Rapid estimation method for ultrasonic thickness measurement sound time of large-curvature cable insulation layer

Abstract

The invention provides a fast estimation method for ultrasonic thickness measurement sound time of a large-curvature cable insulation layer, and belongs to the technical field of ultrasonic measurement of the cable insulation layer, the method combines short-time Fourier transform (STFT), an improved grey wolf algorithm (IGWO) and a matching pursuit algorithm (MP), and fits ultrasonic echo signals based on the matching pursuit algorithm on the basis of a Gabor function model. The algorithm firstly utilizes short-time Fourier transform to optimize an echo parameter search range, then utilizes an improved grey wolf algorithm to replace traversal calculation in matching pursuit, and improves echo parameter search efficiency and estimation precision. The method can effectively solve the problems of insufficient precision and low efficiency in ultrasonic traditional acoustic time estimation and thickness estimation, and has better estimation precision and stability in an acoustic system containing frequency dispersion and phase shift, so that the method meets the application requirements of real-time online thickness measurement.

Description

Technical Field

[0001] This invention relates to the field of ultrasonic measurement technology for cable insulation layers, and in particular to a rapid estimation method for ultrasonic thickness measurement of insulation layers of cables with large curvature. Background Technology

[0002] Ultrasonic thickness measurement technology estimates thickness by extracting the time-of-flight (ToF) characteristics of ultrasonic echo signals. Therefore, accurate and rapid ultrasonic ToF estimation is fundamental to ultrasonic thickness detection. However, ultrasonic echo signals are not only affected by the spatial parameters of the measured object's surface but also closely related to the alignment of the ultrasonic transducer with the object. When the measured object is a static plane, the echo signal is relatively stable. However, when the surface curvature of the measured object is large (such as a thin cable), ultrasonic energy is scattered by the curved surface, leading to increased echo signal redundancy and clutter, a decreased signal-to-noise ratio (SNR), and dispersion and phase shift. This makes accurate ToF estimation difficult and causes measurement errors.

[0003] Traditional Time-of-Flight (ToF) estimation methods mainly include thresholding, peaking, and cross-correlation. The first two methods have low computational cost and are widely used in practical production, but in acoustic systems with low signal-to-noise ratios, large signal amplitude variations, and phase shifts, it is difficult to set appropriate threshold parameters to achieve accurate ToF estimation. Cross-correlation estimates ToF by comparing the similarity of two ultrasonic echo signals. While it is fast and robust, it is prone to multiple fuzzy convolution peaks under the aforementioned conditions, leading to estimation errors. To improve the accuracy of ToF estimation in these environments, current research mainly introduces sparse representation methods such as wavelet decomposition, basis pursuit, and matched pursuit to extract ToF parameters from echo signals. Among these, the matched pursuit (MP) algorithm based on echo model fitting has become a research focus in signal parameter estimation. The MP algorithm constructs a discretized overcomplete parameter dictionary and iteratively searches for the optimal fitting parameters with the goal of minimizing the signal residual energy. However, the MP algorithm, based on a greedy strategy, requires traversing the entire search space. This leads to high computational resource requirements and insufficient parameter fitting accuracy when dealing with the sparsity of the echo signal time-series space and the discreteness of the dictionary, reducing its practicality in online measurement environments. Although time-frequency domain analysis can reduce the search space and lower computational resources and complexity, the parameter estimation accuracy is still affected by the discreteness of the dictionary. To improve parameter search accuracy, some studies have combined intelligent optimization algorithms such as artificial bee colony optimization and particle swarm optimization to improve the MP algorithm, enabling it to search in a continuous space. However, since the parameter search space still relies on prior knowledge, the parameter search efficiency is low and cannot meet the real-time requirements of online measurements.

[0004] The thickness of cable insulation directly affects the efficiency and safety of power transmission, therefore its thickness must be strictly controlled during the production process. However, thin cables typically have a large curvature, and the high production speed coupled with high-frequency vibrations results in a large amount of redundant noise during measurement, thus placing higher demands on the ToF estimation algorithm in ultrasonic thickness measurement for accuracy and real-time performance.

[0005] In view of this, and in response to the need for online ultrasonic thickness measurement of cable insulation, this invention proposes a rapid estimation method for ultrasonic thickness measurement signal acoustic time. Summary of the Invention

[0006] The purpose of this invention is to provide a rapid estimation method for ultrasonic thickness measurement of insulation layers in cables with large curvature, thereby solving the technical problems mentioned in the background art.

[0007] This method combines Short-time Fourier Transform (STFT), Improved Grey Wolf Optimizer (IGWO), and MP algorithm. STFT optimizes the parameter search range of the ultrasonic echo fitting model and improves the computational efficiency of MP algorithm. IGWO enables the reconstruction of multiple echoes in continuous parameter space, improving the accuracy and real-time performance of ToF estimation.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A rapid estimation method for ultrasonic thickness measurement of insulation layer in cables with high curvature, the method comprising the following steps:

[0010] Step 1: Select a mathematical model of the Gabor function characteristics to fit the echo signal;

[0011] Step 2: Optimize the parameter range of the echo model based on the short-time Fourier transform;

[0012] Step 3: Use the improved Grey Wolf (IGWO) algorithm to search for the optimal echo parameters;

[0013] Step 4: Calculate the acoustic time difference based on the optimized echo model and the fitted echo signal.

[0014] 2. The rapid estimation method for ultrasonic thickness measurement of insulation layer of large curvature cable according to claim 1, characterized in that: the specific process of step 1 is as follows:

[0015] The echo signal was fitted using the Gabor function:

[0016]

[0017] In the formula, t represents time, θ represents the parameter set of the echo model, β represents amplitude, α represents bandwidth, τ represents acoustic time, and f c For the center frequency, For phase;

[0018] The ultrasonic thickness measurement signal y(t) of the cable insulation layer with a total duration of T is expressed as:

[0019]

[0020] In the formula, g p (θ p ;t) is the p-th Gabor function echo signal, where p is a positive integer, and ε1(t) and ε2(t) are Gaussian white noise and redundant clutter caused by curvature, respectively;

[0021] To obtain the set of fitting parameters θ, based on the Matching Pursuit (MP) algorithm, the signal is decomposed into a linear combination of an overcomplete dictionary, i.e., the signal y(t) is compressed and approximately fitted as follows:

[0022]

[0023] Where y(t) is the original signal, For the fitted signal, c = (c1, c2, ..., c M ) T Let J be the coefficient vector, representing the weight of each atom, where J is the number of selected non-zero coefficients (i.e., sparsity), M is the total number of signal time series, and D∈R. M×N For an overcomplete dictionary, and D = [d1, d2, ..., dn], ... M ], where N is a complete dictionary combination.

[0024] 3. The rapid estimation method for ultrasonic thickness measurement of insulation layer of large curvature cable according to claim 2, characterized in that: the specific process of step 2 is as follows:

[0025] After obtaining the original signal y(t), the signal is multiplied by a window function w(t) and a complex exponential factor to obtain the frequency domain representation of the corresponding signal. The signal spectrum Y(τ) obtained after short-time Fourier transform is then calculated. i ,f k )for:

[0026]

[0027] In the formula, τ i f is the center time of analysis for the short-time Fourier transform. k To analyze the frequency, where t is time, by analyzing Y(τ) i ,f kThe absolute value can be used to calculate the signal at time τ. i and frequency f k The energy below;

[0028] Because the cable insulation layer is a viscoelastic material, the high-frequency components of the ultrasonic signal attenuate during transmission, making the echo signal frequency unpredictable. However, the transducer center frequency parameter f0 is known. Therefore, a search is performed based on the transducer center frequency characteristics, i.e., the spectral energy near f0, in the spectrum Y(τ) i ,f k In the context of signal echoes, the absolute value of a local maximum within a specific frequency range is selected to represent the presence of signal echoes in the corresponding region. The absolute value of this local maximum is:

[0029]

[0030] In the formula, f s τ is the frequency with the highest energy in the spectrum. s f s The corresponding time, Δf is the frequency search range, which is determined by prior knowledge;

[0031] Therefore, the sound-time dictionary τ d The range of values ​​for is:

[0032]

[0033] In the formula, τ ρ For time-based search parameters, To define the upper and lower limits of the search;

[0034] Frequency dictionary f d The range of values ​​for is:

[0035]

[0036] In the formula, and These are the upper and lower limits of the frequency dictionary, respectively, and δ is the frequency control coefficient. The value of the control coefficient depends on the solution resolution in the short-time Fourier transform.

[0037] For phase range optimization, for τ s The signal y(τ) at time t s Using central difference differentiation, the signal at τ is obtained based on the signal amplitude and gradient. s Phase characteristics at time:

[0038]

[0039] Due to noise, the phase is uncertain; only its range can be determined. Therefore, the phase dictionary... The range of values ​​for is:

[0040]

[0041] When the echo signal noise is greater than the set value, the range of the phase dictionary is expanded. The range of the bandwidth dictionary and the range of the amplitude dictionary are set according to the intrinsic parameters of the transducer and the normalized amplitude of the signal.

[0042] When a signal contains several echoes, a threshold is set on the spectral energy in the characteristic frequency domain to determine whether there are any remaining echo signals. If so, there are no echoes, where p is the power spectrum of the remaining signal after removing p echoes, and is the power spectrum threshold.

[0043] 3. The rapid estimation method for ultrasonic thickness measurement of insulation layer of large curvature cable according to claim 1, characterized in that: the improved Grey Wolf algorithm in step 3 is characterized by:

[0044] Let the position of prey p be S, and the position of the l-th generation gray wolf individual be X(t), then:

[0045] S = |WX p (l)-X(l)|

[0046] X(l+1)=X p (l)-M·S

[0047] In the formula, S is the distance parameter, representing the relative distance between the individual and the prey, W is the random weight coefficient, M is the distance control parameter, M = 2mr1-m, W = 2r2, where r1 and r2 are random numbers between [0,1], m is the distance control factor, l is the gray wolf algebra, and p is the prey;

[0048] m decreases linearly from 2 as the number of iterations increases. β For values ​​as low as 0, the expression is as follows:

[0049]

[0050] In the formula, L is the maximum number of iterations;

[0051] The mathematical model for an individual tracking the location of its prey is as follows:

[0052]

[0053] In the formula, S α S β S δ Let X be the distance parameter between ω wolf and the leader wolf. α (l), X β (l), X δ (l) represents the position of the leader wolf, and W1, W2, and W3 are random weight coefficients;

[0054] Therefore, the position update model for ω wolf is:

[0055]

[0056] ① Initialize the population policy using a dual-policy mapping. To accelerate population convergence and improve optimization accuracy, the Box-Muller transformation is used to ensure that the initial gray wolf population follows a normal distribution, concentrated near the center of the parameter subset υ1∈θ, υ1={f,τ}. Then:

[0057]

[0058] In the formula A random number in (0,1) The location of an individual gray wolf follows a normal distribution N(μ) θ ,σ);

[0059] Meanwhile, to improve the initial population diversity and accelerate the convergence speed, the parameter subset υ2∈θ,

[0060] Initialization is performed using a Logistic chaotic mapping:

[0061]

[0062] In the formula, This is a control parameter, and its value range is [0,4].

[0063] ② Dual-strategy distance control factor. To avoid exceeding the set value of the individual factor |M| and thus bypassing the optimal solution, a nonlinear distance control factor based on a logarithmic function is designed, denoted by m1:

[0064]

[0065] In the formula, μ is the control parameter of the logarithmic function. The larger μ is, the more obvious the decrease of m1 is in the early stage of the iteration.

[0066] Meanwhile, to avoid individuals falling into local optima due to |M| decreasing faster than the set value during the search of amplitude, phase, and bandwidth parameters, a distance nonlinear control factor based on the cosine function is designed, denoted by m2:

[0067]

[0068] In the formula, ξ is the control parameter of the cosine function. The larger ξ is, the smaller the decrease of m2 in the early stage of iteration.

[0069] ③ Leader wolf position optimization based on Gaussian perturbation. To prevent the algorithm from converging earlier than the set value, and to balance global and local search capabilities, Gaussian perturbation is used to replace the random coefficient W to maintain population diversity.

[0070] W Gauss =(2r³-1)σ C

[0071] In the formula, r3 is a random number in the range [0,1], and σ c The standard deviation is denoted as .

[0072] The specific process of step 3 is as follows:

[0073] Step 3.1: Set dictionary atomic parameters The gray wolf in the gray wolf algorithm represents a set of dictionary atomic parameters, where each gray wolf represents a set of dictionary atomic parameters, and the minimum ||y(t) - Dc|| is set. 2 Let be the fitness function. The first three gray wolves with the best fitness are selected as leader wolves (α, β, δ wolves), and the remaining wolves are ω wolves.

[0074] Step 3.2: Initialize the population size Q and individual position x using a two-strategy mapping. ij i = 1, 2, ..., Q, j = 1, 2, 3, 4, 5, initialize the iteration counter k2 = 1;

[0075] Step 3.3: Based on the optimization process in Step 3.1, update the position of the individual using a dual-strategy control factor and Gaussian perturbation;

[0076] Step 3.4: k2 = k2 + 1;

[0077] Step 3.4: If the number of iterations reaches the maximum value, return the optimal parameters; otherwise, return to step 3.3.

[0078] 4. The rapid estimation method for ultrasonic thickness measurement of insulation layer of large curvature cable according to claim 1, characterized in that: the specific process of step 4 is as follows:

[0079] Step 4.1: Initialization, acquire an ultrasound signal y of length T. (0) (t), initialize the iteration counter k1 = 0, and initialize the approximate value. and residual signal R (0) =y (0) (t);

[0080] Step 4.2: Let the iteration counter k1 = k1 + 1;

[0081] Step 4.2: Let the iterative fitting counter k1 = k1 + 1;

[0082] Step 4.3: After fitting the signal using steps 3 and 4, calculate the approximate value of the signal. and residual signal

[0083] Step 4.6: Repeat step 4.2 until the residual signal power spectrum is below the threshold to obtain the best-fit signal. Set the number of times to obtain the best-fit signal to p.

[0084] Step 4.7: Calculate the acoustic time difference t, which characterizes the thickness of the cable insulation layer. TODA :

[0085] t TODA =τ p -τ p-1

[0086] In the formula τ p τ p-1 Let p and p-1 represent the acoustic times of the fitted echo signals, respectively, where p = 2, 3, 4, ..., n.

[0087] 5. A rapid estimation method for ultrasonic thickness measurement of insulation layer of a large curvature cable according to claim 4, characterized in that: in step 1, the reconstructed ultrasonic signal is approximated by the following formula:

[0088]

[0089] The present invention, by adopting the above-described technical solution, has the following beneficial effects:

[0090] This invention addresses the insufficient Time-of-Flight (ToF) estimation accuracy of traditional algorithms in ultrasonic thickness measurement of high-curvature cable insulation caused by signal amplitude, frequency, and phase variations. It proposes a time-of-sound estimation method for ultrasonic signals based on STFT-IGWO-MP. STFT-based time-frequency domain analysis optimizes the search range, improving the algorithm's computational efficiency and accuracy. The dual-strategy nonlinear control factor and Gaussian perturbation accelerate the convergence process of the Grey Wolf algorithm, while simultaneously improving the accuracy of ToF estimation. This method demonstrates significant advantages in estimation accuracy, computation time, and noise resistance, making it suitable for rapid time-of-sound estimation in ultrasonic thickness measurement of high-curvature cable insulation. It can also be used for edge computing and real-time detection in online ultrasonic testing equipment. Attached Figure Description

[0091] Figure 1 This is a flowchart of the overall method of the present invention.

[0092] Figure 2 This is a graph showing the variation of the distance control factor m of the present invention with ξ and μ.

[0093] Figure 3 This is a schematic diagram of the cable offset relative to the transducer according to the present invention.

[0094] Figure 4 This is the fitting result of the ultrasonic thickness measurement signal of the present invention. Detailed Implementation

[0095] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and preferred embodiments. However, it should be noted that many details listed in the specification are merely to provide the reader with a thorough understanding of one or more aspects of the present invention, and these aspects of the invention can be implemented even without these specific details.

[0096] like Figure 1 As shown, a rapid estimation method for ultrasonic thickness measurement of insulation layer in cables with large curvature is disclosed. The method includes the following steps:

[0097] Step 1: Selecting a signal fitting model. Studies have shown that the envelope of an ultrasonic pulse echo signal can be approximated as a Gaussian function. Therefore, a mathematical model following the characteristics of a Gaussian function can be used to fit the echo signal, thereby determining the acoustic time of the echo. This invention uses the Gabor function (Gaussian model) to fit the echo signal:

[0098]

[0099] In the formula, t represents time, θ represents the parameter set of the echo model, β represents amplitude, α represents bandwidth, τ represents acoustic time, and f c For the center frequency, For phase.

[0100] Therefore, the cable insulation layer with a total duration of T exceeds [a certain value]. The acoustic thickness signal y(t) can be expressed as:

[0101]

[0102] In the formula, g p (θ p ;t) is the p-th Gabor function echo signal (p is a positive integer), ε1(t) and ε2(t) are Gaussian white noise and redundant clutter caused by curvature, respectively.

[0103] To extract cable insulation thickness information, the acoustic time of multiple consecutive echo signals is fitted to obtain the acoustic time difference t, which characterizes the thickness. TODA :

[0104] t TODA =τ p -τ p-1

[0105] In the formula τ p τ p-1 Let p and p-1 represent the acoustic time of the fitted echo signals, respectively (p = 2, 3, 4, ..., n).

[0106] Step 2: The estimation speed and accuracy of the echo model g(θ;t) parameters are affected by the dictionary D, while STFT can perform time-frequency domain analysis on non-stationary signals, thereby determining and narrowing the parameter search range. Therefore, the parameter range optimization method based on STFT is as follows.

[0107] After obtaining the original signal y(t), the signal is multiplied by a window function w(t) and a complex exponential factor to obtain the frequency domain representation of the signal. The signal spectrum Y(τ) obtained after STFT is... i ,f k )for:

[0108]

[0109] In the formula, τ i f is the center time of analysis for STFT. k To analyze the frequency, by analyzing Y(τ) i ,f k The absolute value can be used to calculate the signal at time τ. i and frequency f k The energy below.

[0110] Because cable insulation is typically made of viscoelastic materials, high-frequency components of the ultrasonic signal attenuate during transmission, making the echo signal frequency unpredictable. However, the transducer's center frequency parameter f0 is known; therefore, a search can be performed based on the transducer's center frequency characteristics—that is, the spectral energy near f0. In the spectrum Y(τ)... i ,f k In the context of signal echoes, we select the local maxima absolute values ​​within the characteristic frequency domain range to represent the potential presence of signal echoes in that region. For example:

[0111]

[0112] In the formula, f s τ is the frequency with the highest energy in the spectrum. s f s The corresponding time. Δf is the frequency search range, which can be determined through prior knowledge.

[0113] Therefore, the sound-time dictionary τ d The range of values ​​for is:

[0114]

[0115] In the formula, τ ρ For time-based search parameters, This sets the upper and lower limits for the search.

[0116] In summary, the frequency dictionary f d The range of values ​​for is:

[0117]

[0118] In the formula, and These represent the upper and lower limits of the frequency dictionary, respectively. δ is the frequency control coefficient, the value of which depends on the solution resolution in the STFT.

[0119] For phase range optimization, τ can be adjusted. s The signal y(τ) at time t s Using central difference differentiation, the signal at τ is obtained based on the signal amplitude and gradient. s Phase characteristics at time:

[0120]

[0121] Due to noise, phase estimation is uncertain; only its range can be determined. Therefore, a phase dictionary... The range of values ​​for is:

[0122]

[0123] When the echo signal has strong noise, the range of values ​​for the phase dictionary can be expanded. The bandwidth dictionary range and amplitude dictionary range can be set according to the transducer's intrinsic parameters and the normalized amplitude of the signal.

[0124] When a signal contains multiple echoes, a threshold can be set on the spectral energy within the characteristic frequency domain to determine whether there are any remaining echo signals. If not, then there are no echoes, where is the power spectrum of the remaining signal after removing p echoes, and is the power spectrum threshold.

[0125] Step 3: Design an improved Grey Wolf Algorithm (IGWO) to search for optimal echo parameters, thereby improving the efficiency and accuracy of echo parameter search.

[0126] Compared with other swarm intelligence algorithms, GWO performs better in terms of optimization capability, search efficiency, and stability.

[0127] The GWO optimization process simulates the social hierarchy, encirclement, and hunting behavior of gray wolves. At each population update, the top three fittest individuals are selected as leader wolves (α, β, δ) to guide the remaining gray wolves (ω) in the next hunt. Let the position of the prey p be denoted as , and the position of the l-th generation gray wolf individual be X(t), then:

[0128] S = |WX p (l)-X(l)|

[0129] X(l+1)=X p (l)-M·S

[0130] In the formula, S is the distance parameter, representing the relative distance between the individual and the prey. A and W are random weight coefficients, M is the distance control parameter, M = 2mr1 - m, W = 2r2, where r1 and r2 are random numbers between [0,1], and m is the distance control factor.

[0131] m decreases linearly from 2 as the number of iterations increases. β For values ​​as low as 0, the expression is as follows:

[0132]

[0133] In the formula, L represents the maximum number of iterations.

[0134] In a gray wolf pack, α, β, and δ wolves are relatively close to the prey and guide ω wolves to approach the prey based on the position of the alpha wolf. The mathematical model for an individual gray wolf tracking the prey's position is as follows:

[0135]

[0136] In the formula, S α S β S δ Let X be the distance parameter between ω wolf and the leader wolf. α (l), X β (l), X δ (l) represents the position of the leader wolf, and W1, W2, and W3 are random weight coefficients.

[0137] Therefore, the mathematical model for the position update of ω wolf is:

[0138]

[0139] To optimize the speed and accuracy of the Grey Wolf algorithm in searching for and fitting signal parameters, the following improvements were made.

[0140] ① Dual-strategy mapping optimizes the initial population position. The initial population position in the Grey Wolf Algorithm (GWO) affects both optimization accuracy and search speed. Traditional GWO initialization positions are based on random distribution, which is not conducive to fast convergence to meet real-time requirements. The previous section used STFT to optimize the center frequency f of the echo signal. s Harmony τ s A rough identification was performed, and the dictionaries of the f and τ parameters were respectively named after f. s and τ s The optimal solution is most likely to be located at the center of the dictionary. Therefore, to accelerate population convergence and improve optimization accuracy, we utilize...

[0141] The Box-Muller transformation makes the initial population follow a normal distribution, concentrated near the center of the parameter subset υ1∈θ, υ1={f,τ}, with the following:

[0142]

[0143] In the formula A random number in (0,1) The individual location follows a normal distribution N(μ) θ ,σ).

[0144] Meanwhile, to improve the initial population diversity and accelerate the convergence speed, the parameter subset υ2∈θ,

[0145] Initialization is performed using a Logistic chaotic mapping:

[0146]

[0147] In the formula, This is a control parameter, and its value range is [0,4].

[0148] ② Dual-strategy distance control factor. In the distance control parameter M, the distance control factor m is a key parameter for balancing global and local searches in the GWO algorithm. When the distance control parameter |M|≥1, the individual performs a global search; when |M|≤1, the individual performs a local search. Previously, STFT preprocessing narrowed the search range of frequency and acoustic time parameters, and the Box-Muller transform strategy optimized the initial individual distribution. Therefore, to avoid individuals "overshooting" the optimal solution due to an excessively large |M|, this invention proposes a nonlinear distance control factor based on a logarithmic function, denoted by m1:

[0149]

[0150] In the formula, μ is the control parameter of the logarithmic function. The larger μ is, the more significant the decrease in m1 is in the early stage of iteration.

[0151] Meanwhile, to avoid individuals falling into local optima due to excessively rapid decreases in |M| during the search of amplitude, phase, and bandwidth parameters, a distance nonlinear control factor based on a cosine function is proposed, denoted by m2:

[0152]

[0153] In the formula, ξ is the control parameter of the cosine function. The larger ξ is, the smaller the decrease of m2 in the early stage of iteration.

[0154] ③ Leader Wolf Position Optimization Based on Gaussian Perturbation. In the Gaussian Wolf Wolves (GWO), the parameter W plays a crucial role in updating individual positions, providing random weights for the leader wolf's position. This helps improve the random search capability of the optimization process and avoids the algorithm getting trapped in local optima. To prevent premature convergence while considering both global and local search capabilities, this invention replaces the random coefficient W with a Gaussian perturbation to maintain population diversity.

[0155] W Gauss =(2r³-1)σ C

[0156] In the formula, r3 is a random number in the range [0,1], and σ c The standard deviation is denoted as .

[0157] Figure 2 The graph shows the variation curves of the distance control factor under different μ and ξ values ​​during 100 iterations. As can be seen from the graph, the nonlinear distance control factor m1 decreases rapidly in the early stages of iteration, enhancing local search capability and improving optimization accuracy. m2 decreases more slowly in the early stages of iteration, enhancing global search capability and accelerating convergence. It is worth noting that when the population size is large, the algorithm possesses stronger global search capability; therefore, μ should be appropriately increased to accelerate the transition from global search to refined local search. Simultaneously, to improve search efficiency, ξ should be relatively small to avoid insufficient search accuracy due to continued global search in the later stages of iteration.

[0158] The specific process of step 3 is as follows:

[0159] Step 3.1: Set dictionary atomic parameters The gray wolf in the gray wolf algorithm represents a set of dictionary atomic parameters, where each gray wolf represents a set of dictionary atomic parameters, and the minimum ||y(t) - Dc|| is set. 2 Let be the fitness function. The first three gray wolves with the best fitness are selected as leader wolves (α, β, δ wolves), and the remaining wolves are ω wolves.

[0160] Step 3.2: Initialize the population size Q and individual position x using a two-strategy mapping. ij i = 1, 2, ..., Q, j = 1, 2, 3, 4, 5, initialize the iteration counter k2 = 1;

[0161] Step 3.3: Based on the optimization process in Step 3.1, update the position of the individual using a dual-strategy control factor and Gaussian perturbation;

[0162] Step 3.4: k2 = k2 + 1;

[0163] Step 3.4: If the number of iterations reaches the maximum value, return the optimal parameters; otherwise, return to step 3.3.

[0164] If the ultrasonic signal acquisition length is 2100 points, the standard t of the cable insulation layer at the measurement location... PVC =0.89μs. Figure 4 The results are the fitting results of the proposed algorithm for the ultrasonic thickness measurement signals of cable insulation layers with added Gaussian white noise of different intensities. Figure 4 (a) is the echo signal when the cable has not shifted (position 1), with no significant phase change. Figure 4 (b) is the echo signal when the cable deviates to its vertical limit; the redundant noise is significantly increased. Figure 4 (c) shows the echo signal at the horizontal limit offset, where both the echo amplitude and phase change significantly. It is evident that the proposed algorithm achieves accurate fitting under varying noise intensities, demonstrating good robustness. Even when the signal is severely distorted due to interference ( Figure 4 (b)) can still effectively fit signals that contain true echo characteristics.

[0165] 4. The acoustic time difference is calculated by performing calculations on the fitted echo signal based on the optimized echo model and the improved Grey Wolf algorithm.

[0166] The acoustic time difference t, which characterizes the thickness of the cable insulation layer, was calculated. TODA :

[0167] t TODA =τ p -τ p-1

[0168] In the formula τ p τ p-1 Let p and p-1 represent the acoustic times of the fitted echo signals, respectively, where p = 2, 3, 4, ..., n.

[0169] To evaluate the accuracy of the algorithm's thickness estimation, the average error of thickness estimation is defined as follows:

[0170]

[0171] In the formula, N represents the number of measurement locations. PVC The longitudinal wave velocity is for PVC material. This is the estimated acoustic time difference of the cable at position n.

[0172] Table 1 shows the average thickness estimation errors of the peak method, threshold method, cross-correlation (CC) method, ABC-MP, GWO-MP, and STFT-IGWO-MP under noise-free and artificially introduced noise conditions. As shown in Table 1, traditional methods exhibit significant thickness estimation errors in noisy environments. For the test case, the average error of the threshold method exceeds 50 μm, making it unsuitable for accurately characterizing the cable insulation thickness under vibration. When signal characteristics change significantly, traditional Time-of-Flight (ToF) estimation methods fail to effectively adapt to nonlinear changes, resulting in large thickness estimation deviations. CC detection, based on signal similarity, maintains good detection accuracy under interference, but the thickness estimation error increases when the echo has a phase change. The algorithm proposed in this invention demonstrates excellent performance in acoustic systems with dispersion and phase shift, maintaining excellent stability even under strong interference environments, with a maximum thickness estimation error of 4.1 μm.

[0173] Table 1. T values ​​for different algorithms under noise conditions error (Unit: μm)

[0174]

[0175] To evaluate the performance advantage of this invention compared to existing algorithms, the thickness relative error ratio is defined as:

[0176]

[0177] In the formula, G / S represents the traditional algorithm or search algorithm, and minT error,G / S T represents the minimum thickness estimation error for traditional methods or search-based algorithms. error,M To address the thickness estimation error in the algorithm.

[0178] Table 2. Thickness Relative Error Ratio T G / S

[0179]

[0180] As shown in Table 2, the proposed algorithm has better thickness estimation accuracy than other existing algorithms and has good practical value.

[0181] Matters not covered in this invention are common knowledge.

[0182] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A rapid estimation method for ultrasonic thickness measurement of insulation layer in cables with large curvature, characterized in that: The method includes the following steps: Step 1: Select a mathematical model of the Gabor function characteristics to fit the echo signal; Step 2: Optimize the parameter range of the echo model based on the short-time Fourier transform; Step 3: Design an improved Grey Wolf algorithm to search for optimal echo parameters; Step 4: Calculate the acoustic time difference by performing calculations on the fitted echo signal based on the optimized echo model and the improved Grey Wolf algorithm.

2. The rapid estimation method for ultrasonic thickness measurement of insulation layer of large curvature cable according to claim 1, characterized in that: The specific process of step 1 is as follows: The echo signal was fitted using the Gabor function: In the formula, t represents time, θ represents the parameter set of the echo model, β represents amplitude, α represents bandwidth, τ represents acoustic time, and f c For the center frequency, For phase; The cable insulation layer with a total duration of T is over The acoustic thickness signal y(t) is expressed as: In the formula, g p (θ p ;t) is the p-th Gabor function echo signal, where p is a positive integer, and ε1(t) and ε2(t) are Gaussian white noise and redundant clutter caused by curvature, respectively; To obtain the set of fitting parameters θ, the signal is decomposed into a linear combination of an overcomplete dictionary based on the matching pursuit algorithm, that is, the signal y(t) is compressed and approximately fitted as follows: Where y(t) is the original signal, For the fitted signal, c = (c1, c2, ..., c M ) T Let J be the coefficient vector, representing the weight of each atom, J be the number of selected non-zero coefficients (i.e., sparsity), M be the total number of time-series signals, and D ∈ R. M×N For an overcomplete dictionary, and D = [d1, d2, ..., dn], ... M ], where N is a complete dictionary combination.

3. The rapid estimation method for ultrasonic thickness measurement of insulation layer of large curvature cable according to claim 2, characterized in that: The specific process of step 2 is as follows: After obtaining the original signal y(t), the signal is multiplied by a window function w(t) and a complex exponential factor to obtain the frequency domain representation of the corresponding signal. The signal spectrum Y(τ) obtained after short-time Fourier transform is then calculated. i ,f k )for: In the formula, τ i f is the center time of analysis for the short-time Fourier transform. k To analyze the frequency, where t is time, by analyzing Y(τ) i ,f k The absolute value can be used to calculate the signal at time τ. i and frequency f k The energy below; Because the cable insulation layer is a viscoelastic material, the high-frequency components of the ultrasonic signal attenuate during transmission, making the echo signal frequency unpredictable. However, the transducer center frequency parameter f0 is known. Therefore, a search is performed based on the transducer center frequency characteristics, i.e., the spectral energy near f0, in the spectrum Y(τ) i ,f k In the context of signal echoes, the absolute value of a local maximum within a specific frequency range is selected to represent the presence of signal echoes in the corresponding region. The absolute value of this local maximum is: In the formula, f s τ is the frequency with the highest energy in the spectrum. s f s The corresponding time, Δf is the frequency search range, which is determined by prior knowledge; Therefore, the sound-time dictionary τ d The range of values ​​for is: In the formula, τ ρ For time-based search parameters, To define the upper and lower limits of the search; Frequency dictionary f d The range of values ​​for is: In the formula, and These are the upper and lower limits of the frequency dictionary, respectively, and δ is the frequency control coefficient. The value of the control coefficient depends on the solution resolution in the short-time Fourier transform. For phase range optimization, for τ s The signal y(τ) at time t s Using central difference differentiation, the signal at τ is obtained based on the signal amplitude and gradient. s Phase characteristics at time: Due to noise, the phase is uncertain; only its range can be determined. Therefore, the phase dictionary... The range of values ​​for is: When the echo signal noise is greater than the set value, the range of the phase dictionary is expanded. The range of the bandwidth dictionary and the range of the amplitude dictionary are set according to the intrinsic parameters of the transducer and the normalized amplitude of the signal. When a signal contains several echoes, a threshold is set on the spectral energy within the characteristic frequency domain to determine whether there are any remaining echo signals. If max|Y p (τ,f)| 2 <γ Threshold Then there is no echo, where |Y p (τ,f)| 2 To determine the power spectrum of the remaining signal after removing p echoes, γ Threshold This is the power spectrum threshold.

4. The rapid estimation method for ultrasonic thickness measurement of insulation layer of large curvature cable according to claim 1, characterized in that, The improvement to the Grey Wolf algorithm in step 3 is as follows: ① To initialize the population strategy using a dual-strategy mapping, and to accelerate population convergence and improve optimization accuracy, a Box-Muller transformation is used to ensure that the initial gray wolf population follows a normal distribution, concentrated near the center of the parameter subset υ1∈θ, υ1={f,τ}. Then: In the formula A random number in (0,1) The location of an individual gray wolf follows a normal distribution N(μ) θ ,σ); Meanwhile, to improve the initial population diversity and accelerate the convergence speed, the parameter subset υ2∈θ, Initialization is performed using a Logistic chaotic mapping: In the formula, This is a control parameter, and its value range is [0,4]. ② Dual-strategy distance control factor: To avoid exceeding the set value of the individual factor |M| and thus overshooting the optimal solution, a nonlinear distance control factor based on a logarithmic function is designed, denoted by m1: In the formula, μ is the control parameter of the logarithmic function. The larger μ is, the more obvious the decrease of m1 is in the early stage of the iteration. Meanwhile, to avoid individuals falling into local optima due to |M| decreasing faster than the set value during the search of amplitude, phase, and bandwidth parameters, a distance nonlinear control factor based on the cosine function is designed, denoted by m2: In the formula, ξ is the control parameter of the cosine function. The larger ξ is, the smaller the decrease of m2 in the early stage of iteration. ③ For leader wolf position optimization based on Gaussian perturbation, to prevent the algorithm from converging earlier than the set value, and to balance global and local search capabilities, Gaussian perturbation is used to replace the random coefficient W to maintain population diversity. W Gauss =(2r3-1)σ C In the formula, r3 is a random number in the range [0,1], and σ c The standard deviation is denoted as .

5. The rapid estimation method for ultrasonic thickness measurement of insulation layer of large curvature cable according to claim 1, characterized in that: The specific process of searching for the optimal echo parameters in step 3 is as follows: Step 3.1: Set dictionary atomic parameters The gray wolf in the gray wolf algorithm represents a set of dictionary atomic parameters, where each gray wolf represents a set of dictionary atomic parameters, and the minimum ||y(t) - Dc|| is set. 2 The fitness function is defined as follows: the three gray wolves with the best fitness are selected as leader wolves, and the remaining wolves are ω wolves. Step 3.2: Initialize the population size Q and individual position x using a two-strategy mapping. ij i = 1, 2, ..., Q, j = 1, 2, 3, 4, 5, initialize the iteration counter k2 = 1; Step 3.3: Based on the optimization process in Step 3.1, update the position of the individual using a dual-strategy control factor and Gaussian perturbation; Step 3.4: k2 = k2 + 1; Step 3.4: If the number of iterations reaches the maximum value, return the optimal parameters; otherwise, return to step 3.

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6. The rapid estimation method for ultrasonic thickness measurement of insulation layer of large curvature cable according to claim 1, characterized in that: The specific process of step 4 is as follows: Step 4.1: Initialization, acquire an ultrasound signal y of length T. (0) (t), initialize the fitting iteration counter k1 = 0, and initialize the approximate value and residual signal R (0) =y (0) (t); Step 4.2: Let the iterative fitting counter k1 = k1 + 1; Step 4.3: After fitting the signal, calculate the approximate value of the signal. and residual signal Step 4.4: Repeat step 4.2 until the residual signal power spectrum is below the threshold to obtain the best-fit signal. Set the number of times to obtain the best-fit signal to p. Step 4.5: Calculate the acoustic time difference t, which characterizes the thickness of the cable insulation layer. TODA : t TODA =t p -t p-1 In the formula τ p τ p-1 Let p and p-1 represent the acoustic times of the fitted echo signals, respectively, where p = 2, 3, 4, ..., n.

7. A rapid estimation method for ultrasonic thickness measurement of insulation layer of large curvature cable according to claim 4, characterized in that: In step 1, the reconstructed ultrasonic signal is approximated by the following formula:

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