A Joint Denoising Method for Weak Fault Signals of Hydro-Turbine Runners Based on Improved Wavelet Thresholding and Kalman Filtering

Abstract

This invention relates to the field of hydropower system technology, specifically to a joint denoising method for weak fault signals of turbine runners based on improved wavelet thresholding and Kalman filtering. The method includes the following steps: acquiring acoustic signals from the turbine runner under normal, 3-crack, and 8-crack operating conditions; performing wavelet decomposition on the original signal, selecting the optimal wavelet basis function and decomposition level, and calculating the universal threshold and minima threshold; processing the wavelet coefficients using an improved threshold function and reconstructing the signal to obtain a preprocessed signal; inputting the preprocessed signal into a Kalman filter module, executing a prediction and update process to obtain the optimal estimate; and outputting a denoised signal, the denoising effect of which can be evaluated using various metrics. This invention optimizes the suppression effect of high-frequency random noise by improving the wavelet threshold function and combines it with Kalman filtering to remove low-frequency dynamic noise, achieving layered and precise denoising, adapting to different fault conditions, and effectively preserving weak fault characteristics.

Description

Technical Field

[0001] This invention relates to the field of hydropower generation system technology, specifically to a joint denoising method for weak fault signals of turbine runners based on improved wavelet threshold-Kalman filter (IWT-KF). Background Technology

[0002] As the core power equipment of a hydroelectric power generation system, the turbine runner, a key component for energy conversion, is subjected to complex conditions of high-speed rotation, water flow impact, media corrosion, and alternating loads, making it prone to various faults such as cracks, wear, and cavitation. Among these, weak faults such as cracks are characterized by their high degree of concealment and slow development. The initial fault signal amplitude is weak and easily masked by various complex noises such as water flow noise, mechanical vibration noise, and electromagnetic interference noise. If they are not detected and identified in a timely and effective manner, they can lead to runner failure, unit shutdown, and even serious safety accidents and huge economic losses as the fault gradually expands. Therefore, the accurate detection of weak faults in turbine runners has significant engineering application value.

[0003] Acoustic detection technology is widely used in the field of turbine runner fault detection due to its advantages such as non-contact operation, convenient operation, wide detection range, and no impact on the normal operation of the unit. Its core is to extract fault features and complete fault identification by collecting acoustic signals generated during the runner's operation. However, noise interference is a key bottleneck restricting the application of acoustic detection technology in the detection of weak faults in turbine runners. The noise generated during the operation of a turbine is complex, mainly including high-frequency random noise (such as water flow turbulence noise and high-frequency components of pipe vibration) and low-frequency dynamic noise (such as low-frequency components of unit shaft vibration and electromagnetic noise of motors). The superposition of these two types of noise causes the features of weak fault acoustic signals to be severely submerged, making it difficult to directly extract effective fault information. Therefore, denoising the acoustic signals of weak faults in turbine runners to achieve the dual goals of noise suppression and fault feature preservation has become a core prerequisite for improving the accuracy of weak fault detection.

[0004] Currently, methods for denoising acoustic signals from hydro turbines are mainly divided into two categories: single denoising methods and joint denoising methods. Among single denoising methods, wavelet thresholding, due to its excellent time-frequency localization characteristics, can effectively separate the high-frequency and low-frequency components of the signal and is widely used for high-frequency noise suppression in acoustic signals. Its core principle is to decompose the original signal into approximate coefficients and detail coefficients at different scales through wavelet decomposition, and then reconstruct the signal by processing the detail coefficients using a threshold function to achieve denoising. However, the hard threshold function used in traditional wavelet thresholding has the defects of producing oscillations and pseudo-Gibbs phenomena after signal reconstruction, while the soft threshold function will lead to signal amplitude attenuation and fault feature distortion. Moreover, the selection of traditional thresholds often uses fixed general thresholds or empirical thresholds, which are difficult to adapt to the dynamic changes of acoustic signals under different operating conditions of the hydro turbine runner (normal operating conditions, fault conditions with different numbers of cracks), and have insufficient protection capabilities for weak fault signals, resulting in limited denoising effects.

[0005] Kalman filtering, as a linear optimal estimation method, possesses excellent dynamic tracking capabilities and can effectively filter out low-frequency dynamic noise in signals. Its core principle is to achieve optimal estimation of dynamic signals through a cyclical process of state prediction, error covariance prediction, Kalman gain calculation, state update, and error covariance update. It has found some application in suppressing low-frequency noise in mechanical vibration and acoustic signals. However, the denoising effect of Kalman filtering depends on the setting of system model parameters (state matrix, measurement matrix, and noise covariance matrix), and its ability to suppress high-frequency random noise is relatively weak. When applied alone to denoise acoustic signals of weak faults in turbine runners, it cannot effectively filter out high-frequency random noise, making it difficult to achieve comprehensive suppression of various types of noise, and the weak fault characteristics may still be masked by noise.

[0006] To address the shortcomings of single denoising methods, some existing technologies employ joint denoising methods combining wavelet thresholding and Kalman filtering. However, these methods often use traditional wavelet threshold functions and fixed decomposition parameters, failing to specifically address the characteristics of acoustic signals from weak faults in turbine runners. This results in the following drawbacks: First, the selection of wavelet basis functions and decomposition levels lacks a systematic approach, relying heavily on empirical methods without considering the characteristics of acoustic signals under different fault conditions to select optimal parameters, leading to poor stability in denoising performance. Second, the wavelet threshold function design is often flawed, failing to achieve adaptive threshold adjustment, making it difficult to balance high-frequency random noise suppression with weak fault feature preservation, and prone to fault feature distortion or noise residue. Third, the combination of wavelet thresholding and Kalman filtering is relatively simple, lacking a clear division of labor and compatibility between the two methods, failing to achieve precise, layered suppression of high-frequency random noise and low-frequency dynamic noise, and resulting in denoising accuracy insufficient to meet the requirements of weak fault detection.

[0007] Furthermore, existing joint denoising methods are not specifically optimized for weak fault conditions with different numbers of cracks in the turbine runner, and cannot adapt to the differences in acoustic signals under weak faults of different degrees, such as 3 cracks or 8 cracks. Therefore, the denoising effect lacks versatility and stability. Thus, addressing the shortcomings of existing technologies, such as low denoising accuracy, weak fault feature preservation, and poor adaptability, developing a joint denoising method for weak fault acoustic signals in turbine runners that can accurately suppress various types of noise, effectively preserve weak fault features, and adapt to different fault conditions has become an urgent technical problem to be solved in the field of turbine fault detection. Summary of the Invention

[0008] The purpose of this invention is to provide a joint denoising method (IWT-KF) for weak fault signals of turbine runners based on improved wavelet thresholding and Kalman filtering, in order to solve the problems of low denoising accuracy and poor adaptability of existing turbine runner denoising methods mentioned in the background art.

[0009] To achieve the above objectives, the present invention provides the following technical solution: A method for jointly denoising weak fault signals of turbine runners based on improved wavelet thresholding and Kalman filtering, characterized by the following steps: Step 1: Collect acoustic signals of the turbine runner under different operating conditions, including normal operating condition, 3-crack condition, and 8-crack condition; Step 2: Perform wavelet decomposition on the original acoustic signal, select wavelet basis functions and determine the number of wavelet decomposition levels, and calculate the universal threshold. and maximum and minimum threshold ; Step 3: Process the wavelet coefficients obtained from wavelet decomposition using an improved threshold function to obtain approximate wavelet coefficients. Reconstruct the approximate wavelet coefficients to obtain the preprocessed signal. The expression for the improved threshold function is: ; In the formula, These are wavelet coefficients. It is a symbolic function; Step 4: Input the preprocessed signal into the Kalman filter module, and execute the prediction and update processes of the Kalman filter in sequence to obtain the optimal estimate of the signal; Step 5: Output the denoised acoustic signal of the turbine runner to complete the joint denoising.

[0010] Preferably, the wavelet basis function in step 2 is selected from one or more of the following: Haar wavelet, Daubechies wavelet, Symlets wavelet, and Coiflets wavelet; The Daubechies wavelet includes db1-db8 ​​wavelets, the Symlets wavelet includes sym1-sym8 wavelets, and the Coiflets wavelet includes coif1-coif5 wavelets; For the acoustic signal of the turbine runner, the above 21 wavelet basis functions (Haar wavelet is equivalent to db1 wavelet) are traversed, and the optimal wavelet basis function under the corresponding working condition is selected by using the signal-to-noise ratio (SNR) as the evaluation index. For the acoustic signals of the turbine runner under 3 and 8 crack conditions, the optimal wavelet basis function obtained by screening is the db1 wavelet.

[0011] Preferably, in step 2, the general threshold... The calculation formula is: ; In the formula, For standard deviation, The signal length; the standard deviation The estimation algorithm is as follows: ; In the formula, The wavelet decomposition scale, Represents the finest scale after wavelet decomposition. High-frequency wavelet coefficients; The maximum and minimum thresholds The calculation formula is: .

[0012] Preferably, in step 2, the wavelet decomposition level is determined as follows: the traversal range of the wavelet decomposition scale is set to 1-8 levels. For the acoustic signals of the turbine runner under normal operating conditions, 3-crack conditions, and 8-crack conditions, wavelet decomposition and processing with different levels of decomposition are performed within this traversal range. The signal processing results under different levels of decomposition are compared using the signal-to-noise ratio (SNR) as the evaluation index, and the optimal level of decomposition for the corresponding operating conditions is selected. For the turbine runner acoustic signals under 3-crack and 8-crack conditions, the optimal level of decomposition is 8 levels.

[0013] Preferably, in step 4, the Kalman filtering prediction process includes state prediction and error covariance prediction, with the corresponding formulas as follows: State prediction formula: ; Error covariance prediction formula: ; In the formula, The predicted value at the current moment. The state matrix, This is the optimal estimate from the previous moment. For the control matrix, The control input measured by the sensor at the current moment; Let be the covariance matrix of the predicted values ​​at the current time. Let be the covariance matrix of the optimal estimate at the previous time step. This is the transpose of the state matrix. This is the covariance matrix for predicting noise.

[0014] Preferably, in step 4, the Kalman filter update process includes Kalman gain calculation, state update, and error covariance update, with the corresponding formulas as follows: Kalman gain formula: ; State update formula: ; Error covariance update formula: ; In the formula, The Kalman gain at the current moment. For the measurement matrix, To measure the transpose of the matrix, The covariance matrix of the measurement noise; The current measurement value obtained by the sensor. This is the optimal estimate for the current moment; It is the identity matrix. Let be the covariance matrix of the optimal estimate at the current time.

[0015] Preferably, in step 1, an industrial-grade noise sensor CRY2301 is used to collect acoustic signals; the parameters of the sensor are: communication interface is USB audio + USB HID, and size is... mm, sampling rate 48kHz, frequency measurement range 10-20000Hz, dynamic measurement range ≥110dBA, standard measurement range 25-130dBA.

[0016] Preferably, in step 1, an acoustic signal is collected using a test bench; the test bench includes a water storage system, a water supply system, a test section, and a return water system; the water storage system is equipped with a water tank, the water supply system includes a pressure pump and supporting pipelines, the test section uses a hydro-generator set as the core equipment, and the return water system includes a submersible pump and supporting pipelines. The parameters of the hydro-generator set are as follows: rated power 5kW / 5KVA, rated frequency 50Hz, rated speed 1500r / min, rated voltage 230V, rated current 21.8A, excitation voltage 49V, excitation current 2.6A, and power factor 1.0.

[0017] Preferably, the method further includes a noise reduction effect evaluation step, using at least one of the following as evaluation indicators: signal-to-noise ratio (SNR), root mean square error (RMSE), noise energy ratio (NER), Bartholomew's law coefficient (BC), and total variation (TV). The calculation formulas for each evaluation indicator are as follows: ; ; ; ; ; In the formula, For signal length, The original signal, The signal after noise reduction; The number of equal intervals to divide the amplitude range of the standardized signal. It is the probability distribution of the original signal amplitude. It is the probability distribution of the amplitude of the denoised signal; It is a discrete signal.

[0018] Preferably, the improved wavelet threshold (IWT) in step 3 targets high-frequency random noise in the original acoustic signal. The process involves wavelet decomposition of the original acoustic signal to obtain wavelet coefficients at different scales, segmenting the wavelet coefficients using an improved threshold function, and then reconstructing the approximate wavelet coefficients to obtain the preprocessed signal. The Kalman filter (KF) in step 4 targets low-frequency dynamic noise in the preprocessed signal. The process involves inputting the preprocessed signal into the Kalman filter module and sequentially executing state prediction, error covariance prediction, Kalman gain calculation, state update, and error covariance update to obtain the optimal estimate of the signal. This method achieves step-by-step processing of high-frequency random noise and low-frequency dynamic noise through a hierarchical noise reduction process of IWT followed by KF. The turbine runner acoustic signal processed by this method shows a 75.4% improvement in SNR compared to the IWT method alone and a 77.4% improvement compared to the KF method alone, and a 29.4% decrease in RMSE compared to the IWT method alone and a 12.8% decrease compared to the KF method alone.

[0019] Compared with the prior art, the beneficial effects of the present invention are: (1) This invention proposes a method combining wavelet threshold (WT) and Kalman filter (KF) algorithms for noise reduction of turbine runner fault signals. The WT algorithm effectively overcomes the problems of discontinuities and constant deviations in traditional thresholding, preserving key signal information to the greatest extent possible, and solving the problem of high requirements for noise and initial signal quality in KF. The feasibility of the WT-KF method is verified by collecting acoustic signals from turbines under different operating conditions using a test bench. Experimental results show that the WT-KF scheme performs best in acoustic signal processing for normal runners, runners with three cracks, and runners with eight cracks. The SNR is 75.4% higher than WT and 77.4% higher than KF, while the RMSE is 29.4% lower than WT and 12.8% lower than KF. The method balances noise reduction and fidelity preservation, and can completely retain the acoustic time-frequency domain characteristics at each stage.

[0020] (2) The three types of turbine runner characteristics in this invention correspond to the three stages of crack initiation, crack absence, and crack propagation. In the crack-free stage, the time-domain signal shows a stable baseline, and the frequency-domain energy is concentrated in the 0-5000Hz range and evenly distributed. In the crack initiation stage, localized weak distortions appear in the time domain, and significant energy accumulation is observed in the 0-5000Hz frequency band. In the crack propagation stage, high-frequency fluctuations appear in the time-domain signal, and the frequency domain exhibits a wide-band energy distribution and multi-band coupled fluctuations. These characteristics at each stage can provide technical support for monitoring the crack condition of water turbines.

[0021] (3) The IWT-KF denoising method in this invention has good versatility and effectiveness, and the characteristics of crack evolution stages can provide a basis for condition detection. Further research can combine intelligent algorithms to use the IWT-KF processed signals for crack quantity identification and fault early warning model construction, expand the sample optimization model accuracy, and realize the whole process optimization of signal processing and condition diagnosis. Attached Figure Description

[0022] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are explained in detail together with the embodiments of the invention, but do not constitute a limitation thereof.

[0023] Figure 1 The time-domain waveform of the Haar wavelet; Figure 2 The waveform diagram is a time-domain representation of the db2-db8 wavelet. Figure 3 The waveforms of sym2-sym8 wavelets in the time domain; Figure 4 The time-domain waveforms of wavelets coif1-coif5; Figure 5 A line graph comparing the three threshold functions; Figure 6 This is a KF diagram illustrating the architecture of the present invention; Figure 7 This is the original simulation signal diagram of the present invention; Figure 8 This is a comparison chart of the denoising effects of three types of wavelet threshold functions in this invention; Figure 9 This is a comparison chart of the spectrum of the simulated signal and the signal after denoising with the improved threshold function according to the present invention; Figure 10 This is a flowchart of the IWT-KF method of the present invention; Figure 11 This is a flowchart of the experimental steps of the present invention; Figure 12 This is a physical image of the test bench of the present invention; Figure 13 This is a diagram of the experimental rotating wheel of the present invention; Figure 14 This is a diagram illustrating the signal acquisition process of different cracked rotors in this invention; Figure 15 The original waveform diagrams for the three rotating wheel conditions of this invention are shown below; Figure 16 This is a diagram showing the normal rotor signal processing results of the present invention; Figure 17 This is a comparison diagram of the normal rotor frequency domain of the present invention; Figure 18 This is a graph showing the evaluation index values ​​of the normal rotary wheel signal algorithm of the present invention; Figure 19 This is a diagram showing the selection of wavelet basis and decomposition layer number for the crack signal in this invention; Figure 20 This is a diagram showing the signal processing results of the cracked rotor of the present invention; Figure 21 This is a frequency domain comparison diagram of the cracked rotor of the present invention; Figure 22 These are the quantitative index parameters for the cracked impeller of this invention. Detailed Implementation

[0024] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0025] This invention discloses a joint denoising method (IWT-KF) for weak fault signals of turbine runners based on improved wavelet thresholding and Kalman filtering. Using the acoustic signal of a cracked turbine runner as the research subject, it addresses the technical challenge of simultaneously achieving accurate signal denoising and feature preservation in rotating machinery fault monitoring, proposing the IWT-KF joint denoising scheme. The IWT algorithm is used to preprocess the original acoustic signal, effectively adapting to the non-stationary characteristics of the signal and significantly suppressing background noise. After obtaining an initial signal with less noise interference, the KF algorithm is used to process dynamic noise, obtaining a more accurate posterior estimate of the signal, and outputting the final denoised signal. An experimental setup was built to collect and process signals from a turbine under cracked operating conditions, further verifying the feasibility of the scheme, as detailed below: Wavelet transform, depending on the scaling factor, can simultaneously perform localized extraction and analysis of signals in both the time and frequency domains, making it an effective method for denoising non-stationary signals in turbine runner fault diagnosis.

[0026] Wavelet transform can transform signals Represented as wavelet basis functions and signals The inner product is shown in equation (1).

[0027] (1) In the formula: The translation factor; Scale factor; These are wavelet basis functions.

[0028] There are four commonly used wavelet basis functions in signal processing: Haar wavelet, Daubechies wavelet, Symlets wavelet, and Coiflets wavelet.

[0029] Haar wavelet Haar wavelet function The definition is as follows: (2) like Figure 1 The image shown is a time-domain waveform of the Haar wavelet.

[0030] Daubechies wavelet Daubechies wavelet applications are often written as dbN, where N represents the order. The db1 wavelet is equivalent to the Haar wavelet, such as... Figure 2 The image shows the time-domain waveform of the db2-db8 wavelet.

[0031] Symlets wavelet Symlets wavelet applications are often written as symN. The sym1 wavelet is equivalent to the db1 wavelet, such as... Figure 3 The image shows the time-domain waveforms of the sym2-sym8 wavelet.

[0032] Coiflets wavelet Coiflets wavelet applications are often written as coifN. For example... Figure 4 The image shows the time-domain waveforms of the coif1-coif5 wavelets.

[0033] The wavelet thresholding denoising method involves performing wavelet transform on a noisy signal to obtain wavelet coefficients at different scales. Each wavelet coefficient is then thresholded to obtain approximate wavelet coefficients, and the signal is reconstructed using these approximate wavelet coefficients to obtain the denoised signal.

[0034] Thresholding is a crucial step in wavelet thresholding denoising. By selecting an appropriate threshold to process the wavelet coefficients, noise can be suppressed while retaining the effective information in the signal. Thresholding involves selecting both the threshold function and the threshold value itself.

[0035] Based on the characteristics that the wavelet coefficients of useful signals have large amplitudes but few numbers, while the wavelet coefficients of noise signals have small amplitudes but many numbers, and the wavelet coefficients of the two types of signals have consistent distributions, the most widely used threshold functions are the hard threshold function and the soft threshold function, as shown in equations (3) and (4), respectively.

[0036] (3) (4) In the formula: These are wavelet coefficients; These are approximate wavelet coefficients; The threshold value is used.

[0037] From equations (3) and (4), it can be seen that the threshold The magnitude of the threshold directly affects the denoising effect. There are four commonly used threshold selection rules: general threshold, maximum-minimum threshold, unbiased risk estimation threshold, and heuristic threshold.

[0038] General threshold The universal threshold rule is based on the statistical properties of wavelet coefficients and applies a uniform threshold to all wavelet coefficients. Its calculation formula is as follows: (5) In the formula: The standard deviation; The length of the signal.

[0039] Standard deviation The estimation algorithm is as follows: (6) In the formula: The wavelet decomposition scale; Represents the finest scale after wavelet decomposition. High-frequency wavelet coefficients; This indicates taking the middle value.

[0040] Maximum and minimum threshold The minimax threshold rule is a selection mechanism that minimizes the denoising error in the worst-case scenario by controlling an optimal fixed threshold. The threshold calculation formula is as follows: (7) Unbiased risk estimation threshold The unbiased risk estimation threshold rule first sorts the squares of the wavelet decomposition coefficients from smallest to largest, and then constructs an unbiased risk estimate based on the sorted coefficients. By minimizing the unbiased risk estimate, the threshold is ultimately adaptively selected.

[0041] Define coefficient vector , ; Define a risk vector R, whose element expression is: (8) Take the minimum value in R Calculate the risk value and find the corresponding value in W. The unbiased risk estimation threshold is calculated as follows: (9) Heuristic threshold Heuristic thresholding is a hybrid strategy that combines a general threshold with an unbiased risk estimation threshold. When the signal-to-noise ratio (SNR) is high, a fixed threshold is used; when the SNR is low, an unbiased risk estimation threshold is used. The threshold calculation formula is as follows: (10) In the formula: and The calculation formula for the preset comparison value is as follows: (11) In the formula: These are the wavelet decomposition coefficients. This is the signal length.

[0042] The characteristics of the four threshold selection rules are shown in Table 1.

[0043] Table 1 Comparison of Four Wavelet Threshold Selection Rules After wavelet transform, wavelet coefficients are naturally categorized into large, medium, and small types based on their magnitude. At this point, using complementary threshold ranges of two different thresholds can cover the full dynamic range of the signal. Unbiased risk estimation thresholds have strong adaptive capabilities but high computational complexity, poor engineering practicality, and lack universality, making them unsuitable as global boundary thresholds. Heuristic thresholds are flexible but rely on judgments of the signal-to-noise ratio (SNR) state, exhibiting weak stability and making them unsuitable as boundary thresholds. This invention uses a general threshold and a maximum-minimum threshold. Both the general threshold and the maximum-minimum threshold have explicit analytical formulas, exhibit strong complementary characteristics, low computational complexity, and simple engineering implementation. Using the general threshold as the boundary between large and medium magnitude coefficients avoids excessive smoothing of signal details. Using the maximum-minimum threshold as the boundary between medium and small magnitude coefficients ensures robust noise filtering in the worst-case scenario. Nonlinear shrinkage of the medium magnitude coefficients effectively balances noise suppression and detail preservation.

[0044] Based on equations (3) and (4), it is easy to see that in practical signal denoising applications, the hard threshold function is discontinuous throughout the entire wavelet domain. and- The noise reduction signal is discontinuous and has a large variance. The soft threshold function has no discontinuities in the wavelet domain, but its wavelet coefficients above the threshold are compressed to a constant value, which is inconsistent with the trend that the noise component gradually decreases as the wavelet coefficient increases.

[0045] Considering both the choice of threshold and the shortcomings of hard and soft thresholding functions in noise reduction, this paper proposes an improved wavelet thresholding (IWT) function, the formula of which is: (12) In the formula: This is a general threshold; The threshold is the maximum or minimum threshold.

[0046] The IWT function performs well in terms of both continuity and asymptoticity.

[0047] (1) Continuity : Left limit = .

[0048] Right limit = .

[0049] If the left and right limits are equal, the function is continuous.

[0050] : Left limit = .

[0051] Right limit = .

[0052] If the left and right limits are equal, the function is continuous.

[0053] The continuity of the remaining function intervals is determined by the exponential function, absolute value function, and constant. The function is continuous.

[0054] (2) Gradualness The wavelet coefficients shrink nonlinearly, as... The increase, and The error gradually decreases and eventually approaches the value. .

[0055] : hour . The improved threshold function has a sloping asymptote, and the deviation between the two eventually approaches 0.

[0056] like Figure 5 As shown, comparing the coefficient curves of the IWT function, hard thresholding function, and soft thresholding function, IWT, by improving the contraction rule of wavelet coefficients within its domain, ensures the continuity of the function itself and overcomes the local signal oscillations caused by the discontinuity at the threshold point in the hard thresholding function. When the absolute value of the coefficients of the IWT function is extremely large, it closely matches the changing trend of the original wavelet coefficients, solving the problem of constant error present in the soft thresholding function.

[0057] The KF algorithm, based on dynamic system mathematical and observational models, predicts future trends of data in complex environments and updates them by combining them with current data, making the predictions more accurate. Its core lies in minimizing the mean square value of the estimation error, providing an optimal estimate of the system state, and continuously performing prediction and update processes. These two processes are achieved through the following steps: Prediction process ① State prediction, the formula is: (13) In the formula: This is the predicted value for the current time based on information from the previous time step; The state matrix; This is the optimal estimate from the previous moment; For control matrix; This is the control input measured by the sensor at the current moment.

[0058] ② Error covariance prediction, the formula is: (14) In the formula: The covariance matrix of the predicted values ​​at the current time; This is the covariance matrix of the optimal estimate at the previous time step; This is the transpose of the state matrix; This is the covariance matrix for predicting noise.

[0059] Update process ① The Kalman gain is calculated using the following formula: (15) In the formula: The Kalman gain at the current moment; For measurement matrix transpose; This is the covariance matrix for measuring noise.

[0060] ②State update, the formula is: (16) In the formula: This is the optimal estimate for the current moment; This is the measurement value obtained from the sensor at the current moment.

[0061] ③ Error covariance update, the formula is: (17) In the formula: This is the covariance matrix of the optimal estimate at the current moment; It is an identity matrix.

[0062] The KF algorithm flowchart and signal block diagram are as follows: Figure 6 As shown. Initial state estimation is set. And error covariance matrix The dynamic model is used to predict the state at the next time step and the error covariance of the state estimate. Based on the observation model, combined with the actual observations and the predicted state, a new state estimate and error covariance are calculated. At each time step, the prediction and update steps are continuously executed to continuously optimize the state estimate.

[0063] To verify the advantages of the IWT function in signal denoising compared to hard and soft thresholding functions, a simulated signal function with sinusoidal noise plus white noise is constructed as follows: (18) Where: frequency ;frequency ;frequency ; Indicates time.

[0064] Based on frequency characteristics The simulated signal contains three sinusoidal signals with different periods. , and A uniform white noise with a standard deviation of 1 With a sampling frequency of 500Hz and 5000 sampling points, the simulated signal waveform is as follows. Figure 7 As shown, a is the time-domain plot of the simulated signal, and b is the frequency-domain plot of the simulated signal.

[0065] For noise reduction, the db4 wavelet is used to decompose the signal, with a decomposition level of 4. The wavelet coefficient thresholds are calculated according to equations (5) and (7). and The size. These are used respectively for the soft threshold function, hard threshold function, and IWT function, followed by... The signal is processed by subdividing the coefficient range of IWT. The signal after hard thresholding, soft thresholding, and IWT processing is as follows: Figure 8 As shown, a is the time domain image after denoising using the three types of wavelet threshold functions, and b is the frequency domain image after denoising using the three types of wavelet threshold functions.

[0066] A graphical comparison of the denoised signals reveals that the curve denoised using the hard thresholding function exhibits more spikes and a coarser signal. The curve denoised using the soft thresholding function is smoother, but some high-frequency details are weakened during the decomposition process, leading to amplitude attenuation in the reconstructed signal. The curve denoised using IWT is closer to the original signal, achieving a more balanced approach to noise reduction and detail preservation.

[0067] Depend on Figure 9 Comparing the spectra of the simulated signal with those of the signal after IWT denoising shows that the denoised curve has fewer spikes and is smoother overall, demonstrating a better effect in eliminating white noise. To quantitatively evaluate the smoothness of the denoised spectrum and the white noise filtering effect, the signal-to-noise ratio (SNR) and root mean square error (RMSE) are used as evaluation metrics, expressed as follows: (19) (20) In the formula: It is the signal length; It is the original signal; This is the signal after noise reduction.

[0068] SNR represents the effective signal ratio; a higher SNR indicates less noise. RMSE represents the error between the denoised signal and the original signal; a lower RMSE indicates higher fidelity. The evaluation metrics after processing with the three threshold functions are shown in Table 2. The data shows that IWT has the highest SNR and the lowest RMSE, indicating that IWT better balances denoising and signal fidelity requirements compared to traditional threshold functions, making it a superior denoising algorithm.

[0069] Table 2 Comparison of Evaluation Indicators for Three Types of Threshold Functions In dynamic experiments of the turbine unit, the signal changes in real time with the operating conditions. Using the Karl von Ferdinand von Bragg (KF) method, the posterior estimate changes in real time along with the measured value, providing the optimal estimate with the minimum mean square error under certain conditions, thus representing the optimal solution for the application. However, KF requires the system to be strictly linear, and the noise must follow a Gaussian white noise distribution. In actual turbine operation, the system often experiences sudden interference noise and other nonlinear elements. In such cases, the filtering results will deviate significantly from the true value, or even fail completely.

[0070] To reduce the significant errors in spectral analysis caused by the non-stationary characteristics of the original signal after KF processing, noise reduction preprocessing of the acquired signal is necessary. WT is particularly suitable for processing non-stationary signals such as turbine cracks, and can simultaneously locate and separate fault acoustic features from background noise in both the time and frequency domains.

[0071] Traditional thresholding functions often rely on a single threshold choice in practical noise reduction applications. Hard thresholding functions exhibit abrupt and discontinuous changes at the threshold, leading to pseudo-Gibbs effects and high-frequency oscillations in the denoised signal. Soft thresholding functions, on the other hand, produce a constant bias when the wavelet coefficient amplitude exceeds the threshold, resulting in signal distortion. The IWT function proposed in this paper employs a piecewise thresholding approach, better balancing the need for noise suppression and detail preservation. It removes redundant noise while maximizing the retention of key information such as signal abrupt changes and spikes, thus reducing signal distortion.

[0072] This invention employs a joint IWT-KF denoising method. IWT is used to preprocess the original signal. For non-stationary signals, background noise is significantly suppressed, addressing the issue of KF's high requirements for noise and initial signal quality, thus providing a better input signal for filtering. KF processing is applied to dynamic noise to obtain more accurate posterior estimates. This method performs dual denoising for both static and dynamic noise, resulting in stronger denoising adaptability and better denoising performance. The method has a clear division of labor, is easy to debug, and the preprocessed signal can quickly output results, meeting the requirements of engineering practicality and real-time operation. The processing flow is as follows: Figure 10 As shown.

[0073] This invention employs four steps to verify the denoising effect of the IWT-KF method, as follows: Figure 11 As shown.

[0074] First, a 3D model of the designed test rig needs to be created to optimize the layout of each component. The test rig consists of four parts: a water storage system, a water supply system, a test section, and a return water system. The water storage system includes a water tank to store water. The water supply system includes a pressure pump and related pipelines, providing power and a path for water flow. The test section, with a hydroelectric generator set as its core equipment, is the core area for conducting experiments. The return water system includes a submersible pump and supporting pipelines to achieve water return.

[0075] After modeling is completed, an actual test bench is built, such as... Figure 12 As shown in the figure, this test bench was used to measure the sound signal generated when water flows through a hydro-generator with a cracked impeller. Before starting the test bench, an appropriate amount of water was added to the water tank and water trough. A pressure pump extracted water from the water tank and transported it to the hydro-generator through pipelines. After the water flow impacted the impeller blades, it flowed into the water trough, and a submersible pump then pumped the water from the trough back to the water tank, thus achieving water circulation. Before the circulation started, a pre-fabricated cracked impeller was used to measure the signal generated when water flowed through the blades of the cracked impeller. The parameters of the hydro-generator used are shown in Table 3.

[0076] Table 3. Parameters of Hydro-generator The signal acquisition equipment uses the industrial-grade noise sensor CRY2301, which is specifically designed for weak noise detection and has real-time spectrum analysis capabilities. It integrates a DSP processor, preamplifier, high-sensitivity microphone, and data acquisition card. The compact internal structure ensures high accuracy and efficiency in data acquisition and processing. Key performance parameters are shown in Table 4.

[0077] Table 4 Noise Sensor Parameter Table The study selected three identical rotating wheels, and artificially created different numbers of cracks in two of them, such as... Figure 13 As shown, the acoustic signals of (b) 3 cracked rotors, (c) 8 cracked rotors, and (a) normal rotors are compared and analyzed.

[0078] The experimental data acquisition process is as follows: Figure 14 As shown. Before operating the test bench, the required conditions were set up on the impeller. After turning on the pressure pump and submersible pump, the water flow was driven to form a stable closed loop within the pipeline. Once the unit was running stably and the amplitude of the sensor output signal tended to stabilize, the acoustic signal data was collected and recorded.

[0079] like Figure 15 As shown, the original signal waveform is disordered due to the superposition of effective signals and noise from various devices. The waveform contains not only effective signal components from the water flow impacting the turbine blades under various conditions, but also high-frequency noise signal components introduced by the operation of pressure pumps, submersible pumps, and hydro-generators. The coupling of these multiple components results in a highly mixed waveform.

[0080] The waveform of a normal rotating wheel is relatively uniform with a small amplitude, serving as the reference signal waveform under noise interference.

[0081] The waveform of the three cracked rotors exhibits increased irregularity, and the frequency of amplitude abrupt changes near the 4500 characteristic point increases. Due to the masking effect of noise signals, the waveform is less distinguishable from the normal waveform.

[0082] The waveform irregularities of the eight cracked rotors were aggravated. Due to interference from high-frequency noise components, the characteristic signals of the cracks were masked, making it impossible to directly identify the degree of failure.

[0083] The original signal waveforms all exhibit strong noise and weak features. Fault signals are masked by significant background noise and cannot be directly used for fault identification. Therefore, selecting an efficient denoising algorithm to suppress random noise and accurately present waveform features is crucial for subsequent feature extraction and identification of turbine cracks.

[0084] To ensure the success of the experiment, the following key points need to be checked during the experiment.

[0085] (1) Runner machining specifications. The location, geometry, and installation position of the runner crack on the blade must be precisely consistent to eliminate additional noise introduced by differences in machining and assembly.

[0086] (2) The water circulation system operates smoothly. Ensure that the water is clean and free of solid impurities that could interfere with the measurement of pure crack signals. After water injection, allow sufficient time for the system to run and remove air bubbles to ensure smooth operation.

[0087] (3) The sensor is placed reasonably and securely. This paper focuses on the fault signal of the turbine runner. When the sensor collects the signal, it is placed as close as possible to the runner to effectively capture the runner noise and to a certain extent keep it away from interference sources such as the pump body.

[0088] The acquired signals were denoised using KF, IWT, and IWT-KF methods, respectively. The denoising results for the normal rotary wheel signal are as follows: Figure 16 As shown.

[0089] The original signal waveform exhibits obvious high-frequency random fluctuations, strong background noise, frequent and chaotic amplitude fluctuations, and insufficiently prominent transient impact characteristics. Without any processing, the acoustic emission signal contains a large amount of environmental noise and irrelevant interference components, which is detrimental to subsequent feature extraction and fault identification.

[0090] The IWT processing results reduce the overall fluctuation amplitude of the signal to some extent and suppress high-frequency random noise. However, the waveform is still relatively coarse and the background disturbance is still obvious, indicating that the method has a certain ability to suppress noise, but its improvement on signal stability and detailed structure is limited.

[0091] The signal processed by KF exhibits smoother time-domain characteristics, with significantly reduced random fluctuations and further attenuation of background noise. While smoothing noise, some transient details are also weakened, indicating that KF strikes a trade-off between noise suppression and feature preservation.

[0092] The IWT-KF processing results exhibit the most stable and clear time-domain waveforms. The overall signal amplitude distribution is more concentrated, random noise is effectively suppressed, and certain transient fluctuation characteristics are preserved, demonstrating a good balance between noise suppression and feature preservation capabilities.

[0093] In summary, different signal processing methods show significant differences in noise suppression and feature preservation capabilities. Among them, the IWT-KF method is the most outstanding in improving signal stability, reducing background noise, and maintaining effective features, providing higher quality input signals for subsequent acoustic emission feature extraction and fault diagnosis.

[0094] Fast Fourier Transform was performed on the original signal from the normal rotating wheel and the signals after denoising using the three methods, resulting in the following: Figure 17 The spectrum diagrams show that the three methods filtered out high-frequency noise from the original signal to varying degrees.

[0095] The original signal exhibits the largest spectral fluctuation amplitude, with numerous high-frequency amplitude spikes. Interference from equipment operation and environmental noise during signal acquisition masks signal characteristics with significant background noise, making it difficult to distinguish between normal and fault conditions. Directly performing subsequent feature extraction and fault identification severely impacts the accuracy of the identification results.

[0096] The IWT processing results reduce the vibration amplitude of the original signal to a certain extent and suppress static noise to some extent. However, IWT alone is not very adaptable to dynamic noise, and some noise spikes still remain in the high-frequency band. It can only perform preliminary noise reduction and cannot meet the high-precision requirements of feature extraction.

[0097] The amplitude fluctuations in the KF processing result are significantly reduced compared to the original signal, and it has a certain suppressive effect on the dynamic noise of the original signal. However, since KF has limited ability to suppress noise in nonlinear acoustic signals, many glitches in the high-frequency region still remain, and the KF method alone is difficult to meet the accuracy requirements of engineering applications.

[0098] The signal processed by IWT-KF exhibits minimal fluctuation amplitude, with the high-frequency band essentially matching the stable region where the amplitude approaches zero, and the fluctuation trend closely mirroring that of the original signal. IWT and KF algorithms complement each other, providing dual denoising for both static and dynamic noise. The denoising effect is significantly superior to either method alone.

[0099] Overall, single algorithms have limitations such as weak adaptability and incomplete suppression. The IWT-KF method, through algorithm coupling, takes into account both effective suppression of random noise and preservation of transient fluctuation features, providing a more reliable signal basis for subsequent turbine status identification.

[0100] To further quantify the denoising effect, the noise energy ratio (NER), the Barthel Index (BC), and the total variation (TV) are used to evaluate the results, and their expressions are as follows: (twenty one) In the formula: It is the signal length; It is the original signal; This is the signal after noise reduction.

[0101] BC (twenty two) in: (twenty three) In the formula: It is the number of equal intervals that divide the amplitude range of the standardized signal; It is the probability distribution of the original signal amplitude; It is the probability distribution of the amplitude of the denoised signal; It is the number of samples of the signal amplitude in the i-th interval.

[0102] (twenty four) In the formula: It is a discrete signal.

[0103] NER is a key metric for quantifying the proportion of noise energy to total signal energy, used to measure how much noise the algorithm removes. A smaller value indicates weaker residual noise interference and better denoising performance. BC is an important indicator of signal feature fidelity, quantifying the similarity of data distribution before and after noise processing. A value closer to 1 indicates more similar characteristics of the effective signal components before and after denoising, resulting in a more ideal denoising effect. TV evaluates the smoothness and detail retention of the signal after denoising, representing the degree of change between adjacent points; a smaller value indicates a smoother waveform and better denoising performance. The evaluation metrics for the denoised signal are as follows: Figure 18 As shown, the data shows that IWT-KT has the best denoising effect in the comprehensive evaluation of various quantitative indicators. IWT-KF has the smallest NER and TV values, demonstrating better denoising performance; for the BC index, the evaluation results of the three methods are very close to the ideal value of 1. Overall, the IWT-KF method has a better noise suppression effect and can better maintain the original shape of the signal, with the best overall performance. The normal rotor signal processed by IWT-KF was selected as the reference signal for the subsequent crack signal.

[0104] For crack signals, the first step is to select the wavelet basis function and the number of decomposition layers. The selection results are as follows: Figure 19 As shown, (a) represents a wheel with 3 cracks, and (b) represents a wheel with 8 cracks. The figure shows that after traversing 21 wavelet bases (db1-db8, sym1-sym8, coif1-coif5) and decomposition scales of 1-8 levels, the optimal denoising potential parameters are selected using SNR as the evaluation index. The optimal wavelet basis function for the 3-crack wheel signal is db1, and the decomposition scale is 8; the optimal wavelet basis function for the 8-crack wheel signal is also db1, and the decomposition scale is 8.

[0105] The signal denoising results for 3-crack turbines and 8-crack turbines are as follows: Figure 20 As shown, (a) is a wheel with 3 cracks and (b) is a wheel with 8 cracks.

[0106] For the original signal, whether it has 3 cracks or 8 cracks, the waveform exhibits obvious high-frequency noise and fault coupling characteristics. The 3-crack signal fluctuates violently and randomly, with fault features being submerged by background noise; the 8-crack signal has similar amplitude fluctuations, but local fluctuations are more frequent. Increasing the number of cracks intensifies the coupling between background noise and the fault signal, making transient impact features more difficult to identify. The degree of signal confusion also increases with the number of cracks, and directly using the unprocessed acoustic emission signal significantly increases the risk of misjudgment in subsequent feature extraction and fault identification.

[0107] The IWT processing method offers limited improvement to the waveform fluctuations of both types of signals. Because the IWT algorithm struggles to adapt to dynamic noise caused by faults, the signal waveforms still retain a significant amount of random vibration, and spikes in some areas of the eight crack signals are not effectively suppressed. This method can only be used for preliminary noise reduction.

[0108] The KF algorithm has limited filtering performance for non-stationary signals. The oscillation frequencies of the three crack signals are close to the original signal, and the eight crack signals exhibit even greater disorder, obscuring fault characteristics. The increased number of cracks amplifies the signal's non-stationarity, and KF fails to demonstrate effective noise reduction. After IWT-KF processing, the improvement in signal amplitude was most significant. The waveform was compressed to the ±0.1 range, and the local dense spikes of the eight crack signals were greatly reduced, resulting in a significant improvement in overall smoothness, demonstrating the effectiveness of the complementary algorithms.

[0109] In summary, the IWT-KF method effectively overcomes the limitations of single denoising methods when the fault severity increases. It solves the noise masking problem for mild faults and adapts to the increased interference with severe faults. Balancing noise reduction effectiveness and adaptability, it is a more ideal denoising solution.

[0110] Fast Fourier Transform was performed on the original signal of the cracked wheel and the signals after denoising using the three methods, resulting in the following: Figure 21 The spectrum diagrams shown are (a) for a 3-cracked wheel and (b) for an 8-cracked wheel.

[0111] The frequency fluctuations of the original signal increase with the number of cracks, with dense and irregular amplitudes in the high-frequency band. The characteristic frequencies corresponding to the fault are drowned out by environmental noise, especially in severe faults, where effective information is completely masked. Directly using the original spectrum for feature extraction and fault identification will increase matching errors due to interference from high-frequency noise.

[0112] The IWT method offers limited improvement to the original signal. Numerous cluttered peaks remain in the mid-to-high frequency bands, and high-frequency intensity is not effectively compressed. It cannot meet the accuracy requirements for frequency feature extraction under highly coupled conditions. It can only achieve preliminary spectral noise reduction.

[0113] After KF processing, no effective spectral cleanup capability was observed in either type of signal. Due to the poor adaptability of the KF algorithm to non-stationary spectra, some peak enhancements appeared in the high-frequency bands of the eight crack spectra after KF processing, which is difficult to meet the requirements of engineering applications.

[0114] The signal spectrum amplitude after IWT-KF joint processing is significantly improved. The high-frequency peaks of the three cracks are greatly compressed, and the spectral disorder of the eight cracks is significantly reduced. The signals under both operating conditions meet the accuracy requirements for subsequent feature extraction and fault identification.

[0115] Overall, the limitations of a single algorithm increase with the number of cracks. The IWT-KF method, through hierarchical denoising, takes into account the denoising effectiveness of both minor and severe faults, and is a superior denoising solution.

[0116] To further quantify the smoothness of the denoised signal and the white noise filtering effect, SNR and RMSE were used as evaluation metrics. The evaluation results are as follows: Figure 22 As shown, (a) is a wheel with 3 cracks and (b) is a wheel with 8 cracks.

[0117] Data shows that regardless of whether there are 3 or 8 cracks, the signal processing results consistently exhibit low original signal NR and high RMSE. The optimization capabilities of the single IWT and KF methods are limited; however, the IWT-KF combined denoising method shows a significant improvement in SNR and an effective reduction in RMSE. These two indicators quantitatively confirm the IWT-KF combined denoising method's ability to balance noise suppression and detail preservation, making it a superior denoising solution suitable for different fault severity levels.

[0118] Based on the signal processing results of different rotors, the IWT-KF solution shows significant advantages in noise reduction performance, signal fidelity, and parameter adaptability.

[0119] Comparison of the processing effects of IWT, KF, and IWT-KF on normal rotor signals ( Figure 18 As can be seen, the IWT-KF scheme has the smallest NER and TV values, and the BC values ​​of all three algorithms are close to the ideal value of 1, indicating that IWT-KF retains the original signal characteristics while having a better noise suppression effect. The crack-free turbine signal processed by IWT-KF is used as the benchmark for subsequent crack signal analysis.

[0120] To adapt to the signal analysis requirements of different crack development stages, 21 wavelet basis functions and 1-8 level decomposition scales were used to analyze signals from 3 cracks and 8 cracks. The optimal parameters were selected based on the signal-to-noise ratio (SNR). Figure 19 The results show that the optimal wavelet basis for both types of crack signals is db1, and the decomposition scale is 8. The selection of wavelet basis functions and decomposition scales is adapted to the signal characteristics of different crack development stages, providing standard prerequisites for subsequent denoising processing.

[0121] Quantitative analysis was conducted on the noise levels and denoising effects of three types of rotor signals. The normal rotor reference signal exhibited a stable baseline characteristic. The original noisy signals from rotors with 3 and 8 cracks had SNRs of -5.86 and -4.75, respectively, and RMSEs of 0.0577 and 0.0508, respectively, indicating significant noise interference and poor signal quality. After IWT-KF processing, the SNRs of both types of signals increased to -1.41 and -0.55, respectively, the highest among all methods; the RMSEs decreased to 0.0346 and 0.0313, respectively, the lowest among all methods. Figure 22 Regardless of whether it's a 3-crack or 8-crack wheel signal, the SNR after IWT-KF processing is higher than that of the standalone IWT or KF schemes, while the RMSE is lower.

[0122] Based on the aforementioned differences in characteristics, a correspondence was further established between the static characteristics of the three types of turbines after IWT-KF processing and the dynamic change stages of cracks: the normal turbine corresponds to the crack-free baseline stage. The time-domain signal amplitude is stable, exhibiting a smooth baseline with uniform overall fluctuations. Figure 16 The frequency domain signal amplitude is approximately 0.004, with energy concentrated between 0-5000Hz, and no abnormal peaks. Figure 17 The impeller containing three cracks corresponds to the crack initiation stage. The time-domain signal shows a small amount of local distortion. Figure 20 The frequency domain signal amplitude increased to 0.009, and significant energy accumulation occurred in the 0-5000Hz frequency band. Figure 21 The impeller with 8 cracks corresponds to the crack propagation stage. The frequency of time-domain signal fluctuations has significantly increased. Figure 20 The frequency domain signal spreads to the 5000-10000Hz frequency band, exhibiting wideband energy surge and multi-band fluctuation coupling signal characteristics. Figure 21 ).

[0123] This invention proposes a combined IWT and KF method for noise reduction of turbine runner fault signals. The IWT algorithm effectively overcomes the problems of discontinuities and constant deviations in traditional thresholding, preserving key signal information to the greatest extent possible, while addressing the high requirements of KF for noise and initial signal quality. The feasibility of the IWT-KF method is verified by collecting acoustic signals from turbines under different operating conditions using a test rig. Experimental results show that the IWT-KF scheme performs best in processing acoustic signals from normal runners, runners with three cracks, and runners with eight cracks. The SNR is improved by 75.4% compared to IWT and 77.4% compared to KF; the RMSE is reduced by 29.4% compared to IWT and 12.8% compared to KF. The method balances noise reduction and fidelity preservation, completely retaining the acoustic time-frequency domain characteristics at each stage.

[0124] The three types of turbine runner characteristics correspond to the three stages of crack initiation, crack absence, and crack propagation. In the crack-free stage, the time-domain signal shows a stable baseline, with frequency-domain energy concentrated in the 0-5000Hz range and uniformly distributed. In the crack initiation stage, localized weak distortions appear in the time domain, and significant energy accumulation is observed in the 0-5000Hz frequency band. In the crack propagation stage, high-frequency fluctuations occur in the time-domain signal, with a wide-band energy distribution and multi-frequency coupled fluctuations in the frequency domain. These characteristics at each stage can provide technical support for monitoring the crack condition of hydraulic turbines.

[0125] The IWT-KF denoising method exhibits good versatility and effectiveness, and the characteristics of crack evolution stages can provide a basis for condition detection. Future research could combine this method with intelligent algorithms to use the IWT-KF-processed signals for crack quantity identification and fault early warning model construction, expanding the sample size to optimize model accuracy and achieving full-process optimization of signal processing and condition diagnosis.

[0126] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for joint denoising of weak fault signals in turbine runners based on improved wavelet thresholding and Kalman filtering, characterized in that, Includes the following steps: Step 1: Collect acoustic signals of the turbine runner under different operating conditions, including normal operating condition, 3-crack condition, and 8-crack condition; Step 2: Perform wavelet decomposition on the original acoustic signal, select wavelet basis functions and determine the number of wavelet decomposition levels, and calculate the universal threshold. and maximum and minimum threshold ; Step 3: Process the wavelet coefficients obtained from wavelet decomposition using an improved threshold function to obtain approximate wavelet coefficients, and reconstruct the approximate wavelet coefficients to obtain the preprocessed signal; The expression for the improved threshold function is: ； In the formula, These are wavelet coefficients. It is a symbolic function; Step 4: Input the preprocessed signal into the Kalman filter module, and execute the prediction and update processes of the Kalman filter in sequence to obtain the optimal estimate of the signal; Step 5: Output the denoised acoustic signal of the turbine runner to complete the joint denoising.

2. The method for joint denoising of weak fault signals of turbine runners based on improved wavelet thresholding and Kalman filtering according to claim 1, characterized in that, The wavelet basis functions mentioned in step 2 are selected from one or more of the following: Haar wavelet, Daubechies wavelet, Symlets wavelet, and Coiflets wavelet. The Daubechies wavelet includes db1-db8 ​​wavelets, the Symlets wavelet includes sym1-sym8 wavelets, and the Coiflets wavelet includes coif1-coif5 wavelets; For the acoustic signal of the turbine runner, the above 21 wavelet basis functions (Haar wavelet is equivalent to db1 wavelet) are traversed, and the optimal wavelet basis function under the corresponding working condition is selected by using the signal-to-noise ratio (SNR) as the evaluation index. For the acoustic signals of the turbine runner under 3 and 8 crack conditions, the optimal wavelet basis function obtained by screening is the db1 wavelet.

3. The method for joint denoising of weak fault signals of turbine runners based on improved wavelet thresholding and Kalman filtering according to claim 1, characterized in that, In step 2, the general threshold The calculation formula is: ； In the formula, For standard deviation, The signal length; the standard deviation The estimation algorithm is as follows: ； In the formula, The wavelet decomposition scale, Represents the finest scale after wavelet decomposition. High-frequency wavelet coefficients; The maximum and minimum thresholds The calculation formula is: 。 4. The method for joint denoising of weak fault signals of turbine runners based on modified wavelet thresholding and Kalman filtering according to claim 1, characterized in that, In step 2, the wavelet decomposition level is determined as follows: the traversal range of the wavelet decomposition scale is set to 1-8 levels. For the acoustic signals of the turbine runner under normal operating conditions, 3-crack conditions, and 8-crack conditions, wavelet decomposition and processing with different levels of decomposition are performed within this traversal range. The signal processing results under different levels of decomposition are compared using the signal-to-noise ratio (SNR) as the evaluation index, and the optimal level of decomposition for the corresponding operating conditions is selected. For the turbine runner acoustic signals under 3-crack and 8-crack conditions, the optimal level of decomposition is 8 levels.

5. The method for joint denoising of weak fault signals of turbine runners based on improved wavelet thresholding and Kalman filtering according to claim 1, characterized in that, In step 4, the Kalman filter prediction process includes state prediction and error covariance prediction, with the corresponding formulas as follows: State prediction formula: ； Error covariance prediction formula: ； In the formula, The predicted value at the current moment. The state matrix, This is the optimal estimate from the previous moment. For the control matrix, The control input measured by the sensor at the current moment; Let be the covariance matrix of the predicted values ​​at the current time. Let be the covariance matrix of the optimal estimate at the previous time step. This is the transpose of the state matrix. This is the covariance matrix for predicting noise.

6. The method for joint denoising of weak fault signals of turbine runners based on improved wavelet thresholding and Kalman filtering according to claim 5, characterized in that, In step 4, the Kalman filter update process includes Kalman gain calculation, state update, and error covariance update, with the corresponding formulas as follows: Kalman gain formula: ； State update formula: ； Error covariance update formula: ； In the formula, The Kalman gain at the current moment. For the measurement matrix, To measure the transpose of the matrix, The covariance matrix of the measurement noise; The current measurement value obtained by the sensor. This is the optimal estimate for the current moment; It is the identity matrix. Let be the covariance matrix of the optimal estimate at the current time.

7. The method for joint denoising of weak fault signals of turbine runners based on improved wavelet thresholding and Kalman filtering according to claim 1, characterized in that, In step 1, an industrial-grade noise sensor, CRY2301, is used to collect acoustic signals. The sensor's parameters are: a communication interface of USB audio + USB HID, and a size of [missing information]. mm, sampling rate 48kHz, frequency measurement range 10-20000Hz, dynamic measurement range ≥110dBA, standard measurement range 25-130dBA.

8. The method for joint denoising of weak fault signals of turbine runners based on improved wavelet thresholding and Kalman filtering according to claim 1, characterized in that, In step 1, an acoustic signal is collected using a test bench; the test bench includes a water storage system, a water supply system, a test section, and a return water system; the water storage system is equipped with a water tank, the water supply system includes a pressure pump and supporting pipelines, the test section uses a hydro-generator set as the core equipment, and the return water system includes a submersible pump and supporting pipelines; The parameters of the hydro-generator set are as follows: rated power 5kW / 5KVA, rated frequency 50Hz, rated speed 1500r / min, rated voltage 230V, rated current 21.8A, excitation voltage 49V, excitation current 2.6A, and power factor 1.

0.

9. The method for joint denoising of weak fault signals of turbine runners based on improved wavelet thresholding and Kalman filtering according to claim 1, characterized in that, The method further includes a noise reduction effect evaluation step, using at least one of the following as evaluation indicators: signal-to-noise ratio (SNR), root mean square error (RMSE), noise energy ratio (NER), Bartholomew's law coefficient (BC), and total variation (TV). The calculation formulas for each evaluation indicator are as follows: ； ； ； ； ； In the formula, For signal length, The original signal, The signal after noise reduction; The number of equal intervals to divide the amplitude range of the standardized signal. It is the probability distribution of the original signal amplitude. It is the probability distribution of the amplitude of the denoised signal; It is a discrete signal.

10. The method for joint denoising of weak fault signals of turbine runners based on improved wavelet thresholding and Kalman filtering according to claim 1, characterized in that, The improved wavelet thresholding in step 3 targets high-frequency random noise in the original acoustic signal. The process involves wavelet decomposition of the original acoustic signal to obtain wavelet coefficients at different scales, segmenting the wavelet coefficients using an improved threshold function, and then reconstructing the processed approximate wavelet coefficients using wavelets to obtain the preprocessed signal. The Kalman filtering in step 4 targets low-frequency dynamic noise in the preprocessed signal. The process involves inputting the preprocessed signal into the Kalman filtering module and sequentially executing the state prediction, error covariance prediction, Kalman gain calculation, state update, and error covariance update steps to obtain the optimal estimate of the signal.

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