A noise reduction method for CNC machine tool power tool holder based on UUSGSR

Abstract

The present invention discloses a noise reduction method for a CNC machine tool power tool holder based on UUSGSR, which belongs to the technical field of monitoring the power tool holder of a CNC machine tool servo tool holder. The method of the present invention comprises the following steps: performing Hilbert transform and elliptic filtering preprocessing on the vibration signal of the bearing in the monitored tool holder power tool holder; constructing a non-saturated scaled Gaussian potential stochastic resonance model to process the signal; proposing a high-order weighted harmonic noise ratio (HWR) HWHNR As the objective function, reflecting the nonlinear characteristics of the signal, the Gray Wolf Optimization Algorithm is used to optimize the structural parameters and damping factors, resulting in the optimal underdamped, unsaturated, scaled Gaussian potential stochastic resonance model (UUSGSR) containing these model structural parameters and damping factors. This model is then used to perform stochastic resonance processing on the bearing vibration signal within the toolholder power toolholder, reducing the noise contained in the bearing vibration signal and improving the signal-to-noise ratio. In summary, the method disclosed in the present invention can achieve noise reduction for the bearing vibration signal within the toolholder power toolholder.

Description

Technical Field

[0001] The present invention belongs to the technical field of noise reduction of a servo tool holder of a CNC machine tool, and in particular relates to a noise reduction method of a CNC machine tool power tool holder based on UUSGSR. Background Art

[0002] The powered toolholder of a servo toolholder is a key component for rotary cutting in CNC machine tools. Its core supporting bearing is highly susceptible to failure under high speeds, heavy loads, and harsh operating conditions, threatening processing safety and equipment reliability. Monitoring its status through vibration signals is a common method. However, the fault characteristic signals of the bearings within the powered toolholder are inherently nonlinear and non-stationary, and are submerged in the extremely strong background noise within the toolholder, primarily from multiple sources such as gear meshing, motor electromagnetics, and cutting vibrations. These noises are highly coupled with the bearing signals within the compact space of the toolholder, resulting in an extremely low signal-to-noise ratio. This makes it difficult for traditional time-domain or frequency-domain analysis methods to effectively extract and identify early, weak fault characteristics of the bearing. Therefore, developing efficient noise reduction technologies suitable for the complex and high-noise environments of powered toolholders and improving their signal-to-noise ratio is a key prerequisite for improving their bearing status monitoring and fault diagnosis capabilities.

[0003] Current noise reduction methods rely on noise suppression and signal decomposition, such as wavelet transform, empirical mode decomposition, and variational mode decomposition. While these methods suppress noise, they also weaken useful fault signature information to a certain extent, inevitably damaging the useful signal. Compared to wavelet transform, empirical mode decomposition, and variational mode decomposition, stochastic resonance is a new approach that has emerged in recent years with the rapid advancement of nonlinear dynamics and statistical physics. Unlike traditional noise reduction techniques, which rely on noise suppression and signal decomposition, stochastic resonance does not directly reduce noise. Instead, it achieves noise reduction by optimizing the matching of the signal, nonlinear system, and noise, converting some noise energy into useful signal. However, in practical applications, traditional stochastic resonance methods have poor detection performance in certain complex noise environments and are prone to severe sideband interference.

[0004] The classic bistable stochastic resonance model suffers from output saturation when processing weak signals from incipient faults. Most current research focuses on analyzing and resolving this issue using first-order differential equations when the model is overdamped. However, when the model is underdamped, second-order differential equations are required to address the stochastic resonance issue. This state is equivalent to double filtering of the signal, theoretically allowing for more effective signal feature extraction.

[0005] The traditional signal-to-noise ratio (SNR) is widely used as the objective function for stochastic resonance, but it has several drawbacks. First, the SNR relies on prior knowledge and requires determining the fault frequency of the measured signal before calculating the SNR. Second, the SNR primarily focuses on the target frequency of the signal, while ignoring the overall periodic characteristics of the signal. Summary of the Invention

[0006] The purpose of the present invention is to solve the above technical problems and achieve effective noise reduction of the bearing vibration signal in the tool holder power tool holder, and to provide a noise reduction method for the CNC machine tool power tool holder based on UUSGSR.

[0007] The present invention is achieved by adopting the following technical solutions:

[0008] A method for reducing noise of a CNC machine tool power tool holder based on UUSGSR, comprising the following steps:

[0009] Step 1: Obtain the vibration signal of the bearing inside the tool holder power tool holder;

[0010] Step 2: Add Gaussian white noise to the original signal to better simulate the actual working conditions with low signal-to-noise ratio. The stochastic resonance dynamics model of the multistable system includes the memory of time, making the stochastic resonance process non-Markov.

[0011] Step 3: Preprocess the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise so that the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise meets the parameter restriction condition of stochastic resonance;

[0012] The preprocessing method includes: performing Hilbert-Huang transform on the vibration signal of the internal bearing of the tool holder power tool holder containing Gaussian white noise to remove the DC component, and using a low-pass elliptic filter to perform filtering processing to reduce the low-frequency influence, thereby obtaining a signal to be detected that meets the parameter restriction conditions of stochastic resonance after preprocessing;

[0013] Step 4: Build an improved gray wolf optimization algorithm, providing an adaptive stepping strategy that updates the gray wolf's position by dynamically adjusting weights to better balance global search and local exploration. Also, introduce proportional weights based on the improved step-size Euclidean distance, allowing the algorithm to more flexibly adjust the search direction when updating the position.

[0014] Step 5: Construct an underdamped unsaturated scaled Gaussian potential stochastic resonance (UUSGSR) model;

[0015] Step 6: Taking the constructed high-order weighted harmonic noise ratio (HWHNR) as the objective function, the underdamped unsaturated scaled Gaussian potential stochastic resonance (UUSGSR) model is optimized using the gray wolf optimization algorithm. When the number of iterations is When the maximum number of iterations is reached, the iteration is stopped and the optimal parameter pair is output. , and maximum HWHNR.

[0016] The adaptive step strategy expression in the gray wolf optimization algorithm is as follows:

[0017] (1)

[0018] in, Representative The position vector of the gray wolf individual, Represents the three individual position vectors with the best fitness in the current generation of gray wolf population, and Respectively represent the current number of iterations and the maximum number of iterations of the Grey Wolf Optimization Algorithm;

[0019] The proportional weight expression of the Euclidean distance of the improved step size is as follows:

[0020] (2)

[0021] (3)

[0022] (4)

[0023] in, is a very small positive real number, ensuring that the denominator of the fraction is not 0;

[0024] The final gray wolf position update method can be expressed as:

[0025] (5)

[0026] The improved gray wolf optimization algorithm can be used to optimize the structural parameters , structural parameters and damping factor Perform optimization.

[0027] The potential function of the underdamped unsaturated scaled Gaussian stochastic resonance (UUSGSR) model is:

[0028] (6)

[0029] in, represents the scaled Gaussian potential function, and is a positive real structural parameter, is the input vibration signal of the tool holder's internal bearing containing Gaussian white noise;

[0030] Under underdamped conditions, the Langevin equation driven by the UUSGSR model can be described as:

[0031] (7)

[0032] in, is the damping factor, and is a positive real structural parameter, The input is the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise, and are amplitude and frequency respectively, The mean is 0 and the variance is Gaussian white noise, Represents the noise intensity.

[0033] Under underdamped conditions, the behavior of the UUSGSR model under the influence of noise and periodic signals can be analyzed by deriving and measuring the steady-state probability density function (SPD) and mean first passage time (MFPT) of the model under the adiabatic approximation theory; the second-order differential equation (7) is transformed into two first-order differential equations:

[0034] (8)

[0035] Assumed amplitude , noise intensity , we get three singular points:

[0036] (9)

[0037] Let the potential function be The partial derivative of , the potential function pair The partial derivative of , then formula (8) can be written as:

[0038] (10)

[0039] The linearization matrix of formula (8) is obtained as follows:

[0040] (11)

[0041] Further, at the singularity The linearization matrix at can be described as:

[0042] (12)

[0043] By solving equation (12), the corresponding eigenvalues ​​are calculated:

[0044] (13)

[0045] Similarly, The linearization matrix is:

[0046] (14)

[0047] The eigenvalue corresponding to formula (14) is:

[0048] (15)

[0049] Assumptions is the probability density function (PDF) of the random process, and the corresponding Fokker-Planck equation is:

[0050] (16)

[0051] in, is the damping factor, and is a positive real structural parameter, and are amplitude and frequency respectively, is the noise intensity.

[0052] Then the steady-state probability density function (SPD) corresponding to the UUSGSR model can be expressed as:

[0053] (17)

[0054] in, is the normalization constant:

[0055] (18)

[0056] in, is the generalized potential function:

[0057] (19)

[0058] The transition rate of particles at singular points in the UUSGSR model is:

[0059] (20)

[0060] in, and is the eigenvalue corresponding to formula (14), and To solve the eigenvalue obtained by equation (12), is the noise intensity, is the amplitude;

[0061] The particle transition rate (MFPT) is:

[0062] (twenty one)

[0063] The analytical expression of the theoretical output signal-to-noise ratio (SNR) of the UUSGSR model is derived as follows:

[0064] (twenty two)

[0065] Among them, the parameters It can be expressed as:

[0066] (twenty three)

[0067] The higher-order weighted harmonic-to-noise ratio (HWHNR) is a new stochastic resonance objective function disclosed in the present invention, and is an improvement on the harmonic-to-noise ratio (HNR). The HWHNR analyzes the ratio of the periodic component to the non-periodic component (noise) of the signal, which can better reflect the nonlinear characteristics of the signal without requiring prior knowledge.

[0068] For the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise , autocorrelation function As a time delay The function is defined as:

[0069] (twenty four)

[0070] This function It reaches the global maximum when There is also a global maximum at the position of There is no global maximum at the position of , but there is a local maximum, and its position is recorded as ; If these local maxima If it is large enough, then the signal can be considered to have a periodic part; the local maximum of the normalized autocorrelation , expressed as the following formula (25);

[0071] (25)

[0072] Take a period of The periodic signal And add noise According to formula (24), if the two parts are uncorrelated, the autocorrelation function of the entire signal is equal to the sum of the autocorrelation functions of each part; for zero lag, ,in and Represents periodic signals and noise The autocorrelation function of ; if the noise is white, then the lag A local maximum is found at ;

[0073] Since the autocorrelation function of a signal at zero lag is equal to the power in the signal, The normalized autocorrelation function at represents the relative power of the signal periodic component, while its complement represents the relative power of the noise component. The local maximum of the normalized autocorrelation Expressed as:

[0074] (26)

[0075] in, and Represents the periodic signal at time 0 and noise The autocorrelation function of .

[0076] The harmonic-to-noise ratio (HNR) is defined as:

[0077] (27)

[0078] Before introducing the high-order weighted harmonic noise ratio, we first consider the high-order statistical signal processing indicator kurtosis; the kurtosis is a dimensionless parameter that describes the peak degree of the waveform. is defined as:

[0079] (28)

[0080] To emphasize the periodic component of the signal, HNR is rewritten as a higher-order statistic of the signal, and the higher-order harmonic-to-noise ratio (HHNR) is defined as the ratio of the cubed autocorrelation function of the periodic signal to the cube of the autocorrelation function of the noise signal; therefore, HHNR can be expressed as:

[0081] (29)

[0082] Where, The vibration signal of the bearing inside the tool holder power tool holder containing Gaussian white noise, is the local maximum of the normalized autocorrelation function, is the relative power of the periodic signal, is the non-periodic signal (noise) power;

[0083] In order to further consider the amplitude of the overall autocorrelation function of the signal, the indicator is expanded to the higher-order weighted harmonic noise ratio (HWHNR). By calculating the sum of the peak weights of multiple autocorrelation functions, the periodic characteristics of the signal are more comprehensively reflected. The HWHNR is expressed as:

[0084] (30)

[0085] in, is the sampling time point of the bearing vibration signal in the tool holder power tool holder containing Gaussian white noise, Indicates time delay; and Represent the sum of the time accumulation and the delay part respectively.

[0086] On this basis, an adaptive method is introduced to dynamically adjust the weights according to the characteristics of noise and signal, making HWHNR more flexible:

[0087] (31)

[0088] in, For the frequency band The relevant weight factors can be used to analyze the energy distribution of the signal in different frequency bands using the signal's autocorrelation function or power spectral density (PSD), and then adjusted according to the energy distribution. For frequency bands with obvious periodic components, higher weights are given. , while lower weights are given to frequency bands dominated by noise; is an attenuation factor related to noise intensity, which controls the effect of noise intensity on HWHNR. For cases where low-frequency noise is strong, you can set Larger to suppress the interference of low-frequency noise on the signal. For the The noise power in a frequency band.

[0089] When the HWHNR reaches its maximum value, optimal stochastic resonance is generated, and a high signal-to-noise ratio bearing vibration signal of the tool holder power tool holder is output.

[0090] The present invention provides a noise reduction method for a CNC machine tool power tool holder based on UUSGSR. The method performs Hilbert transform and elliptic filtering preprocessing on the monitored bearing vibration signal of the tool holder power tool holder, and constructs a non-saturated scaled Gaussian potential stochastic resonance model to process the signal. The proposed high-order weighted harmonic noise ratio (HWHNR) of the bearing vibration signal of the tool holder power tool holder is used as an optimization index, and the gray wolf optimization algorithm is used to perform combined optimization on the structural parameters and the damping factor to obtain the optimal under-damped non-saturated scaled Gaussian potential stochastic resonance model UUSGSR containing the model structural parameters and the damping factor. The stochastic resonance model is used to perform stochastic resonance processing on the bearing vibration signal of the tool holder power tool holder, thereby weakening the noise contained in the bearing vibration signal of the tool holder power tool holder and improving the signal-to-noise ratio.

[0091] The present invention has the following beneficial effects:

[0092] 1. The present invention discloses a noise reduction method for a CNC machine tool power tool holder based on UUSGSR. The method takes the high-order weighted harmonic noise ratio (HWHNR) of the bearing vibration signal in the tool holder power tool holder as the optimization index, adopts the improved grey wolf optimization algorithm to perform combined optimization on the structural parameters and the damping factor, and obtains the optimal underdamped non-saturated scaled Gaussian potential stochastic resonance model UUSGSR containing the model structural parameters and the damping factor; utilizes this stochastic resonance model to perform stochastic resonance processing on the bearing vibration signal in the tool holder power tool holder, thereby weakening the noise contained in the bearing vibration signal and improving the improved signal-to-noise ratio of the bearing vibration signal.

[0093] 2. This paper improves the gray wolf optimization algorithm and proposes a new adaptive stepping strategy. It updates the gray wolf's position by dynamically adjusting weights, thereby better balancing global search and local development. At the same time, by introducing proportional weights based on the improved step-size Euclidean distance, the algorithm can more flexibly adjust the search direction when updating the position.

[0094] 3. The underdamped unsaturated scaled Gaussian potential stochastic resonance model UUSGSR disclosed in the present invention processes the stochastic resonance problem through a second-order differential equation. This state is equivalent to double filtering of the signal, which can more effectively extract signal features.

[0095] 4. The high-order weighted harmonic-to-noise ratio (HWHNR) disclosed in the present invention can more comprehensively reflect the periodic characteristics of the signal by calculating the sum of the peak weights of multiple autocorrelation functions, avoiding interference from accidental autocorrelation function peaks. HWHNR not only considers the high-order statistics of the signal and enhances the characterization of periodicity, but also suppresses noise through weight adjustment. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 It is a flow chart of a noise reduction method for a CNC machine tool power tool holder based on UUSGSR of the present invention;

[0097] Figure 2 It is the original vibration signal of the bearing part in the tool holder power tool holder collected by detection;

[0098] Figure 3 is the SPD with respect to different noise intensities an image of Figure 3 (a) is the noise intensity Schematic diagram of SPD of UUSGSR model when ; Figure 3 (b) is the noise intensity Schematic diagram of SPD of UUSGSR model when ; Figure 3 (c) is the noise intensity Schematic diagram of SPD of UUSGSR model when ;

[0099] Figure 4 is the ln MFPT+ change image under different parameter changes; Figure 4 (a) is the structural parameter Schematic diagram of the impact of changes in ln MFPT+ in the UUSGSR model; Figure 4 (b) is the structural parameter Schematic diagram of the impact of changes in ln MFPT+ in the UUSGSR model; Figure 4 (c) is the damping factor Schematic diagram of the impact of changes in ln MFPT+ in the UUSGSR model;

[0100] Figure 5 This is a comparison chart of the signal-to-noise ratio (SNR) output using different methods. DETAILED DESCRIPTION

[0101] Example 1

[0102] See attached Figure 1 As shown, a noise reduction method for a CNC machine tool power tool holder based on UUSGSR includes the following steps:

[0103] Step 1: Obtain the vibration signal of the bearing in the tool holder power tool holder. The CNC servo tool holder reliability test bench developed by the Key Laboratory of CNC Equipment Reliability of the Ministry of Education of Jilin University was used for the test. The torque was 10 N·m, the speed was 1400 r / min, the sampling frequency was 10 kHz, and the sampling frequency was 5s. The original vibration signal of the power tool holder was monitored and collected using a vibration sensor. The vibration signal was obtained. See the attached Figure 2 ;

[0104] Step 2: Add Gaussian white noise to the original signal to better simulate the actual working conditions with low signal-to-noise ratio. Due to the presence of Gaussian white noise, the stochastic resonance dynamics model of the multistable system includes time memory, making the stochastic resonance process non-Markov, thus making the system exhibit more different characteristics.

[0105] Step 3: Preprocess the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise so that the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise meets the parameter restriction condition of stochastic resonance;

[0106] The preprocessing method includes: performing Hilbert-Huang transform on the internal bearing vibration signal of the tool holder power tool holder containing Gaussian white noise to remove the DC component, and using an elliptical filter to perform filtering processing to reduce the low-frequency influence, thereby obtaining a preprocessed signal to be detected, so that the internal bearing vibration signal of the tool holder power tool holder containing Gaussian white noise meets the parameter restriction conditions of stochastic resonance;

[0107] The elliptical filter is a low-pass elliptical filter, and its cut-off frequency is set according to the frequency characteristics of the bearing vibration signal in the tool holder power tool holder;

[0108] Step 4: The gray wolf optimization algorithm has a simple structure, is easy to implement, and has few parameters, making it easy to adjust. By simulating the hunting behavior of gray wolves, it can achieve a certain balance between global search and local search, and is suitable for solving various optimization problems.

[0109] This paper improves the gray wolf optimization algorithm and proposes a new adaptive stepping strategy. It updates the gray wolf's position by dynamically adjusting weights, thereby better balancing global search and local development. At the same time, by introducing proportional weights based on the improved step-length Euclidean distance, the algorithm can more flexibly adjust the search direction when updating the position.

[0110] Step 5: Construct an underdamped unsaturated scaling Gaussian potential stochastic resonance (UUSGSR) model.

[0111] Step 6: Using the high-order weighted harmonic noise ratio (HWHNR) as the objective function, the underdamped unsaturated scaled Gaussian potential stochastic resonance (UUSGSR) model is optimized using the Gray Wolf optimization algorithm. When the maximum number of iterations is reached, the iteration is stopped and the optimal parameter pair is output. , and maximum HWHNR.

[0112] The adaptive stepping strategy is expressed as follows:

[0113] (1)

[0114] in, Representative The position vector of the gray wolf individual, Represents the three individual position vectors with the best fitness in the current generation of gray wolf population, and Respectively represent the current number of iterations and the maximum number of iterations of the Grey Wolf Optimization Algorithm;

[0115] The proportional weight expression of the Euclidean distance of the improved step size is as follows:

[0116] (2)

[0117] (3)

[0118] (4)

[0119] in, is a very small positive real number, ensuring that the denominator of the fraction is not 0;

[0120] The final gray wolf position update method can be expressed as

[0121] (5)

[0122] The improved gray wolf optimization algorithm for structural parameters 、 and damping factor For optimization, the population size of the improved gray wolf optimization algorithm is , the maximum number of iterations is , the structural parameters and damping factor ranges are set to: .

[0123] The potential function of the underdamped unsaturated scaled Gaussian stochastic resonance (UUSGSR) model is:

[0124] (6)

[0125] in represents the scaled Gaussian potential function, and is a positive real structural parameter, is the input vibration signal of the tool holder's internal bearing containing Gaussian white noise;

[0126] Under underdamped conditions, the Langevin equation driven by the UUSGSR model can be described as:

[0127] (7)

[0128] in, is the damping factor, and is a positive real structural parameter, The input is the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise, and are amplitude and frequency respectively, The mean is 0 and the variance is Gaussian white noise, Represents the noise intensity.

[0129] To further explore the behavior of the underdamped UUSGSR model under the influence of noise and periodic signals, the steady-state probability density function (SPD) and the analytical expression of the mean first passage time (MFPT) of the model were derived and measured under the adiabatic approximation theory. This can further explore the behavior of the underdamped UUSGSR model under the influence of noise and periodic signals.

[0130] Formula (7) is a second-order differential equation. To facilitate the solution, the second-order differential equation can be transformed into two first-order differential equations:

[0131] (8)

[0132] Assumed amplitude , noise intensity , we get three singular points:

[0133] (9)

[0134] Let the potential function be The partial derivative of , the potential function pair The partial derivative of , then formula (8) is written as:

[0135] (10)

[0136] The linearization matrix of formula (8) is obtained as follows:

[0137] (11)

[0138] Further, at the singularity The linearization matrix at can be described as:

[0139] (12)

[0140] By solving equation (12), the corresponding eigenvalues ​​are calculated:

[0141] (13)

[0142] Similarly, The linearization matrix is:

[0143] (14)

[0144] The eigenvalue corresponding to formula (14) is:

[0145] (15)

[0146] Assumptions is the probability density function (PDF) of the random process, and the corresponding Fokker-Planck equation is:

[0147] (16)

[0148] in, is the damping factor, and is a positive real structural parameter, and are amplitude and frequency respectively, is the noise intensity.

[0149] Then the steady-state probability density function (SPD) corresponding to the underdamped unsaturated scaled Gaussian potential stochastic resonance (UUSGSR) model can be expressed as:

[0150] (17)

[0151] in, is the normalization constant:

[0152] (18);

[0153] in, is the generalized potential function:

[0154] (19)

[0155] See attached Figure 3 As shown, when hour, Figure 3 (a) shows the noise intensity When , the SPD function has only one obvious peak, indicating that in the UUSGSR model under weak noise environment, the particles stay in a potential well and no transition occurs;

[0156] Figure 3 (b) shows the noise intensity When , the SR phenomenon occurs, particles jump between potential wells, and the noise energy is converted into periodic signal energy;

[0157] Figure 3 (c) shows the noise intensity When the noise intensity is large, the SPD peak at the potential well is no longer obvious, the particles have deviated from the regular transition form, and will interfere with the periodic signal. It can be seen that the UUSGSR model in an underdamped environment can produce SR phenomenon under the action of random noise and periodic signal, and appropriate noise intensity is required to achieve the ideal effect.

[0158] The transition rate of particles at singular points in the UUSGSR model:

[0159] (20)

[0160] in, and is the eigenvalue corresponding to formula (14), and To solve the eigenvalue obtained by equation (12), is the noise intensity, is the amplitude;

[0161] The particle transition rate (MFPT) is:

[0162] (twenty one)

[0163] See attached Figure 4 To facilitate the analysis of the changing trend, we also take the logarithm on both sides of the equation and analyze the lnMFPT+ curve; when changing the structural parameters 、 or damping factor When the noise intensity 𝐷 increases, ln MFPT+ decreases monotonically, which indicates that as the noise intensity As the noise intensity 𝐷 increases, the time it takes for the particle to jump from the left potential well to the right potential well decreases, that is, the particle transition rate increases; the particle becomes more active as the noise intensity 𝐷 increases, indicating that noise helps the particle jump between potential wells; when the noise intensity As it approaches 0, the initial ln MFPT+ approaches infinity, which means that the particle no longer jumps between two potential wells, but oscillates in a single potential well.

[0164] See attached Figure 4 (a), ln MFPT+ This indicates that the appropriate It is beneficial for particles to transition between the two potential wells at the required rate, thereby obtaining the required SR effect;

[0165] Attachment Figure 4 (b) shows the Figure 4 (a) Similar trends, with As MFPT+ increases, ln MFPT+ decreases, that is, Increasing can reduce the transition rate of particles and inhibit the SR effect;

[0166] See attached Figure 4 (c), with varying damping factors When , ln MFPT+ will increase with the increase of 𝛾, that is, Increasing can increase the transition rate of particles and enhance the SR effect;

[0167] In summary, the analysis of the transient characteristics of the UUSGSR model by calculating MFPT proves that under underdamping conditions, the potential function of the UUSGSR model can still excite the occurrence of stochastic resonance and adjust the structural parameters. , and damping factor Can affect the motion of particles in nonlinear systems.

[0168] The traditional signal-to-noise ratio (SNR) is widely used as the objective function of stochastic resonance. The analytical expression of the theoretical output signal-to-noise ratio (SNR) of the UUSGSR model is derived as follows:

[0169] (twenty two)

[0170] Among them, the parameters It can be expressed as:

[0171] (twenty three)

[0172] However, using the traditional signal-to-noise ratio (SNR) as an objective function has some shortcomings: First, the SNR relies on prior knowledge and can only be calculated after the fault frequency of the measured signal is determined; second, the SNR focuses primarily on the target frequency of the signal, while ignoring the overall periodic characteristics of the signal;

[0173] To address these pain points, this paper proposes a new stochastic resonance objective function: the Higher-order Weighted Harmonic Noise Ratio (HWHNR). HWHNR analyzes the ratio of the signal's periodic components to its non-periodic components (noise), better reflecting the nonlinear characteristics of the signal. Compared with the traditional signal-to-noise ratio (SNR), HWHNR does not require prior knowledge and can directly focus on the harmonic components of the signal, thereby reducing the deviation caused by inaccurate prior information.

[0174] To derive HWHNR, we first need to understand the harmonic-to-noise ratio (HNR). HNR analyzes the ratio of the periodic component to the non-periodic component (noise) of a signal, enabling it to better reflect the nonlinear characteristics of the signal and effectively combining the considerations of periodicity and sparsity.

[0175] For the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise , autocorrelation function As a time delay The function is defined as:

[0176] (twenty four)

[0177] This function is in The global maximum is reached when There is also a global maximum at the position of , which indicates that the signal is periodic and has a specific hysteresis period ; All these maxima occur at The position of each integer , ; The fundamental frequency of the periodic signal Defined as If in There is no global maximum at the location of , but there are local maxima, and the locations of these local maxima are recorded as ; If these local maxima is large enough, then the signal can be considered to have a periodic part; its harmonic intensity is a number between 0 and 1 equal to the local maximum of the normalized autocorrelation , which can be expressed as the following formula (25); This shows that there are significant periodic components in the signal, and its periodic characteristics can be identified by these local maxima;

[0178] (25)

[0179] Take a period of The periodic signal And add noise According to formula (24), if the two parts are uncorrelated, the autocorrelation function of the entire signal is equal to the sum of the autocorrelation functions of each part; for zero lag, ,in and Represents periodic signals and noise The autocorrelation function of ; if the noise is white, then the lag A local maximum is found at ;

[0180] Since the autocorrelation function of a signal at zero lag is equal to the power in the signal, The normalized autocorrelation function at represents the relative power of the signal periodic component (or harmonic component), while its complement represents the relative power of the noise component. The local maximum of the normalized autocorrelation Expressed as:

[0181] (26)

[0182] in, and Represents the periodic signal at time 0 and noise The autocorrelation function of .

[0183] HNR is the ratio of the periodic component of the signal to the non-periodic component (noise), so it is defined as:

[0184] (27)

[0185] Before introducing the high-order weighted harmonic noise ratio, we can first consider a common high-order statistical signal processing indicator, kurtosis. Kurtosis is a dimensionless parameter that describes the peak degree of a waveform and is widely used in early equipment fault identification. The kurtosis value is is defined as:

[0186] (28)

[0187] Kurtosis value The calculation involves the fourth-order central moment and the second-order central moment (i.e., variance) of the signal data distribution. If there are many extreme values ​​or outliers in the data set, then these values ​​far from the mean will have a greater impact on the fourth-order central moment, causing the numerator to grow faster. Because these values ​​are raised to the fourth power, the fourth-order central moment is very sensitive to extreme values. The variance measures the average of the squares of the differences between the data points and the mean. If the dispersion of the data points increases, the variance will also increase.

[0188] However, the variance is less sensitive to extreme values ​​than the fourth-order central moment because they are only raised to the second power. Therefore, considering that HNR is a simple ratio of harmonic power to noise power, in order to accurately denoise the bearing vibration signal and obtain a representation of the fault-induced impulse signal, the periodicity and sparsity of the signal must be considered simultaneously. As a possible solution, we can refer to the calculation method of kurtosis. Because kurtosis calculates the high-order statistics of the signal, it is mainly sensitive to the impulse component (periodic signal) of the signal. Therefore, in order to emphasize the periodic component of the signal, HNR is rewritten as a high-order statistic of the signal, and the higher-order harmonic noise ratio (HHNR) is defined as the ratio of the cube of the autocorrelation function of the periodic signal to the cube of the autocorrelation function of the noise signal. Therefore, HHNR can be expressed as:

[0189] (29)

[0190] Where, The vibration signal of the bearing inside the tool holder power tool holder containing Gaussian white noise, is the local maximum of the normalized autocorrelation function, is the relative power of the periodic signal, is the non-periodic signal (noise) power.

[0191] To further consider the overall autocorrelation function amplitude of the signal, the indicator is expanded to the Higher-order Weighted Harmonic Noise Ratio (HWHNR). By calculating the sum of the peak weights of multiple autocorrelation functions, it can more comprehensively reflect the periodic characteristics of the signal and avoid interference from occasional autocorrelation function peaks. Therefore, HWHNR not only considers the higher-order statistics of the signal and enhances the representation of periodicity, but also suppresses noise through weight adjustment:

[0192] (30)

[0193] in, is the sampling time point of the bearing vibration signal in the tool holder power tool holder containing Gaussian white noise, Indicates time delay; and Represent the sum of the time accumulation and the delay part respectively.

[0194] On this basis, an adaptive method is introduced to dynamically adjust the weights according to the characteristics of noise and signal, making HWHNR more flexible:

[0195] (31)

[0196] in, For the frequency band The relevant weight factors can be used to analyze the energy distribution of the signal in different frequency bands using the signal's autocorrelation function or power spectral density (PSD), and then adjusted according to the energy distribution. For frequency bands with obvious periodic components, higher weights are given. , while lower weights are given to frequency bands dominated by noise; is an attenuation factor related to noise intensity, which controls the effect of noise intensity on HWHNR. For cases where low-frequency noise is strong, you can set Larger to suppress the interference of low-frequency noise on the signal. For the The noise power in a frequency band.

[0197] When the HWHNR reaches its maximum value, optimal random resonance is generated, which weakens the noise contained in the bearing vibration signal of the tool holder power tool holder, eliminates the sideband interference near the characteristic frequency, improves the characteristic frequency amplitude and the signal-to-noise ratio of the bearing vibration signal of the tool holder power tool holder, and outputs a high signal-to-noise ratio bearing vibration signal of the tool holder power tool holder.

[0198] There is no need to input the fault frequency of the bearing in the tool holder power tool holder in advance. The signal is processed using the underdamped unsaturated scaled Gaussian potential stochastic resonance (UUSGSR) model with HWHNR as the objective function, and the structural parameters are optimized using the Grey Wolf optimization algorithm. , and damping factor Optimize and finally obtain the optimal parameter pair that maximizes HWHNR =(16.3121, 6.8724, 0.0113);

[0199] At the same time, in order to further illustrate the superiority of the method of the present invention, M1: overdamped unsaturated scaled stochastic resonance (USGSR) model, M2: classical bistable stochastic resonance (CBSR) model, M3: wavelet transform (WT) method, M4: UUSGSR method with SNR as the objective function, M5: UUSGSR method with HNR as the objective function and M6: the method proposed by the present invention are compared. Here, the signal-to-noise ratio (SNR) is used as the evaluation index. The results are shown in the attached figure. Figure 5 As shown in Table 1 below:

[0200] Table 1 Comparison results of different methods

[0201] index original signal M1 M2 M3 M4 M5 M6 SNR / dB -30.1932 -15.1725 -22.3256 -24.3701 -14.1165 -14.3062 -13.0598

[0202] From Table 1 and the attached Figure 5 From the results, it can be seen that a noise reduction method for CNC machine tool power tool holder based on UUSGSR has advantages in noise suppression, and can significantly improve the SNR of the signal compared with other methods; the above experiments have verified that this method can achieve the purpose of noise reduction and has certain application feasibility; the signal processed by the model shows more excellent output characteristics and higher output signal-to-noise ratio; at the same time, HWHNR can effectively reflect the nonlinear characteristics in the signal by analyzing the ratio of the periodic component to the non-periodic component of the signal and integrating the considerations of periodicity and sparsity; compared with the traditional objective function SNR of the stochastic resonance model, HWHNR does not rely on prior knowledge, but directly focuses on the harmonic component of the signal, which can reduce the deviation caused by inaccurate prior information. In summary, using HWHNR as the objective function can effectively improve the signal-to-noise ratio; the method of the present invention can achieve effective noise reduction of the bearing vibration signal in the tool holder power tool holder.

Claims

1. A noise reduction method for a CNC machine tool power tool holder based on UUSGSR, characterized by: The steps include: 1) Obtain the vibration signal of the bearing inside the tool holder power tool holder; 2) Gaussian white noise is added to the original signal to better simulate the actual working conditions with low signal-to-noise ratio. The stochastic resonance dynamics model of the multistable system includes the memory of time, making the stochastic resonance process non-Markovian. 3) Preprocessing the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise so that the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise meets the parameter restriction conditions of stochastic resonance; 4) Construct an improved gray wolf optimization algorithm; 5) Construct an underdamped non-saturated scaling Gaussian potential stochastic resonance model; 6) Taking the constructed high-order weighted harmonic noise ratio HWHNR as the objective function, the gray wolf optimization algorithm is used to optimize the underdamped unsaturated scaled Gaussian potential stochastic resonance UUSGSR model. When the number of iterations is When the maximum number of iterations is reached, the iteration is stopped and the optimal parameter pair is output. , and maximum HWHNR; The potential function of the underdamped unsaturated scaled Gaussian potential stochastic resonance UUSGSR model in step 5) is: (6)； in represents the scaled Gaussian potential function, and is a positive real structural parameter, is the input vibration signal of the tool holder's internal bearing containing Gaussian white noise; Under underdamped conditions, the Langevin equation driven by the UUSGSR model is described as: (7)； in, is the damping factor, and is a positive real structural parameter, The input is the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise, and are amplitude and frequency respectively, The mean is 0 and the variance is Gaussian white noise, represents the noise intensity; Step 6) The higher-order weighted harmonic noise ratio HWHNR is obtained by analyzing the ratio of the periodic component to the non-periodic component of the signal; For the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise , autocorrelation function As a time delay The function is defined as: (24)； By calculating the sum of the peak weights of multiple autocorrelation functions, the periodic characteristics of the signal can be more comprehensively reflected, and the high-order weighted harmonic noise ratio HWHNR is obtained.

2. The noise reduction method for a CNC machine tool driven tool holder based on UUSGSR according to claim 1 is characterized in that: The adaptive step strategy expression in the gray wolf optimization algorithm is as follows: (1)； in, Representative The position vector of the gray wolf individual, Represents the three individual position vectors with the best fitness in the current generation of gray wolf population, and Respectively represent the current number of iterations and the maximum number of iterations of the Grey Wolf Optimization Algorithm; The proportional weight expression of the Euclidean distance of the improved step size is as follows: (2)； (3)； (4)； in, is a very small positive real number, ensuring that the denominator of the fraction is not 0; The final gray wolf position update is expressed as: (5)； The improved gray wolf optimization algorithm for structural parameters , structural parameters and damping factor Perform optimization.

3. The noise reduction method for a CNC machine tool driven tool holder based on UUSGSR according to claim 2 is characterized in that: The preprocessing in step 2) includes: performing Hilbert-Huang transform on the bearing vibration signal of the tool holder power tool holder containing Gaussian white noise to remove the DC component, and filtering it with a low-pass elliptic filter to reduce the low-frequency effect, thereby obtaining a signal to be detected that meets the parameter restriction conditions of stochastic resonance after preprocessing.

4. The noise reduction method for a CNC machine tool driven tool holder based on UUSGSR according to claim 3 is characterized in that: Step 5) Under the underdamped condition, the behavior of the UUSGSR model under the influence of noise and periodic signals is analyzed by deriving and measuring the steady-state probability density function SPD and the mean first passage time MFPT of the model under the adiabatic approximation theory; the second-order differential equation (7) is transformed into two first-order differential equations: (8)； Assumed amplitude , noise intensity , we get three singular points: (9)； Let the potential function be The partial derivative of , the potential function pair The partial derivative of , then formula (8) is written as: (10)； The linearization matrix of formula (8) is obtained as follows: (11)； Further, at the singularity The linearization matrix at is described as: (12)； By solving equation (12), the corresponding eigenvalues ​​are calculated: (13)； Similarly, The linearization matrix is: (14)； The eigenvalue corresponding to formula (14) is: (15)； Assumptions is the probability density function (PDF) of the random process, and the corresponding Fokker-Planck equation is: (16)； in, is the damping factor, and is a positive real structural parameter, and are amplitude and frequency respectively, is the noise intensity; Then the steady-state probability density function (SPD) corresponding to the UUSGSR model is expressed as: (17)； in, is the normalization constant: (18)； in, is the generalized potential function: (19)。 5. The noise reduction method for a CNC machine tool driven tool holder based on UUSGSR according to claim 4 is characterized in that: The transition rate of particles at the singular point in the UUSGSR model described in step 5) is: (20)； in, and is the eigenvalue corresponding to formula (14), and To solve the eigenvalue obtained by equation (12), is the noise intensity, is the amplitude; The particle transition rate (MFPT) is: (21)； The analytical expression of the theoretical output signal-to-noise ratio (SNR) of the UUSGSR model is derived as follows: (22)； Among them, the parameters Expressed as: (23)。 6. A method for reducing noise of a CNC machine tool driven tool holder based on UUSGSR according to any one of claims 1 to 5, characterized in that: This function It reaches the global maximum when There is also a global maximum at the position of There is no global maximum at the position of , but there is a local maximum, and its position is recorded as ; If these local maxima If it is large enough, then the signal can be considered to have a periodic part; the local maximum of the normalized autocorrelation , expressed as the following formula (25); (25)； Take a period of The periodic signal And add noise According to formula (24), if the two parts are uncorrelated, the autocorrelation function of the entire signal is equal to the sum of the autocorrelation functions of each part; for zero lag, ,in and Represents periodic signals and noise The autocorrelation function of If the noise is white, then the lag A local maximum is found at ; Since the autocorrelation function of a signal at zero lag is equal to the power in the signal, The normalized autocorrelation function at represents the relative power of the signal periodic component, while its complement represents the relative power of the noise component. The local maximum of the normalized autocorrelation Expressed as: (26)； in, and Represents the periodic signal at time 0 and noise The autocorrelation function of The harmonic noise ratio HNR is defined as: (27)； Before introducing the high-order weighted harmonic noise ratio, we first consider the high-order statistical signal processing indicator kurtosis; the kurtosis is a dimensionless parameter that describes the peak degree of the waveform. is defined as: (28)； To emphasize the periodic component of the signal, Rewrite it as a high-order statistic of the signal and convert the high-order harmonic noise ratio It is defined as the ratio of the cube of the autocorrelation function of the periodic signal to the cube of the autocorrelation function of the noise signal; therefore, It can be expressed as: (29)； Where, The vibration signal of the bearing inside the tool holder power tool holder containing Gaussian white noise, is the local maximum of the normalized autocorrelation function, is the relative power of the periodic signal, is the non-periodic signal power; Considering the amplitude of the overall autocorrelation function of the signal, the indicator is expanded to the high-order weighted harmonic noise ratio HWHNR, which is expressed as: (30)； in, is the sampling time point of the bearing vibration signal in the tool holder power tool holder containing Gaussian white noise, Indicates time delay; and Represent the sum of the time accumulation and the delay part respectively; On this basis, an adaptive method is introduced to dynamically adjust the weights according to the characteristics of noise and signal, making HWHNR more flexible: (31)； in, For the frequency band The relevant weight factors are used to analyze the energy distribution of the signal in different frequency bands using the signal's autocorrelation function or power spectral density PSD, and then adjusted according to the energy distribution. For frequency bands with obvious periodic components, higher , while lower weights are given to frequency bands dominated by noise; is an attenuation factor related to noise intensity, which controls the effect of noise intensity on HWHNR. For cases where low-frequency noise is strong, set Larger to suppress the interference of low-frequency noise on the signal; For the The noise power in a frequency band.

7. The noise reduction method for a CNC machine tool driven tool holder based on UUSGSR according to claim 6, characterized in that: When the HWHNR reaches its maximum value, optimal stochastic resonance is generated, and a high signal-to-noise ratio bearing vibration signal of the tool holder power tool holder is output.

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