Method for identifying time-varying modal parameters in machining process of thin-wall structure

Abstract

The invention discloses a method for identifying time-varying modal parameters in the machining process of a thin-wall structure. The method comprises the following steps: acquiring response signals in different time periods in the machining process of the thin-wall structure; detecting an effective modal peak frequency in the response signal by using a joint spectral peak-to-peak value detection method; the combined spectrum peak-to-peak value detection method is a peak value detection method based on a singular value spectrum peak and a PSD spectrum peak; performing signal enhancement on the effective modal peak frequency to obtain an enhanced signal; performing modal identification on the enhanced signal based on a random subspace method to obtain modal parameters; stability judgment is carried out on the modal parameters in different time periods, and time-varying modal parameters in the thin-wall structure machining process are obtained; according to the method, the response signal is detected based on a combined spectrum peak-to-peak value detection method of a singular value spectrum peak and a PSD spectrum peak, frequency components related to inherent characteristics in the machining process of the thin-wall structure are accurately detected, and the identification precision of modal parameters is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural health monitoring, and in particular relates to a method for identifying time-varying modal parameters in a thin-wall structure processing process. Background Art

[0002] In the field of structural health monitoring (SHM) and system identification, accurate identification of modal parameters is the key to ensuring the safety and functionality of engineering structures. Modal parameter identification of thin-walled structures in working state is one of the important means to ensure the smooth progress of the processing process. The modal parameter identification using random subspace method (SSI) first collects the response signal of the identification object, detects the peak value of the response signal spectrum peak, obtains the frequency component related to the mode in the response signal, and then further identifies the modal parameters based on the frequency component related to the mode. However, in the actual thin-walled structure processing process, the response signal under the tool-workpiece contact state is a dynamic response signal, which may be mixed with environmental noise or other interference signals, resulting in the introduction of invalid peaks in the peak detection process, thereby affecting the identification accuracy of the modal parameters. Summary of the invention

[0003] The purpose of the present invention is to provide a method for identifying time-varying modal parameters in a thin-wall structure machining process, so as to improve the identification accuracy of the modal parameters.

[0004] The present invention adopts the following technical solutions:

[0005] A method for identifying time-varying modal parameters in a thin-wall structure machining process comprises the following steps:

[0006] Obtain response signals at different time periods during the processing of thin-walled structures;

[0007] The effective modal peak frequency in the response signal is detected by using the joint spectrum peak detection method; the joint spectrum peak detection method is a peak detection method based on the singular value spectrum peak and the PSD spectrum peak;

[0008] Perform signal enhancement on the effective mode peak frequency to obtain an enhanced signal;

[0009] Based on the random subspace method, the modal identification of the enhanced signal is carried out to obtain the modal parameters;

[0010] The stability of the modal parameters in different time periods is judged respectively, and the time-varying modal parameters of the thin-walled structure processing are obtained.

[0011] Furthermore, the effective modal peak frequency in the detection response signal is detected by using the joint spectrum peak-to-peak detection method, including:

[0012] Calculate the singular values ​​and PSD of the response signal to obtain the singular value spectrum and PSD spectrum;

[0013] The spectral peaks that meet both the height condition and the prominence condition in the singular value spectrum and the PSD spectrum are selected, and the frequency of the spectral peak is the effective mode peak frequency.

[0014] Furthermore, the peaks that meet both the height condition and the prominence condition in the singular value spectrum and the PSD spectrum are selected to include:

[0015] Calculate the first height condition threshold according to the median of the singular value spectrum, the median absolute deviation of the singular value spectrum and the standard deviation of the singular value spectrum; calculate the first decibel value of all spectral peaks in the singular value spectrum; select the first decibel value greater than or equal to the first height condition threshold, and the spectral peak corresponding to the first decibel value is the first height spectral peak;

[0016] Calculate the first protrusion condition threshold according to the median absolute deviation of the singular value spectrum and the standard deviation of the singular value spectrum; calculate the first protrusion decibel value according to the first decibel value, the decibel value from the first height spectrum peak to the lowest spectrum peak on the left, and the decibel value from the first height spectrum peak to the lowest spectrum peak on the right; select the first protrusion decibel value that is greater than or equal to the first protrusion condition threshold, and the spectrum peak corresponding to the first protrusion decibel value is the first protrusion spectrum peak;

[0017] Calculate the second height condition threshold according to the median of the PSD spectrum, the median absolute deviation of the PSD spectrum and the standard deviation of the PSD spectrum; calculate the second decibel value of all spectral peaks in the PSD spectrum; select the second decibel value greater than or equal to the second height condition threshold, and the spectral peak corresponding to the second decibel value is the second height spectral peak;

[0018] The second protrusion condition threshold is calculated according to the median absolute deviation of the PSD spectrum and the standard deviation of the PSD spectrum; the second protrusion decibel value is calculated according to the second decibel value, the decibel value from the second height spectrum peak to the lowest spectrum peak on the left, and the decibel value from the second height spectrum peak to the lowest spectrum peak on the right; the second protrusion decibel value that is greater than or equal to the second protrusion condition threshold is selected, and the spectrum peak corresponding to the second protrusion decibel value is the second protrusion spectrum peak;

[0019] A spectrum peak that exists in both the first protrusion spectrum peak and the second protrusion spectrum peak is selected, and the frequency of the spectrum peak is the effective modal peak frequency.

[0020] Furthermore, the effective modal peak frequency is signal enhanced to obtain an enhanced signal including:

[0021] Performing signal enhancement based on time-frequency domain characteristics on the frequency range of the effective mode peak frequency to obtain a first enhanced signal; the signal enhancement based on time-frequency domain characteristics includes wavelet transform enhancement and STFT enhancement;

[0022] Performing signal enhancement based on the time domain scaling coefficient on the response signal to obtain a second enhanced signal;

[0023] The first enhanced signal and the second enhanced signal are combined to obtain an enhanced signal.

[0024] Furthermore, the enhancement coefficient of the signal enhancement is 1+amplification_factor, where amplification_factor is the enhancement factor.

[0025] Furthermore, the modal identification of the enhanced signal based on the random subspace method includes:

[0026] constructing a joint matrix using the response signal, the first enhanced signal, and the second enhanced signal;

[0027] Construct multi-domain enhanced extended Hankel matrix based on joint matrix;

[0028] The modal parameters are solved using the multi-domain enhanced extended Hankel matrix to obtain the modal parameters.

[0029] Furthermore, the stability of the modal parameters in different time periods is judged, and the time-varying modal parameters of the thin-walled structure processing process are obtained, including:

[0030] The stability of the modal parameters in different time periods is preliminarily judged to obtain the stable mode in each time period;

[0031] Based on the joint spectrum peak detection method, the secondary stability is judged to obtain the true mode of each time period;

[0032] Select the intersection of the stable mode and the true mode to obtain the stable true mode;

[0033] The stable real modes of all time periods are integrated to obtain the time-varying modal parameters of the thin-walled structure machining process.

[0034] Furthermore, based on the joint spectrum peak detection method, the secondary stability judgment is performed to obtain the true mode of each time period, including:

[0035] In the singular value spectrum, the frequency of the spectrum peak is subtracted from the center frequency of the spectrum peak of the singular value spectrum to obtain a first difference value;

[0036] In the PSD spectrum, the frequency of the spectrum peak is subtracted from the center frequency of the spectrum peak of the PSD spectrum to obtain a second difference value;

[0037] The spectrum peak whose absolute values ​​of the first difference and the second difference are both less than or equal to the frequency matching tolerance is retained, and the mode corresponding to the spectrum peak is the true mode.

[0038] An electronic device, comprising:

[0039] at least one processor;

[0040] and, a memory communicatively coupled to the at least one processor;

[0041] The memory stores instructions that can be executed by at least one processor, and the instructions are executed by at least one processor so that the at least one processor can execute any one of the above methods for identifying time-varying modal parameters in a thin-walled structure processing process.

[0042] The beneficial effects of the present invention are as follows: the present invention detects the response signal based on a joint spectrum peak detection method of singular value spectrum peaks and PSD spectrum peaks, filters out invalid peaks caused by factors such as environmental noise through a peak detection method based on the two spectrum peaks, accurately detects frequency components related to inherent characteristics during thin-wall structure processing, and improves the identification accuracy of modal parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 The figure is a flow chart of the method of the present invention.

[0044] Figure 2 It is a schematic diagram of the height condition and the protrusion condition in the peak detection condition of the present invention;

[0045] Figure 3 It is a flow chart of the signal enhancement method based on the time-frequency domain characteristics of a specific frequency range in the present invention;

[0046] Figure 4 It is a flow chart of the method for automatic filtering and integration of real modes based on joint spectrum peak value in the present invention;

[0047] Figure 5 It is a schematic diagram of the finite element model of the thin-walled structure in the present invention;

[0048] Figure 6 It is a schematic diagram of the vibration response of point R of the finite element model of thin-walled structure;

[0049] Figure 7 This is a comparison chart of the frequency domain characteristics of the vibration response of the finite element model of the thin-walled structure;

[0050] Figure 8 This is a comparison diagram of the time-frequency domain characteristics of the enhanced signal for the vibration response of the finite element model of the thin-walled structure;

[0051] Fig. 9 Comparison diagram of modal stability diagram identification effect of the method of the present invention under different model orders;

[0052] Fig.10 This is a comparison diagram of the modal stability diagram identification effect of the method of the present invention at different sampling time lengths. DETAILED DESCRIPTION

[0053] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] In the field of structural health monitoring (SHM) and system identification, accurate identification of modal parameters is the key to ensure the safety and functionality of engineering structures. Traditional thin-walled structure modal parameter identification is mainly based on experimental modal analysis, but this method can only obtain static thin-walled structure modal parameters in the uncut contact state, and cannot consider the dynamic modal parameters of thin-walled structures in the tool-workpiece cutting contact state during machining. The operating modal analysis method is a modal analysis method that obtains structural modal parameters through structural response signals. The modal parameters of thin-walled structures in the cutting contact state can be accurately identified through operating modal analysis, but traditional operating modal analysis methods rely on input and output data. In practical applications, only output data can be obtained, which limits their application in engineering practice. For example, the frequency function response method measures the input and output data of the system when it is subjected to external excitation, calculates the frequency response function, and reflects the dynamic characteristics of the system at each frequency. The input-output autoregressive moving average model analyzes the dynamic characteristics of the system by establishing an autoregressive moving average relationship between the input signal and the output signal. The random subspace method (SSI) modal parameter identification technology estimates the dynamic characteristics of the structure through statistical characteristics such as the autocovariance and cross-correlation matrix of the data. It can handle modal analysis problems based only on output data. It has unique advantages in the application of scenarios where only output data can be obtained, so it has been widely used in various fields. However, the SSI method still faces challenges in processing complex data structures or in multiple noise environments. In addition, the traditional SSI method needs to rely on manual mode separation during application, which is very inefficient and prone to misjudgment. Therefore, in engineering practice, how to accurately and efficiently extract modal parameters from limited measurement data has always been a research hotspot and difficulty in this field. In addition, the traditional SSI method is based on the Hankel matrix of a single time domain signal to identify the system state, but the single signal data may mask its own characteristics due to factors such as noise, or because some high-order inherent frequency components are not prominent, resulting in inaccurate system identification results. If the diversity of signals can be improved when constructing the Hankel matrix and the system state matrix, and the signal processing technology of multiple information domains can be introduced, the identifiability of the dynamic characteristics of the signal can be significantly improved; at the same time, if the modes can be automatically filtered and the modal parameters can be integrated according to the precise modal identification and separation criteria without manual intervention, it will not only significantly improve the identification accuracy of the modal parameters, but also greatly shorten the calculation time, and realize the online automatic and accurate identification of the modal parameters, which has important scientific research significance and extensive engineering practice value. In summary, the existing thin-walled structure modal parameter identification method and the random subspace method working modal analysis method have the following problems:

[0055] (1) The response signal may be mixed with environmental noise or other interference signals, resulting in the introduction of invalid peaks in the peak detection process, thus affecting the identification accuracy of the modal parameters.

[0056] (2) The existing thin-walled structure modal parameter identification is mainly based on the experimental modal analysis method. The static modal parameters in the uncut contact state are identified by the hammering modal method. Since the dynamic modal parameters of the thin-walled structure in the tool-workpiece contact state in the actual processing process are different from the static modal parameters in the uncut contact state, and the hammering process is interfered by interference factors such as human operation errors and hammer head jumping, the traditional experimental modal analysis method cannot accurately identify the time-varying modal parameters in the thin-walled structure processing process. It is necessary to use the working modal analysis method to accurately identify the time-varying modal parameters in the thin-walled structure processing process.

[0057] (3) The system state matrix of the existing working modal analysis method based on the random subspace method is constructed by a Hankel matrix based on a single time domain signal. Since the input signal of this matrix is ​​single, it is easy for interference factors such as noise in the signal to mask the dynamic characteristics of the signal itself, resulting in the inability to accurately extract the inherent characteristics of the signal.

[0058] (4) In the existing random subspace method, the determination of stable modes requires manual determination of modal stability based on stability diagrams. This determination method is extremely inefficient and prone to misjudgment, especially in the case of high-order models or dense modes, where accurate modal identification and separation is almost impossible to achieve.

[0059] Therefore, the specific implementation methods of the present invention are as follows:

[0060] A method for identifying time-varying modal parameters in thin-walled structure machining process, such as Figure 1 As shown, the following steps are included:

[0061] S110, obtaining response signals at different time periods during the thin-wall structure processing, specifically:

[0062] In order to identify the time-varying modal parameters of thin-walled structure machining, the machining process needs to be discretized into multiple time periods, and the modal parameters of the thin-walled structure need to be accurately identified in each time period. Figure 5 The finite element model of a thin-walled structure is shown in Table 1. Figure 5 Sinusoidal excitation is applied in the Z direction at point P in the middle. The blue area in the figure is set as a completely fixed constraint, the sampling frequency is 5KHz, and the damping ratios of the first three modals are set to 2.00%, 2.50% and 3.00% respectively. The following can be obtained through modal dynamics calculation: Figure 6 The Z-direction vibration acceleration response signal of point R shown is used as the input of the random subspace method.

[0063] Table 1 Material parameters of finite element model of thin-walled structure

[0064]

[0065] In the actual application of thin-wall structure processing, the response signal is the response signal of the thin-wall structure caused by the milling force excitation.

[0066] The present invention detects the response signal based on a joint spectrum peak detection method of singular value spectrum peaks and PSD spectrum peaks. The invalid peaks caused by factors such as environmental noise are filtered out by a peak detection method based on the two spectrum peaks, and the frequency components related to the inherent characteristics in the thin-wall structure processing process are accurately detected, thereby improving the identification accuracy of the modal parameters.

[0067] S120, using the joint spectrum peak detection method to detect the effective modal peak frequency in the response signal; the joint spectrum peak detection method is a peak detection method based on singular value spectrum peaks and PSD spectrum peaks, specifically: calculate the singular values ​​and PSD of the signal, and use the joint spectrum peak detection method based on the singular value spectrum peaks and PSD spectrum peaks to accurately detect the modal-related frequency components in the signal.

[0068] S121, calculating the singular value and PSD of the response signal to obtain a singular value spectrum and a PSD spectrum;

[0069] S122, selecting a spectrum peak that satisfies both the height condition and the prominence condition in the singular value spectrum and the PSD spectrum, and the frequency of the spectrum peak is the effective mode peak frequency;

[0070] The present invention proposes a peak detection method based on the joint peak of the singular value spectrum peak and the PSD spectrum peak, which is used to accurately detect the modal-related frequency components in the signal. Figure 2 As shown, the method defines that the peak value in the detected signal must satisfy both the height condition and the protrusion condition in the peak detection condition to be counted as a valid modal peak value related to the inherent characteristics of the signal, otherwise it is regarded as an invalid peak value caused by noise or other factors, and it is considered that the peak value has nothing to do with the inherent characteristics of the signal. The height condition and protrusion condition for peak detection proposed in the present invention are as follows:

[0071] Height conditions:

[0072] In order to make the newly proposed peak detection method applicable to different signal conditions, the present invention proposes a peak detection strategy based on the peak height condition of the median, median absolute deviation (MAD) and standard deviation of the singular value spectrum and PSD spectrum.

[0073] This strategy states that for each significant modal peak, the following height conditions need to be met:

[0074]

[0075] Among them, the dynamic threshold θ of the peak detection of the singular value spectrum and PSD spectrum is SV and θ PSD The settings are as follows:

[0076]

[0077] Among them, a, b and c, d are the adjustment coefficients of the dynamic thresholds of the singular value spectrum and PSD spectrum, and their value range is [0.1, 3].

[0078] To calculate the dynamic threshold for peak detection, it is necessary to calculate the median, median absolute deviation (MAD) and standard deviation of the singular value spectrum and PSD spectrum of the signal. The calculation process is as follows:

[0079] First, the calculation formula of the singular value spectrum is shown in equations (3) to (5):

[0080]

[0081] in, is the Fourier transform of Y, E[·] denotes expectation, and H denotes conjugate transpose.

[0082] Then, perform singular value decomposition on the signal:

[0083] S yy (f)=U(f)∑(f)V H (f) (4)

[0084] Among them, ∑(f) is a diagonal matrix, and the elements on its diagonal are singular values ​​σ i (f), U(f) and V(f) are the left and right singular vector matrices, respectively.

[0085] Then, the first singular value σ1(f) is extracted and converted to decibels:

[0086] SV dB (f) = 10log 10 (σ1(f)) (5)

[0087] The calculation method of PSD spectrum is shown in formula (6):

[0088]

[0089] Similarly, in order to more clearly distinguish the signal peak, facilitate threshold setting, and make data processing easier, the PSD value is also converted into decibel value:

[0090] PSD dB (f) = 10log 10P xx ((f)) (7)

[0091] Then, the medians of the singular value spectrum and the PSD spectrum are calculated according to the decibel values ​​of the singular value spectrum and the PSD spectrum. The median calculation formula is shown in formula (8):

[0092]

[0093] Wherein, X is the singular value spectrum SV or power spectrum density PSD of the measured signal, and N represents the number of values.

[0094] In practical applications, in order to make MAD and standard deviation have the same scale, they are often multiplied by a constant factor, usually 1.4826 (this is the adjustment factor when assuming that the data follows a normal distribution). The following is the calculation formula for the median absolute deviation MAD of the transformed singular value spectrum and PSD spectrum as shown in formula (9):

[0095]

[0096] Where X is the singular value spectrum decibel value SV of the measured signal dB Or power spectral density decibel value PSD dB .

[0097] Finally, the standard deviation of the singular value spectrum and PSD is calculated, and the calculation formula is shown in formula (10):

[0098]

[0099] Prominence conditions:

[0100] In order to find the effective peak value that meets the requirements, the present invention stipulates that the effective modal peak value must also meet the following prominence conditions:

[0101]

[0102] Among them, prominence p or prominence q It is the vertical distance between the peak value p or peak value q and the higher point of the lowest point on its left and right sides:

[0103]

[0104] Among them, SV dB [p] and PSD dB [q] are the singular value at the peak p and the decibel value of SV and PSD at the peak q, SV dB [l SV ] and SV dB [r SV] are the minimum values ​​on the left and right sides of the peak value p in the singular value spectrum, PSD dB [l PSD ] and PSD dB [r PSD ] are the minimum values ​​on the left and right sides of the peak q in the PSD spectrum.

[0105] For each peak point p or q, find the lowest point l in the search interval to its left:

[0106]

[0107] Where i is the point to the left of p or q until the next local minimum point or data boundary is reached. For each peak point p or q, find the lowest point r in the search interval to its right:

[0108]

[0109] where j is a point to the right of p or q until the next local minimum or data boundary is reached.

[0110] When the peak detected in the signal satisfies the height condition and prominence condition based on the dynamic threshold in both the singular value spectrum and the PSD spectrum, the peak can be regarded as an effective modal peak, and the effective modal peak set of the signal can be obtained as follows:

[0111]

[0112] f peaks ={F sv,p |p∈P}∩{F psd,q |q∈Q}(16)

[0113] Among them, P or Q is the index set that satisfies the above height condition and prominence condition at the same time, f peaks is the effective modal peak frequency finally detected and related to the inherent characteristics of the signal, F sv,p represents the set of effective modal peak frequencies detected in the singular value spectrum, F psd,q Represents the set of effective modal peak frequencies detected in the ## power spectrum.

[0114] The specific steps are:

[0115] Calculate the first height condition threshold according to the median of the singular value spectrum, the median absolute deviation of the singular value spectrum and the standard deviation of the singular value spectrum; calculate the first decibel value of all spectral peaks in the singular value spectrum; select the first decibel value greater than or equal to the first height condition threshold, and the spectral peak corresponding to the first decibel value is the first height spectral peak;

[0116] Calculate the first protrusion condition threshold according to the median absolute deviation of the singular value spectrum and the standard deviation of the singular value spectrum; calculate the first protrusion decibel value according to the first decibel value, the decibel value from the first height spectrum peak to the lowest spectrum peak on the left, and the decibel value from the first height spectrum peak to the lowest spectrum peak on the right; select the first protrusion decibel value that is greater than or equal to the first protrusion condition threshold, and the spectrum peak corresponding to the first protrusion decibel value is the first protrusion spectrum peak;

[0117] Calculate the second height condition threshold according to the median of the PSD spectrum, the median absolute deviation of the PSD spectrum and the standard deviation of the PSD spectrum; calculate the second decibel value of all spectral peaks in the PSD spectrum; select the second decibel value greater than or equal to the second height condition threshold, and the spectral peak corresponding to the second decibel value is the second height spectral peak;

[0118] The second protrusion condition threshold is calculated according to the median absolute deviation of the PSD spectrum and the standard deviation of the PSD spectrum; the second protrusion decibel value is calculated according to the second decibel value, the decibel value from the second height spectrum peak to the lowest spectrum peak on the left, and the decibel value from the second height spectrum peak to the lowest spectrum peak on the right; the second protrusion decibel value that is greater than or equal to the second protrusion condition threshold is selected, and the spectrum peak corresponding to the second protrusion decibel value is the second protrusion spectrum peak;

[0119] A spectrum peak that exists in both the first protrusion spectrum peak and the second protrusion spectrum peak is selected, and the frequency of the spectrum peak is the effective modal peak frequency.

[0120] The frequency components related to the inherent characteristics of the system are accurately detected based on the joint spectral peaks of the singular value spectrum and the PSD spectrum of the system response signal, wherein the spectral peaks of the singular value spectrum and the PSD spectrum need to meet both the height condition and the prominence condition, wherein the height condition is that the height of the peak value of the detected spectral peak must be greater than the dynamic threshold of the height condition composed of the median, median absolute deviation (MAD) and standard deviation of the singular value spectrum or PSD spectrum, and the prominence condition is that the vertical distance between the peak value of the detected spectral peak and the higher point of the lowest points on its left and right sides must be greater than the prominence threshold composed of the median absolute deviation and the standard deviation. Only when the peak value of the spectral peak of the signal satisfies both the height condition and the prominence condition in the singular value spectrum and the PSD spectrum can the peak value of the spectral peak be considered to be related to the inherent characteristics of the signal, otherwise it is regarded as an invalid peak caused by factors such as noise. The peak detection method based on the joint spectral peak can accurately detect the frequency components related to the inherent characteristics of the system, and because the dynamic threshold can be automatically adjusted, it can be applied to different signal conditions. It solves the problem that the traditional peak detection method of signal spectrum peak cannot accurately detect the frequency components related to the inherent characteristics of the signal under different signal conditions, and may be mixed with invalid peaks caused by factors such as environmental noise, resulting in identification accuracy errors in subsequent processing. It has strong engineering application value.

[0121] S130, performing signal enhancement on the effective modal peak frequency to obtain an enhanced signal, specifically:

[0122] The following is done for a specific frequency range near the detected effective modal peak frequency: Figure 3 The signal enhancement based on time-frequency domain features and the signal enhancement based on time-domain scaling coefficient shown in FIG. 1 highlight the inherent characteristic-related frequency components in the signal and effectively suppress the useless information in the signal. The frequency domain feature comparison diagram and the time-frequency domain feature comparison diagram of the enhanced signal are shown in FIG. Figure 7 and Figure 8 shown.

[0123] S131, performing signal enhancement based on time-frequency domain characteristics on the frequency range of the effective modal peak frequency to obtain a first enhanced signal; the signal enhancement based on time-frequency domain characteristics includes wavelet transform enhancement and STFT (short-time Fourier transform) enhancement, specifically:

[0124] Wavelet transform signal enhancement method based on a specific frequency range:

[0125] For a given signal Y(t), firstly perform wavelet transform to obtain wavelet coefficients at different scales and translations. Using the wavelet function ψ(t), the wavelet transform can be expressed as:

[0126]

[0127] Among them, a is the scale parameter, which controls the expansion and contraction of the wavelet; b is the translation parameter, which controls the position of the wavelet; ψ * (t) is the complex conjugate of the wavelet function ψ(t).

[0128] In order to achieve wavelet transform enhancement based on a specific frequency range, we first need to solve its center frequency. The center frequency ω0 of the wavelet transform refers to the main frequency of the wavelet function ψ(t) in the frequency domain. For a given wavelet, the center frequency ω0 can be determined by analyzing the amplitude spectrum of its Fourier transform. The calculation formula is as follows:

[0129]

[0130] in, is the Fourier transform of the wavelet function ψ(t):

[0131]

[0132] Then, the target center frequency f is mapped to the corresponding wavelet scale a:

[0133]

[0134] Among them, F sis the sampling frequency, and f is the effective modal peak frequency.

[0135] In order to prevent the signal from being over-enhanced due to an excessively large enhancement factor, thereby losing some important information or introducing some undesirable effects that cause signal distortion, the present invention sets the enhancement factor to 1+amplification_factor. Such an enhancement factor is relatively gentle and can finely control the degree of enhancement, which helps to maintain the original characteristics and quality of the signal while enhancing it, avoiding excessive processing and possible distortion. Thus, the enhanced wavelet coefficient C can be obtained. enhanced (a,b) are as follows:

[0136] C enhanced (a,b)=C(a,b)·(1+amplification_factor)(21)

[0137] Where C(a,b) is the original wavelet coefficient and amplification_factor is the predetermined enhancement factor.

[0138] Finally, the enhanced wavelet coefficients C enhanced (a, b) The reconstructed wavelet enhanced signal Y is obtained by inverse wavelet transform enhanced (t):

[0139]

[0140] Among them, ψ a,b (t) is the wavelet function adjusted according to scale a and translation b, and its calculation formula is:

[0141] STFT signal enhancement method based on a specific frequency range:

[0142] First, perform STFT transformation on the signal, and its transformation expression is as follows:

[0143] S(t,f)=∫Y(τ)ω(t-τ)e -i2πfτ dτ (23)

[0144] Among them, Y(τ) is the input signal, ω(t-τ) is the window function, usually a Hamming window or a Gaussian window, t is the time variable, indicating the center position of the time window, and f is the frequency variable.

[0145] Then, for each detected significant modal peak frequency f, the specific frequency range of STFT enhancement is as follows:

[0146] freq_indices={i:f-Δf≤F[i]≤f+Δf}(24)

[0147] Where F[i] is the frequency array calculated by STFT, Δf is the selected frequency bandwidth, f is the effective modal peak frequency detected by the peak detection method based on joint spectrum peaks, and f-Δf and f+Δf are specific frequency ranges around the peak frequency.

[0148] From this, we can get the STFT enhancement coefficient S for a specific frequency range: enhanced (t,f):

[0149] S enhanced (t,f)=|S(t,f)|·(1+amplification_factor)(25)

[0150] Among them, S(t,f) is the original STFT enhancement coefficient, and amplification_factor is the predefined enhancement factor.

[0151] Finally, the enhanced STFT coefficient S enhanced (t, f) The reconstructed STFT enhanced signal Y is obtained by inverse STFT transformation enhanced (t):

[0152] Y enhanced (t) = ∫S enhanced (t,f)e i2πft df (26)

[0153] S132, performing signal enhancement based on the time domain scaling coefficient on the response signal to obtain a second enhanced signal, which is expressed as:

[0154] Y enhanced (t)=Y(t)×(1+amplification_factor)(27)

[0155] Where amplification_factor is a predefined amplitude scaling factor of the time domain signal.

[0156] The second enhanced signal includes two signals with different time domain scaling factors.

[0157] After detecting the frequency components related to the inherent characteristics in the signal, multi-domain signal enhancement is performed based on the detected specific frequency range. The wavelet coefficients and STFT coefficients of the signal are obtained through wavelet transform and STFT transform. The detected specific frequency range is converted to the corresponding wavelet coefficients or STFT coefficients for targeted signal enhancement, and a relatively smooth signal enhancement method is selected to prevent the inherent characteristics of the signal from changing due to over-enhancement. Then, the enhanced reconstructed signal is obtained through inverse wavelet transform and inverse STFT transform. This enhancement method can highlight the frequency components related to the inherent characteristics in the signal, effectively suppress the useless information in the signal, and will not cause signal distortion due to over-enhancement. At the same time, the time domain of the signal is smoothly enhanced based on the time domain scaling coefficient;

[0158] S140, perform modal identification on the enhanced signal based on the random subspace method to obtain modal parameters, specifically:

[0159] S141, construct a joint matrix using the response signal, the first enhanced signal, and the second enhanced signal. Specifically:

[0160] Arrange the response signal, the first enhanced signal, and the second enhanced signal in columns to obtain a joint matrix containing the response signal, the first enhanced signal, and the second enhanced signal. Its specific form is shown as follows:

[0161]

[0162] Y combined is the joint matrix containing the response signal and the enhanced signal, where y i,j (t) represents the value at the nt moment of the jth response signal or enhanced signal of the ith sensor; ns is the number of sensors, 1 ≤ i ≤ ns; nt is the number of time points, 0 < t ≤ nt; ne is the number of enhanced signals, ne ≥ 1; j is the response signal when it is original, and j is the ne-th enhanced signal when it is enhanced_ne. The enhanced signals in the joint matrix Y combined constructed in the present invention are composed of two enhanced signals (the first enhanced signal) based on the time-frequency domain characteristics of a specific frequency range and two enhanced signals (the second enhanced signal) based on the time domain scaling coefficient.

[0163] S142, construct a multi-domain enhanced extended Hankel matrix based on the joint matrix, specifically:

[0164] Based on the joint matrix Y combined established above, a multi-domain enhanced extended Hankel matrix composed of the original signal and the enhanced signal with multi-domain feature enhancement can be established by extracting data from it through a sliding window as follows:

[0165]

[0166] Y h From Y combined The multi-domain enhanced extended Hankel matrix constructed by extracting data through sliding windows consists of a response signal and multiple enhanced signals with feature enhancements from different information domains. For the starting column i of each sliding window, Y combined All rows from column i to nt-2s+i are copied to Y h In this way, Y h Each row of contains the data of all sensors starting from a certain time point until the time point nt-2s+1, s is the number of block rows, and its value is generally 2 or 3 times the model order.

[0167] The above original signal and multi-domain enhanced signal are arranged in columns to obtain a joint matrix containing the original signal and the multi-domain enhanced signal. By extracting data from it through a sliding window, a multi-domain enhanced extended Hankel matrix consisting of the original signal and the enhanced signal with multi-domain feature enhancement can be established. Then, based on the multi-domain enhanced extended Hankel matrix, a system state matrix is ​​established to solve the modal parameters. Compared with the system state matrix constructed based on the traditional Hankel matrix, the system state matrix constructed based on the multi-domain enhanced extended Hankel matrix can more completely extract the dynamic characteristics of the signal, and effectively alleviates the problem that the system state matrix constructed based on the traditional Hankel matrix may not be able to completely extract the dynamic characteristics of the system due to interference factors such as noise in the signal, and has high scientific research significance.

[0168] S143, using the multi-domain enhanced extended Hankel matrix to solve the modal parameters, the modal parameters are obtained, specifically:

[0169] Y h Perform QR decomposition to extract orthogonal features of the data and reduce the complexity of data calculation:

[0170] Y h =QR (30)

[0171] Perform singular value decomposition on the upper triangular matrix R after QR decomposition to extract the main singular values ​​and singular vectors of the data:

[0172] R=USV T (31)

[0173] U is an m×m orthogonal matrix whose column vectors are the left singular vectors of R, forming an orthogonal basis of the column space of R. S is an m×n diagonal matrix whose diagonal elements are singular values, arranged in descending order. V is an n×n orthogonal matrix whose column vectors are the right singular vectors of R.

[0174] Divide the U matrix into U past and U future , where U past Contains the first ns×(s-1) rows of the U matrix, where ns is the number of sensors, used to represent the past state of the system; U future Contains the part of the U matrix from ns×(s-1)+1 row to the last row, which is used to represent the future state of the system. m represents the number of columns in the U matrix, which is also the number of rows in the R matrix.

[0175]

[0176] According to U past and U future The system's state transfer matrix A, output matrix C, and output covariance matrix G can be constructed as follows:

[0177]

[0178] C=U 1:ns,1:m (34)

[0179]

[0180] A is the state transfer matrix, which describes the dynamic characteristics of the system state from the past to the future. It's U past Pseudo-inverse; the output matrix C is directly extracted from the first row of the matrix U, which is used to describe the dynamic behavior of the system output and transform the system's state variables into output variables; the output covariance matrix G is used to represent the covariance of future state outputs, describing the uncertainty or noise characteristics of the system's output.

[0181] By extracting the modal frequency f and modal damping ratio ζ from the system state transfer matrix A, it can be expressed as:

[0182] λ=eig(A) (36)

[0183]

[0184] Among them, λ represents the eigenvalue of the system state matrix, f represents the modal frequency, and ζ represents the modal damping ratio

[0185] S150, performing stability judgment on the modal parameters in different time periods, respectively, to obtain the time-varying modal parameters of the thin-walled structure processing process, specifically:

[0186] After dividing the stable modes and unstable modes by judging whether the relative errors of frequency, damping ratio and modal vibration shape under adjacent model orders exceed the corresponding error threshold, the modes with different stability are marked differently to obtain the modal stability diagram under different model orders, and then the stable modes are manually determined through the modal stability diagram.

[0187] S151, preliminarily determine the stability of the modal parameters in different time periods to obtain the stable mode of each time period, specifically:

[0188] The frequency stability criterion, damping ratio stability criterion, and modal assurance (MAC) stability criterion are as follows:

[0189] Frequency stability criteria:

[0190]

[0191] This criterion requires that for the jth modal frequency f1 j , there is at least one modal frequency f2 k In the i+1th order model, their relative difference is made not to exceed the frequency error threshold err1, where err1 is 1%, and k represents the mode closest to j.

[0192] Damping stability criteria:

[0193]

[0194] This criterion requires that for the jth modal frequency ψ1 j , there is at least one modal frequency ψ2 k In the (i+1)th order model, their relative difference is made not to exceed the frequency error threshold err2, where err2 is 5%.

[0195] Modal Assurance Criteria (MAC) Stability Criteria:

[0196]

[0197] This criterion requires that for the jth modal frequency Φ1 j , there is at least one modal frequency Φ2 k In the i+1th order model, their relative difference is made not to exceed the frequency error threshold err3, where err3 is 98%. Finally, the adjacent model orders need to meet these three criteria at the same time to be considered as stable modes:

[0198] IDs i ={j|j∈δ f ∩δ ψ ∩δ Φ}(42)

[0199] Collection IDs i The modal index set that is determined to be stable in the i-th order model is the mode that satisfies the frequency stability, damping stability and modal assurance criteria at the same time.

[0200] S152, perform secondary stability discrimination based on the joint spectrum peak detection method to obtain the true mode of each time period: use the true mode automatic filtering and integration method based on the joint spectrum peak to automatically filter and accurately identify and separate the effective true stable modes in the stability diagram, and obtain the final modal parameters by integrating the filtered effective true modes, specifically:

[0201] In the singular value spectrum, the frequency of the spectrum peak is subtracted from the center frequency of the spectrum peak of the singular value spectrum to obtain a first difference value;

[0202] In the PSD spectrum, the frequency of the spectrum peak is subtracted from the center frequency of the spectrum peak of the PSD spectrum to obtain a second difference value;

[0203] The spectrum peak whose absolute values ​​of the first difference and the second difference are both less than or equal to the frequency matching tolerance is retained, and the mode corresponding to the spectrum peak is the true mode.

[0204] S153, selecting the intersection of the stable mode and the true mode to obtain the stable true mode;

[0205] Firstly, the peak detection method based on joint spectrum peak proposed in the present invention is used to determine the effective real mode peak frequency range, which is composed of the peak center frequency and the frequency matching tolerance. Then, all the modal frequencies that exist in the peak frequency range of both the singular value spectrum peak and the PSD spectrum peak are marked as effective real modes, and all the modal parameters under different model orders i are integrated to construct the effective real mode set valid_modes. i As shown in the formula:

[0206]

[0207] Where tolerance is the frequency matching tolerance, f i is the effective true modal frequency, f CMIF and f PSD are the peak center frequencies of the singular value spectrum and PSD spectrum respectively.

[0208] Then, all stable modes that have been initially filtered based on the modal stability criterion are combined with the effective true mode set to obtain the final effective true stable mode:

[0209]

[0210] S154, integrate the stable real modes of all time periods to obtain the time-varying modal parameters of the thin-walled structure processing process, specifically:

[0211] After filtering to the effective real stable modes, for each detected effective mode peak frequency f peak , the modal parameters of the effective stable real modes under all model orders are integrated to obtain the final modal parameters. The specific integration process is as follows:

[0212] First, initialize each peak frequency f peak The modal parameter set of:

[0213]

[0214] all_frequencies represents the set of all modal frequencies, and all_damping_ratios represents the set of all modal damping ratios.

[0215] Then, for each valid mode valid_modes in model order i i Define the modal integration range valid_indices:

[0216] mode_range=[f peak -tolerance,f peak +tolerance] (46)

[0217] The valid modal index range within the modal integration range is selected accordingly:

[0218] valid_indices = {j|f i,j ∈valid_modes i ,f i,j ∈[f peak -tolerance,f peak +tolerance]}(47)

[0219] Then, sort all modal parameters that are within the valid modal index range:

[0220]

[0221] Then, the 3x MAD criterion is used to filter out singular values ​​in the modal parameters for all model orders:

[0222]

[0223] The median and median absolute deviation (MAD) of the modal frequency and modal damping ratio are calculated as follows:

[0224]

[0225] Finally, the final modal parameters after filtering are obtained by integration:

[0226] final_frequencies={all_frequencies[j]|j∈valid_indices} (52)

[0227] final_damping_ratios={all_damping_ratios[j]|j∈valid_indices} (53)

[0228]

[0229] final_frequencies represents the final set of modal frequencies, final_damping_ratios represents the final set of modal damping ratios, and final_modes represents the final set of modal parameters.

[0230] Use Figure 4 The method of automatic filtering and integration of true modes based on the joint spectrum peak value shown in FIG. automatically filters and accurately distinguishes and separates the effective true stable modes in the stability diagram, and obtains the final modal parameters by integrating the filtered effective true modes. The stability diagrams before and after filtering under different model orders and different sampling times are shown in FIG. Fig. 9 and Fig.10 As shown in Figure 2 (the left side of each figure is the stable diagram before filtering, and the right side is the stable diagram after filtering, where × represents stable mode and · represents unstable mode), the final modal parameters obtained by integration are shown in Table 2 and Table 3. From the comparison results, it can be seen that although the modal frequency estimation accuracy of the traditional SSI method is within ±1 Hz, the modal damping ratio identification accuracy is only 88%. The new method proposed in the present invention has significantly improved the calculation accuracy compared with the traditional SSI method. The modal frequency estimation accuracy is maintained within ±1 Hz, while the modal damping ratio identification accuracy is improved to within 96%, and its calculation time is only increased by about 1 s under the same calculation conditions. Fig. 9 Among, (a) order = 20, (b) order = 60, (c) order = 100, (t = 10s, noiselevel = 10%), Fig.10 Among them, (a)t=3s, (b)t=6s, (c)t=8s, (order=100, noise level=10%).

[0231] Table 2 Comparison of modal frequency identification results of thin-walled structures

[0232]

[0233] Table 3 Comparison of identification results of modal damping ratio of thin-walled structure

[0234]

[0235] After solving the modal parameters through the system state matrix constructed based on the multi-domain enhanced extended Hankel matrix, a preliminary modal stability judgment is performed through the traditional modal parameter stability criterion, and then the stable modes are further filtered through the real mode automatic filtering and integration method based on the joint spectral peak value. This method mainly filters the modes after preliminary filtering based on the detected effective modal peak frequency, so as to establish the final effective real stable mode. Compared with the traditional modal stability judgment method, this method can further accurately filter out the effective real stable mode of the system from the stable mode filtered out by the traditional method, and efficiently and accurately eliminate the false modes, which solves the problem that the traditional modal filtering method may introduce a large number of false modes when the model order is high and cannot effectively eliminate the false modes, and solves the problem of low efficiency and possible misjudgment in the traditional manual filtering method based on the modal stability diagram, and has high engineering practice value.

[0236] Based on the automatic working modal analysis method of the multi-domain enhanced extended Hankel matrix, the time-varying modal parameters in the cutting contact state during the processing of thin-walled structures can be accurately identified through the response signals during the processing of thin-walled structures. This effectively solves the problem that the traditional experimental modal analysis method of modal parameters of thin-walled structures based on the hammer modal method cannot consider the time-varying dynamic characteristics of the system under the dynamic cutting state. It can effectively improve the identification accuracy of the time-varying modal parameters in the processing of thin-walled structures, more accurately characterize the time-varying dynamic characteristics in the processing of thin-walled structures, and has high engineering practice value.

Claims

1. A method for identifying time-varying modal parameters in a thin-walled structure machining process, characterized in that: The following steps are involved: Obtain response signals at different time periods during the processing of thin-walled structures; The effective modal peak frequency in the response signal is detected by using a joint spectrum peak detection method; the joint spectrum peak detection method is a peak detection method based on the singular value spectrum peak and the PSD spectrum peak; Perform signal enhancement on the effective mode peak frequency to obtain an enhanced signal; Based on the random subspace method, the modal identification of the enhanced signal is carried out to obtain the modal parameters; The stability of the modal parameters in different time periods is judged respectively, and the time-varying modal parameters of the thin-walled structure processing are obtained.

2. The method for identifying time-varying modal parameters in a thin-walled structure machining process according to claim 1, characterized in that: Using the joint spectrum peak-to-peak detection method, the effective modal peak frequencies in the detection response signal include: Calculate the singular values ​​and PSD of the response signal to obtain the singular value spectrum and PSD spectrum; A spectrum peak that satisfies both the height condition and the prominence condition in the singular value spectrum and the PSD spectrum is selected, and the frequency of the spectrum peak is the effective modal peak frequency.

3. The method for identifying time-varying modal parameters in a thin-walled structure machining process according to claim 2, characterized in that: The peaks that meet both the height condition and the prominence condition in the singular value spectrum and PSD spectrum are selected as follows: Calculate the first height condition threshold according to the median of the singular value spectrum, the median absolute deviation of the singular value spectrum and the standard deviation of the singular value spectrum; calculate the first decibel value of all spectral peaks in the singular value spectrum; select the first decibel value greater than or equal to the first height condition threshold, and the spectral peak corresponding to the first decibel value is the first height spectral peak; Calculate the first protrusion condition threshold according to the median absolute deviation of the singular value spectrum and the standard deviation of the singular value spectrum; calculate the first protrusion decibel value according to the first decibel value, the decibel value from the first height spectrum peak to the lowest spectrum peak on the left, and the decibel value from the first height spectrum peak to the lowest spectrum peak on the right; select the first protrusion decibel value that is greater than or equal to the first protrusion condition threshold, and the spectrum peak corresponding to the first protrusion decibel value is the first protrusion spectrum peak; Calculate the second height condition threshold according to the median of the PSD spectrum, the median absolute deviation of the PSD spectrum and the standard deviation of the PSD spectrum; calculate the second decibel value of all spectral peaks in the PSD spectrum; select the second decibel value greater than or equal to the second height condition threshold, and the spectral peak corresponding to the second decibel value is the second height spectral peak; The second protrusion condition threshold is calculated according to the median absolute deviation of the PSD spectrum and the standard deviation of the PSD spectrum; the second protrusion decibel value is calculated according to the second decibel value, the decibel value from the second height spectrum peak to the lowest spectrum peak on the left, and the decibel value from the second height spectrum peak to the lowest spectrum peak on the right; the second protrusion decibel value that is greater than or equal to the second protrusion condition threshold is selected, and the spectrum peak corresponding to the second protrusion decibel value is the second protrusion spectrum peak; A spectrum peak that exists in both the first protrusion spectrum peak and the second protrusion spectrum peak is selected, and the frequency of the spectrum peak is the effective modal peak frequency.

4. The method for identifying time-varying modal parameters in a thin-walled structure machining process according to claim 3, characterized in that: The effective modal peak frequency is signal enhanced, and the enhanced signal includes: Performing signal enhancement based on time-frequency domain characteristics on the frequency range of the effective modal peak frequency to obtain a first enhanced signal; the signal enhancement based on time-frequency domain characteristics includes wavelet transform enhancement and STFT enhancement; Performing signal enhancement based on the time domain scaling coefficient on the response signal to obtain a second enhanced signal; The first enhanced signal and the second enhanced signal are combined to obtain an enhanced signal.

5. The method for identifying time-varying modal parameters in a thin-walled structure machining process according to claim 4, characterized in that: The enhancement factor of the signal enhancement is 1+amp l i f ication_ f actor ,in, amp l i f ication_ f actor is the enhancement factor.

6. The method for identifying time-varying modal parameters in a thin-walled structure machining process according to claim 5, characterized in that: Modal identification of enhanced signals based on random subspace method includes: constructing a joint matrix using the response signal, the first enhanced signal, and the second enhanced signal; Construct multi-domain enhanced extended Hankel matrix based on joint matrix; The modal parameters are solved using the multi-domain enhanced extended Hankel matrix to obtain the modal parameters.

7. The method for identifying time-varying modal parameters in a thin-walled structure machining process according to claim 6, characterized in that: The stability of the modal parameters in different time periods is judged respectively, and the time-varying modal parameters of the thin-walled structure processing process are obtained, including: The stability of the modal parameters in different time periods is preliminarily judged to obtain the stable mode in each time period; Based on the joint spectrum peak detection method, the secondary stability is judged to obtain the true mode of each time period; Select the intersection of the stable mode and the true mode to obtain the stable true mode; The stable real modes of all time periods are integrated to obtain the time-varying modal parameters of the thin-walled structure machining process.

8. The method for identifying time-varying modal parameters in a thin-walled structure machining process according to claim 7, characterized in that: Based on the joint spectrum peak detection method, the secondary stability is judged and the real mode of each time period is obtained, including: In the singular value spectrum, the frequency of the spectrum peak is subtracted from the center frequency of the spectrum peak of the singular value spectrum to obtain a first difference value; In the PSD spectrum, the frequency of the spectrum peak is subtracted from the center frequency of the spectrum peak of the PSD spectrum to obtain a second difference value; The spectrum peak whose absolute values ​​of the first difference and the second difference are both less than or equal to the frequency matching tolerance is retained, and the mode corresponding to the spectrum peak is the real mode.

9. An electronic device, characterized in that: include: at least one processor; and, a memory communicatively coupled to at least one of the processors; Wherein, the memory stores instructions that can be executed by at least one of the processors, and the instructions are executed by at least one of the processors so that at least one of the processors can execute a method for identifying time-varying modal parameters in a thin-walled structure processing process as described in any one of claims 1 to 8.

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