A ball screw pair fault diagnosis method based on short-time window energy kurtosis spectrum

Abstract

The application discloses a kind of ball screw pair fault diagnosis methods based on short-time window energy kurtosis spectrum, current, position and speed and other servo control signals in the running process of ball screw pair are collected, according to position signal and speed signal extract stable running section;Zero-mean processing is carried out to stable running section current signal and short-time Fourier transform is used to construct time-frequency spectrum matrix;According to preset bandwidth, sub-band division is carried out to time-frequency spectrum matrix and the energy of each sub-band in each short-time window is calculated;Further combined with position signal, the energy of sub-band is mapped to lead space, and lead-energy matrix is formed;The kurtosis and / or negative entropy of the energy distribution sequence of each sub-band in the lead direction is calculated, to determine the fault sensitive band;According to the lead energy anomaly corresponding to fault sensitive band, fault diagnosis, fault location and fault degree evaluation are completed;The application has the advantages of strong working condition adaptability, small amount of calculation, good interpretability and easy engineering deployment.

Description

Technical Field

[0001] This invention relates to the field of ball screw condition monitoring and intelligent fault diagnosis technology, and in particular to a ball screw pair fault diagnosis method based on short time window energy kurtosis spectrum. Background Technology

[0002] Ball screw assemblies are key transmission components that convert rotary motion into linear motion. They offer advantages such as high transmission accuracy, high efficiency, and fast response, and are widely used in precision machining, aerospace, industrial robotics, and intelligent personal equipment. As high-end equipment develops towards high speed, heavy load, long stroke, and high precision, ball screw assemblies operate in complex environments with varying speeds, loads, strokes, and multi-physics coupling. Their failure evolution often exhibits characteristics of early, weak failures, multi-source coupling, and gradual degradation. Typical failures include ball wear, ball pitting, ball breakage, raceway wear, raceway scratches, preload loosening, lubrication failure, nut jamming, and coupling loosening.

[0003] Current ball screw pair condition monitoring largely relies on vibration sensors, accelerometers, or additional measurement hardware. However, ball screw pairs have a compact structure and limited installation space. Adding sensors not only increases hardware costs and maintenance workload but also leads to problems such as difficult placement, asynchronous data acquisition, and insufficient signal stability. In contrast, servo systems can natively output control signals such as current, position, speed, torque, and tracking error during operation, providing a feasible path for ball screw pair fault monitoring without the need for additional vibration sensors.

[0004] Existing methods for ball screw pair fault diagnosis using built-in servo signals mainly include signal processing-based methods (Qibo Yang, Xiang Li, Yinglu Wang, et al. Fault Diagnosis of Ball Screwin Industrial Robots Using Non-Stationary Motor Current Signals, ProcediaManufacturing.48(2020),1102-1108) and data-driven methods (Fei Jiang, Qin Liang, Zhaoqian Wu, et al. A zero-cost unsupervised transfer method based on non-vibration signals fusion for ball screw fault diagnosis, Knowledge-BasedSystems.288(2024),111475). The former typically relies on time-domain statistics, frequency-domain features, or time-frequency analysis results; the latter relies on a large number of labeled fault samples for training. Since ball screw pairs often operate under varying conditions in actual industrial scenarios, the servo signals exhibit significant non-stationarity, making it difficult for traditional single-signal analysis and fixed-band analysis methods to stably extract local fault features. At the same time, while deep learning methods have the ability to learn features automatically, they often require a large amount of labeled data and high computing power, which is not conducive to deployment in resource-constrained industrial terminals.

[0005] Furthermore, existing technologies often only determine whether a fault exists, but struggle to simultaneously determine the severity of the fault and its specific lead location (Qibo Yang, Xiang Li, Yinglu Wang, et al. Fault Diagnosis of Ball Screw in Industrial Robots Using Non-Stationary Motor Current Signals, Procedia Manufacturing. 48(2020), 1102-1108; V. Pandhare, M. Miller, GW Vogl and J. Lee. Ball Screw Health Monitoring With Inertial Sensors, IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS. 19(2023), 7323-7334; FeiJiang, Qin Liang, Zhaoqian Wu, et al. A zero-cost unsupervised transfer method based on non-vibration signals fusion for ball screw fault diagnosis, Knowledge-Based). Systems. 288 (2024), 111475); many methods still rely on manual selection of sensitive frequency bands, which is highly subjective and lacks an interpretable adaptive screening mechanism. Therefore, it is of great significance to propose a lightweight ball screw pair fault diagnosis method that does not require additional vibration sensors, can adapt to varying operating conditions, and can realize fault location in lead space. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, the present invention aims to provide a ball screw pair fault diagnosis method based on short time window energy kurtosis spectrum. This method fully utilizes the original control signals of the servo system, such as current, position, and speed, and achieves local fault feature extraction, fault-sensitive frequency band identification, and fault location by following the technical route of "operating condition division - time-frequency analysis - sub-band energy extraction - lead space reconstruction - statistical enhancement - anomaly discrimination".

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A fault diagnosis method for ball screw pairs based on short-time window energy kurtosis spectrum includes the following steps: acquiring servo control signals during the operation of the ball screw pair, wherein the servo control signals include at least current signals, position signals, and speed signals, or speed signals obtained by differentiating the position signals; dividing the original servo control signals into operating conditions based on the variation range of the position signals, the directional consistency of the speed signals, and the degree of speed fluctuation, and extracting stable operating segments; performing zero-mean processing on the current signals corresponding to the stable operating segments, and constructing a time-frequency spectrum matrix using short-time Fourier transform; and performing fault diagnosis according to a preset bandwidth. The frequency axis of the time-spectrum matrix is ​​divided into sub-bands, and the energy of each sub-band within each short time window is calculated to form a sub-band-time-energy matrix. Using the position signal corresponding to the stable operating segment, the sub-band-time-energy matrix is ​​mapped to the lead space of the ball screw pair to obtain the lead-energy matrix. Statistical characteristics are calculated for the energy distribution sequence of each sub-band in the lead direction, and fault-sensitive frequency bands are identified based on the statistical characteristics. Anomaly criteria are established based on the lead energy distribution corresponding to the fault-sensitive frequency bands to perform fault diagnosis, fault location, and fault severity assessment of the ball screw pair.

[0008] The servo control signal also includes at least one of torque signal, position deviation signal, and following error signal.

[0009] The position signal is used to characterize the axial movement position of the ball screw pair, the current signal is used to characterize the dynamic response of the servo motor under mechanical state changes and load disturbances, and the speed signal is used to characterize the movement direction and operational stability of the ball screw pair.

[0010] The extraction of stable operating segments includes: determining the start and end positions of the ball screw pair entering the effective working range based on the position signal to eliminate start-stop phases and invalid motion ranges; distinguishing between forward and reverse motion based on the sign of the speed signal; and selecting continuous signal segments with small speed changes as stable operating segments based on whether the speed standard deviation, speed deviation rate, or local speed fluctuation amplitude meets the preset stability conditions.

[0011] The short-time Fourier transform uses a preset physical time length. Analysis window and overlap rate Frame-by-frame analysis is performed on the current signal during the stable operation phase, with the window length satisfying... The sliding step size satisfies ,in The sampling frequency is ; for the , After applying a window function to the signal segments within each time window, a Fast Fourier Transform is performed to obtain the spectral amplitude of the corresponding time window, which forms the time-spectrum matrix. The short-time Fourier transform corresponding to the r-th time window is expressed as follows: in, , Total number of time windows; This is a discrete signal sequence after zero-mean processing; For analysis window functions; The window length is the number of sample points contained in a single time window. This is the sliding step size between two adjacent time windows; Index of local sampling points within the time window ; Angular frequency; The imaginary unit is used here. The Hanning window is used as the rotation window function. The spectral results of each time window are arranged column-wise to obtain the time-spectrum matrix. Its magnitude matrix satisfy .

[0012] The frequency axis sub-band is divided into equal-width or non-equal-width divisions; for the first Sub-band and the first The sub-band energy is obtained by summing or integrating the spectral amplitude within the sub-band within a time window, thereby forming the sub-band-time energy matrix.

[0013] The process of mapping the sub-band-time energy matrix to the lead space includes: determining the total number of leads experienced based on the relationship between the start and end positions of the stable operating segment and the lead length of a single ball screw; establishing a correspondence between the center position of the time window and the position signal to determine the lead interval to which each time window belongs; and accumulating or averaging the sub-band energy of each time window belonging to the same lead interval to obtain the lead-energy matrix. .

[0014] The statistical features include kurtosis or negative entropy; wherein, when kurtosis is used... As a statistical feature, kurtosis values ​​are calculated for the energy sequence at each lead position for each sub-band to characterize the degree of energy concentration of that sub-band at a few lead positions. In the formula, For the first Kurtosis values ​​of individual frequency bands; The total lead number covered by the stable operating section of the ball screw pair; For the guide number, and ; Indicates the first The sub-band is in the first Energy at each lead position; For the first The average energy of each sub-band at each lead position; Let be the standard deviation of the corresponding energy sequence, and ; When using negative entropy as a statistical feature, the lead energy sequence of each sub-band is first standardized. Then, the expected difference between the nonlinear function and the standard Gaussian variable is used to construct a negative entropy approximation to characterize the degree to which the energy sequence of that sub-band deviates from the Gaussian distribution. Let... If the variable is a standard Gaussian variable, then the first... The approximate negative entropy of each sub-band can be written as: In the formula, For the first The approximate negative entropy of each sub-band; This represents the mathematical expectation operation; and For nonlinear functions as defined; is the independent variable of the nonlinear function; Standard Gaussian variables; For the first The normalized lead-range energy sequence of each sub-band, the first in this sequence The elements are ; For the first The sub-band is in the first Standardized energy value at each lead position; Indicates the first The sub-band is in the first Energy at each lead; For the first The average energy of each sub-band at each lead position; This represents the standard deviation of the corresponding energy sequence.

[0015] The anomaly criterion is obtained by establishing a normal energy fluctuation range for the lead energy sequence corresponding to the fault-sensitive frequency band. The normal energy fluctuation range is obtained by adding or subtracting three standard deviations from the mean or by robust statistical estimation. When the lead energy corresponding to a certain lead position exceeds the normal energy fluctuation range, it is determined that there is an abnormal response at that lead position, and the severity of the fault is characterized by the degree to which the abnormal peak deviates from the mean.

[0016] A ball screw pair fault diagnosis system based on short-time-window energy kurtosis spectrum includes: Signal acquisition and working condition division module: used to acquire servo control signals during the operation of the ball screw pair, and extract stable operating segments based on position and speed signals; Time-frequency analysis and sub-band energy calculation module: used to preprocess and perform short-time Fourier transform on the current signal corresponding to the stable operation segment to construct the time-frequency spectrum matrix, and to divide the time-frequency spectrum matrix into sub-bands and calculate the energy of each sub-band in each short time window; Lead space reconstruction and feature recognition and fault determination module: It is used to combine position signals to map sub-band energy to lead space to form lead-energy matrix, calculate the statistical features corresponding to each sub-band and identify fault-sensitive frequency bands, and complete fault diagnosis, fault location and fault severity assessment based on the lead energy anomaly corresponding to the fault-sensitive frequency band.

[0017] The system is deployed in a servo controller, industrial computer, or edge computing terminal. The diagnostic output module is used to output the abnormal lead number, abnormality level index, and alarm information.

[0018] Compared with existing technologies, this invention has at least the following advantages: First, it can perform online diagnosis directly using the native signals of the servo system without relying on additional vibration sensors; second, by mapping sub-band energy to lead space, it achieves spatially interpretable expression of fault characteristics, which is beneficial for accurately locating fault positions; third, by using statistical indicators sensitive to non-Gaussianity such as kurtosis and negative entropy, it can amplify the weak impact characteristics caused by local faults, which is suitable for early fault identification; fourth, it adopts a sub-band adaptive screening mechanism to avoid misjudgment caused by noise interference in a single frequency band; fifth, the overall algorithm is lightweight and computationally inexpensive, making it easy to deploy on servo controllers, industrial computers, or edge terminals. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the process of an embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of the speed and current signals corresponding to the stable operation segment in an embodiment of the present invention.

[0021] Figure 3 This is a schematic diagram of the lead-frequency energy distribution and statistical characteristic curves of each sub-band in an embodiment of the present invention.

[0022] Figure 4 This is a lead energy distribution diagram of the sensitive frequency band in an embodiment of the present invention.

[0023] Figure 5 This is a bar chart showing the lead energy distribution in the sensitive frequency band according to an embodiment of the present invention.

[0024] Figure 6 This is a schematic diagram of the abnormality index corresponding to different fault types in embodiments of the present invention. Detailed Implementation

[0025] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings. It should be understood that the following embodiments are only for illustrating the present invention and are not intended to limit the scope of protection of the present invention; all equivalent substitutions or modifications made based on the technical concept of the present invention should fall within the scope of protection of the present invention.

[0026] like Figure 1 As shown, a fault diagnosis method for ball screw pairs based on short-time-window energy kurtosis spectrum is proposed, targeting servo drive systems under variable speed, variable load, and variable stroke conditions. The acquired servo control signals include current signals. Position signal and speed signal When the system does not directly output a velocity signal, the velocity estimate can be obtained from the position signal using a center differential method. ,in The sampling frequency.

[0027] Step S001: Acquire servo control signals and construct the original data sequence. In this embodiment, current, speed, and position data are read from the servo system log file. The current signal can correspond to the phase current of the servo motor or the equivalent drive current, and the position signal is the axial displacement or angular position conversion value of the ball screw pair. For decimal data stored in string format, the format is first converted and then a unified timing input is formed. Step S002: Extract the stable operating segment. During start-up, stop-reversal, and acceleration / deceleration phases, ball screw pairs typically contain a large number of transient components unrelated to faults. Therefore, firstly, the effective operating range is determined based on the position signal; then, the forward or reverse motion is identified based on the sign of the speed signal; finally, the stable segment is selected based on whether the local speed fluctuation is less than a preset threshold. Let the start and end times of the effective operating range be... and The signal for the stable operating segment can then be expressed as: In a preferred embodiment, the stable operating segment satisfies the following conditions: first, the position signal is within the effective working stroke range; second, the speed sign remains consistent to distinguish between forward and reverse motion; and third, local speed fluctuations meet preset stability constraints. The length can be set to... The sliding interval satisfies: in, and Let represent the mean and standard deviation of the velocity sequence within this interval, respectively. To preset a stable threshold, To prevent extremely small positive numbers with a denominator of zero, continuous intervals satisfying the above conditions are considered stationary segments for subsequent analysis. For example... Figure 2The diagram illustrates the speed and current waveforms of the stationary signal captured in this embodiment. It shows that within the captured stationary operating range, the servo motor speed remains essentially stable, exhibiting only minor periodic fluctuations near the mean, without significant acceleration or deceleration abrupt changes. Simultaneously, the corresponding current signal amplitude also remains within a relatively stable range during this period, exhibiting continuous and uniform periodic oscillation characteristics, effectively eliminating transient impact interference generated during the ball screw's start-stop and commutation phases. This indicates that the captured signal segment satisfies the preset stationarity conditions well, providing a reliable data foundation for accurately constructing the time-frequency spectrum and extracting the weak energy characteristics of local faults. Step S003: Preprocess the current signal during the stable operation phase and construct the time-spectrum matrix. First, zero-mean processing is performed on the current signal during the stable operation phase to eliminate the influence of DC components and static bias; then, short-time Fourier transform is used to perform frame-by-frame analysis on the current signal; let the sampling frequency be... The physical duration of the analysis window is Window overlap rate Then the window length is The sliding step size between two adjacent windows is ; for the first There is a time window. ;in, , Total number of time windows; This is a discrete signal sequence after zero-mean processing; For analysis window functions; The window length is the number of sample points contained in a single time window. This is the sliding step size between two adjacent time windows; Index of local sampling points within the time window ; Angular frequency; The Hanning window is used here as the imaginary unit for the rotation window function. In this embodiment, the Hanning window is preferably used, with a sampling frequency of 16000Hz, a window length of 0.08s, an overlap rate of 0.5, and a short-time Fourier transform calculated with a frequency resolution of 2Hz.

[0028] Step S004: Divide the time-frequency spectrum matrix into sub-bands and calculate the sub-band energy. Arrange the frequency axes of the time-frequency spectrum matrix according to a preset bandwidth. Divided into Sub-band, the first The frequency range corresponding to each sub-band is For each time window, sum or integrate the spectral amplitude within the corresponding sub-band to obtain the first... The sub-band is in the first Energy within a time window A segmented bandpass filter can be used to divide the spectral amplitude, forming a sub-band-time energy matrix of all sub-bands across all time windows. In this embodiment, the decomposition level is 7, corresponding to a sub-band bandwidth of 62.5Hz, resulting in a total of 128 sub-bands. Step S005: Map the sub-band time-energy matrix to the lead space. Let the ball screw lead length be L, and the starting position corresponding to the stable operating segment be... The termination position is The total number of leads can then be calculated based on the relationship between displacement change and lead length. Furthermore, a mapping relationship is established between the center position of each time window and the position signal to determine its corresponding lead interval. The energy of each time window sub-band within the same lead interval is then accumulated or averaged to obtain the lead-energy matrix. ,See Figure 3 The left figure shows the energy distribution in the frequency domain for different leads in this embodiment. After spatial domain reconstruction, the spectral energy that originally varied with time has been successfully mapped and aligned to the physical lead space of the ball screw. This two-dimensional matrix diagram intuitively shows the changes in energy of each frequency band with the lead position throughout the entire stable operating stroke: the background energy of most frequency bands in the figure is low (shown in dark blue), but there are obvious horizontal high energy bands in certain specific frequency ranges. This matrix representation, which precisely binds energy to physical spatial position, not only effectively eliminates the time axis stretching or compression effect caused by small speed fluctuations in the actual operation of the servo motor on the time domain analysis, making the characteristics of each position highly comparable, but also lays an intuitive and reliable data foundation for the next step of independently calculating the statistical characteristics (such as energy kurtosis) of each sub-frequency band along the lead direction and thereby adaptively screening out fault-sensitive frequency bands. Step S006: Identify fault-sensitive frequency bands. For each sub-band in the lead-energy matrix, identify the lead energy sequence... Calculate its statistical characteristics; preferably, kurtosis is used as the statistical characteristic. ,in and These are the mean and standard deviation of the lead energy sequence for this sub-band, respectively. The larger the value, the more concentrated the energy of that sub-band is at a few lead positions. Alternatively, negative entropy can be used as a statistical feature. First, the lead energy sequence is standardized to obtain... redefine the nonlinear function and ,set up If the variable is a standard Gaussian variable, then the negative entropy approximation can be expressed as: The sub-band with the largest statistical eigenvalue is selected as the fault-sensitive frequency band. Figure 3 The right figure shows that the selected instance is most sensitive in the 91st sub-band; Step S007: Establish anomaly criteria and complete fault location. For the lead energy sequence corresponding to the fault-sensitive frequency band... Calculate its mean and standard deviation Construct normal fluctuation threshold and When a certain lead position satisfies When an abnormal response is detected at a certain lead position, it can be identified as a potential fault location. See [link to relevant documentation]. Figure 4 and Figure 5 As can be seen, the lead screw in this embodiment failed at the 19th lead. To describe the severity of the failure, an anomaly severity index can be further constructed. ,in To prevent extremely small positive numbers with a denominator of zero, a method is adopted... Similar indicators to scores differentiate fault severity, see... Figure 6 According to The fault is classified by score in this embodiment. The score is 4.07.

[0029] By combining the above steps, this invention can achieve local fault feature extraction, lead position localization, and anomaly degree assessment of ball screw pairs without relying on a large number of fault samples or additional vibration sensors. This method is particularly suitable for industrial scenarios where servo control signals already exist but additional sensors are inconvenient to deploy, and can serve as important technical support for online health monitoring and maintenance decision-making for ball screw pairs.

Claims

1. A method for fault diagnosis of ball screw pairs based on short-time-window energy kurtosis spectrum, characterized in that, Includes the following steps: Servo control signals during the operation of the ball screw pair are acquired. These servo control signals include at least current signals, position signals, and speed signals, or speed signals derived from the position signals. Based on the variation range of the position signals, the directional consistency of the speed signals, and the degree of speed fluctuation, the original servo control signals are divided into operating conditions to extract stable operating segments. The current signals corresponding to the stable operating segments are zero-mean processed, and a time-frequency spectrum matrix is ​​constructed using short-time Fourier transform. The frequency axes of the time-frequency spectrum matrix are divided into sub-bands according to a preset bandwidth, and the energy of each sub-band within each short time window is calculated to form a sub-band-time energy matrix. Using the position signal corresponding to the stable operating segment, the sub-band-time energy matrix is ​​mapped to the lead space of the ball screw pair to obtain the lead-energy matrix; Statistical characteristics are calculated for the energy distribution sequence of each sub-band in the lead direction, and fault-sensitive frequency bands are identified based on the statistical characteristics. Anomaly criteria are established based on the lead energy distribution corresponding to the fault-sensitive frequency band to perform fault diagnosis, fault location and fault severity assessment on the ball screw pair.

2. The method for diagnosing ball screw pair faults according to claim 1, characterized in that, The position signal is used to characterize the axial movement position of the ball screw pair, the current signal is used to characterize the dynamic response of the servo motor under mechanical state changes and load disturbances, and the speed signal is used to characterize the movement direction and running stability of the ball screw pair. The servo control signal also includes at least one of torque signal, position deviation signal, and following error signal.

3. The method for diagnosing ball screw pair faults according to claim 1, characterized in that, The extraction of stable operating segments includes: determining the start and end positions of the ball screw pair entering the effective working range based on the position signal to eliminate start-stop phases and invalid motion ranges; distinguishing between forward and reverse motion based on the sign of the speed signal; and selecting continuous signal segments with small speed changes as stable operating segments based on whether the speed standard deviation, speed deviation rate, or local speed fluctuation amplitude meets the preset stability conditions.

4. The method for diagnosing ball screw pair faults according to claim 1, characterized in that, The short-time Fourier transform uses a preset physical time length. Analysis window and overlap rate Frame-by-frame analysis is performed on the current signal during the stable operation phase, with the window length satisfying... The sliding step size satisfies ,in The sampling frequency is ; for the , After applying a window function to the signal segments within each time window, a Fast Fourier Transform is performed to obtain the spectral amplitude of the corresponding time window, which forms the time-spectrum matrix. The short-time Fourier transform corresponding to the r-th time window is expressed as follows: in, , Total number of time windows; This is a discrete signal sequence after zero-mean processing; For analysis window functions; The window length is the number of sample points contained in a single time window. This is the sliding step size between two adjacent time windows; This serves as an index for local sampling points within a time window. ; Angular frequency; The imaginary unit is used here. The Hanning window is used as the rotation window function. The spectral results of each time window are arranged column-wise to obtain the time-spectrum matrix. Its magnitude matrix satisfy .

5. The method for diagnosing ball screw pair faults according to claim 4, characterized in that, The frequency axis sub-band is divided into equal-width or non-equal-width divisions; for the first Sub-band and the first The sub-band energy is obtained by summing or integrating the spectral amplitude within the sub-band within a time window, thereby forming the sub-band-time energy matrix.

6. The method for diagnosing ball screw pair faults according to claim 1, characterized in that, The process of mapping the sub-band-time energy matrix to the lead space includes: determining the total number of leads experienced based on the relationship between the start and end positions of the stable operating segment and the lead length of a single ball screw; establishing a correspondence between the center position of the time window and the position signal to determine the lead interval to which each time window belongs; and accumulating or averaging the sub-band energy of each time window belonging to the same lead interval to obtain the lead-energy matrix. .

7. The method for diagnosing ball screw pair faults according to claim 1, characterized in that, The statistical features include kurtosis or negative entropy; wherein, when kurtosis is used... As a statistical feature, kurtosis values ​​are calculated for the energy sequence at each lead position for each sub-band to characterize the degree of energy concentration of that sub-band at a few lead positions. In the formula, For the first Kurtosis values ​​of individual frequency bands; The total lead number covered by the stable operating section of the ball screw pair; For the guide number, and ; Indicates the first The sub-band is in the first Energy at each lead position; For the first The average energy of each sub-band at each lead position; Let be the standard deviation of the corresponding energy sequence, and ; When using negative entropy as a statistical feature, the lead energy sequence of each sub-band is first standardized. Then, the expected difference between the nonlinear function and the standard Gaussian variable is used to construct a negative entropy approximation to characterize the degree to which the energy sequence of that sub-band deviates from the Gaussian distribution. Let... If the variable is a standard Gaussian variable, then the first... The approximate negative entropy of each sub-band can be written as: In the formula, For the first The approximate negative entropy of each sub-band; This represents the mathematical expectation operation; and For nonlinear functions as defined; is the independent variable of the nonlinear function; Standard Gaussian variables; For the first The normalized lead-range energy sequence of each sub-band, the first in this sequence The elements are ; For the first The sub-band is in the first Standardized energy value at each lead position; Indicates the first The sub-band is in the first Energy at each lead; For the first The average energy of each sub-band at each lead position; This represents the standard deviation of the corresponding energy sequence.

8. The method for diagnosing ball screw pair faults according to claim 1, characterized in that, The anomaly criterion is obtained by establishing a normal energy fluctuation range for the lead energy sequence corresponding to the fault-sensitive frequency band. The normal energy fluctuation range is obtained by adding or subtracting three standard deviations from the mean or by robust statistical estimation. When the lead energy corresponding to a certain lead position exceeds the normal energy fluctuation range, it is determined that there is an abnormal response at that lead position, and the severity of the fault is characterized by the degree to which the abnormal peak deviates from the mean.

9. A ball screw pair fault diagnosis system based on short-time window energy kurtosis spectrum, implementing the ball screw pair fault diagnosis method based on short-time window energy kurtosis spectrum as described in any one of claims 1-8, characterized in that, include: Signal acquisition and working condition division module: used to acquire servo control signals during the operation of the ball screw pair, and extract stable operating segments based on position and speed signals; Time-frequency analysis and sub-band energy calculation module: used to preprocess and perform short-time Fourier transform on the current signal corresponding to the stable operation segment to construct the time-frequency spectrum matrix, and to divide the time-frequency spectrum matrix into sub-bands and calculate the energy of each sub-band in each short time window; Lead space reconstruction and feature recognition and fault determination module: It is used to combine position signals to map sub-band energy to lead space to form lead-energy matrix, calculate the statistical features corresponding to each sub-band and identify fault-sensitive frequency bands, and complete fault diagnosis, fault location and fault severity assessment based on the lead energy anomaly corresponding to the fault-sensitive frequency band.

10. The ball screw pair fault diagnosis system according to claim 9, characterized in that, The system is deployed in a servo controller, industrial computer, or edge computing terminal. The diagnostic output module is used to output the abnormal lead number, abnormality level index, and alarm information.

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