Giant magnetostriction bar health state evaluation method considering subharmonic content

Abstract

The invention discloses a giant magnetostrictive bar health state evaluation method considering subharmonic content, which comprises the following steps of: firstly, obtaining output displacement data of a giant magnetostrictive bar through a built giant magnetostrictive bar test platform; in order to select the filter length and the mode decomposition number of the characteristic mode decomposition method, combining with the Shannon entropy coefficient, taking the square envelope spectrum kurtosis as a weight, constructing a weighted square envelope spectrum kurtosis Shannon entropy coefficient objective function, and performing parameter optimization by using a Harris eagle optimization algorithm; according to the method, the principle of maximum square envelope spectrum kurtosis is taken as a principle to select a main mode component, finally, envelope spectrum analysis is carried out, the health state of the giant magnetostrictive bar is evaluated by counting the sub-harmonic content in the envelope spectrum, and the method plays a guiding role in development and application of a giant magnetostrictive transducer. And the service life of the subsequent transducer can be detected and evaluated.

Description

Technical Field

[0001] The present invention relates to the technical field of transducers, and in particular to a health status assessment method for a giant magnetostrictive rod taking subharmonic content into consideration. Background Art

[0002] Giant magnetostrictive transducers (GMTs) are electro-acoustic energy conversion devices based on a giant magnetostrictive rod (GMR) as their core excitation unit. They are widely used in fields such as sonar detection and marine communications. As a core component of a GMT, the health of the GMR directly impacts the device's operating efficiency and safety. When excited by an alternating magnetic field, the GMR periodically expands and contracts, generating force. Due to its high electrical conductivity, the GMR generates eddy currents in the alternating magnetic field. At high frequencies, the skin effect is significant, further exacerbating heating and degrading GMR performance. Therefore, to reduce eddy current losses, the GMR is often cut, but this creates stress concentrations at the cut seams. The GMR's metal substrate has poor ductility and high brittleness, making it highly sensitive to mechanical stress concentrations. Cutting significantly reduces its mechanical strength, predisposing it to fatigue cracks and accelerating crack growth. However, due to its sealed assembly within the GMT and its typical use at deep water, the GMR's condition cannot be directly observed, making assessing its health a significant challenge. By collecting the output displacement data of a giant magnetostrictive rod, its condition can be detected. In the present invention, the raw data collected is the vibration displacement data of the giant magnetostrictive rod. GMR is essentially a ferromagnetic material, with inherent hysteresis between its magnetic field strength and magnetization intensity, resulting in a hysteresis-like nonlinearity between input and output. When subjected to an AC excitation magnetic field, GMR only undergoes elongation and deformation regardless of the direction of the field, inherently exhibiting a frequency-doubling effect. Using superharmonics often fails to detect crack faults. Furthermore, in actual experiments, high-frequency signals are easily affected by nonlinear factors introduced 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. However, the subharmonic components of nonlinear ultrasound are only generated during impact, collision, and vibration contact at solid interfaces, and under specific excitation conditions. They are unrelated to the testing process, making subharmonics more suitable for GMR crack damage detection. Based on the operating characteristics and failure mechanisms of GMR, a periodic pulse signal is generated after a fault occurs, stimulating resonance throughout the entire system. However, GMR vibration signals collected at the worksite are easily overwhelmed by the strong background noise in the operating environment. Fault-related repetitive pulses in the vibration signal are often weak, making it difficult to extract their subharmonic characteristics. There is an urgent need to develop methods that can effectively extract GMR subharmonic characteristics in the presence of 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 unique advantages in extracting periodic fault pulses. This is because the fault signal collected by an accelerometer or laser displacement sensor can be regarded as the convolution of the fault source signal and the noise signal. Blind deconvolution realizes inverse deconvolution by constructing an inverse filter to extract the periodic pulses. It can recover the periodic pulses related to the fault in the vibration signal under conditions such as unknown vibration source and noise intensity.

[0003] In order to better extract the periodic pulse characteristics of faults under strong background noise, a new characteristic mode decomposition (FMD) method is proposed. The fault period of the vibration signal is estimated by the autocorrelation function, and a continuously iterative finite impulse response (FMD) filter bank is used to ensure that the filtered signal is as close as possible to the maximum correlate kurtosis deconvolution (MCKD) correlation kurtosis objective function. The signal is effectively decomposed into independent modal components, which can fully extract the periodic pulses of faults in the vibration signal.

[0004] Glossary:

[0005] Subharmonic: The frequency is 1 / 2, 3 / 2, 1 / 3, 2 / 3 times the excitation frequency, that is, the periodic component whose frequency is a fractional multiple of the fundamental frequency.

[0006] HHO optimization algorithm: Harris Hawk optimization algorithm, a metaheuristic algorithm proposed by Heidari et al. in 2019. Its core is to imitate the hunting behavior of Harris Hawk. It consists of three phases: global search phase, transition phase, and local development phase.

[0007] FMD algorithm: also known as the characteristic mode decomposition algorithm, can accurately decompose the fault mode 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 evaluating the health status of a giant magnetostrictive rod taking into account the subharmonic content, in view of the shortcomings of the existing technology.

[0009] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0010] A method for evaluating the health status of giant magnetostrictive rods considering subharmonic content includes:

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

[0012] Step 2: Use the squared envelope spectrum kurtosis as the weight and combine it with the Shannon entropy coefficient to construct the objective function;

[0013] Step 3: Optimizing the two parameters of the filter length L and the number of decomposed modes n of the eigenmode decomposition method FMD. When the objective function is minimized, the optimal filter length L and the number of decomposed modes n are obtained, and the optimized eigenmode decomposition method FMD is obtained.

[0014] Step 4: Decompose the original data set using the optimized modal decomposition method FMD, and select the main modal component based on the principle of maximum square envelope spectrum kurtosis;

[0015] Step 5: Perform envelope spectrum analysis on the selected main modal component, calculate the subharmonic content of the main modal component, and compare the subharmonic content of the main modal component with the preset threshold to obtain a health status assessment of the giant magnetostrictive rod.

[0016] For further improvement, in step 2, the objective function is:

[0017]

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

[0019] For further improvement, in step 2, the objective function is constructed as follows:

[0020] Step 2.1 uses 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 is the fast Fourier transform, Hilbert is the Hilbert transform, abs() represents the modulus, j represents the imaginary unit, S SES (x) represents the square envelope spectrum of the original vibration signal x;

[0023] Step 2.2: Construct the Shannon entropy SESES to evaluate the squared envelope spectrum coefficient: 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 ) represents the original vibration signal x at frequency f i The square envelope spectrum value at , Indicates the accumulation of energy at all frequency points; p i Indicates the square envelope spectrum of the ith frequency in the total S SES The probability distribution value in the spectrum; N represents the total number of frequency points;

[0026] Step 2.3: Assign weights to the squared envelope spectrum kurtosis and increase the weight of the main modal component:

[0027]

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

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

[0030]

[0031] Where u i (t) represents the i-th modal component decomposed by the eigenmode decomposition method FMD, N is the total number of modal components decomposed by FMD, and t is the time scale;

[0032]

[0033] As a further improvement, in step 1, the vibration displacement data of the giant magnetostrictive rod is collected and obtained by a laser displacement sensor.

[0034] For further improvement, the specific steps of step three are as follows:

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

[0036] Step 3.2: Perform a global search. Harris's hawk randomly perches at certain locations and waits for prey according to two strategies. The specific expressions are as follows (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] Where t is the current iteration number; X(t+1) is the position vector of the Harris Hawk in the next iteration; X rabbit (t) is the location of the prey; X(t) is the current position vector of the hawk; r1, r2, r3, r4 and q are random numbers in the range [0, 1], where q controls the roosting strategy of the Harris hawk; L and U represent the upper and lower limits of the search range; X rand (t) represents a randomly selected Harris hawk individual; X m (t) represents the average position of all eagles, and its expression is:

[0040]

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

[0042] Step 3.3: Transition phase: As the prey escapes, its energy gradually decreases. The Harris hawk transforms the phases based on the prey's energy. The energy change simulation 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] at each iteration; as the number of iterations increases, the escape energy E decreases continuously; 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. During this phase, the Harris hawk uses different pursuit styles to attack its prey: r is set as a parameter that determines whether the prey can escape. r is a random number in [0,1]. When r is less than 0.5, the prey is considered to have a probability of successfully escaping; when r is greater than 0.5, the prey is considered to have failed to escape. Specifically, there are 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 siege strategy is implemented, and when |E| < 0.5, a hard siege strategy is implemented.

[0049] The fitness function Fitness for optimizing the eigenmode decomposition method FMD using the HHO optimization algorithm is as follows:

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

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

[0052] For further improvement, the specific steps of step 4 are as follows:

[0053] Step 4.1: Input the original vibration signal x, the number of decomposed modes n and the filter length L of the FMD obtained in step 3 to the optimized modal decomposition method FMD;

[0054] Step 4.2: Use K Hanning windows i represents the number of iterations, k represents the kth filter at the i-th iteration, initializes the FIR filter bank, and starts 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, J is the total length of the window; w(j) represents the Hanning window used;

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

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

[0059] Step 4.5: Determine whether the current number of iterations has reached the maximum number of iterations. 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 each two modal components, select the two modal components with the largest correlation coefficient, and use the previously estimated fault cycle Calculate its related kurtosis, then select the modal component with the largest square envelope spectrum kurtosis as the decomposed modal 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 decomposition modes n; if not, return to step 4.3, otherwise go to step 4.8.

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

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

[0064]

[0065] S SESK The main modal component is selected based on the principle of maximum (x).

[0066] For further improvement, the specific steps of step five are as follows:

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

[0068] Step 5.1.1: De-mean the selected main modal component to obtain the de-meaned signal x remean :

[0069]

[0070] Among them, x(t) is the original signal, represents the mean of x(t).

[0071] Step 5.1.2: Demean the signal x remean Perform Hilbert transform to obtain the analytical signal z(t):

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

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

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

[0075]

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

[0077] Step 5.1.3: Based on the analytical signal z(t), obtain the envelope signal e(t).

[0078]

[0079] Step 5.1.4: Remove the mean of the envelope signal e(t) again to obtain the envelope signal after removing the mean remean (t);

[0080]

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

[0082] Step 5.1.4: De-average the envelope signal e remean (t) Perform fast Fourier transform to obtain the envelope spectrum E(f)

[0083]

[0084] e -i2πft represents the complex exponential function;

[0085] Step 5.2: Count the subharmonic content of the envelope spectrum E(f) to evaluate 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 of the energy value of the subharmonic frequency band to the total energy, η.

[0090]

[0091] in, Represents the total energy value of all frequency bands; |E(k)| represents the energy value of the kth frequency band. Finally, based on the subharmonic content value, the health status of the giant magnetostrictive rod is evaluated:

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

[0093] If 0%<η≤10%, the giant magnetostrictive rod is in a slightly damaged state;

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

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

[0096] Compared with the prior art, the present invention has the following beneficial effects:

[0097] 1. The present invention proposes using subharmonic content to assess the health of giant magnetostrictive rods. Because GMR is inherently a ferromagnetic material, there is a natural hysteresis between its magnetic field strength and magnetization intensity, resulting in a hysteresis-nonlinear relationship between input and output. When subjected to an AC excitation magnetic field, it undergoes only elongation deformation regardless of the magnetic field's direction, inherently exhibiting a frequency-doubling effect. Furthermore, in actual experiments, high-frequency signals are susceptible to nonlinear factors caused by sensors, power amplifiers, and other measurement equipment. These components, acting as background noise, can mask damage signals and reduce the signal-to-noise ratio, adversely affecting health assessment. Therefore, the present invention proposes using subharmonic content to assess the health of GMR rods, enabling health assessment of giant magnetostrictive rods and providing guidance for the development and application of transducers.

[0098] 2. The present invention proposes to use the FMD method to extract fault features from the collected vibration displacement data. In order to solve the problem of determining the filter length L and the number of modal decompositions n, the 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 the Shannon entropy coefficient value of the square envelope spectrum is assigned appropriate weights. The weight of the main modal component is increased, which is conducive to the subsequent optimization algorithm to select the most effective parameters and effectively extract the fault information of GMR.

[0099] 3. In order to solve the problem of difficulty in selecting the main mode after FMD decomposition, the present invention proposes to use the principle of maximum envelope spectrum kurtosis to select the main mode. The larger the value, the better the cyclostationarity of the fault information. Using it as a parameter for selecting the main mode can effectively solve the problem of selecting the main mode. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 This is a flow chart of a health status assessment method for giant magnetostrictive rods considering subharmonic content;

[0101] Figure 2 Construct a process for the Shannon entropy coefficient of the weighted squared envelope spectrum;

[0102] Figure 3 It is the original displacement map method of giant magnetostrictive rod;

[0103] Figure 4 This is the envelope spectrum of a perfect giant magnetostrictive rod;

[0104] Figure 5 This is the envelope spectrum of a slightly damaged giant magnetostrictive rod.

[0105] Figure 6 This is the envelope spectrum of a moderately damaged giant magnetostrictive rod.

[0106] Figure 7 This is the envelope spectrum of a severely damaged giant magnetostrictive rod.

[0107] Figure 8 Intact and differently damaged giant magnetostrictive rods used in the experiment: (a) an intact giant magnetostrictive rod, (b) a slightly damaged giant magnetostrictive rod, (c) a moderately damaged giant magnetostrictive rod, and (d) a severely damaged giant magnetostrictive rod. DETAILED DESCRIPTION

[0108] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0109] The present invention discloses a health status assessment of a giant magnetostrictive rod. First, output displacement data of the giant magnetostrictive rod is obtained by constructing a giant magnetostrictive rod test platform. In order to select the filter length and the number of modal decompositions of the characteristic mode decomposition method, a weighted square envelope spectrum kurtosis Shannon entropy coefficient objective function is constructed in combination with the Shannon entropy coefficient and with the square envelope spectrum kurtosis as a weight, and the Harris Eagle optimization algorithm is used for parameter optimization. The main modal component is selected based on the principle of maximizing the square envelope spectrum kurtosis. Finally, envelope spectrum analysis is performed and the subharmonic content thereof is statistically analyzed to achieve the health status assessment of the giant magnetostrictive rod. This method plays a guiding role in the development and application of giant magnetostrictive transducers and plays a role in detecting and evaluating the service life of subsequent transducers.

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

[0111] Figure 1This is a brief flow chart of a method for evaluating the health status of a giant magnetostrictive rod considering subharmonic content corresponding to this embodiment. Figure 1 As shown, the implementation of this embodiment may include:

[0112] Step 1: Collect the displacement signal of the giant magnetostrictive rod.

[0113] In this embodiment, step 1 may include: building a giant magnetostrictive bar vibration test platform, collecting displacement signals through a laser displacement sensor, and obtaining an original vibration data set.

[0114] Step 2: Construct the weighted square envelope spectrum Shannon entropy coefficient as the objective function

[0115] Step 2.1 uses 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 is the fast Fourier transform, Hilbert is the Hilbert transform, and abs(·) represents the modulo.

[0118] Step 2.2: Construct the Shannon entropy SESES to evaluate the square envelope spectrum coefficient. 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 square envelope spectrum value at , Indicates the accumulation of energy at all frequency points.

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

[0122]

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

[0124]

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

[0126]

[0127] SESES can effectively represent the fault characteristics of the square envelope spectrum and has strong robustness, and W i can effectively represent the cyclostationarity of GMR faults. Therefore, parameter optimization is performed in the WSESES minimum principle, which can not only retain the sparsity index advantage of SESES, but also increase the weight of the modal containing fault characteristics in the objective function, which is beneficial to the optimization algorithm to select the optimal parameters

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

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

[0130] Step 3.2: global search, in this stage, Harris hawks randomly perch in some positions and wait for prey according to two strategies, and the specific expressions are as follows (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(U-L)],q<0.5 (1.51)

[0133] In the formula, t is the current iteration number; X(t+1) is the position vector of Harris hawks in the next iteration; X rabbit (t) is the position of the prey; X(t) is the current position vector of the hawk; r1, r2, r3, r4 and q are random numbers in [0, 1], wherein q controls the selection of the perching strategy of Harris hawks; L and U represent the upper and lower bounds of the search range; X rand (t) represents a randomly selected Harris hawk individual; X m (t) represents the average position of all hawks, and its expression is as follows:

[0134]

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

[0136] Step 3.3: During the transition phase, the prey's energy gradually decreases as it flees. The Harris's hawk will transition between phases based on the prey's energy. The energy change simulation is shown in the following equation:

[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 varies randomly within the range [-1, 1] with each iteration. As the number of iterations increases, the escape energy E decreases. When |E| ≥ 1, HHO performs a global search phase; when |E| < 1, HHO performs a local exploitation phase.

[0139] Step 3.4: Local development phase. During this phase, the Harris's hawk will use different pursuit styles to ambush its prey. Let r be a parameter that determines whether the prey can escape. r is a random number between 0 and 1. If r is less than 0.5, the prey is considered to have a probability of escaping successfully; if r is greater than 0.5, the prey is considered to have failed to escape. Specifically, there are two siege strategies: soft siege and hard siege.

[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. When |E| ≥ 0.5, a soft siege strategy is implemented, and when |E| < 0.5, a hard siege strategy is implemented.

[0143] In summary, the HHO algorithm is used to optimize FMD, and its fitness function is as follows:

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

[0145] Among them, S WSESES Formula (1.5) represents the objective function for the proposed extraction of giant magnetostrictive bar fault features. By calculating the S of the FMD decomposition result WSESES , by selecting the filter length L of the FMD and the number of modal decompositions n corresponding to the minimum Shannon entropy of the weighted square envelope spectrum, the best parameter combination can be obtained, that is, the optimized FMD method can be obtained.

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

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

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

[0149]

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

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

[0152] Step 4.4: Using the original signal x, the decomposed mode and estimated failure cycles Update the filter coefficients, where the estimated failure period is The autocorrelation function reaches a local maximum after passing through zero After one iteration is completed, the iteration counter i=i+1.

[0153] Step 4.5: Determine whether the current number of iterations has reached the maximum number of iterations. 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 each two modal components, select the two modal components with the largest correlation coefficient, and use the previously estimated fault cycle The relevant kurtosis is calculated, and then the modal component with the larger relevant kurtosis is selected as the decomposed modal component, and the number of filters is set to K=K-1.

[0155] Step 4.7: Determine whether 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 square envelope spectrum kurtosis of each mode separately.

[0158]

[0159] S SESKThe main mode is selected based on the maximum principle, and the resulting envelope spectrum can better reflect the fault characteristic frequency.

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

[0161] Step 5.1: Perform envelope spectrum analysis on the selected main mode.

[0162] Step 5.1.1: Remove the mean of the original signal:

[0163]

[0164] Among them, x(t) is the original signal, represents the mean of x(t).

[0165] Step 5.1.2: Demean the signal x remean Perform Hilbert transform to obtain the analytical signal z(t):

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

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

[0168]

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

[0170]

[0171] Step 5.1.4: Remove the mean of the envelope signal e(t) again.

[0172]

[0173] Step 5.1.4: De-average the envelope signal e remean (t) Perform fast Fourier transform to obtain the envelope spectrum E(f)

[0174]

[0175] Step 5.2: Count the subharmonic content and evaluate the health status of the giant magnetostrictive 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, which 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, Indicates the total energy value of all frequency bands.

[0182] Finally, the health status of the giant magnetostrictive rod is evaluated based on the subharmonic content value.

[0183]

[0184] in, Figure 4-Figure 7 As shown, corresponding to Figure 8 Envelope spectra of giant magnetostrictive rods in (a)-(d),

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

[0186] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A method for evaluating the health status of a giant magnetostrictive rod considering subharmonic content, characterized in that: include: Step 1: Collect the vibration displacement data of the giant magnetostrictive rod and obtain the original data set as the original vibration signal x; Step 2: Use the squared envelope spectrum kurtosis as the weight and combine it with the Shannon entropy coefficient to construct the objective function; Step 3: Optimizing the two parameters of the filter length L and the number of decomposed modes n of the eigenmode decomposition method FMD. When the objective function is minimized, the optimal filter length L and the number of decomposed modes n are obtained, and the optimized eigenmode decomposition method FMD is obtained. Step 4: Decompose the original data set using the optimized modal decomposition method FMD, and select the main modal component based on the principle of maximum square envelope spectrum kurtosis; Step 5: Perform envelope spectrum analysis on the selected main modal component, calculate the subharmonic content of the main modal component, and compare the subharmonic content of the main modal component with the preset threshold to obtain a health status assessment of the giant magnetostrictive rod.

2. The method for evaluating the health status of a giant magnetostrictive rod considering subharmonic content according to claim 1, wherein: In the step 2, the objective function is: Among them, W i is the weight of each modal component of the i-th mode, H SESES is the Shannon entropy coefficient of the weighted square envelope spectrum.

3. The method for evaluating the health status of a giant magnetostrictive rod considering subharmonic content according to claim 2, wherein: In the step 2, the objective function is constructed as follows: Step 2.1 uses 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 is the fast Fourier transform, Hilbert is the Hilbert transform, abs() represents the modulus, j represents the imaginary unit, S SES (x) represents the square envelope spectrum of the original vibration signal x; Step 2.2: Construct the Shannon entropy SESES to evaluate the squared envelope spectrum coefficient: H 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 ) represents the original vibration signal x at frequency f i The square envelope spectrum value at Indicates the accumulation of energy at all frequency points; p i Indicates the square envelope spectrum of the ith frequency in the total S SES The probability distribution value in the spectrum; N represents the total number of frequency points; Step 2.3: Assign weights to the squared envelope spectrum kurtosis and increase the weight of the main modal component: S SESK (x) represents the square envelope spectrum kurtosis of the original vibration signal x, S SES (x i ) represents the pf envelope spectrum value of the i-th point, Represents the average value of the square envelope spectrum of all frequency points; Among them, the weight W assigned to each modal component is i for: Where u i (t) represents the i-th modal component decomposed by the eigenmode decomposition method FMD, N is the total number of modal components decomposed by FMD, and t is the time scale; 4. The method for evaluating the health status of a giant magnetostrictive rod considering subharmonic content according to claim 1, wherein: In the step 1, the vibration displacement data of the giant magnetostrictive rod is collected by a laser displacement sensor.

5. The method for evaluating the health status of a giant magnetostrictive rod 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 N and maximum number of iterations T of the HHO optimization algorithm: Step 3.2: Perform a global search. Harris's hawk randomly perches at certain locations and waits for prey according to two strategies. The specific expressions are as follows (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[L+r4(U-L)],q<0.5(1.7) Where t is the current iteration number; X(t+1) is the position vector of the Harris Hawk in the next iteration; X rabbit (t) is the location of the prey; X(t) is the current position vector of the hawk; r1, r2, r3, r4 and q are random numbers in the range [0, 1], where q controls the roosting strategy of the Harris hawk; L and U represent the upper and lower limits of the search range; X rand (t) represents a randomly selected Harris hawk individual; X m (t) represents the average position of all eagles, and its expression is: Where, X i (t) represents the position of the i-th eagle; Q is the total number of eagles; Step 3.3: Transition phase: As the prey escapes, its energy gradually decreases. The Harris hawk transforms the phases based on the prey's energy. The energy change simulation 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] at each iteration; as the number of iterations increases, the escape energy E decreases continuously; when |E| ≥ 1, HHO executes the global search phase; when |E| < 1, HHO executes the local development phase; Step 3.4: Local development phase. During this phase, the Harris hawk uses different pursuit styles to attack its prey: r is set as a parameter that determines whether the prey can escape. r is a random number in [0,1]. When r is less than 0.5, the prey is considered to have a probability of successfully escaping; when r is greater than 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|JX 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 J is the random jump intensity. When |E| ≥ 0.5, a soft siege strategy is implemented, and when |E| < 0.5, a hard siege strategy is implemented. The fitness function Fitness for optimizing the eigenmode decomposition method FMD using the HHO optimization algorithm is as follows: Fitness=min(S WSESES ) (1.12) Among them, min() means taking the minimum value.

6. The method for evaluating the health status of a giant magnetostrictive rod considering subharmonic content according to claim 1, characterized in that: The specific steps of step 4 are as follows: Step 4.1: Input the original vibration signal x, the number of decomposed modes n and the filter length L of the FMD obtained in step 3 to the optimized modal decomposition method FMD; Step 4.2: Use K Hanning windows i represents the number of iterations, k represents the kth filter at the i-th iteration, initializes the FIR filter bank, and starts 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, J is the total length of the window; w(j) represents the Hanning window used; Step 4.3: Use Obtaining the decomposed modes Where k = 1, 2, ..., k, * represents convolution operation; Step 4.4: Use the original vibration signal x and the decomposed mode and estimated failure cycles Update the coefficients of the filter FIR filter bank, where the estimated fault period is The autocorrelation function reaches a local maximum after passing through zero The corresponding time is determined; after completing one iteration, the iteration counter i=i+1; Step 4.5: Determine whether the current number of iterations has reached the maximum number of iterations. 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 each two modal components, select the two modal components with the largest correlation coefficient, and use the previously estimated fault cycle Calculate its related kurtosis, then select the modal component with the largest square envelope spectrum kurtosis as the decomposed modal 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 decomposition modes n; if not, return to step 4.3, otherwise go to step 4.

8. Step 4.8: The obtained n modal components are taken as the final decomposition modes; Step 4.9: After obtaining the decomposition results, calculate the square envelope spectrum kurtosis of each mode separately: S SESK The main modal component is selected based on the principle of maximum (x).

7. The method for evaluating the health status of a giant magnetostrictive rod by optimizing the characteristic mode decomposition of the parameter L considering the 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 main modal components: Step 5.1.1: De-mean the selected main modal component to obtain the de-meaned signal x remean : Among them, x(t) is the original signal, represents the mean of x(t). Step 5.1.2: Demean the signal x remean Perform Hilbert transform to obtain the analytical signal z(t): z(t)=x remean (t)+i·H{x remean (t)} (1.16) H{} represents the Hilbert transform of the signal x, and i represents the imaginary unit; Among them, H{x remean (t)} is defined as t is the current calculation time, τ is the resolution, x remean (τ) is the value of the original signal after removing the mean at time τ; Step 5.1.3: Based on the analytical signal z(t), obtain the envelope signal e(t). Step 5.1.4: Remove the mean of the envelope signal e(t) again to obtain the envelope signal after removing the mean remean (t); Represents the time average of the envelope signal; Step 5.1.4: De-average the envelope signal e remean (t) Perform fast Fourier transform to obtain the envelope spectrum E(f) e -i2πft represents the complex exponential function; Step 5.2: Count the subharmonic content of the envelope spectrum E(f) to evaluate 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 of the energy value of the subharmonic frequency band to the total energy, η. in, Represents the total energy value of all frequency bands; |E(k)| represents the energy value of the kth frequency band. Finally, based on the subharmonic content value, the health status of the giant magnetostrictive rod is evaluated: If η = 0%, the giant magnetostrictive rod is in a healthy state; If 0%<η≤30%, the giant magnetostrictive rod is in a slightly damaged state; If 30%<η≤50%, the giant magnetostrictive rod is in a state of slight to moderate damage; If η>50%, the giant magnetostrictive rod is in a state of slight or severe damage.

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