A multi-order evidence constraint-based rotating machinery non-tachometer rotation frequency estimation method

Abstract

The application discloses a rotating machinery non-tachometer rotational frequency estimation method based on multi-order evidence constraint, and belongs to the technical field of rotating machinery state monitoring and signal processing. The method takes a single-channel vibration signal as input, constructs robust spectrum evidence through background suppression, short-time Fourier transform, quantile normalization and nonlinear compression; combines to generate direct spectrum peak candidates and order anti-projection candidates, and fuses local amplitude evidence, multi-order consistency and dynamic continuity to establish a multi-hypothesis dynamic path search on a candidate fundamental frequency graph. Then, the start-up section protection mechanism and the harmonic lock protection mechanism are respectively used to conditionally correct the start-up section false lock caused by low-speed weak evidence and the frequency multiplication false lock caused by strong harmonics. The application does not need to take the tachometer signal as an estimation input, and can obtain continuous instantaneous rotational frequency and rotational speed estimation results based on only the vibration signal, thereby providing a reliable rotational speed benchmark for order analysis, fault diagnosis and state monitoring of variable-speed rotating machinery.

Description

Technical Field

[0001] This invention relates to the field of rotating machinery condition monitoring and signal processing technology, specifically to a rotating machinery frequency estimation method without a tachometer based on multi-order evidence constraints. Background Technology

[0002] During the start-up, acceleration, stabilization, deceleration, and load changes of rotating machinery, the fault modulation component, rotational order component, and structural response in its vibration signal will change with the instantaneous rotational frequency. If a reliable instantaneous rotational frequency trajectory cannot be obtained, conventional spectrum analysis, envelope analysis, and order analysis are prone to spectral line diffusion, order aliasing, and characteristic position shifts, which in turn affect the equipment condition identification and fault diagnosis results.

[0003] Existing methods for acquiring rotational frequency typically rely on speed encoders, photoelectric tachometers, or key-phase signals. In enclosed gearboxes, port cranes, and temporary monitoring scenarios, external speed sensors may be limited by installation space, wiring costs, and synchronous acquisition conditions; existing speed channels may also be affected by pulse loss, installation misalignment, or asynchronous sampling. Therefore, there is a practical need for a tachometer-less method that estimates instantaneous rotational frequency solely based on vibration signals.

[0004] Existing tachometer-less frequency estimation methods typically search for local maximum spectral peaks or trace single high-energy spectral ridges in the time-frequency representation and infer the frequency based on a pre-defined order relationship. However, in situations such as low-speed start-up, weak fundamental frequency amplitude, dominance of higher harmonics, low-frequency background drift, or strong structural resonance, the maximum spectral ridge in the time-frequency representation may not correspond to the true fundamental frequency. Frame-by-frame peak search lacks cross-time continuity constraints and is prone to jumping between different spectral ridges; while single-path search can limit frequency abrupt changes, it may prematurely lock onto low-frequency background or higher harmonics when initial evidence is insufficient, and continue to propagate along erroneous branches under subsequent continuity constraints.

[0005] Furthermore, when the true fundamental frequency itself is weak but its multiple integer harmonics are still visible, evaluating only the local amplitude at the candidate frequency location will lose the order structure information that can be used to identify the true fundamental frequency. Therefore, a frequency estimation method is needed that can jointly utilize local spectral evidence at candidate points, integer order consistency, and frequency shift dynamic continuity, and that sets up a conditional correction mechanism for false locking due to weak evidence in the initiation phase and false locking due to harmonic branches. Summary of the Invention

[0006] To address the limitations of existing technologies, this invention proposes a rotational frequency estimation method for rotating machinery without a tachometer, based on multi-order evidence constraints. Without inputting an external tachometer signal, this method reduces the occurrence of candidate fundamental frequency loss, path mislocking, and trajectory jumps caused by weak fundamental frequencies during low-speed startup, dominance of higher-order harmonics, low-frequency background, and strong local interference in the vibration signals of variable-speed rotating machinery, thereby improving the continuity and stability of instantaneous rotational frequency estimation.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows: A method for estimating the rotational frequency of rotating machinery without a tachometer based on multi-order evidence constraints, the specific steps of which are as follows: Step S1: Collect vibration signals and determine the analysis range.

[0008] A single-channel vibration signal is collected from the rotating machinery during variable speed operation, denoted as... , For time, the sampling frequency is denoted as . The candidate frequency search range is determined based on the equipment's permissible speed, transmission ratio, or the operating range of the monitored object. ,in These are the lower and upper limits of the candidate frequency transition, respectively. Determine the set of integer orders used for multi-order consensus evaluation. ,in, For the first Integer order.

[0009] Step S2: Construct robust spectrum evidence.

[0010] Low-frequency background suppression and robust amplitude normalization are performed on single-channel vibration signals with obvious slow-varying backgrounds to obtain preprocessed vibration signals. Perform a short-time Fourier transform on the preprocessed vibration signal and calculate the power time spectrum. Robust background at each frequency position is estimated along the time direction, and background normalization and nonlinear compression are performed on the power time spectrum to obtain robust spectral evidence.

[0011] Trend subtraction and robust amplitude normalization are performed on vibration signals with a slowly varying background to obtain preprocessed vibration signals: (1) In the formula, To preprocess the vibration signal; when low-frequency background suppression is not required, let .

[0012] For zero-phase filtering operators, This represents the median absolute deviation. To prevent the denominator from being too small, a positive stability constant is required; Time scale The above uses the moving median estimation for slow-varying trend estimation: (2) In the formula, It is a local time variable; Indicated by t Centered on, with a length of TThe median of the signal within the time interval, This is the median estimation function.

[0013] Perform short-time Fourier transform on the preprocessed vibration signal and calculate the power-time spectrum: (3) (4) In the formula, For the first One time frame, For frequency and time frame The complex short-time Fourier transform coefficients at the location; For time integration variables; For analysis window; It is an exponential function; The imaginary unit; This is for modular arithmetic operations on complex numbers.

[0014] Robust background at each frequency location is estimated along the time direction, and background normalization and nonlinear compression are performed to obtain robust spectral evidence. : (5) (6) In the formula, Robust spectral evidence after background normalization and nonlinear compression. Spectral evidence after background normalization; To prevent stable terms with excessively small denominators, for Quantile operator, Preset quantile level; For frequency From frame 1 to frame 2 The power sequence of the frames; The compression factor is greater than zero.

[0015] Step S3: Generate a candidate fundamental frequency set.

[0016] Direct spectral peak candidates and order backprojection candidates are generated simultaneously from the local maxima spectral peaks of each time frame. Direct spectral peak candidates retain directly observable fundamental frequency peaks, while order backprojection candidates map higher-order rotational components back to the potential fundamental frequency position, thus avoiding candidate loss when weak fundamental frequencies do not form significant spectral peaks.

[0017] In the Time frames Internally, extract the set of local maxima spectral peaks from robust spectral evidence. The search range will be within the specified range. The maximum spectral peaks within the range are used as the direct spectral peak candidate set: (7) In the formula, For the first The direct spectral peak candidate set of time frames; For the first k The first time frame p The frequency of the maximum spectral peak.

[0018] The maximum spectral peaks are back-projected onto the candidate frequency transition search interval according to the integer order relationship, resulting in the candidate set of order back-projections: (8) In the formula, For the first The order backprojection candidate set of time frames; This represents the upper limit of the frequency of evaluation of order evidence.

[0019] Merging the direct spectral peak candidate set and the order back projection candidate set, the candidate fundamental frequency set is: (9) In the formula, For the first The set of candidate fundamental frequencies for a time frame.

[0020] Step S4: Calculate the local amplitude evidence and multi-order consistency evidence of the candidate fundamental frequency respectively, and combine the two into the candidate node score.

[0021] For any candidate fundamental frequency First, calculate its local amplitude evidence score: (10) In the formula, Candidate fundamental frequency In the Local amplitude evidence score over time. This is to read the positive half-bandwidth of the candidate frequency neighborhood.

[0022] Subsequently, robust spectral evidence near each integer harmonic of the candidate fundamental frequency was read, providing multi-order observational support: (11) in, Candidate fundamental frequency In the Support for unnormalized multi-order observations obtained from time frames; For the first Non-negative weights of order, For the first h The half-bandwidth of the frequency neighborhood, This is an indicator function. It takes the value 1 when the condition inside the parentheses is true, indicating that the condition is true; otherwise, it takes the value 0 when the condition inside the parentheses is false, indicating that the condition is false.

[0023] Normalization of multi-order observations within the same time frame: (12) In the formula, for After the first Multi-order consistency score obtained by intra-temporal normalization u To iterate through the variables of candidate fundamental frequencies, It is a positive stability constant.

[0024] The candidate node score is: (13) In the formula, Candidate fundamental frequency In the Candidate node scores for each time frame; The weights are non-negative multi-order consensus weights. Local amplitude evidence reflects the spectral intensity of the candidate itself, while the multi-order consensus score reflects the degree to which its integer harmonic positions receive common support.

[0025] Step S5: Perform multi-hypothesis dynamic programming and obtain the main candidate fundamental frequency sequence.

[0026] A directed candidate graph is established with time frames as layers and candidate fundamental frequencies as nodes. The main candidate fundamental frequency sequence is searched through joint optimization of node scores and dynamic penalties for adjacent frames.

[0027] The dynamic penalty between candidate fundamental frequencies of adjacent time frames is defined as follows: (14) In the formula, For from the first Time frame candidate fundamental frequency Transfer to the Time frame candidate fundamental frequency Dynamic penalties; and These are non-negative continuous weights; This is an optional reference frequency increment; it is set to 0 when there is no reference increment. This is the normalization scale for incremental bias.

[0028] make Representing the complete candidate fundamental frequency sequence, the first... The first time frame The candidate fundamental frequency is labeled as Its dynamic programming cumulative score is initialized and recursively calculated as follows: (15) (16) In the formula, For the first The first time frame The cumulative score of dynamic programming for each candidate fundamental frequency. For the first The first time frame Candidate fundamental frequencies In the Candidate node scores for time frames. For from the first The first time frame Candidate fundamental frequencies Transfer to the The first time frame Candidate fundamental frequencies Dynamic penalties.

[0029] In each frame, the candidate fundamental frequency sequences are sorted from high to low according to their cumulative scores, and the end frequency intervals are retained sequentially. The sequence, at most, retains B Among them, The end-frequency separation threshold, B The number of candidate sequences to retain.

[0030] For the final reserved b Calculate the second-order smoothing cost for each candidate fundamental frequency sequence: (17) In the formula, For the first b A complete candidate sequence, For the first b The candidate fundamental frequency sequence in the first k Candidate fundamental frequency values ​​at each time frame. For the first b The smoothing cost of candidate fundamental frequency sequences.

[0031] In satisfying Among the candidate fundamental frequency sequences, the one with the highest cumulative score is selected as the primary candidate fundamental frequency, denoted as . ,in, This is the second-order smoothing threshold. The main candidate fundamental frequency sequence is determined by the following formula: (18) In the formula, The candidate fundamental frequency sequence that maximizes the difference between the cumulative node score and the dynamic penalty. For the first Time frame candidate fundamental frequency In the Candidate node scores for time frames.

[0032] Step S6: Perform protection and correction on the low-trust startup segment.

[0033] First, determine whether start-up protection is needed. When the score of the primary candidate fundamental frequency sequence within the start-up candidate interval is below the threshold or an abnormal jump occurs, filter subsequent anchor points with a continuous acceleration trend and perform a reverse search for the start-up candidate fundamental frequency sequence. If the backtracking sequence meets the preset evaluation conditions, replace the primary candidate fundamental frequency sequence before the anchor point; otherwise, leave it unchanged, resulting in the candidate fundamental frequency sequence after start-up protection. After triggering start-up protection, using the primary candidate fundamental frequency sequence obtained in step S5 as input, examine each time frame of the primary candidate fundamental frequency sequence within the start-up candidate interval. If the length after this time frame is... If the frequency generally increases within the interval and the set of positive increments in equation (19) is not empty, then this time frame is taken as a candidate anchor point. The length after the anchor point is The stability range is estimated with reference to the acceleration step size: (19) (20) in, The main candidate fundamental frequency sequence obtained in step S5 is in the first... k Frequency values ​​at each time frame For reference acceleration step size, Its normalization scale, It is a positive stability constant.

[0034] Using the main frequency at the anchor point as the endpoint, the reverse search starts the backtracking trajectory of the initiation segment. Its objective function is: (twenty one) in, For the start-up phase, backtrack the candidate fundamental frequency sequence. The objective function value, For the backtracking sequence at the 1st k The candidate baseband node scores at each time frame. For the backtracking sequence at the 1st k Candidate fundamental frequency values ​​at each time frame. ; Weighting for consistency of the acceleration trend. For the reverse fall penalty weight, It is a positive part function.

[0035] Equation (21) is the constrained form of Equation (18) within the candidate interval for starting: retaining the cumulative term of node scores, and adding the consistency constraint of acceleration trend and the penalty for reverse fall.

[0036] Step S7: Detect and correct harmonic mislocking.

[0037] First, a statistical reference is constructed based on the multi-order consistency score, and it is determined whether the input sequence consistently exhibits an integer harmonic relationship. If no second-order or higher harmonic relationship that meets the persistence ratio threshold exists, this step is skipped; if a persistent harmonic relationship is detected, a potential fundamental frequency sequence is constructed and its scores are compared.

[0038] Within each time frame, select the candidate fundamental frequency with the highest multi-order consistency score and construct a multi-order statistical reference: (twenty two) In the formula, For the first Multi-order statistical reference frequency conversion of time frames; Let the input trajectory of harmonic lockout protection be ,for and In length of Detection window Internal calculation of harmonic relationship indication: (twenty three) And the duration of the harmonic relationship: (twenty four) In the formula, For the first Time frame about the A binary indicator of whether the harmonic relationship holds true; For the first At the time frame position The duration of the harmonic relationship within the detection window; r This is the index of the time frame within the detection window. For the first h Tolerance for harmonic frequency relationship.

[0039] when When it holds true continuously, the corresponding largest continuous interval is denoted as ,in, This is the trigger threshold for the frequency multiplication relationship. For the trigger order... Construct a potential fundamental frequency trajectory within the risk range: (25) In the formula, For triggering order The potential fundamental frequency is obtained by reverse calculation.

[0040] Substituting the input primary candidate fundamental frequency sequence and potential fundamental frequency sequence into equation (18) respectively, within the risk interval... Calculate cumulative score and .

[0041] When the potential fundamental frequency trajectory is located Inside, and The input frequency transition trajectory within the risk interval is replaced with the potential fundamental frequency trajectory; otherwise, the original input main candidate fundamental frequency sequence is retained. This yields the final instantaneous frequency transition estimate. .

[0042] Step S8: Output the instantaneous frequency and speed estimation results.

[0043] The result obtained in step S7 As the first k The final instantaneous rotational frequency estimate for the time frame, converted to revolutions per minute: (26) in, For the first The final instantaneous frequency estimate of the time frame, in units of ; For the first The estimated rotational speed for the corresponding time frame, in units of The obtained instantaneous frequency or speed trajectory is used for subsequent order resampling, order spectrum analysis, fault feature extraction, condition monitoring, or maintenance decision-making.

[0044] The beneficial effects of this invention are: This invention jointly constructs direct spectral peak candidates and order back-projection candidates, utilizes integer harmonic evidence to preserve weak fundamental frequencies, and integrates local spectral intensity, multi-order consistency, and dynamic continuity for multi-hypothesis path search to reduce candidate loss, non-physical jumps, and early false locking. Furthermore, it corrects low-confidence start-up trajectories and harmonic false locking intervals through a start-up segment protection mechanism and a harmonic locking protection mechanism, respectively. This method requires no external speed signal and can improve the continuity, accuracy, and robustness of instantaneous frequency estimation under complex variable speed conditions. Attached Figure Description

[0045] Figure 1 This is an overall flowchart of the tachometer-less frequency estimation method based on multi-order evidence constraints of the present invention; Figure 2 The time-domain waveform and time-frequency representation of the sample are shown, where (a) is the time-domain waveform of the sample and (b) is the time-frequency representation of the sample. Figure 3 The diagram illustrates candidate generation and multi-hypothesis dynamic path search, where (a) shows the schematic positions of the direct spectral peak and the back-projected candidate fundamental frequency in the time-frequency diagram, and (b) shows the schematic results of the multi-hypothesis path search. Figure 4 The results of the method comparison are based on the sample. Detailed Implementation

[0046] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0047] A method for estimating the rotational frequency of rotating machinery without a tachometer based on multi-order evidence constraints, such as... Figure 1 As shown, the specific steps are as follows: In this embodiment, a vibration acceleration sensor is arranged near the input shaft of the gear transmission device, and a photoelectric speed sensor that outputs one pulse per revolution is arranged at the shaft. The photoelectric speed sensor signal is only used to obtain the reference rotational frequency and calculate the evaluation error, and does not participate in candidate generation, path search, or parameter determination. Single-channel vibration signals are collected during the device's start-up, acceleration, near-constant speed operation, and deceleration processes. The highest rotational frequency selected is approximately of Variable speed sample. The original sampling frequency is... To reduce computational load, while preserving the low-frequency components of the target signal, anti-aliasing resampling is used to downsample the vibration signal to a lower frequency. .

[0048] Figure 2 Figures (a) and (b) show the time-domain waveform and time-frequency representation of the sample, respectively. The time-domain signal exhibits significant impulses and amplitude fluctuations; in the time-frequency diagram, the fundamental spectral ridge near the actual frequency transition is not always the strongest component, and there is stronger spectral energy at approximately the second harmonic position. Therefore, using only the maximum spectral peak frame by frame can easily lead to misselection of harmonics.

[0049] Step S1: Based on the allowed frequency of the experimental setup and the highest frequency of the sample, set the candidate frequency search interval to... The set of integer orders used for multi-order consistency evaluation is set as follows: The search range covers the acceleration, near-constant speed, and deceleration processes of the sample, and reserves an upper limit margin for local fluctuations.

[0050] Step S2: Select an analysis window that can cover a finite number of low-speed rotation cycles based on the low-speed end of the search interval. This embodiment uses a 1024-point analysis window, corresponding to... The time length and FFT points are 4096. For signals with obvious slow-varying backgrounds, slow trend subtraction and robust amplitude normalization based on median absolute deviation are first performed according to equations (1) and (2). In this embodiment, no continuous slow-varying trend requiring separate subtraction is detected, and robust amplitude normalization is retained. Subsequently, the short-time Fourier transform and power time spectrum are calculated according to equations (3) and (4), and quantile normalization and logarithmic compression are performed on the time background at each frequency position according to equations (5) and (6). In this embodiment, the quantile level is... We set it to 0.12. This weakens the dominance of persistent background lines and local abnormally strong peaks, resulting in robust spectral evidence for candidate extraction.

[0051] Step S3: Extract significant spectral peaks within each time frame based on local maxima and spectral salience. (Located in...) to The main spectral peaks within the range are generated as direct spectral peak candidates according to formula (7); significant spectral peaks located in a wider evaluation frequency band are divided by the first, second, and third orders respectively, and those falling into the search interval are included. The results are used as candidates for the order back projection. The two types of candidates are merged according to Equation (9), and duplicate candidates with frequency intervals smaller than the merging tolerance are removed. No more than 12 candidate nodes are retained in each time frame.

[0052] Step S4: Read robust spectral evidence near each candidate frequency as local amplitude evidence, then read spectral evidence from the first to third harmonic positions of the candidate frequencies and sum them with weights. Normalize the multi-order observations within the same time frame to obtain... The node scores are generated according to equation (13). This embodiment uses multi-level consistency weights. The value is set to 0.55 to balance the candidate's own spectral intensity and integer harmonics. The multi-order score only participates in the candidate evaluation and is not directly used as the frequency conversion output.

[0053] Step S5: Establish a directed candidate graph with time frames as layers and candidate base frequencies as nodes. Calculate the dynamic penalty between adjacent frame candidates according to equation (14), assuming the path incremental cost weight is 0.10 and the path second-order smoothing cost weight is 0.05. Perform dynamic programming recursion according to equations (15) and (16), and retain competitive paths whose cumulative score differs from the current optimal path's unit frame score by no more than 0.60 and whose terminal frequencies are separated. After completing the recursion of all time frames, evaluate the second-order smoothness of each retained path according to equation (17), and select the path that satisfies the smoothing condition and has the highest cumulative score as the main path. Figure 3 In the diagram, (a) shows the schematic positions of the direct spectral peak and the candidate fundamental frequency of the back projection in the time-frequency diagram, and (b) shows the schematic results of the multi-hypothesis path search.

[0054] After obtaining the main path, proceed to step S6. to After checking the main path node scores and anchor points frame by frame within the candidate launch range, The acceleration trend of the neighborhood. For anchor points that meet the conditions, the reference acceleration step size is estimated according to Equations (19) and (20), and the candidate at the anchor point is used as the backtracking endpoint to search for the starting segment path forward according to Equation (21).

[0055] Step S7: Select the candidate with the highest multi-order consistency score in each time frame according to equation (22) to form a multi-order statistical reference, and make the harmonic-locked input path for protection. For second-order and third-order relations, calculate the duration ratio of the harmonic relationship between the input path and the multi-order statistical reference window by window according to equations (23) and (24). Only when Reaching the trigger threshold and forming a continuous risk range Only when the input path is divided by the corresponding order to construct the potential fundamental frequency path, and then the cumulative scores of the potential path and the input path are compared according to step S5.

[0056] Step S8: Use the path after the gating checks in steps S6 and S7 as the final instantaneous frequency estimate. And convert it to rotational speed according to equation (26). The obtained trajectory can be used as a phase reference for order resampling, or directly input into rotating machinery fault diagnosis and condition monitoring programs. Figure 4 Results from the proposed method, along with those from the multi-order probabilistic method MOPA, the graph search dynamic programming method GraphSearch-DP, and the time-frequency ridge estimation method TFRE, are presented. All methods use the same vibration input and reference rotational frequency evaluation interval. The quantification results are shown in Table 1 below.

[0057] Table 1

[0058] As can be seen from the above results, the MAE of the method of the present invention is... RMSE is The maximum absolute error is Compared with the three comparison methods, the method of the present invention does not show obvious low-frequency branches or double-frequency branches within the complete speed range.

Claims

1. A method for estimating the rotational frequency of rotating machinery without a tachometer based on multi-order evidence constraints, characterized in that, The specific steps are as follows: Step S1: Acquire vibration signals and determine the analysis range; Step S2: Construct robust spectrum evidence; Low-frequency background suppression and robust amplitude normalization are performed on single-channel vibration signals with obvious slow-varying backgrounds to obtain preprocessed vibration signals; short-time Fourier transform is performed on the preprocessed vibration signals and the power time spectrum is calculated; robust background at each frequency position is estimated along the time direction, and background normalization and nonlinear compression are performed on the power time spectrum to obtain robust spectral evidence. Step S3: Generate a candidate fundamental frequency set; Direct spectral peak candidates and order backprojection candidates are generated simultaneously from the local maximum spectral peaks of each time frame. Direct spectral peak candidates retain the directly observable fundamental frequency peaks, while order backprojection candidates map higher-order rotational components back to the potential fundamental frequency position, thereby avoiding candidate loss when weak fundamental frequencies do not form significant spectral peaks. Step S4: Calculate the local amplitude evidence and multi-order consistency evidence of the candidate fundamental frequency respectively, and combine the two into the candidate node score; Step S5: Perform multi-hypothesis dynamic programming and obtain the main candidate fundamental frequency sequence; A directed candidate graph is established with time frames as layers and candidate fundamental frequencies as nodes. The main candidate fundamental frequency sequence is searched through joint optimization of node scores and dynamic penalties for adjacent frames. Step S6: Perform protection and correction on the low-trust startup segment; First, determine whether start-up protection is required; when the score of the main candidate fundamental frequency sequence in the start-up candidate interval is lower than the threshold or an abnormal jump occurs, screen the subsequent anchor points with a continuous acceleration trend, and search the start-up candidate fundamental frequency sequence in reverse; if the backtracking sequence meets the preset evaluation conditions, replace the main candidate fundamental frequency sequence before the anchor point; otherwise, leave it unchanged to obtain the candidate fundamental frequency sequence after start-up protection; step S7: detect and correct harmonic mislocking; First, a statistical reference is constructed based on the multi-order consistency score, and it is determined whether the input sequence continuously exhibits an integer harmonic relationship. If there is no second-order or higher harmonic relationship that meets the continuity ratio threshold, this step is skipped. If a continuous harmonic relationship is detected, a potential fundamental frequency sequence is constructed and a score comparison is performed. Step S8: Output the instantaneous frequency and speed estimation results.

2. The method for estimating the rotational frequency of rotating machinery without a tachometer based on multi-order evidence constraints according to claim 1, characterized in that, Step S1 is as follows: A single-channel vibration signal is collected from the rotating machinery during variable speed operation, denoted as... , For time, the sampling frequency is denoted as . The candidate frequency search range is determined based on the equipment's permissible speed, transmission ratio, or the operating range of the monitored object. ,in These are the lower limit and upper limit of candidate frequency conversion, respectively; Determine the set of integer orders for multi-order consistency evaluation ,in, For the first Integer order.

3. The method for estimating the rotational frequency of rotating machinery without a tachometer based on multi-order evidence constraints according to claim 1, characterized in that, Step S2 is as follows: Trend subtraction and robust amplitude normalization are performed on vibration signals with a slowly varying background to obtain preprocessed vibration signals: (1) In the formula, To preprocess the vibration signal; when low-frequency background suppression is not required, let ; For zero-phase filtering operators, This represents the median absolute deviation. To prevent the denominator from being too small, a positive stability constant is required; Time scale The above uses the moving median estimation for slow-varying trend estimation: (2) In the formula, It is a local time variable; Indicated by t Centered on, with a length of T The median of the signal within the time interval, It is the median estimation function; Perform short-time Fourier transform on the preprocessed vibration signal and calculate the power-time spectrum: (3) (4) In the formula, For the first One time frame, For frequency and time frame The complex short-time Fourier transform coefficients at the location; For time integration variables; For analysis window; It is an exponential function; The imaginary unit; For modular arithmetic of complex numbers; Robust background at each frequency location is estimated along the time direction, and background normalization and nonlinear compression are performed to obtain robust spectral evidence. : (5) (6) In the formula, Robust spectral evidence after background normalization and nonlinear compression. Spectral evidence after background normalization; To prevent stable terms with excessively small denominators, for Quantile operator, Preset quantile level; For frequency From frame 1 to frame 2 The power sequence of the frames; The compression factor is greater than zero.

4. The method for estimating the rotational frequency of rotating machinery without a tachometer based on multi-order evidence constraints according to claim 1, characterized in that, Step S3 is as follows: In the Time frames Internally, extract the set of local maxima spectral peaks from robust spectral evidence. ; will be located in the search range The maximum spectral peaks within the range are used as the direct spectral peak candidate set: (7) In the formula, For the first The direct spectral peak candidate set of time frames; For the first k The first time frame p The frequency of the spectral peaks at their maximum values; The maximum spectral peaks are back-projected onto the candidate frequency transition search interval according to the integer order relationship, resulting in the candidate set of order back-projections: (8) In the formula, For the first The order backprojection candidate set of time frames; This represents the upper limit of the frequency of evaluation of order of evidence. Merging the direct spectral peak candidate set and the order back projection candidate set, the candidate fundamental frequency set is: (9) In the formula, For the first The set of candidate fundamental frequencies for a time frame.

5. The method for estimating the rotational frequency of rotating machinery without a tachometer based on multi-order evidence constraints according to claim 1, characterized in that, Step S4 is as follows: For any candidate fundamental frequency First, calculate its local amplitude evidence score: (10) In the formula, Candidate fundamental frequency In the Local amplitude evidence score over time. To read the positive half-bandwidth of the candidate frequency neighborhood; Subsequently, robust spectral evidence near each integer harmonic of the candidate fundamental frequency was read, providing multi-order observational support: (11) in, Candidate fundamental frequency In the Support for unnormalized multi-order observations obtained from time frames; For the first Non-negative weights of order, For the first h The half-bandwidth of the frequency neighborhood, This is an indicator function. It takes the value 1 when the condition inside the parentheses is true, indicating that the condition is true; otherwise, it takes the value 0 when the condition inside the parentheses is false, indicating that the condition is false. Normalization of multi-order observations within the same time frame: (12) In the formula, for After the first Multi-order consistency score obtained by intra-temporal normalization u To iterate through the variables of candidate fundamental frequencies, It is a positive stability constant; The candidate node score is: (13) In the formula, Candidate fundamental frequency In the Candidate node scores for each time frame; It is a non-negative multi-order consistency weight.

6. The method for estimating the rotational frequency of rotating machinery without a tachometer based on multi-order evidence constraints according to claim 1, characterized in that, Step S5 is as follows: The dynamic penalty between candidate fundamental frequencies of adjacent time frames is defined as follows: (14) In the formula, For from the first Time frame candidate fundamental frequency Transfer to the Time frame candidate fundamental frequency Dynamic penalties; and These are non-negative continuous weights; This is an optional reference frequency increment; it is set to 0 when there is no reference increment. The normalization scale for incremental bias; make Representing the complete candidate fundamental frequency sequence, the first... The first time frame The candidate fundamental frequency is labeled as Its dynamic programming cumulative score is initialized and recursively calculated as follows: (15) (16) In the formula, For the first The first time frame The cumulative score of dynamic programming for each candidate fundamental frequency. For the first The first time frame Candidate fundamental frequencies In the Candidate node scores for time frames. For from the first The first time frame Candidate fundamental frequencies Transfer to the The first time frame Candidate fundamental frequencies Dynamic penalties; In each frame, the candidate fundamental frequency sequences are sorted from high to low according to their cumulative scores, and the end frequency intervals are retained sequentially. The sequence, at most, retains B Among them, The end-frequency separation threshold, B Retain the number of candidate sequences; For the final reserved b Calculate the second-order smoothing cost for each candidate fundamental frequency sequence: (17) In the formula, For the first b A complete candidate sequence, For the first b The candidate fundamental frequency sequence in the first k Candidate fundamental frequency values ​​at each time frame. For the first b The smoothing cost of candidate fundamental frequency sequences; In satisfying Among the candidate fundamental frequency sequences, the one with the highest cumulative score is selected as the primary candidate fundamental frequency, denoted as . ,in, The second-order smoothing threshold is used; the main candidate fundamental frequency sequence is determined by the following formula: (18) In the formula, The candidate fundamental frequency sequence that maximizes the difference between the cumulative node score and the dynamic penalty. For the first Time frame candidate fundamental frequency In the Candidate node scores for time frames.

7. The method for estimating the rotational frequency of rotating machinery without a tachometer based on multi-order evidence constraints according to claim 1, characterized in that, Step S6 is as follows: Within the candidate start interval, examine each time frame of the primary candidate fundamental frequency sequence sequentially; if the length after that time frame is... If the frequency generally increases within the interval and the set of positive increments in equation (19) is not empty, then this time frame is taken as a candidate anchor point. ; Based on the length after the anchor point The stability range is estimated with reference to the acceleration step size: (19) (20) in, The main candidate fundamental frequency sequence obtained in step S5 is in the first... k Frequency values ​​at each time frame For reference acceleration step size, Its normalization scale, It is a positive stability constant; Using the main frequency at the anchor point as the endpoint, the reverse search starts the backtracking trajectory of the initiation segment. Its objective function is: (21) in, For the start-up phase, backtrack the candidate fundamental frequency sequence. The objective function value, For the backtracking sequence at the 1st k The candidate baseband node scores at each time frame. For the backtracking sequence at the 1st k Candidate fundamental frequency values ​​at each time frame; ; Weighting for consistency of the acceleration trend. For the reverse fall penalty weight, It is a positive part function.

8. The method for estimating the rotational frequency of rotating machinery without a tachometer based on multi-order evidence constraints according to claim 1, characterized in that, Step S7 is as follows: Within each time frame, select the candidate fundamental frequency with the highest multi-order consistency score and construct a multi-order statistical reference: (22) In the formula, For the first Multi-order statistical reference frequency conversion of time frames; Let the input trajectory of harmonic lockout protection be ,for and In length of Detection window Internal calculation of harmonic relationship indication: (23) And the duration of the harmonic relationship: (24) In the formula, For the first Time frame about the A binary indicator of whether the harmonic relationship holds true; For the first At the time frame position The duration of the harmonic relationship within the detection window; r This is the index of the time frame within the detection window. For the first h Tolerance for harmonic frequency order; when When it holds true continuously, the corresponding largest continuous interval is denoted as ,in, The trigger threshold is the frequency multiplication factor; for the trigger order... Construct a potential fundamental frequency trajectory within the risk range: (25) In the formula, For triggering order The potential fundamental frequency obtained by reverse calculation; Substituting the input primary candidate fundamental frequency sequence and potential fundamental frequency sequence into equation (18) respectively, within the risk interval... Calculate cumulative score and ; When the potential fundamental frequency trajectory is located Inside, and The input frequency shift trajectory within the risk interval is replaced with the potential fundamental frequency trajectory; otherwise, the original input main candidate fundamental frequency sequence is retained; thus, the final instantaneous frequency shift estimate is obtained. .

9. The method for estimating the rotational frequency of rotating machinery without a tachometer based on multi-order evidence constraints according to claim 1, characterized in that, Step S8 is as follows: The result obtained in step S7 As the first k The final instantaneous rotational frequency estimate for the time frame, converted to revolutions per minute: (26) in, For the first The final instantaneous frequency estimate of the time frame, in units of ; For the first The estimated rotational speed for the corresponding time frame, in units of The obtained instantaneous frequency or speed trajectory is used for subsequent order resampling, order spectrum analysis, fault feature extraction, condition monitoring, or maintenance decision-making.

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