A health state evaluation method of a giant magnetostrictive rod considering sub-harmonic content

Abstract

The application discloses a health state evaluation method of a giant magnetostrictive rod considering sub-harmonic content, and first obtains output displacement data of the giant magnetostrictive rod through a built giant magnetostrictive rod test platform; in order to select a filter length and a modal decomposition number of a characteristic modal decomposition method, a weighted square envelope spectrum kurtosis Shannon entropy coefficient objective function is constructed by taking a square envelope spectrum kurtosis as a weight value in combination with a Shannon entropy coefficient, and a Harris eagle optimization algorithm is used for parameter optimization; the selection of a main modal component is performed according to the principle that the square envelope spectrum kurtosis is maximum, envelope spectrum analysis is further performed, the sub-harmonic content is counted, and the health state evaluation of the giant magnetostrictive rod is realized, which plays a guiding role for the development and application of the giant magnetostrictive transducer and plays a detection and evaluation role for the service life of the subsequent transducer.

Description

Technical Field

[0001] This invention relates to the field of transducer technology, and more specifically to a method for assessing the health status of supermagnetostrictive rods considering subharmonic content. Background Technology

[0002] A giant magnetostrictive transducer (GMT) is an electro-acoustic energy conversion device using a giant magnetostrictive rod (GMR) as its core excitation unit, widely used in sonar detection, marine communications, and other fields. As the core component of the GMT, the health of the GMR directly affects the equipment's efficiency and safety. Under alternating magnetic field excitation, the GMR undergoes periodic expansion and contraction, thus outputting force. Due to the high conductivity of the GMR, eddy currents are generated in an alternating magnetic field, and the skin effect is significant at high frequencies, further exacerbating heat generation and leading to a decline in GMR performance. Therefore, to reduce eddy current losses, the GMR is usually cut, but this creates stress concentration at the cut seam. The metal matrix of the GMR has poor ductility and high brittleness, making it very sensitive to mechanical stress concentration. Cutting significantly reduces its mechanical strength, easily leading to fatigue cracks and accelerating crack propagation. However, because it is sealed inside the GMT and is generally used in deep water, the condition of the GMR cannot be directly observed, making the assessment of its health a significant challenge. By collecting the output displacement data of the giant magnetostrictive (GMR) rod, its state can be detected. In this invention, the collected raw data is the vibration displacement data of the GMR rod. GMR is essentially a ferromagnetic material, and its magnetic field strength and magnetization naturally exhibit hysteresis, resulting in a nonlinear lag between input and output. When subjected to an AC excitation magnetic field, GMR only undergoes elongation deformation regardless of the direction of the magnetic field, inherently possessing a frequency doubling effect. Superharmonic waves often fail to detect crack faults. Furthermore, in actual experiments, high-frequency signals are easily affected by nonlinear factors caused by sensors, power amplifiers, and other measuring equipment. These components, acting as background noise, mask the damage signal and reduce the signal-to-noise ratio. The subharmonic components of nonlinear ultrasound only occur during impact collisions and vibrations at solid interfaces, and under specific excitation conditions, independent of the testing process, making subharmonic waves more suitable for identifying crack damage in GMR. Based on the operating characteristics and fault mechanism of GMR, a periodic pulse signal is generated after a fault occurs, exciting the resonance of the entire system. However, GMR vibration signals collected at the work site are easily submerged by the large amount of strong background noise in the operating environment. The repetitive pulses related to the fault in the vibration signal are often very weak, making it difficult to extract their subharmonic features. There is an urgent need to develop methods that can effectively extract GMR subharmonic features under strong background noise. In recent years, methods such as Variational Mode Decomposition (VMD), Empirical Wavelet Transform (EWT), neural networks, and blind deconvolution have been proposed to extract periodic fault pulses.Among them, blind deconvolution (BD) has a unique advantage in extracting periodic fault pulses. This is because the fault signal collected by the accelerometer or laser displacement sensor can be regarded as the convolution of the fault source signal and the noise signal. Blind deconvolution extracts the periodic pulses by constructing an inverse filter to achieve inverse deconvolution, which can recover the periodic pulses related to the fault in the vibration signal under unknown vibration source and noise intensity.

[0003] To better extract the periodic pulse features of faults under strong background noise, a novel Feature Mode Decomposition (FMD) method is proposed. This method estimates the fault period of the vibration signal through the autocorrelation function and uses an iterative finite impulse response filter bank to ensure that the filtered signal is as close as possible to the correlation kurtosis objective function of maximum correlated kurtosis deconvolution (MCKD). This effectively decomposes the signal into independent modal components, which can fully extract the periodic pulses of faults in the vibration signal.

[0004] Definitions:

[0005] Subharmonics: Periodic components whose frequencies are 1 / 2, 3 / 2, 1 / 3, 2 / 3 times the excitation frequency, that is, periodic components whose frequencies are fractional multiples of the fundamental frequency.

[0006] The Harris Eagle Optimization Algorithm (HHO) is a metaheuristic algorithm proposed by Heidari et al. in 2019. Its core principle is to mimic the hunting behavior of the Harris Eagle, and it comprises three phases: a global search phase, a transition phase, and a local exploration phase.

[0007] FMD algorithm: also known as Eigenmode Decomposition algorithm, can accurately decompose fault modes and is robust to other interference and noise. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a method for assessing the health status of supermagnetostrictive rods that takes into account the subharmonic content, in order to address the shortcomings of the existing technology.

[0009] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0010] A method for assessing the health status of supermagnetostrictive rods considering subharmonic content includes:

[0011] Step 1: Collect vibration displacement data of the giant magnetostrictive rod to obtain the raw dataset as the original vibration signal x;

[0012] Step 2: Construct the objective function by using the squared envelope spectrum kurtosis as weights and combining it with the Shannon entropy coefficient;

[0013] Step 3: Optimize the two parameters of the Eigenmode Decomposition method FMD, namely the filter length L and the number of decomposed modes n. When the objective function is minimized, the optimal filter length L and the number of decomposed modes n are obtained, thus obtaining the optimized Eigenmode Decomposition method FMD.

[0014] Step 4: Decompose the original dataset using the optimized mode decomposition method FMD, and select the principal mode components based on the principle of maximizing the kurtosis of the squared envelope spectrum;

[0015] Step 5: Perform envelope spectrum analysis on the selected principal modal components, and count the subharmonic content of the principal modal components. Compare the subharmonic content of the principal modal components with the preset threshold to obtain the health status assessment of the supermagnetostrictive rod.

[0016] In a further improvement, the objective function in step two is:

[0017]

[0018] Among them, W i H represents the weights of each modal component in the i-th mode. SESES is the Shannon entropy coefficient of the weighted squared envelope spectrum.

[0019] In a further improvement, the objective function is constructed in step two as follows:

[0020] Step 2.1 Use Shannon entropy to evaluate the sparsity of the squared envelope spectrum:

[0021] S SES (x)=abs(T FFT (|x+j·Hilbert(x)| 2 (1.1)

[0022] Among them, T FFT It is the Fast Fourier Transform, Hilbert is the Hilbert Transform, abs() represents the modulus, j represents the imaginary unit, and S SES (x) represents the square envelope spectrum of the original vibration signal x;

[0023] Step 2.2: Construct the Shannon entropy (SESES) for evaluating the squared envelope spectral coefficients: H SESES H SESES The smaller the value, the more obvious the fault characteristics reflected by the envelope spectrum. The specific expression is:

[0024]

[0025] in S SES (f i () indicates that the original vibration signal x at frequency f i The squared envelope spectrum value at that location, This indicates the accumulation of energy at all frequency points; p i This represents the square envelope spectrum of the i-th frequency in the total S. SES The probability distribution values ​​in the spectrum; N represents the total number of frequency points;

[0026] Step 2.3: Assign weights to the kurtosis of the squared envelope spectrum, increasing the weights of the principal modal components:

[0027]

[0028] S SESK (x) represents the square envelope kurtosis of the original vibration signal x, S SES (x i ) represents the pf envelope spectrum value at the i-th point. This represents the average of the squared envelope spectrum at all frequency points;

[0029] Among them, the weight W assigned to each modal component i for:

[0030]

[0031] In the formula, u i (t) represents the i-th mode component of the Eigenmode Decomposition (FMD) method, N is the total number of mode components in the FMD decomposition, and t is the time scale;

[0032]

[0033] In a further improvement, in step one, the vibration displacement data of the giant magnetostrictive rod is collected by a laser displacement sensor.

[0034] Further improvements are made, and the specific steps of step three are as follows:

[0035] Step 3.1: Initialize the population size N and maximum number of iterations T for the HHO optimization algorithm:

[0036] Step 3.2: Perform a global search. The Harris Eagle randomly perches in certain locations and waits for prey according to two strategies, as shown in expressions (1.6) and (1.7):

[0037] X(t+1)=X rand (t)-r1|X rand (t)-2r2X(t)|,q≥0.5 (1.6)

[0038] X(t+1)=(X rabbit (t)-X m (t))-r3[L+r4(UL)],q<0.5 (1.7)

[0039] In the formula, t is the current iteration number; X(t+1) is the position vector of the Harris Hawk in the next iteration; X rabbit (t) represents the location of the prey; X(t) is the current position vector of the eagle; r1, r2, r3, r4 and q are random numbers in the range [0,1], where q controls the eagle's roosting strategy; L and U represent the upper and lower limits of the search range; X rand (t) represents a randomly selected Harris Eagle individual; X m (t) represents the average position of all eagles, and its expression is:

[0040]

[0041] In the formula, X i (t) represents the position of the i-th eagle; Q is the total number of eagles;

[0042] Step 3.3: Transition Phase. During the prey's escape, its energy gradually decreases. The Harris Eagle transitions between phases based on the prey's energy level, and the simulated energy change process is shown in the following formula:

[0043]

[0044] Where E is the escape energy of the current prey; T is the maximum number of iterations; E0 is the initial energy of the prey, which changes randomly in the range of [-1, 1] in each iteration; as the number of iterations increases, the escape energy E continuously decreases; when |E|≥1, HHO executes the global search phase; when |E|<1, HHO executes the local development phase.

[0045] Step 3.4: Local development phase. In this phase, Harris Eagle uses different pursuit styles to ambush prey: set r as a parameter to determine whether the prey can escape. r is a random number in [0,1]. When r < 0.5, it is considered that the prey has a chance to escape successfully; when r > 0.5, it is considered that the prey has failed to escape. Specifically, it is divided into the following two siege strategies: soft siege and hard siege.

[0046] X(t+1)=ΔX(t)-E|JX rabbit (t)-X(t)|,|E|≥0.5 (1.10)

[0047] X(t+1)=X rabbit (t)-E|ΔX(t)|,|E|<0.5 (1.11)

[0048] Where ΔX(t) is the distance between the prey and the current individual, and J is the random jump intensity; when |E|≥0.5, a soft encirclement strategy is implemented, and when |E|<0.5, a hard encirclement strategy is implemented.

[0049] The fitness function for optimizing the Eigenmode Decomposition (FMD) method using the HHO optimization algorithm is as follows:

[0050] Fitness = min(S WSESES (1.12)

[0051] Here, min() means taking the minimum value.

[0052] Further improvements are made, and the specific steps of step four are as follows:

[0053] Step 4.1: Input the original vibration signal x into the optimized mode decomposition method FMD, as well as the number of decomposition modes n and filter length L of FMD obtained in Step 3;

[0054] Step 4.2: Use K Hanning windows i represents the iteration number, k represents the k-th filter in the i-th iteration, initialize the FIR filter bank and start the iteration count, i = 1; the number of filters used k is 5-10:

[0055]

[0056] Where j represents the discrete-time index, j = 1, 2, 3, ... J-1, and J is the total length of the window; w(j) represents the Hanning window used.

[0057] Step 4.3: Use Obtain the decomposed modes Where k = 1, 2, ..., k, and * denotes convolution operation;

[0058] Step 4.4: Using the original vibration signal x, the decomposed modes and estimated failure cycle Update the coefficients of the FIR filter bank, where the estimated fault period is... It is by The autocorrelation function reaches a local maximum after passing through the zero. The corresponding time is determined; after one iteration is completed, the iteration counter i = i + 1;

[0059] Step 4.5: Determine if the current iteration count has reached the maximum iteration count. If not, return to step 4.3; otherwise, continue to step 4.6.

[0060] Step 4.6: Construct the correlation matrix CC (K×K)Calculate the correlation coefficient between every two modal components, select the two modal components with the largest correlation coefficient, and then apply the previously estimated fault cycle. Calculate its correlation kurtosis, then select the mode component with the largest square envelope spectrum kurtosis as the decomposed mode component, and set the number of filters K = K-1;

[0061] Step 4.7: Determine whether the current number of filters K is equal to the set number of decomposed modes n; if not, return to step 4.3, otherwise proceed to step 4.8.

[0062] Step 4.8: The obtained n modal components are used as the final decomposition modes;

[0063] Step 4.9: After obtaining the decomposition results, calculate the squared envelope kurtosis of each mode:

[0064]

[0065] With S SESK (x) The principal modal component is selected based on the principle of maximizing (x).

[0066] Further improvements are made, and the specific steps of step five are as follows:

[0067] Step 5.1: Perform envelope spectrum analysis on the selected principal modal components:

[0068] Step 5.1.1: Perform mean-removal processing on the selected principal mode components to obtain the mean-removed signal x. remean :

[0069]

[0070] Where x(t) is the original signal, Let x(t) represent the mean of x(t).

[0071] Step 5.1.2: Process the mean-removed signal x remean Performing the Hilbert transform, we obtain the analytic signal z(t):

[0072] z(t) = x remean (t)+i·H{x remean (t)}(1.16)

[0073] H{} represents the Hilbert transform of signal x, where i represents the imaginary unit;

[0074] Wherein, H{x remean (t)} is defined as

[0075]

[0076] t is the current calculation time, τ is the resolution, and x is the value of τ. remean (τ) represents the value of the original signal after mean removal at time τ;

[0077] Step 5.1.3: Obtain the envelope signal e(t) based on the analytic signal z(t).

[0078]

[0079] Step 5.1.4: Mean the envelope signal e(t) again to obtain the mean-reduced envelope signal e. remean (t);

[0080]

[0081] e represents the time average value of the envelope signal;

[0082] Step 5.1.4: For the mean-removed envelope signal e... remean Perform a Fast Fourier Transform on (t) to obtain the envelope spectrum E(f).

[0083]

[0084] e -i2πft Represents a complex exponential function;

[0085] Step 5.2: Statistically analyze the subharmonic content of the envelope spectrum E(f) to assess the health status of the giant magnetostrictive rod.

[0086] Step 5.2.1: Calculate the energy value E of the subharmonic frequency band. y :

[0087] E y =|E f1 | 2 +|E f2 | 2 +…|E fn | 2 (1.21)

[0088] Where n = 1, 2, ..., N, represents the number of frequencies containing subharmonics;

[0089] Step 5.2.2: Calculate the ratio η of the energy value of the subharmonic frequency band to the total energy.

[0090]

[0091] in, The total energy value across all frequency bands is represented by |E(k)|; |E(k)| represents the energy value of the k-th frequency band. Finally, the health status of the supermagnetostrictive rod is assessed based on the subharmonic content.

[0092] If η = 0%, then the supermagnetostrictive rod is in a healthy state;

[0093] If 0% < η ≤ 10%, the supermagnetostrictive rod is in a state of slight damage.

[0094] If 10% < η ≤ 20%, the supermagnetostrictive rod is in a state of slight to moderate damage.

[0095] If η > 20%, the supermagnetostrictive rod is in a state of slight severe damage.

[0096] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0097] 1. This invention proposes using subharmonic content to evaluate the health status of giant magnetostrictive (GMR) rods. Since GMR is essentially a ferromagnetic material, a natural hysteresis phenomenon exists between its magnetic field strength and magnetization, exhibiting a hysteresis nonlinearity between input and output. When subjected to an AC excitation magnetic field, it only undergoes elongation deformation regardless of the magnetic field direction, inherently possessing a frequency doubling effect. Furthermore, in actual experiments, high-frequency signals are easily affected by nonlinear factors caused by sensors, power amplifiers, and other measuring equipment. These components, acting as background noise, can mask damage signals and reduce the signal-to-noise ratio, which is detrimental to health status assessment. Therefore, this invention proposes using subharmonic content to evaluate the health status of GMR, achieving a comprehensive assessment of the health status of giant magnetostrictive (GMR) rods and providing guidance for the development and application of transducers.

[0098] 2. This invention proposes using the FMD method to extract fault features from collected vibration displacement data. To address the need to determine the filter length L and the number of mode decompositions n, a weighted square envelope spectrum Shannon entropy coefficient is proposed as the objective function. The sparsity of the square envelope spectrum is evaluated by Shannon entropy, and appropriate weights are assigned to the Shannon entropy coefficient values ​​of the square envelope spectrum, increasing the weights of the principal mode components. This facilitates the selection of optimal parameters in subsequent optimization algorithms, effectively extracting fault information from GMR.

[0099] 3. In this invention, to solve the problem of difficulty in selecting the principal mode after FMD decomposition, it is proposed to use the principle of maximizing envelope spectrum kurtosis to select the principal mode. The larger the value, the better the cyclic stability of the fault information. Using it as a parameter for selecting the principal mode can effectively solve the problem of principal mode selection. Attached Figure Description

[0100] Figure 1 A flowchart of a method for assessing the health status of supermagnetostrictive rods that takes into account subharmonic content;

[0101] Figure 2 The process of constructing the Shannon entropy coefficients for the weighted squared envelope spectrum;

[0102] Figure 3 The original displacement diagram method for supermagnetostrictive rods;

[0103] Figure 4 A complete envelope spectrum of the supermagnetostrictive rod;

[0104] Figure 5 Envelope spectrum of a slightly damaged supermagnetostrictive rod.

[0105] Figure 6 The image shows the envelope spectrum of a moderately damaged supermagnetostrictive rod.

[0106] Figure 7 The image shows the envelope spectrum of a severely damaged supermagnetostrictive rod.

[0107] Figure 8 These are intact and differently damaged giant magnetostrictive rods used in the experiment. Among them, (a) is an intact giant magnetostrictive rod, (b) is a slightly damaged giant magnetostrictive rod, (c) is a moderately damaged giant magnetostrictive rod, and (d) is a severely damaged giant magnetostrictive rod. Detailed Implementation

[0108] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0109] This invention discloses a health status assessment method for giant magnetostrictive rods. First, output displacement data of the giant magnetostrictive rods is obtained through a constructed experimental platform. To select the filter length and number of modes for the characteristic mode decomposition method, a weighted squared envelope spectrum kurtosis-Shannon entropy coefficient objective function is constructed, using the squared envelope spectrum kurtosis as the weight, combined with the Shannon entropy coefficient. The Harris Eagle optimization algorithm is then used to optimize the parameters. The principal mode components are selected based on maximizing the squared envelope spectrum kurtosis. Finally, envelope spectrum analysis is performed, and the subharmonic content is statistically analyzed to achieve a health status assessment of the giant magnetostrictive rods. This provides guidance for the development and application of giant magnetostrictive transducers and plays a role in detecting and evaluating the service life of subsequent transducers.

[0110] To make the implementation process of the present invention clearer and easier to understand, the invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0111] Figure 1This is a simplified flowchart of a method for assessing the health status of supermagnetostrictive rods considering subharmonic content, corresponding to this embodiment. Figure 1 As shown, the implementation of this embodiment may include:

[0112] Step 1: Acquire displacement signals of the giant magnetostrictive rod.

[0113] In this embodiment, step 1 may include: building a vibration testing platform for giant magnetostrictive rods, collecting displacement signals through a laser displacement sensor, and obtaining the original vibration dataset.

[0114] Step 2: Construct the weighted squared envelope spectrum with Shannon entropy coefficients as the objective function.

[0115] Step 2.1 Use Shannon entropy to evaluate the sparsity of the squared envelope spectrum:

[0116] S SES (x)=abs(T FFT (|x+j·Hilbert(x)| 2 ))(1.45)

[0117] Among them, T FFT It is the Fast Fourier Transform, Hilbert is the Hilbert Transform, and abs(·) represents the modulo operation.

[0118] Step 2.2: Construct the Shannon entropy (SESES) for evaluating the squared envelope spectrum coefficients. The smaller the value, the more obvious the fault characteristics reflected by the envelope spectrum. The specific expression is:

[0119]

[0120] in S SES (x i ) indicates that the signal is at frequency f i The squared envelope spectrum value at that location, This indicates that the energy at all frequency points is accumulated.

[0121] Step 2.3: Assign appropriate weights to the Square Envelope Spectral Kurtosis (SESK) to increase the weights of the principal modal components:

[0122]

[0123] Among them, the weight W assigned to each modal component i for

[0124]

[0125] In the formula, u i(t) represents the i-th modal component of the FMD decomposition, and N is the total number of modal components in the FMD decomposition;

[0126]

[0127] Among them, SESES can effectively characterize the fault features of the square envelope spectrum and has strong robustness. The W obtained from SESK i It can effectively characterize the cyclic stationarity of GMR faults. Therefore, using the WSEESES minimization principle for parameter optimization can both retain the sparsity advantage of SESES and increase the weight of fault-containing characteristic modes in the objective function, which is beneficial for the optimization algorithm to select the optimal parameters.

[0128] In this embodiment, step 3 may include:

[0129] Step 3.1: Initialize the population size N and maximum number of iterations T of HHO:

[0130] Step 3.2: Perform a global search. In this stage, the Harris Eagle randomly perches in certain locations and waits for prey according to two strategies, as shown in expressions (1.6) and (1.7):

[0131] X(t+1)=X rand (t)-r1|X rand (t)-2r2X(t)|,q≥0.5 (1.50)

[0132] X(t+1)=(X rabbit (t)-X m (t))-r3[L+r4(UL)],q<0.5 (1.51)

[0133] In the formula, t is the current iteration number; X(t+1) is the position vector of the Harris Hawk in the next iteration; X rabbit (t) represents the location of the prey; X(t) is the current position vector of the eagle; r1, r2, r3, r4 and q are random numbers in the range [0,1], where q controls the eagle's roosting strategy; L and U represent the upper and lower limits of the search range; X rand (t) represents a randomly selected Harris Eagle individual; X m (t) represents the average position of all eagles, and its expression is:

[0134]

[0135] In the formula, X i (t) represents the position of the i-th eagle; N is the total number of eagles.

[0136] Step 3.3: Transition Phase. During the prey's escape, its energy gradually decreases. The Harris Eagle transitions between phases based on the prey's energy level, and the simulated energy change process is shown in the following formula:

[0137]

[0138] Where E is the escape energy of the current prey; T is the maximum number of iterations; and E0 is the initial energy of the prey, which changes randomly within the range of [-1, 1] in each iteration. As the number of iterations increases, the escape energy E continuously decreases. When |E|≥1, HHO executes the global search phase; when |E|<1, HHO executes the local development phase.

[0139] Step 3.4: Local Development Phase. In this phase, the Harris Eagle will use different pursuit styles to ambush its prey. Let r be a parameter indicating whether the prey can escape. r is a random number in the range [0,1]. If r < 0.5, the prey is considered to have a chance of successfully escaping; if r > 0.5, the prey is considered to have failed to escape. Specifically, there are two attack strategies: soft encirclement and hard encirclement.

[0140] X(t+1)=ΔX(t)-E|JX rabbit (t)-X(t)|,|E|≥0.5 (1.54)

[0141] X(t+1)=X rabbit (t)-E|ΔX(t)|,|E|<0.5 (1.55)

[0142] Where ΔX(t) is the distance between the prey and the current individual, and J is the random jump intensity. A soft encirclement strategy is implemented when |E|≥0.5, and a hard encirclement strategy is implemented when |E|<0.5.

[0143] In summary, the fitness function of the HHO algorithm for optimizing FMD is as follows:

[0144] Fitness = min(S WSESES (1.56)

[0145] Among them, S WSESES Equation (1.5) represents the proposed objective function for fault feature extraction of supermagnetostrictive rods. The S function is calculated from the FMD decomposition results. WSESES By selecting the filter length L and the number of mode decompositions n of the FMD corresponding to the minimum weighted squared envelope spectrum Shannon entropy, the best parameter combination can be obtained, which is the optimized FMD method.

[0146] In this embodiment, step 4 may include:

[0147] Step 4.1: Input the original vibration signal x, and the number of decomposed modes n and filter length L of FMD obtained in Step 2.

[0148] Step 4.2: Use K Hanning windows Initialize the FIR filter bank and begin iteration counting, i = 1. It is recommended to use a filter number k of 5-10.

[0149]

[0150] Where n represents the discrete-time index, n = 1, 2, 3, ... N-1, and N is the total length of the window.

[0151] Step 4.3: Use Obtain the filtered signal, where k = 1, 2, ..., k, and * denotes convolution operation.

[0152] Step 4.4: Using the original signal x, the decomposed modes and estimated failure cycle Update the filter coefficients, where the estimated fault period is... It is by The autocorrelation function reaches a local maximum after passing through the zero. The corresponding time is used to determine this. After one iteration is completed, the iteration counter i = i + 1.

[0153] Step 4.5: Determine if the current iteration count has reached the maximum iteration count. If not, return to step 3; otherwise, continue to step 4.6.

[0154] Step 4.6: Construct the correlation matrix CC (K×K) Calculate the correlation coefficient between every two modal components, select the two modal components with the largest correlation coefficient, and then apply the previously estimated fault cycle. Calculate its correlation kurtosis, then select the mode component with the larger correlation kurtosis as the decomposed mode component, and set the number of filters K = K-1.

[0155] Step 4.7: Determine if the current number of filters K is equal to the set number of decomposition modes n. If not, return to step 3; otherwise, proceed to step 4.8.

[0156] Step 4.8: The obtained n modal components are used as the final decomposition modes.

[0157] Step 4.9: After obtaining the decomposition results, calculate the squared envelope kurtosis of each mode.

[0158]

[0159] With S SESKThe principal mode is selected based on the principle of maximizing the frequency of faults, and the resulting envelope spectrum can better reflect the fault characteristic frequencies.

[0160] In this embodiment, step 5 may include:

[0161] Step 5.1: Perform envelope spectrum analysis on the selected principal modes.

[0162] Step 5.1.1: Mean removal processing of the original signal:

[0163]

[0164] Where x(t) is the original signal, Let x(t) represent the mean of x(t).

[0165] Step 5.1.2: Process the mean-removed signal x remean Performing the Hilbert transform, we obtain the analytic signal z(t):

[0166] z(t) = x remean (t)+i·H{x remean (t)}(1.60)

[0167] Wherein, H{x remean (t)} is defined as

[0168]

[0169] Step 5.1.3: Take the analytic signal z(t) to obtain the envelope signal e(t).

[0170]

[0171] Step 5.1.4: Mean the envelope signal e(t) again.

[0172]

[0173] Step 5.1.4: For the mean-removed envelope signal e... remean Perform a Fast Fourier Transform on (t) to obtain the envelope spectrum E(f).

[0174]

[0175] Step 5.2: Statistically analyze the subharmonic content to assess the health status of the supermagnetostrictive rod.

[0176] Step 5.2.1: Calculate the energy value of the subharmonic frequency band.

[0177] E y =|E f1 | 2 +|E f2| 2 +...|E fn | 2 (1.65)

[0178] Where n = 1, 2, ..., N, represents the number of frequencies containing subharmonics.

[0179] Step 5.2.2: Calculate the ratio of the energy value of the subharmonic frequency band to the total energy.

[0180]

[0181] in, This represents the total energy value across all frequency bands.

[0182] Finally, the health status of the supermagnetostrictive rod is assessed based on the subharmonic content value.

[0183]

[0184] in, Figures 4-7 As shown, they correspond to Figure 8 Envelope spectra of the supermagnetostrictive rods in (a)-(d)

[0185] The subharmonic content increases significantly with the degree of damage.

[0186] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for assessing the health status of supermagnetostrictive rods considering subharmonic content, characterized in that, include: Step 1: Collect vibration displacement data of the giant magnetostrictive rod to obtain the raw dataset as the original vibration signal x; Step 2: Construct the objective function by using the squared envelope spectrum kurtosis as weights and combining it with the Shannon entropy coefficient; Step 3: Optimize the two parameters of the Eigenmode Decomposition method FMD: filter length L and number of decomposed modes R. When the objective function is minimized, the optimal filter length L and number of decomposed modes R are obtained, thus obtaining the optimized Eigenmode Decomposition method FMD. Step 4: Decompose the original dataset using the optimized Feature Mode Decomposition (FMD) method, and select the principal mode components based on the principle of maximizing the kurtosis of the squared envelope spectrum. Step 5: Perform envelope spectrum analysis on the selected principal modal components, and count the subharmonic content of the principal modal components. Compare the subharmonic content of the principal modal components with the preset threshold to obtain the health status assessment of the giant magnetostrictive rod. In step two, the objective function is: Among them, W r H represents the weight of the r-th modal component. SESES The weighted squared envelope spectrum Shannon entropy coefficients; In step two, the objective function is constructed as follows: Step 2.1 Use Shannon entropy to evaluate the sparsity of the squared envelope spectrum: S SES (x)=abs(T FFT (|x+j·Hilbert(x)| 2 )) (1.1) Among them, T FFT It is the Fast Fourier Transform, Hilbert is the Hilbert Transform, abs() represents the modulus, j represents the imaginary unit, and S SES (x) represents the square envelope spectrum of the original vibration signal x; Step 2.2: Construct the weighted squared envelope spectrum Shannon entropy coefficient H for evaluating the squared envelope spectrum coefficients. SESES H SESES The smaller the value, the more obvious the fault characteristics reflected by the envelope spectrum. The specific expression is: in S SES (f i () indicates that the original vibration signal x at frequency f i The squared envelope spectrum value at that location, This indicates the accumulation of energy at all frequency points; p i This represents the square envelope spectrum of the i-th frequency in the total S. SES The probability distribution values ​​in the spectrum; N represents the total number of frequency points; Step 2.3: Assign weights to the kurtosis of the squared envelope spectrum, increasing the weights of the principal modal components: S SESK (x) represents the square envelope kurtosis of the original vibration signal x, S SES (x i () represents the pf envelope spectrum value of the i-th point. This represents the average of the squared envelope spectrum at all frequency points; Among them, the weight W assigned to each modal component r for: In the formula, u r (t) represents the r-th modal component of the Eigenmode Decomposition (FMD) method, where t is the time scale; 2. The method for assessing the health status of supermagnetostrictive rods considering subharmonic content as described in claim 1, characterized in that, In step one, the vibration displacement data of the giant magnetostrictive rod is collected by a laser displacement sensor.

3. The method for assessing the health status of supermagnetostrictive rods considering subharmonic content according to claim 1, characterized in that, The specific steps of step three are as follows: Step 3.1: Initialize the population size F and maximum number of iterations T for the HHO optimization algorithm: Step 3.2: Perform a global search. The Harris Eagle randomly perches in certain locations and waits for prey according to two strategies, as shown in expressions (1.6) and (1.7): X(t+1)=X rand (t)-r1|X rand (t)-2r2X(t)|,q≥0.5 (1.6) X(t+1)=(X rabbit (t)-X m (t))-r3[P+r4(U-P)],q<0.5 (1.7) In the formula, t is the current iteration number; X(t+1) is the position vector of the Harris Eagle in the next iteration; X rabbit X(t) is the location of the prey; X(t) is the current position vector of the eagle; r1, r2, r3, r4 and q are random numbers in the range [0,1], where q controls the harrier eagle's roosting strategy; P and U represent the upper and lower limits of the search range; X rand (t) represents a randomly selected Harris Eagle individual; X m (t) represents the average position of all eagles, and its expression is: In the formula, X j (t) represents the position of the j-th eagle; Q is the total number of eagles; Step 3.3: Transition Phase. During the prey's escape, the prey's energy gradually decreases. The Harris Eagle transitions between phases based on the prey's energy level, and the simulated energy change process is shown in the following formula: Where E is the escape energy of the current prey; T is the maximum number of iterations; E0 is the initial energy of the prey, which changes randomly in the range of [-1, 1] in each iteration; as the number of iterations increases, the escape energy E continuously decreases; when |E|≥1, HHO executes the global search phase; when |E|<1, HHO executes the local development phase. Step 3.4: Local development phase. In this phase, the Harris Eagle uses different pursuit styles to ambush its prey: set r as a parameter to determine whether the prey can escape. r is a random number in [0,1]. When r < 0.5, the prey is considered to have a chance of successfully escaping; when r > 0.5, the prey is considered to have failed to escape. Specifically, there are two siege strategies: soft siege and hard siege. X(t+1)=ΔX(t)-E|DX rabbit (t)-X(t)|,|E|≥0.5 (1.10) X(t+1)=X rabbit (t)-E|ΔX(t)|,|E|<0.5 (1.11) Where ΔX(t) is the distance between the prey and the current individual, and D is the random jump intensity; when |E|≥0.5, a soft encirclement strategy is implemented, and when |E|<0.5, a hard encirclement strategy is implemented. The fitness function for optimizing the Eigenmode Decomposition (FMD) method using the HHO optimization algorithm is as follows: Fitness=min(S WSESES ) (1.12) Here, min() means taking the minimum value.

4. The method for assessing the health status of supermagnetostrictive rods considering subharmonic content according to claim 1, characterized in that, The specific steps of step four are as follows: Step 4.1: Input the original vibration signal x into the optimized mode decomposition method FMD, the number of decomposition modes R, and the filter length L; Step 4.2: Use K Hanning windows i represents the iteration number, k represents the k-th filter in the i-th iteration, initialize the FIR filter bank and start the iteration count, i = 1; the number of filters used k is 5-10: Where j represents the discrete-time index, j = 1, 2, 3, ... J-1, and J is the total length of the window; w(j) represents the Hanning window used; Step 4.3: Use Obtain the decomposed modes Where k = 1, 2, ..., k, and * denotes convolution operation; Step 4.4: Using the original vibration signal x, the decomposed modes and estimated failure cycle Update the coefficients of the FIR filter bank, where the estimated fault period is... It is by The autocorrelation function reaches a local maximum after passing through the zero. The corresponding time is determined; after one iteration is completed, the iteration counter i = i + 1; Step 4.5: Determine if the current iteration count has reached the maximum iteration count. If not, return to step 4.3; otherwise, continue to step 4.

6. Step 4.6: Construct the correlation matrix CC (K×K) Calculate the correlation coefficient between every two modal components, select the two modal components with the largest correlation coefficient, and then apply the previously estimated fault cycle. Calculate its correlation kurtosis, then select the mode component with the largest square envelope spectrum kurtosis as the decomposed mode component, and set the number of filters K = K-1; Step 4.7: Determine whether the current number of filters K is equal to the set number of decomposed modes R; if not, return to step 4.3, otherwise proceed to step 4.8; Step 4.8: The obtained R modal components are used as the final decomposition modes; Step 4.9: After obtaining the decomposition results, calculate the squared envelope kurtosis of each mode: With S SESK (x) The principal modal component is selected based on the principle of maximizing (x).

5. The method for assessing the health status of supermagnetostrictive rods considering subharmonic content according to claim 1, characterized in that, The specific steps of step five are as follows: Step 5.1: Perform envelope spectrum analysis on the selected principal modal components: Step 5.1.1: Perform mean-removal processing on the selected principal mode components to obtain the mean-removed signal x. remean : Where x(t) is the original signal, Let x(t) represent the mean of x(t); Step 5.1.2: Process the mean-removed signal x remean Performing the Hilbert transform, we obtain the analytic signal z(t): z(t)=x remean (t)+i·H{x remean (t)} (1.16) H{} represents the Hilbert transform of signal x, where i represents the imaginary unit; Wherein, H{x remean (t)} is defined as t is the current calculation time, τ is the resolution, and x is the value of τ. remean (τ) represents the value of the original signal after mean removal at time τ; Step 5.1.3: Obtain the envelope signal e(t) based on the analytic signal z(t). Step 5.1.4: Mean the envelope signal e(t) again to obtain the mean-reduced envelope signal e. remean (t); This represents the time average value of the envelope signal; Step 5.1.4: For the mean-removed envelope signal e... remean Perform a Fast Fourier Transform on (t) to obtain the envelope spectrum E(f). e -i2πft Represents a complex exponential function; Step 5.2: Statistically analyze the subharmonic content of the envelope spectrum E(f) to assess the health status of the giant magnetostrictive rod. Step 5.2.1: Calculate the energy value E of the subharmonic frequency band. y : AND y =|E f1 | 2 +|E f2 | 2 +…|And fn | 2 (1.21) Where n = 1, 2, ..., N, represents the number of frequencies containing subharmonics; Step 5.2.2: Calculate the ratio η of the energy value of the subharmonic frequency band to the total energy. in, |E(k)| represents the total energy value across all frequency bands; |E(k)| represents the energy value of the k-th frequency band. Finally, the health status of the supermagnetostrictive rod is assessed based on the subharmonic content value: If η = 0%, then the supermagnetostrictive rod is in a healthy state; If 0% < η ≤ 30%, the supermagnetostrictive rod is in a state of slight damage. If 30% < η ≤ 50%, the supermagnetostrictive rod is in a state of slight to moderate damage. If η > 50%, the supermagnetostrictive rod is in a state of slight severe damage.

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