rotational speed trajectory of the rotating machinery in the physical world. The observation cost matrix forms a steep "canyon" at the time-frequency energy ridge, greatly reducing the probability of the algorithm jumping to sidelobes or noise paths.

[0187] Figure 7 This is a flowchart of a method for determining a time-frequency amplitude matrix according to an embodiment of this application. See also... Figure 7 In this embodiment, the method for obtaining the mechanical rotation speed is described using a computer device as an example. The method includes the following steps: 701. Based on the maximum rate of change of rotational speed of the rotating machinery, determine the maximum rate of change of the target frequency in the vibration signal of the rotating machinery. The maximum rate of change of rotational speed indicates the physical limit of the rotational speed of the rotating machinery, and the target frequency is the vibration frequency in the vibration signal that is related to the rotational speed.

[0188] In this embodiment, the computer device acquires the vibration signal of the rotating machinery and the inherent maximum rate of change of rotational speed of the machinery. The maximum rate of change of rotational speed refers to the maximum acceleration (or deceleration) that the rotating machinery can physically achieve, usually expressed in RPM / s. It is a physical limit determined by the dynamic characteristics of the machinery itself (such as maximum torque, moment of inertia, etc.). The target frequency refers to the frequency component in the vibration signal that has a fixed proportional relationship with the rotational speed, such as the fundamental frequency (1st order) of the rotating shaft or other harmonic orders. Based on the proportional relationship between the rotational speed and the target frequency, and the maximum rate of change of rotational speed, the computer device calculates the maximum rate of change of the target frequency in the vibration signal. This maximum rate of change reflects the maximum possible change in the target frequency per unit time under physical limits.

[0189] In this embodiment, a computer device receives vibration signals from rotating machinery collected by a vibration sensor and determines the target frequency to be tracked from the vibration signal. This target frequency is a vibration frequency component that is proportional to the rotational speed, such as the fundamental frequency (1st order) or other harmonic orders of the rotating shaft. Based on the proportional relationship between the target frequency and the rotational speed and the maximum rate of change of rotational speed, the computer device can determine the maximum possible change in the target frequency per unit time.

[0190] In some embodiments, the computer device may calculate the maximum rate of change of the target frequency using the following formula (16).

[0191] (16); in, The maximum rate of change of the target frequency; This represents the maximum rate of change of rotational speed of the rotating machinery. The order of the target frequency. The order represents the ratio between the frequency of the vibration or noise and the rotational frequency of the reference axis (usually the spindle).

[0192] For example, if the maximum speed change rate of a motor is 3000 RPM / s, and it is tracking the fundamental frequency (order 1), then the maximum speed change rate of the target frequency is 50 Hz / s. This value provides an objective physical basis for subsequent window length selection and transfer cost setting, avoiding the blindness of traditional methods that rely on empirically preset parameters.

[0193] 702. Taking the constraint that the frequency change of the signal within a single time window is less than the frequency resolution of the short-time Fourier transform, the length of the first window is determined based on the maximum rate of change of the target frequency.

[0194] In this embodiment, the computer device needs to determine the first window length used for time-frequency analysis. The determination of the first window length is based on a physical constraint: ensuring that within any single time window, the change in target frequency due to rotational speed variation is less than the smallest frequency interval that the short-time Fourier transform itself can resolve. If the window length is too long, the frequency change within the window will exceed the frequency resolution, leading to spectral energy smearing and blurred peaks. Accordingly, the computer device calculates the maximum permissible window length that satisfies the requirement of "frequency change within the window being less than the frequency resolution" based on the maximum rate of change of the target frequency obtained in step 201, combined with the above constraint, and then selects a window length less than or equal to this maximum permissible window length as the first window length. This process ensures that the spectrum within each time window maintains a clear single-peak shape.

[0195] In this embodiment of the application, the computer device measures the frequency change of the signal within a single time window. Frequency resolution less than that of short-time Fourier transform As a constraint, the maximum rate of change based on the target frequency. Frequency resolution of short-time Fourier transform and permissible smearing coefficient Determine the maximum allowable window length that satisfies the constraints. Maximum permissible window length Equal to the allowable smearing coefficient With the maximum rate of change The square root of the ratio. Then, the computer device determines the first window length as any value that does not exceed (is less than or equal to) the maximum permissible window length.

[0196] Wherein, the frequency change of the signal within a single time window is Frequency resolution of short-time Fourier transform With window length The relationship between them is However, considering the need for sufficiently clear spectral peaks in practical engineering, the frequency variation within the window is typically required to be much smaller than the frequency resolution. Therefore, an allowable smearing factor is introduced. , is used to indicate the permissible frequency of application, and its value ranges from greater than 0 to less than 1. The smaller the value, the more strictly the smearing is suppressed, and the shorter the window length needs to be. The specific value can be preset according to the requirements for spectral peak clarity in actual applications. For example, in scenarios requiring high-precision tracking, a value of [value] can be set. The value is 0.1 or 0.2, and this application does not limit this to the embodiments.

[0197] Accordingly, to ensure that the signal within the window is approximately stable, it must meet the following requirements. , can be rewritten as The length of the time window can be obtained by organizing the data. That is, the maximum allowable window length that satisfies the constraints. (Permissible application coefficient) With the maximum rate of change (The square root of the ratio).

[0198] The solution provided in this application uses the constraint that the frequency change of the signal within a single time window is less than the frequency resolution. Based on the maximum rate of change of the target frequency, the frequency resolution, and the allowable smearing coefficient, the maximum allowable window length that satisfies this constraint is determined, and any value not exceeding this maximum allowable window length is used as the first window length. This determination method has clear physical meaning and mathematical basis. The maximum allowable window length is equal to the square root of the ratio of the allowable smearing coefficient to the maximum rate of change. This formula quantitatively gives the upper limit of the window length to ensure that the spectrum within the window does not undergo severe smearing under a given maximum rate of change of frequency. By selecting a window length less than this upper limit, it is ensured that the signal within each time window is approximately stable, and the spectral energy is concentrated rather than dispersed. This provides a clear, tail-free time-frequency amplitude matrix for subsequent path search, fundamentally solving the energy smearing problem caused by improper window length selection under high dynamic conditions and improving the reliability of speed extraction.

[0199] For example, when At that time, the maximum allowable window length is approximately 0.141 seconds. If the sampling rate is 12000 Hz, a window length of 512 points can be selected (corresponding to...). This value is much less than 0.141 seconds, fully satisfying the constraints. This determination method fundamentally solves the energy smearing problem caused by improper window length selection under high dynamic conditions.

[0200] 703. Based on the time window of the first window length and the first step length, perform a short-time Fourier transform on the vibration signal to obtain the first time-frequency amplitude matrix. The first step length is smaller than the first window length. The first time-frequency amplitude matrix indicates the distribution of the vibration signal amplitude with time and frequency.

[0201] In this embodiment, after determining the first window length, the computer device also needs to set a first step length. This step length must be smaller than the first window length, meaning that adjacent time windows overlap, and the overlap rate is high. Using a step length smaller than the window length is to increase the temporal density of the time-frequency analysis, making the generated time frames sufficiently dense to capture details during rapid changes in rotational speed. Then, the computer device performs frame processing on the vibration signal of the rotating machinery according to the first window length and the first step length, performs a Fourier transform on each frame signal segment (or sub-signal), and takes the amplitude of the transform result. The computer device then arranges the amplitudes of each frame in chronological order, thus forming the first time-frequency amplitude matrix. This first time-frequency amplitude matrix includes multiple elements (points), each element corresponding to a time point and a frequency, and the value of each element is the amplitude of the corresponding frequency at the corresponding time point. That is, the first time-frequency amplitude matrix uses time and frequency as two-dimensional coordinates, and the value of each element reflects the energy strength of the frequency component at that moment, providing a data foundation for subsequent path searching.

[0202] In this embodiment, the computer device frames the vibration signal based on a first window length and a first step length, obtaining signal segments with multiple time windows. Then, the computer device performs a Fourier transform on each signal segment within the multiple time windows to obtain the spectrum corresponding to each time window. Finally, the computer device arranges the spectra corresponding to each time window in chronological order to obtain a first time-frequency amplitude matrix. This first time-frequency amplitude matrix includes multiple elements, each corresponding to a time point and a frequency, with each element's value being the amplitude at the corresponding frequency at that time point.

[0203] In some embodiments, the ratio of the first step length to the first window length is less than a preset value. This ensures that the overlap rate is higher than a certain level. For example, if the preset overlap rate is 87.5%, then the first step length should be 1 / 8 of the first window length. This high overlap rate setting gives the time-frequency matrix a high temporal density, enabling it to meticulously depict every minute fluctuation during rapid changes in rotational speed.

[0204] The solution provided in this application frames the vibration signal based on a first window length and a first step length. After windowing each frame, a Fourier transform is performed, and the spectra of each frame are arranged in chronological order. This standardized processing flow ensures the integrity and reproducibility of the time-frequency analysis. The setting that the first step length is less than the first window length ensures overlap between adjacent time windows, resulting in a high temporal density in the time-frequency amplitude matrix, capable of meticulously depicting every minute fluctuation during rapid changes in rotational speed. Frame-based processing ensures that the signal is analyzed by stabilizing each segment, windowing effectively suppresses spectral leakage, and arranging the spectrum in chronological order visually presents the distribution of signal energy with time and frequency. Through this systematic processing, a time-frequency amplitude matrix with both clear spectral peaks and high temporal resolution is generated, laying a solid data foundation for subsequent accurate path searching.

[0205] Specifically, vibration signal It is a length of For a discrete digital signal with a sampling rate of 12kHz and a duration of 1 second, then Point. The length of the first window is... Points, for example, 512 points. The first step is of length [missing information]. Points, for example, 64 points, correspond to That is, the first step length is 1 / 8 of the first window length, at which point the overlap rate is 87.5%. Then, the computer equipment, based on the first window length and the first step length, transmits the original vibration signal... The signal is divided into several overlapping segments (which can be called "frames"), for example, the first frame is taken as... arrive Since the step size is 64 points, the second frame takes... arrive ; Take the 3rd frame arrive This process continues until the vibration signal ends. Thus, we obtain... Frame signal segment, Then, for each frame of signal, the computer multiplies it by a smoothing window function (such as a Hanning window) to reduce spectral leakage (i.e., reduce spurious frequency components caused by signal truncation). Then, for each windowed frame, the computer performs a Fast Fourier Transform (FFT) and calculates its amplitude. For example, performing an FFT on the first frame yields a complex result. Then perform the modulo operation: , to obtain a length of The vector of (one-sided spectrum) represents the energy at different frequencies at that moment. This process is repeated to obtain the spectral amplitude vector for each frame of the signal. Then, the computer device stacks the spectral amplitude vectors obtained from each frame in chronological order to form the first time-frequency amplitude matrix. First time-frequency amplitude matrix The number of rows represents the number of time frames; the first time-frequency amplitude matrix The number of columns is the number of frequency points, usually 1. First time-frequency amplitude matrix The elements in Indicates the first At frame time, the frequency is The vibration amplitude at that location.

[0206] In some embodiments, before performing the short-time Fourier transform, in order to ensure that the first and last frames of the signal also have complete window length data, the computer device can also perform continuation processing on the boundaries of the vibration signal. This continuation processing may include at least one of even-symmetric continuation, mirror continuation, and periodic continuation.

[0207] Even-symmetric continuation (boundary='even' / Symmetric Padding) refers to mirror reflection with the signal endpoints as the axis of symmetry. For example, for a vibration signal [a, b, c, d, e], in the leftward continuation: with index 0 as the axis, the first point to the left is the mirror image of index 1, i.e., b; the next point to the left is the mirror image of index 2, i.e., c, and so on. In the rightward continuation: with index 4 as the axis, the first point to the right is the mirror image of index 3, i.e., d; the next point to the right is the mirror image of index 2, i.e., c. This method ensures that the first derivative is continuous at the endpoints (smooth waveform transition) without abrupt changes, thus introducing minimal high-frequency noise.

[0208] Mirror padding, similar to even symmetry, is also a reflection, but it typically refers to including the endpoint itself as the axis. For example, in the vibration signal [a, b, c, d, e], during leftward padding: with index 0 as the axis, the first point on the left can be a mirror image of index 0 itself (a) or a mirror image of index 1 (b), with slight differences in implementation across different libraries. The difference between even symmetric padding and mirror padding is that even symmetric padding usually does not copy the endpoint itself, while mirror padding sometimes copies the endpoint.

[0209] Periodic padding / wrap-around refers to assuming the signal is periodic and connecting the end of the signal to the beginning. For example, for a vibration signal [a, b, c, d, e], in the leftward extension: take the last data point of the signal, i.e., the first point on the left is e, the second point is d, and so on. In the rightward extension: take the first data point of the signal, i.e., the first point on the right is a, the second point is b, and so on.

[0210] The computer equipment, based on a set mode (e.g., boundary='even'), responds to vibration signals. The front-end and back-end were added respectively. The length of the data is used to obtain the expanded signal. Then, in the expanded signal The signal is divided into frames. This way, even frames covering the very beginning and end of the original signal can be fully captured in the extended signal. The data is processed by taking points, and then windowing and fast Fourier transform are performed on each extracted frame (which may contain virtual data with extensions) to finally generate a time-frequency amplitude matrix.

[0211] The solution provided in this application extends the boundary of the vibration signal before performing the short-time Fourier transform, specifically including at least one of even-symmetric extension, mirror extension, or periodic extension. This preprocessing step solves the problem of spectral distortion caused by truncation at the beginning and end of the signal. Traditional zero-padding introduces abrupt changes at the signal boundary, resulting in high-frequency artifacts in the spectrum, affecting the frequency positioning accuracy at the start moment, i.e., the "start-off" phenomenon. Even-symmetric extension maintains the continuity of the signal at the endpoints, while mirror extension and periodic extension can effectively smooth the boundary transition, allowing the signal segment at the boundary to obtain complete data support, thereby obtaining accurate spectral analysis results. Through this boundary processing, reliable time-frequency information is ensured from the first frame to the last frame of signal acquisition, making the rotational speed extraction stable throughout the entire time range without edge blind spots.

[0212] This application provides a method for determining a time-frequency amplitude matrix. First, the maximum rate of change of rotational speed of the rotating machinery is introduced as a physical limit, providing an objective basis for subsequent parameter settings from the source and avoiding the blindness of relying on empirical presets in traditional methods. Then, the first window length is determined by the constraint that the frequency change within a single time window is less than the frequency resolution, ensuring that the spectrum within each time window can still maintain a clear peak shape when the rotational speed changes rapidly, effectively suppressing the energy smearing phenomenon. At the same time, a short-time Fourier transform is performed using a first step length that is less than the first window length to generate a high-time-density first time-frequency amplitude matrix, so that the frequency transition details during the rapid rotational speed change process can be completely preserved.

[0213] In this embodiment of the application, by Figure 2 or Figure 3 After obtaining the target frequency, the embodiment can further correct the target frequency to obtain a more accurate rotational speed. This process is carried out through the following steps: Figure 8 and Figure 9 The implementation of the example.

[0214] Figure 8 This is a flowchart of a frequency correction method provided in an embodiment of this application. This embodiment is executed by a computer device. See also... Figure 8The method includes the following steps.

[0215] 801. Obtain the time-frequency amplitude matrix and frequency sequence of the vibration signal of rotating machinery. The time-frequency amplitude matrix includes the amplitude of the vibration signal at multiple frequencies at multiple time points, and the frequency sequence indicates the first instantaneous frequency of the vibration signal at each of the multiple time points, and the first instantaneous frequency belongs to multiple frequencies.

[0216] It should be noted that the time-frequency amplitude matrix in this embodiment can be... Figure 4-8 The embodiments are determined by any one of the embodiments.

[0217] A frequency sequence indicates the first instantaneous frequency of a vibration signal at multiple time points. It is a sequence of instantaneous frequencies extracted from multiple discrete time points in the time-frequency amplitude matrix. At a given time point, the vibration signal generates multiple frequency components, such as those generated by the rotation of rotating machinery or by noise. The first instantaneous frequency is the dominant frequency component of the vibration signal at that particular time point. This first instantaneous frequency can be considered as the rotational frequency of the rotating machinery and is directly related to its rotational speed. This frequency sequence reflects the change of the dominant frequency in the vibration signal over time.

[0218] 802. For each of the multiple time points, based on the time-frequency amplitude matrix and frequency sequence, determine the target amplitude, the first adjacent amplitude, and the second adjacent amplitude of the vibration signal at that time point.

[0219] The target amplitude is the amplitude at the first instantaneous frequency at each time point, the first adjacent amplitude is the amplitude at the previous frequency at the first instantaneous frequency at that time point, and the second adjacent amplitude is the amplitude at the next frequency at the first instantaneous frequency at that time point.

[0220] In this embodiment, the frequency sequence is determined based on a time-frequency amplitude matrix, where multiple frequencies are discrete. The first instantaneous frequency of the vibration signal at each time point in the frequency sequence belongs to these discrete frequencies within the time-frequency amplitude matrix, resulting in low precision. Alternatively, the first instantaneous frequency at each time point can be the target frequency at each time point determined based on the time-frequency amplitude matrix, a process described above. Figure 2-3 The implementation is as follows. Therefore, steps 802-804 are used to correct the first instantaneous frequency at each time point.

[0221] For any given time point among multiple time points, the computer searches the time-frequency amplitude matrix for the amplitude at a first instantaneous frequency at that time point, and uses the found amplitude as the target amplitude for that time point. The discrete frequencies in the time-frequency amplitude matrix are arranged in ascending order. The computer determines the previous frequency and the next frequency among the multiple frequencies at the first instantaneous frequency. The search in the time-frequency amplitude matrix for the amplitude at the previous frequency at the first instantaneous frequency at that time point is used as the first adjacent amplitude for that time point. Similarly, the search in the time-frequency amplitude matrix for the amplitude at the next frequency at the first instantaneous frequency at that time point is used as the second adjacent amplitude for that time point.

[0222] For example, taking time point t as an example, the frequency at the first instant of time point t is: First instantaneous frequency The previous frequency is First instantaneous frequency The previous frequency is Therefore, the target amplitude is equal to the x-coordinate of the time-frequency amplitude matrix, where the y-coordinate is t. The amplitude at point t, the first adjacent amplitude is equal to the amplitude at point t on the time-frequency amplitude matrix, where the x-axis is t and the y-axis is t. The amplitude at point t, the second adjacent amplitude is equal to the amplitude at point t on the time-frequency amplitude matrix, where the x-axis is t and the y-axis is t. The amplitude at that point.

[0223] 803. Determine the offset parameter based on the difference between the target amplitude, the first adjacent amplitude, and the second adjacent amplitude.

[0224] The offset parameter reflects the offset of the first instantaneous frequency at a given time point, and it indicates the offset direction and amount.

[0225] Since the actual instantaneous frequencies (dominant frequencies) at various time points typically form a continuously varying curve, and the currently determined first instantaneous frequency is an approximate sample of this continuous curve, if the currently determined first instantaneous frequency happens to coincide with the actual instantaneous frequency, then the target amplitude at that first instantaneous frequency will generally exhibit symmetry or smoothness between adjacent frequencies. However, when the first instantaneous frequency deviates from the actual instantaneous frequency, the symmetry or smoothness between adjacent frequencies will be broken, meaning the target amplitude will tilt to one side in frequency distribution. The degree of asymmetry in the target amplitude reflects the direction and extent of the deviation of the first instantaneous frequency relative to the actual instantaneous frequency.

[0226] Therefore, the difference between the target amplitude at a given time point, the first adjacent amplitude, and the second adjacent amplitude can quantify the degree of amplitude asymmetry, thereby inferring the offset of the first instantaneous frequency relative to the true instantaneous frequency, which is the offset parameter. Subsequently, the original first instantaneous frequency can be corrected based on this offset parameter.

[0227] 804. Correct the first instantaneous frequency at the time point according to the offset parameter to obtain the second instantaneous frequency at the time point.

[0228] After obtaining the offset parameter, the computer equipment corrects the first instantaneous frequency at that time point based on the offset parameter, thereby obtaining a more accurate second instantaneous frequency. This moves the finally determined instantaneous frequency from the position of the discrete frequency to a position closer to the true frequency, achieving refinement of the instantaneous frequency and improving the accuracy and continuity of frequency tracking.

[0229] The method provided in this application embodiment, based on the frequency sequence, for each time point, uses the difference between the target amplitude at the instantaneous frequency at that time point, the first adjacent amplitude at the previous frequency at that time point, and the second adjacent amplitude at the next frequency at that time point to reflect the amplitude variation relationship of adjacent frequencies. Based on this variation relationship, the continuous variation characteristics of frequency amplitude are characterized, thereby determining the offset parameter of the instantaneous frequency at that time point. The offset parameter is used to correct the instantaneous frequency at that time point to obtain a more accurate instantaneous frequency, effectively breaking through the frequency resolution limitation of the time-frequency amplitude matrix on the accuracy of the instantaneous frequency, and improving the accuracy of the extracted frequency.

[0230] The above Figure 8 The diagram shown is only the basic process of this application. The following is a further explanation of the solution provided in this application based on a specific implementation method. Figure 9 This is a flowchart of another frequency correction method provided in this application embodiment. This application embodiment is executed by a computer device. See also... Figure 9 The method includes the following steps.

[0231] 901. Obtain the time-frequency amplitude matrix of the vibration signal of the rotating machinery. The time-frequency amplitude matrix includes the amplitude of the vibration signal at multiple frequencies at multiple time points.

[0232] The process of obtaining the time-frequency amplitude matrix in step 901 is the same as the process of obtaining the time-frequency amplitude matrix in step 801 above, and will not be repeated here.

[0233] 902. Based on the amplitude and frequency corresponding to multiple elements in the time-frequency amplitude matrix, search for the path with the lowest path cost in the time-frequency amplitude matrix. The path includes one element corresponding to each time point in multiple time points. The path cost is used to measure the degree of unreasonableness of taking the frequency corresponding to each element in the path as the instantaneous frequency of each time point.

[0234] 903. Based on the time points and frequencies corresponding to multiple elements in the path, construct a frequency sequence. The frequency sequence indicates the first instantaneous frequency of the vibration signal at multiple time points, and the first instantaneous frequency belongs to multiple frequencies.

[0235] It should be noted that the path in this embodiment can be derived from... Figure 2-3 In this embodiment, the target frequency is composed of multiple time points, that is, the frequency of the time point corresponding to each element in the path in this embodiment is... Figure 2-3 The target frequency at this time point in the embodiment.

[0236] Specifically, by arranging the frequencies corresponding to multiple elements in the path in chronological order according to the time points corresponding to the multiple elements in the path, and taking the sequentially arranged frequencies as the first instantaneous frequency of each time point, a frequency sequence can be obtained. This frequency sequence indicates the first instantaneous frequency of the vibration signal at multiple time points, and the first instantaneous frequency of each time point is the frequency component of the vibration signal that is dominant at that time point.

[0237] In related technologies, the peak-finding method is used to take the frequency corresponding to the maximum amplitude at each time point as the instantaneous frequency, without considering the continuity constraint in the time dimension. However, in the vibration signal of rotating machinery, the spectrum often contains noise, multiple frequency components, and closely spaced order components, so the amplitude of the dominant frequency may not be at its maximum at some time points. In this case, the peak-finding method may misidentify local noise peaks as instantaneous frequencies, resulting in abrupt changes in the extracted frequency between different time points.

[0238] In this implementation, the amplitude at a specific frequency at a given time point in the time-frequency amplitude matrix is ​​considered as an element. Based on the amplitudes corresponding to each element in the matrix, a path with the lowest cost is searched among multiple elements of the matrix. This path covers a more reasonable instantaneous frequency at each time point, thus constructing a more accurate frequency sequence. This method avoids the instability caused by relying solely on local peaks in traditional point-by-point peak-finding methods. The resulting frequency sequence considers not only the amplitude of individual elements but also the continuity and rationality of the time dimension, effectively suppressing misjudgments caused by noise, reducing frequency jumps, and improving the accuracy of the frequency sequence.

[0239] In one possible implementation, the computer device determines the frequency indices of multiple elements in the path, which indicate the frequencies. The frequency indices are then sorted according to the chronological order of the time points corresponding to the elements in the path, resulting in a frequency sequence. This frequency sequence includes the frequency indices of the vibration signal at multiple time points, with each time point's frequency index indicating the frequency at the first instant at that time point.

[0240] In this context, the frequency index can be understood as the position number of multiple discrete frequencies in the time-frequency amplitude matrix. In the time-frequency amplitude matrix, the frequencies are not continuous but discretized into multiple equally spaced frequencies arranged in ascending order. Each frequency corresponds to a unique position number, which is the frequency index. For example, the 0th frequency point, the 1st frequency point, and so on up to the Kth frequency point; each frequency index uniquely corresponds to a specific frequency.

[0241] Furthermore, a definite mapping relationship exists between the frequency index and the frequency, which is typically determined by both the sampling frequency and the transform length. In scenarios based on the short-time Fourier transform, the frequency interval is fixed, and its size is determined by the sampling frequency and the transform length. Specifically, if the sampling frequency is... If the transform length is N, then the interval between two adjacent frequencies is The frequency corresponding to the k-th frequency index can be represented as Therefore, through this mapping relationship, the frequency can be determined based on the frequency index.

[0242] In this embodiment, the frequencies corresponding to multiple elements in the path are taken as the first instantaneous frequencies at the corresponding time points. The frequency indices of these first instantaneous frequencies are then arranged sequentially according to the time points corresponding to the multiple elements in the path, from earliest to latest, to obtain the frequency sequence. For example, this frequency sequence can be represented as follows: , The index representing the first instantaneous frequency at time point t.

[0243] In this implementation, the frequency corresponding to each element in the path is represented by a frequency index, and the frequency index is sorted according to the time order to construct the frequency sequence, which reduces the complexity of the frequency sequence and helps to improve the efficiency of data processing.

[0244] 904. For each of the multiple time points, based on the time-frequency amplitude matrix and frequency sequence, determine the target amplitude, the first adjacent amplitude, and the second adjacent amplitude of the vibration signal at that time point.

[0245] The target amplitude is the amplitude at the first instantaneous frequency at a given time point, the first adjacent amplitude is the amplitude at the previous frequency at the first instantaneous frequency at a given time point, and the second adjacent amplitude is the amplitude at the next frequency at the first instantaneous frequency at a given time point.

[0246] Wherein, the time point is denoted as t, and the target amplitude, the first adjacent amplitude and the second adjacent amplitude at the time point can be represented by the following formulas (17)-(19).

[0247] (17); (18); (19); in, Indicates the first adjacent amplitude. This represents the amplitude of the previous frequency at the first instant of time t. The frequency index is the frequency of the first instant. It is the frequency index of the previous frequency of the first instantaneous frequency. Indicates the target amplitude. It represents the amplitude of the frequency at the first instant at time point t. Indicates the second adjacent amplitude. This represents the amplitude of the next frequency at the first instant of time t. This is the frequency index of the next frequency after the first instantaneous frequency.

[0248] 905. Determine the index offset parameter based on the difference between the target amplitude, the first adjacent amplitude, and the second adjacent amplitude.

[0249] The frequency sequence includes frequency indices of the vibration signal at multiple time points, with each time point's frequency index indicating the first instantaneous frequency at that point. The index offset parameter reflects the offset of the frequency index at the first instantaneous frequency at that time point, indicating both the direction and amount of the offset.

[0250] In one possible implementation, the computer device subtracts the second adjacent amplitude from the first adjacent amplitude to obtain a first difference; subtracts twice the target amplitude from the sum of the first and second adjacent amplitudes to obtain a second difference; and multiplies the scaling factor, the first difference, and the reciprocal of the second difference to obtain an index offset parameter.

[0251] The computer equipment constructs three data points based on the target amplitude, the first adjacent amplitude, and the second adjacent amplitude of the vibration signal at a given time point: , , Based on these three data points, construct a quadratic polynomial passing through these three data points: The parabola vertex of the quadratic polynomial is determined relative to the frequency index using the principle of extrema. index offset parameter The derivation process is as follows.

[0252] The formula for determining the vertex of a parabola is: (20).

[0253] Substituting the three data points above into the quadratic polynomial, we can determine the coefficients a and b of the quadratic polynomial: (twenty one); (twenty two); Substituting the above formulas (21) and (22) into formula (20), we can obtain the parabola vertex relative to the frequency index. index offset parameter

[0254] (twenty three); Therefore, the index offset parameter can be determined according to formula (23), which is the product of the scaling factor, the reciprocal of the first difference, and the second difference. Optionally, the value range of this index offset parameter is within... between.

[0255] In this implementation, a first difference and a second difference are constructed based on the target amplitude, the first adjacent amplitude, and the second adjacent amplitude. The index offset parameter is determined based on these first and second differences. This approach utilizes the amplitude's variation trend within a local range to reflect the true frequency's positional distribution among discrete frequency points, achieving accurate estimation of the frequency offset with lower computational complexity. Compared to interpolation methods, this method reduces the complexity of determining the index offset parameter and improves its efficiency.

[0256] 906. Correct the frequency index of the time point according to the index offset parameter to obtain the corrected frequency index, and convert the corrected frequency index into the second instantaneous frequency of the time point.

[0257] Here, the frequency index at that time point refers to the frequency index of the first instantaneous frequency in the frequency sequence at that time point. The computer device adds the frequency index of the first instantaneous frequency to the index offset parameter to obtain the corrected frequency index, and converts the corrected frequency index into the second instantaneous frequency at that time point.

[0258] In one possible implementation, the computer device uses the following formulas (24)-(25) to determine the second instantaneous frequency.

[0259] (twenty four); (25); in, The frequency index represents the frequency at the first instant. Indicates the index offset parameter. Indicates the corrected frequency index. Indicates the second instantaneous frequency. The sampling frequency of the short-time Fourier transform is represented by , and N represents the transform length of the short-time Fourier transform.

[0260] In this embodiment, frequency is represented as a frequency index. An index offset parameter is first determined based on the difference between the amplitudes of adjacent elements. Then, the frequency index is corrected using the index offset parameter, and finally, the corrected frequency index is converted back to a frequency. This method achieves sub-pixel-level frequency correction for multiple discrete frequencies, obtaining results that are closer to the true frequency position, thereby significantly improving the accuracy of frequency confirmation.

[0261] It should be noted that steps 905-906 above determine the offset parameter based on the difference between the target amplitude, the first adjacent amplitude, and the second adjacent amplitude; and correct the first instantaneous frequency at the time point according to the offset parameter to obtain the second instantaneous frequency at the time point.

[0262] 907. Smooth the second instantaneous frequencies at multiple time points to obtain the third instantaneous frequencies at multiple time points.

[0263] By executing steps 901-906 above, the computer device can obtain a more accurate second instantaneous frequency of the vibration signal at each of multiple time points. The computer device can then smooth the second instantaneous frequency at these multiple time points to obtain a smoother third instantaneous frequency, thereby reducing high-frequency jitter in the instantaneous frequency.

[0264] In this embodiment of the application, after frequency correction is completed, the instantaneous frequencies at multiple time points after correction are smoothed, so that the instantaneous frequencies at multiple time points are more continuous and smooth in the time dimension, reducing jitter caused by noise interference or calculation errors, thereby suppressing local abnormal fluctuations and further improving the accuracy of the determined frequency.

[0265] In one possible implementation, the process of smoothing the second instantaneous frequency at multiple time points by the computer device includes: for each of the multiple time points, selecting M neighboring time points centered on that time point, where M is an odd number greater than 1; wherein each neighboring time point and the second instantaneous frequency of each neighboring time point constitute a data point, and the M neighboring time points include that time point; performing polynomial fitting on the M data points to obtain a P-order polynomial, where P is an integer greater than 1; and determining the function value of the P-order polynomial at the time point to obtain the third instantaneous frequency at that time point.

[0266] Taking time point t as an example among multiple time points, select M neighboring time points centered on time point t. Here, M = 2n + 1, and the M neighboring time points include time point t, the n time points preceding time point t, and the n time points following time point t.

[0267] Based on M neighboring time points and their second instantaneous frequencies, M data points are constructed, with the x-axis representing the time point and the y-axis representing the second instantaneous frequency. Then, the least squares method is used to fit a P-order polynomial to the M data points, resulting in a P-order polynomial. The function value of this P-order polynomial at time point t is determined, and this function value is used as the third instantaneous frequency at time point t, thus obtaining the smoothed instantaneous frequency.

[0268] Optionally, the number of neighborhood time points M and the order P of the polynomial can be determined experimentally or otherwise. For example, M equals 8 and P equals 3.

[0269] In this implementation, M neighboring time points are selected centered on the current time point. A polynomial fit is then performed on the data points corresponding to these M neighboring time points, and the instantaneous frequency at each time point is adjusted according to the fitted polynomial. This method can model the frequency change trend within a local range, thereby smoothing the frequency at a given time point. Compared to simple averaging methods, it better preserves local shape features and transient changes, improving the accuracy of smoothing frequencies across multiple time points.

[0270] It should be noted that this embodiment of the application describes step 907 as being performed after step 906. In another embodiment, step 907 may not be performed, that is, the second instantaneous frequency may not be smoothed.

[0271] The method provided in this application addresses the issue that the instantaneous frequencies of the vibration signal at each time point in the frequency sequence belong to multiple discrete frequencies in the time-frequency amplitude matrix, resulting in low accuracy. Therefore, this application, based on the frequency sequence, for each time point, utilizes the difference between the target amplitude at that time point, the first adjacent amplitude at the previous frequency, and the second adjacent amplitude at the next frequency to reflect the amplitude variation relationship between adjacent frequencies. This variation relationship characterizes the continuous amplitude variation of the frequency, thereby determining the offset parameter of the instantaneous frequency at that time point. The offset parameter is then used to correct the instantaneous frequency at that time point, resulting in a more accurate instantaneous frequency. This effectively overcomes the limitation of frequency resolution in the time-frequency amplitude matrix on the accuracy of the instantaneous frequency, improving the accuracy of the extracted frequency.

[0272] In some embodiments, based on the above embodiments, after performing step 906, a frequency curve or a rotational speed curve may also be generated.

[0273] (1) Based on the second instantaneous frequency at multiple time points, generate the frequency curve of the vibration signal. The frequency curve is used to reflect the change of the instantaneous frequency of the vibration signal over time.

[0274] In this context, the horizontal axis of the frequency curve of the vibration signal represents the time point, and the vertical axis represents the second instantaneous frequency.

[0275] After obtaining the second instantaneous frequency at multiple time points, the computer device maps each time point to its second instantaneous frequency, forming multiple discrete data points. The horizontal axis of each data point represents the time point, and the vertical axis represents the second instantaneous frequency. Connecting the data points in chronological order yields a frequency curve. Alternatively, curve fitting can be performed on the multiple discrete data points to obtain a smoother, continuous frequency curve across time points, thus visually reflecting the change of the instantaneous frequency of the vibration signal over time.

[0276] (2) Based on the second instantaneous frequency at multiple time points, the rotational speed curve of the vibration signal is generated. The rotational speed curve is used to reflect the change of the rotational speed of the vibration signal over time.

[0277] In this context, the horizontal axis of the rotational speed curve of the vibration signal represents the time point, and the vertical axis represents the rotational speed corresponding to the second instantaneous frequency.

[0278] After obtaining the second instantaneous frequency at multiple time points, the computer equipment converts the second instantaneous frequency at each time point into rotational speed, and establishes a one-to-one correspondence between each time point and its rotational speed, forming multiple discrete data points. The horizontal axis of each data point represents the time point, and the vertical axis represents the rotational speed. Connecting the data points in chronological order yields the rotational speed curve. Alternatively, curve fitting can be performed on multiple discrete data points to obtain a smoother, continuous rotational speed curve at different time points, thus intuitively reflecting the change of rotational speed of rotating machinery over time.

[0279] It should be noted that there is a direct correspondence between the speed curve and the frequency curve mentioned above. They are different representations of the same physical process. The speed curve can be regarded as the result of scaling the frequency curve.

[0280] In some embodiments, based on the above embodiments, after performing step 907, a frequency curve or a rotational speed curve may also be generated.

[0281] (1) Based on the third instantaneous frequency at multiple time points, generate the frequency curve of the vibration signal. The frequency curve is used to reflect the change of the instantaneous frequency of the vibration signal over time.

[0282] The process of generating a frequency curve based on the third instantaneous frequency is the same as the process of generating a frequency curve based on the second instantaneous frequency, and will not be repeated here.

[0283] (2) Based on the third instantaneous frequency at multiple time points, the rotational speed curve of the vibration signal is generated. The rotational speed curve is used to reflect the change of rotational speed of the vibration signal over time.

[0284] The process of generating the speed curve based on the third instantaneous frequency is the same as the process of generating the speed curve based on the second instantaneous frequency, and will not be repeated here.

[0285] In this embodiment, frequency curves or rotational speed curves are generated based on instantaneous frequencies corrected at multiple time points. These curves can intuitively reflect the dynamic characteristics of rotating machinery during operation, providing an important basis for condition monitoring and fault diagnosis of rotating machinery. Compared to curves obtained based on the original discrete instantaneous frequencies, the frequency curves or rotational speed curves generated by this method are smoother and more accurate, accurately reflecting the changing trends of rotating machinery and improving the reliability of condition monitoring and fault diagnosis of rotating machinery.

[0286] Once the accurate rotational speed is obtained, this speed data has a wide range of engineering application value, mainly reflected in the following aspects.

[0287] First, motor closed-loop control and performance calibration: In motor drive systems such as electric vehicles and high-speed spindles, instantaneous speed is a key feedback quantity in vector control algorithms. The real-time, high-precision speed data provided in this application can be directly input into the controller to achieve high-precision torque control and speed regulation. Especially under rapid acceleration conditions, accurate speed feedback can prevent motor step loss, optimize current output, and improve dynamic response performance. Simultaneously, during motor factory testing, by acquiring the instantaneous speed curves during rapid acceleration and deceleration, key performance indicators such as the motor's dynamic response time and speed overshoot can be accurately evaluated, verifying whether it meets design standards.

[0288] Secondly, transient characteristic analysis and fault diagnosis of rotating machinery: During the start-up, shutdown, or variable operating condition processes of equipment such as aero-engines, gas turbines, and large compressors, the instantaneous speed curves obtained are the core data for analyzing their dynamic characteristics. For example, by analyzing the entire speed change trajectory from the lowest stable speed to the highest speed, the critical speed points of the rotor system can be identified, preventing prolonged stagnation at these speed points that could lead to resonance. Furthermore, synchronous analysis of speed and vibration signals allows for order tracking. When the speed changes, the fault characteristic frequencies of various components of the equipment change accordingly. By locking the vibration signal onto the speed, the order corresponding to faults such as broken gear teeth or damaged bearings can be accurately identified, thereby achieving early fault warning.

[0289] Third, measurement verification for high-dynamic tests: In various high-dynamic tests conducted in laboratories or test tracks (such as vehicle launch control and engine rapid loading tests), this method can serve as a fundamental measurement tool. Its output high-time-resolution rotational speed trajectory can be used as benchmark data to verify the accuracy of simulation models, and also as a time reference for other testing equipment (such as fuel consumption meters and power analyzers), ensuring the synchronization and accuracy of multi-physical quantity test data.

[0290] Figure 10 This is a block diagram illustrating a speed determining device according to an exemplary embodiment. (Refer to...) Figure 10 The device includes: The acquisition module 1001 is used to acquire the time-frequency diagram of the vibration signal of the rotating machinery and the constraint frequencies at multiple first time points. The time-frequency diagram includes the spectral intensity of the vibration signal at multiple frequencies at multiple time points, and the multiple time points include multiple first time points. The determination module 1002 is used to determine the local cost of multiple frequencies at the first time point for each first time point based on the constraint frequency at the first time point and the spectral intensity of multiple frequencies at the first time point respectively. The local cost of each frequency is used to measure the degree of matching between the frequency and the time-frequency energy ridge of the time-frequency map. The determination module 1002 is also used to determine, for each second time point, the local cost of multiple frequencies at the second time point based on the spectral intensity of multiple frequencies at the second time point, wherein the second time point is a time point other than the first time point among multiple time points; The determination module 1002 is also used to determine the target frequency of each of the multiple time points based on the local cost of multiple frequencies at multiple time points, wherein the target frequency of each time point refers to the frequency selected by the time-frequency energy ridge at the time point. The determination module 1002 is also used to determine the rotational speed of the rotating machinery at each time point based on the target frequency at each time point.

[0291] In some embodiments, the determining module 1002 is configured to: For each first time point, based on the spectral intensity and data function of multiple frequencies at the first time point, the first sub-cost of multiple frequencies at the first time point is determined respectively. The data function is used to constrain the target frequency at the first time point to the vicinity of the frequency with high spectral intensity. Based on the constraint frequency, multiple frequencies, and trap function at the first time point, the second sub-cost of multiple frequencies at the first time point is determined respectively. The trap function is used to constrain the target frequency at the first time point to be near the constraint frequency at the first time point. For each frequency, the local cost of the frequency at the first time point is determined based on the first sub-cost and the second sub-cost of the frequency at the first time point.

[0292] In some embodiments, the trap function includes a trap strength coefficient, which is used to constrain the degree of influence of the second sub-cost on the local cost. The determining module 1002 is further configured to: For each time point, the potential depression intensity coefficient is determined based on at least one of the signal-to-noise ratio, local spectral peak contrast, and noise floor estimate of the time-frequency plot at that time point. The local spectral peak contrast is used to indicate the prominence of the peak with the largest spectral intensity at that time point in the time-frequency plot, and the noise floor estimate is used to indicate the overall level of background noise at that time point in the time-frequency plot.

[0293] In some embodiments, for each first time point, if the difference between the frequency with the largest spectral intensity at the first time point in the time-frequency diagram and the constraint frequency is less than the difference threshold, the trap function is a quadratic function. If the difference between the frequency with the largest spectral intensity at the first time point in the time-frequency graph and the constraint frequency is not less than the difference threshold, the trap function is a linear function.

[0294] In some embodiments, the determining module 1002 is configured to: Based on the local costs of multiple frequencies at multiple time points, the minimum cumulative cost of multiple frequencies at multiple time points is determined. The minimum cumulative cost of each frequency at each time point is used to measure the degree of matching between the path corresponding to the frequency and the time-frequency energy ridge. The path refers to the frequency path from the first time point of the time-frequency graph to the time point, with the frequency at the time point as the endpoint. The target frequency for each of the multiple time points is determined based on the minimum cumulative cost of multiple frequencies at multiple time points.

[0295] In some embodiments, the determining module 1002 is configured to: For each time point, based on the minimum cumulative cost of multiple frequencies at the previous time point, the transfer cost of each frequency at the time point relative to the multiple frequencies at the previous time point is determined. The transfer cost of each frequency at each time point relative to the multiple frequencies at the previous time point refers to the cost of frequency jump when transferring from the multiple frequencies at the previous time point to the frequency at the time point. The minimum cumulative cost of multiple frequencies at the first time point in the time-frequency diagram is the local cost of multiple frequencies at the first time point. For each frequency at each time point, the minimum value of the transfer cost of the frequency relative to multiple frequencies is determined as the minimum transfer cost of the frequency at the time point. Based on the minimum transfer cost of the frequency at the time point and the local cost, the minimum cumulative cost of the frequency at the time point is determined.

[0296] In some embodiments, the determining module 1002 is configured to: For each frequency at a given time point, the smoothing cost between the frequency and multiple frequencies at the previous time point is determined based on a smoothing function. The smoothing function is used to constrain the smoothness of the time-frequency energy ridge. Based on the minimum cumulative cost of multiple frequencies at the previous time point and the smoothing cost between frequencies, the transfer cost of each frequency at a given time point relative to the multiple frequencies at the previous time point is determined.

[0297] In some embodiments, the smoothing function includes a smoothing coefficient, which is used to constrain the degree to which the smoothing cost affects the transfer cost; the determining module 1002 is further configured to: The smoothing coefficient is determined based on the degree of interference from interfering factors in the time-frequency graph.

[0298] In some embodiments, the target frequency at the last time point among a plurality of time points is the frequency corresponding to the minimum value among a plurality of minimum cumulative costs at the last time point. The determining module 1002 is configured to: Starting with the target frequency at the last time point, the transfer frequency corresponding to the target frequency at each time point is determined as the target frequency at the previous time point. The transfer frequency refers to the frequency corresponding to the minimum transfer cost from multiple frequencies at the previous time point to the target frequency at this time point.

[0299] In some embodiments, the plurality of first time points includes the first time point and the last time point among a plurality of time points.

[0300] This application provides a rotational speed determination scheme that applies a local cost constraint based on spectral intensity only at the first time point, thus ensuring the frequency accuracy at the critical time point. However, there are no trajectory shape constraints for the second time point other than the first time point. The target frequency at the second time point is determined entirely based on free optimization of the time-frequency energy ridge. This avoids trajectory jumps caused by noise when there are no constraints, and retains the true nonlinear rotational speed characteristics through optimization of the time-frequency energy ridge, thereby improving the accuracy of rotational speed determination.

[0301] Regarding the apparatus in the above embodiments, the specific manner in which each unit performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0302] In some embodiments, the computer device is provided as a terminal. Figure 11 This illustration shows a schematic diagram of a terminal 1100 provided in an exemplary embodiment of this application. The terminal 1100 may be a smartphone, tablet computer, MP3 player (Moving Picture Experts Group Audio Layer III), MP4 player (Moving Picture Experts Group Audio Layer IV), laptop computer, or desktop computer. The terminal 1100 may also be referred to as a user device, portable terminal, laptop terminal, desktop terminal, or other names.

[0303] Typically, terminal 1100 includes a processor 1101 and a memory 1102.

[0304] Processor 1101 may include one or more processing cores, such as a quad-core processor, an octa-core processor, etc. Processor 1101 may be implemented using at least one hardware form selected from DSP (Digital Signal Processing), FPGA (Field-Programmable Gate Array), and PLA (Programmable Logic Array). Processor 1101 may also include a main processor and a coprocessor. The main processor, also known as a CPU (Central Processing Unit), is used to process data in the wake-up state; the coprocessor is a low-power processor used to process data in the standby state. In some embodiments, processor 1101 may integrate a GPU (Graphics Processing Unit), which is responsible for rendering and drawing the content to be displayed on the screen. In some embodiments, processor 1101 may also include an AI (Artificial Intelligence) processor, which is used to handle computational operations related to machine learning.

[0305] The memory 1102 may include one or more computer-readable storage media, which may be non-transitory. The memory 1102 may also include high-speed random access memory and non-volatile memory, such as one or more disk storage devices or flash memory devices. In some embodiments, the non-transitory computer-readable storage media in the memory 1102 are used to store at least one program code, which is executed by the processor 1101 to implement the rotational speed determination method provided in the method embodiments of this application.

[0306] In some embodiments, the terminal 1100 may also optionally include a peripheral device interface 1103 and at least one peripheral device. The processor 1101, memory 1102, and peripheral device interface 1103 can be connected via a bus or signal line. Each peripheral device can be connected to the peripheral device interface 1103 via a bus, signal line, or circuit board. Specifically, the peripheral device includes at least one of the following: a radio frequency circuit 1104, a display screen 1105, a camera assembly 1106, an audio circuit 1107, and a power supply 1108.

[0307] Peripheral device interface 1103 can be used to connect at least one I / O (Input / Output) related peripheral device to processor 1101 and memory 1102. In some embodiments, processor 1101, memory 1102 and peripheral device interface 1103 are integrated on the same chip or circuit board; in some other embodiments, any one or two of processor 1101, memory 1102 and peripheral device interface 1103 can be implemented on separate chips or circuit boards, which is not limited in this embodiment.

[0308] The radio frequency (RF) circuit 1104 is used to receive and transmit RF (Radio Frequency) signals, also known as electromagnetic signals. The RF circuit 1104 communicates with communication networks and other communication devices via electromagnetic signals. The RF circuit 1104 converts electrical signals into electromagnetic signals for transmission, or converts received electromagnetic signals back into electrical signals. Optionally, the RF circuit 1104 includes: an antenna system, an RF transceiver, one or more amplifiers, a tuner, an oscillator, a digital signal processor, a codec chipset, a user identity module card, etc. The RF circuit 1104 can communicate with other terminals through at least one wireless communication protocol. This wireless communication protocol includes, but is not limited to: metropolitan area networks (MANs), various generations of mobile communication networks (2G, 3G, 4G, and 5G), wireless local area networks (WLANs), and / or WiFi (Wireless Fidelity) networks. In some embodiments, the RF circuit 1104 may also include circuitry related to NFC (Near Field Communication), which is not limited in this application.

[0309] Display screen 1105 is used to display a UI (User Interface). This UI may include graphics, text, icons, videos, and any combination thereof. When display screen 1105 is a touch display screen, it also has the ability to collect touch signals on or above its surface. These touch signals can be input as control signals to processor 1101 for processing. In this case, display screen 1105 can also be used to provide virtual buttons and / or a virtual keyboard, also known as soft buttons and / or a soft keyboard. In some embodiments, there may be one display screen 1105, which serves as the front panel of terminal 1100; in other embodiments, there may be at least two display screens, respectively disposed on different surfaces of terminal 1100 or in a folded design; in still other embodiments, display screen 1105 may be a flexible display screen, disposed on a curved or folded surface of terminal 1100. Furthermore, display screen 1105 may also be configured as a non-rectangular, irregular shape, i.e., a non-rectangular screen. The display screen 1105 can be made of materials such as LCD (Liquid Crystal Display) and OLED (Organic Light-Emitting Diode).

[0310] The camera assembly 1106 is used to acquire images or videos. Optionally, the camera assembly 1106 includes a front-facing camera and a rear-facing camera. Typically, the front-facing camera is located on the front panel of the terminal, and the rear-facing camera is located on the back of the terminal. In some embodiments, there are at least two rear-facing cameras, which are any one of a main camera, a depth-sensing camera, a wide-angle camera, and a telephoto camera, to achieve background blurring by fusion of the main camera and the depth-sensing camera, panoramic shooting by fusion of the main camera and the wide-angle camera, VR (Virtual Reality) shooting, or other fusion shooting functions. In some embodiments, the camera assembly 1106 may also include a flash. The flash can be a single-color temperature flash or a dual-color temperature flash. A dual-color temperature flash refers to a combination of a warm light flash and a cool light flash, which can be used for light compensation at different color temperatures.

[0311] The audio circuit 1107 may include a microphone and a speaker. The microphone is used to collect sound waves from the user and the environment, converting the sound waves into electrical signals that are input to the processor 1101 for processing, or input to the radio frequency circuit 1104 for voice communication. For stereo sound acquisition or noise reduction purposes, multiple microphones may be used, each positioned at a different location on the terminal 1100. The microphone may also be an array microphone or an omnidirectional microphone. The speaker is used to convert electrical signals from the processor 1101 or the radio frequency circuit 1104 into sound waves. The speaker may be a conventional diaphragm speaker or a piezoelectric ceramic speaker. When the speaker is a piezoelectric ceramic speaker, it can convert electrical signals not only into audible sound waves but also into inaudible sound waves for purposes such as distance measurement. In some embodiments, the audio circuit 1107 may also include a headphone jack.

[0312] Power supply 1108 is used to power the various components in terminal 1100. Power supply 1108 can be AC ​​power, DC power, a disposable battery, or a rechargeable battery. When power supply 1108 includes a rechargeable battery, the rechargeable battery can support wired charging or wireless charging. The rechargeable battery can also be used to support fast charging technology.

[0313] Those skilled in the art will understand that Figure 11 The structure shown does not constitute a limitation on terminal 1100 and may include more or fewer components than shown, or combine certain components, or use different component arrangements.

[0314] Figure 12 This is a schematic diagram of a server structure according to an embodiment of this application. The server 1200 can vary considerably due to different configurations or performance. It may include one or more Central Processing Units (CPUs) 1201 and one or more memories 1202. The memories 1202 are used to store executable program code, and the processors 1201 are configured to execute the executable program code to implement the speed determination method provided in the various method embodiments described above. Of course, the server may also have wired or wireless network interfaces, a keyboard, and input / output interfaces for input and output. The server may also include other components for implementing device functions, which will not be elaborated here.

[0315] In an exemplary embodiment, a computer-readable storage medium is also provided, which, when executed by a processor of a computer device, enables the computer device to perform the above-described speed determination method. Optionally, the computer-readable storage medium may be a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, or optical data storage device, etc.

[0316] In an exemplary embodiment, a computer program product is also provided, the computer program product including a computer program that, when executed by a processor, implements the above-described speed determination method.

[0317] In some embodiments, the computer program product involved in the present application can be deployed and executed on a computer device, or on multiple computer devices located in one location, or on multiple computer devices distributed in multiple locations and interconnected through a communication network. Multiple computer devices distributed in multiple locations and interconnected through a communication network can form a blockchain system.

[0318] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims. All the above-described optional technical solutions can be combined in any way to form optional embodiments of this application, and will not be elaborated upon here.

[0319] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A method for determining rotational speed, characterized in that, The method includes: The vibration signal of the rotating machinery is obtained from a time-frequency diagram and a constraint frequency at multiple first time points. The time-frequency diagram includes the spectral intensity of the vibration signal at multiple frequencies at multiple time points, and the multiple time points include the multiple first time points. For each first time point, based on the constraint frequency at the first time point and the spectral intensity of the plurality of frequencies at the first time point, the local cost of the plurality of frequencies at the first time point is determined. The local cost of each frequency is used to measure the degree of matching between the frequency and the time-frequency energy ridge of the time-frequency map. For each second time point, based on the spectral intensity of the plurality of frequencies at the second time point, the local cost of the plurality of frequencies at the second time point is determined, wherein the second time point is a time point other than the first time point among the plurality of time points; Based on the local costs of the multiple frequencies at the multiple time points, the target frequencies of the multiple time points are determined respectively, and the target frequency of each time point refers to the frequency selected by the time-frequency energy ridge at the time point. The rotational speed of the rotating machinery at each time point is determined based on the target frequency at that time point.

2. The method according to claim 1, characterized in that, For each first time point, determining the local cost of each of the plurality of frequencies at the first time point based on the constraint frequency at the first time point and the spectral intensity of the plurality of frequencies at the first time point includes: For each first time point, based on the spectral intensity and data function of the plurality of frequencies at the first time point, a first sub-cost of the plurality of frequencies at the first time point is determined, wherein the data function is used to constrain the target frequency at the first time point to the vicinity of the frequency with a large spectral intensity. Based on the constraint frequency at the first time point, the plurality of frequencies and the trap function, the second sub-cost of the plurality of frequencies at the first time point is determined respectively, and the trap function is used to constrain the target frequency at the first time point to be near the constraint frequency at the first time point. For each frequency, the local cost of the frequency at the first time point is determined based on the first sub-cost and the second sub-cost of the frequency at the first time point.

3. The method according to claim 2, characterized in that, The potential trap function includes a potential trap strength coefficient, which is used to constrain the degree of influence of the second sub-cost on the local cost. The method further includes: For each time point, the potential depression intensity coefficient for that time point is determined based on at least one of the signal-to-noise ratio, local spectral peak contrast, and noise floor estimate of the time-frequency plot at that time point. The local spectral peak contrast is used to indicate the prominence of the peak with the largest spectral intensity at that time point in the time-frequency plot, and the noise floor estimate is used to indicate the overall level of background noise at that time point in the time-frequency plot.

4. The method according to claim 2, characterized in that, The method further includes: For each first time point, if the difference between the frequency with the largest spectral intensity at the first time point in the time-frequency diagram and the constraint frequency is less than the difference threshold, the trap function is a quadratic function; If the difference between the frequency with the largest spectral intensity at the first time point in the time-frequency graph and the constraint frequency is not less than the difference threshold, the trap function is a linear function.

5. The method according to claim 1, characterized in that, The step of determining the target frequency for each of the multiple time points based on the local costs of the multiple frequencies at the multiple time points includes: Based on the local costs of the multiple frequencies at the multiple time points, the minimum cumulative cost of the multiple frequencies at the multiple time points is determined. The minimum cumulative cost of each frequency at each time point is used to measure the degree of matching between the path corresponding to the frequency and the time-frequency energy ridge. The path refers to the frequency path from the first time point of the time-frequency graph to the time point, with the frequency at the time point as the endpoint. The target frequency for each of the multiple time points is determined based on the minimum cumulative cost of the multiple frequencies at the multiple time points.

6. The method according to claim 5, characterized in that, The step of determining the minimum cumulative cost of the multiple frequencies at the multiple time points based on the local costs of the multiple frequencies at the multiple time points includes: For each time point, based on the minimum cumulative cost of the plurality of frequencies at the previous time point, the transfer cost of each frequency at the time point relative to the plurality of frequencies at the previous time point is determined. The transfer cost of each frequency at the time point relative to the plurality of frequencies at the previous time point refers to the cost of frequency jump when transferring from the plurality of frequencies at the previous time point to the frequency at the time point. The minimum cumulative cost of the plurality of frequencies at the first time point of the time-frequency diagram is the local cost of the plurality of frequencies at the first time point. For each frequency at each time point, the minimum value of the transfer costs of the frequency relative to the plurality of frequencies is determined as the minimum transfer cost of the frequency at that time point. Based on the minimum transfer cost of the frequency at that time point and the local cost, the minimum cumulative cost of the frequency at that time point is determined.

7. The method according to claim 6, characterized in that, The step of determining the transfer cost of each frequency at the given time point relative to the plurality of frequencies at the previous time point, based on the minimum cumulative cost of the plurality of frequencies at the given time point, includes: For each frequency at the time point, a smoothing cost is determined between the frequency and multiple frequencies at the previous time point based on a smoothing function, wherein the smoothing function is used to constrain the smoothness of the time-frequency energy ridge. Based on the minimum cumulative cost of the plurality of frequencies at the previous time point and the smoothing cost between the frequencies and the plurality of frequencies, the transfer cost of the frequency at the time point relative to the plurality of frequencies at the previous time point is determined.

8. The method according to claim 7, characterized in that, The smoothing function includes a smoothing coefficient, which is used to constrain the degree of influence of the smoothing cost on the transition cost; the method further includes: The smoothing coefficient is determined based on the degree of interference from the interfering factors in the time-frequency graph.

9. The method according to claim 6, characterized in that, The target frequency at the last time point among the plurality of time points is the frequency corresponding to the minimum value among the plurality of minimum cumulative costs of the plurality of frequencies at the last time point. Determining the target frequency for each of the plurality of time points based on the minimum cumulative costs of the plurality of frequencies at the plurality of time points includes: Starting from the target frequency at the last time point, the transfer frequency corresponding to the target frequency at each time point is determined as the target frequency of the previous time point. The transfer frequency refers to the frequency corresponding to the minimum transfer cost from multiple frequencies at the previous time point to the target frequency at the current time point.

10. The method according to claim 1, characterized in that, The plurality of first time points includes the first time point and the last time point among the plurality of time points.

11. A speed determining device, characterized in that, The device includes: The acquisition module is used to acquire the time-frequency diagram of the vibration signal of the rotating machinery and the constraint frequencies at multiple first time points. The time-frequency diagram includes the spectral intensity of the vibration signal at multiple frequencies at multiple time points, and the multiple time points include the multiple first time points. The determination module is used to determine the local cost of the plurality of frequencies at the first time point for each first time point, based on the constraint frequency at the first time point and the spectral intensity of the plurality of frequencies at the first time point respectively. The local cost of each frequency is used to measure the degree of matching between the frequency and the time-frequency energy ridge of the time-frequency diagram. The determining module is further configured to, for each second time point, determine the local cost of the plurality of frequencies at the second time point based on the spectral intensity of the plurality of frequencies at the second time point, wherein the second time point is a time point other than the first time point among the plurality of time points; The determining module is further configured to determine the target frequency of each of the multiple time points based on the local cost of the multiple frequencies at the multiple time points respectively, wherein the target frequency of each time point refers to the frequency selected by the time-frequency energy ridge at the time point; The determining module is also used to determine the rotational speed of the rotating machinery at each time point based on the target frequency at each time point.

12. A computer device, characterized in that, include: processor; Memory used to store the processor's executable instructions; The processor is configured to execute the instructions to implement the rotational speed determination method as described in any one of claims 1 to 10.

13. A computer-readable storage medium, characterized in that, When the instructions in the computer-readable storage medium are executed by the processor of a computer device, the computer device is able to perform the rotational speed determination method according to any one of claims 1 to 10.

14. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the rotational speed determination method according to any one of claims 1 to 10.

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