Material crack prediction method, system and equipment fused with damage factors and medium

Abstract

The invention relates to the technical field of structure detection, in particular to a damage factor fused material crack prediction method, system, equipment and medium, firstly, multi-path and multi-frequency ultrasonic guided wave signals of a composite material structure to be detected are obtained, and multiple damage factors in a time domain and a frequency domain are extracted respectively; performing weighted fusion on the multiple damage factors by using a principal component analysis method to obtain a comprehensive damage factor; constructing a multi-task Gaussian process regression model adopting a joint kernel function, wherein the joint kernel function comprises an input kernel for representing the similarity of input features and a task kernel for representing the similarity between tasks; and finally, inputting the comprehensive damage factor into the model, and outputting a crack length predicted value and a confidence interval thereof. According to the method, through feature fusion and multi-task joint modeling, the problem of poor generalization ability under small sample and cross-regional working conditions in the prior art is effectively solved, high-precision prediction and uncertainty quantification of crack propagation are realized, and the reliability of structural health monitoring is improved.

Description

Technical Field

[0001] This invention relates to the field of structural testing technology, and in particular to a method, system, device and medium for predicting material cracks by incorporating damage factors. Background Technology

[0002] In rail transit systems, critical components such as car bodies and bogies are subjected to vibration and impact loads over long periods of time, making them highly susceptible to cracks that can gradually propagate. The appearance of cracks not only reduces the overall strength and stiffness of the structure but may also lead to catastrophic failures, seriously threatening the operational safety of trains.

[0003] In addition, the visual inspection and traditional non-destructive testing (such as ultrasonic C-scan and X-ray inspection) commonly used in existing technologies have problems such as low efficiency, poor real-time performance, and difficulty in covering large areas. Although the imaging method based on ultrasonic guided waves can intuitively reflect the location and morphology of cracks, it is not accurate enough in quantitative prediction of crack length and has high computational cost, which limits its engineering applicability.

[0004] Meanwhile, existing technologies also attempt to apply Gaussian processes to structural health monitoring and quantitative assessment of fatigue cracks. Although these methods consider the uncertainty of time-varying variance, they still lack integration with guided wave damage signals and rely on a large amount of experimental data. When the sample size is insufficient, they will face performance degradation. Although this method can provide predicted values, it cannot provide prediction intervals, which reduces the engineering reference value of the model. Summary of the Invention

[0005] The main objective of this invention is to provide a material crack prediction method that integrates damage factors, aiming to solve the problems of existing methods lacking integration with multi-path and multi-frequency guided wave signals, poor adaptability to small samples and cross-regional working conditions, and insufficient uncertainty quantification.

[0006] To achieve the above objectives, the present invention provides a material crack prediction method incorporating damage factors, the method comprising the following steps: Acquire the ultrasonic guided wave signal of the composite material structure under test in its current state; The ultrasonic guided wave signal is preprocessed to extract various damage factors in the time domain and frequency domain, respectively; The multiple damage factors under different paths and frequencies are weighted and fused according to principal component analysis to obtain a comprehensive damage factor. A multi-task Gaussian process regression model is constructed, wherein the multi-task Gaussian process regression model adopts a joint kernel function, which includes an input kernel for characterizing the similarity of input features and a task kernel for characterizing the similarity between tasks; The comprehensive damage factor is input into the multi-task Gaussian process regression model, and the predicted crack length and its confidence interval of the composite material structure under test are output according to the multi-task Gaussian process regression model.

[0007] Optionally, the multiple damage factors include: time-domain amplitude damage factor, frequency-domain amplitude damage factor, time-domain energy damage factor, and frequency-domain energy damage factor; The time-domain amplitude impairment factor is obtained by calculating the maximum absolute value of the difference between the time-domain reference signal and the time-domain signal in the current state, and dividing it by the maximum absolute value of the time-domain reference signal. The frequency domain amplitude impairment factor is obtained by calculating the maximum absolute value of the difference between the frequency domain reference signal and the frequency domain signal in the current state, and dividing it by the maximum absolute value of the frequency domain reference signal. The time-domain energy damage factor is obtained by calculating the square integral of the difference between the time-domain reference signal and the time-domain signal in the current state, and dividing it by the square integral of the time-domain reference signal. The frequency domain energy impairment factor is obtained by calculating the square integral of the difference between the frequency domain reference signal and the frequency domain signal in the current state, and then dividing it by the square integral of the frequency domain reference signal.

[0008] Optionally, the weighted fusion of the multiple damage factors under different paths and frequencies based on principal component analysis includes the following steps: Multiple damage factors of different paths and frequencies under several sample lengths are extracted, a data matrix is ​​constructed, and the data matrix is ​​standardized. Calculate the covariance matrix of the standardized data matrix, and perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalue matrix and eigenvector matrix; Based on the magnitude of the cumulative contribution rate, select the first few principal components and construct a projection matrix composed of the corresponding eigenvectors; The standardized data is projected onto the principal component space to obtain the principal component scores.

[0009] Optionally, after obtaining the principal component scores, the principal component scores are weighted and fused using the variance contribution rate of the principal components as weights to obtain the comprehensive damage factor.

[0010] Optionally, the joint kernel function is composed of the Hadamard product of the input kernel and the task kernel.

[0011] Optionally, the task kernel is constructed based on the cosine similarity between principal components. The specific process includes: calculating the dot product of the principal component components of different tasks and dividing it by the product of the moduli of their respective principal component components to characterize the similarity of the fused features between different tasks.

[0012] Optionally, the step of outputting the predicted crack length and its confidence interval of the composite material structure under test based on the multi-task Gaussian process regression model includes the following steps: The crack length prediction is calculated based on the posterior mean formula of multi-task Gaussian process regression. The prediction variance is calculated based on the posterior variance formula of multi-task Gaussian process regression, and a 95% confidence interval is determined based on the prediction variance as the range of uncertainty of the prediction result.

[0013] To achieve the above objectives, the present invention also provides a prediction system, the system comprising: A data acquisition module is used to acquire the ultrasonic guided wave signal of the composite material structure under test in its current state. The feature extraction module is used to preprocess the ultrasonic guided wave signal and extract multiple damage factors in the time domain and frequency domain, respectively. The feature fusion module is used to perform weighted fusion of the multiple damage factors under different paths and frequencies according to the principal component analysis method to obtain a comprehensive damage factor. The prediction and evaluation module is used to construct a multi-task Gaussian process regression model. The multi-task Gaussian process regression model adopts a joint kernel function, which includes an input kernel for characterizing the similarity of input features and a task kernel for characterizing the similarity between tasks. The prediction and evaluation module is also used to input the comprehensive damage factor into the multi-task Gaussian process regression model, and output the predicted crack length of the composite material structure under test and its confidence interval according to the multi-task Gaussian process regression model.

[0014] To achieve the above objectives, the present invention also provides a computer device, which includes a memory and a processor, wherein the memory stores a computer program and the processor executes the computer program to implement the above-described method.

[0015] To achieve the above objectives, the present invention also provides a computer-readable storage medium storing a computer program, wherein a processor executes the computer program to implement the above-described method.

[0016] The beneficial effects that this invention can achieve are as follows: This invention provides comprehensive structural response data through multi-path detection. Addressing the issues of poor adaptability to small samples and cross-regional operating conditions, principal component analysis weighted fusion and a multi-task Gaussian process regression model design enhance the model's generalization ability under limited samples. By synchronously outputting predicted crack length values ​​and their confidence intervals, the invention quantifies prediction uncertainty, providing a reliable risk assessment basis for engineering decisions and overcoming the shortcomings of existing methods that only provide point estimates and lack uncertainty characterization. By deploying piezoelectric sensor arrays on the structural surface to acquire guided wave signals under multiple paths and frequencies, damage factor features in the time and frequency domains are extracted, and feature fusion is achieved based on principal component analysis. Subsequently, a multi-task Gaussian process regression model is used to predict crack propagation and quantify uncertainty, thereby achieving high-precision, small-sample, cross-regional prediction of cracks in rail transit structures. Attached Figure Description

[0017] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0018] Figure 1 This is a flowchart illustrating the method in Embodiment 1 of the present invention; Figure 2 This is a structural block diagram of the system in Embodiment 6 of the present invention; The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0019] 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 a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0020] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a specific posture. If the specific posture changes, the directional indication will also change accordingly.

[0021] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral part; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0022] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the meaning of "and / or" throughout the text includes three parallel solutions; for example, "A and / or B" includes solution A, solution B, or a solution where both A and B are satisfied simultaneously. Furthermore, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0023] To make the technical solution of the present invention clearer, the abbreviations and key terms in the present invention are explained and defined herein, wherein: SHM (Structural Health Monitoring): refers to a technical system that uses sensor networks, signal processing, and intelligent algorithms to monitor and assess the damage status of structures during service.

[0024] PZT (Lead Zirconate Titanate): A commonly used piezoelectric sensor material that can convert mechanical vibration signals into electrical signals and vice versa, and is widely used in ultrasonic guided wave excitation and reception.

[0025] Lamb wave (ultrasonic guided wave): a type of ultrasonic wave that propagates in plate-like structures. It has low energy attenuation, long propagation distance, and is sensitive to structural damage such as cracks and corrosion. It is often used in SHM (Structured Shock Measuring).

[0026] Damage Index (DI): A characterization measure extracted from guided wave signals in healthy and damaged states, used to quantitatively describe the degree of structural damage. This invention includes the following four types of damage factors: Temporal amplitude impairment factor: reflects the change in temporal signal amplitude as impairment occurs; Frequency domain amplitude impairment factor: reflects the change in spectral amplitude; Time-domain energy damage factor: reflects the change in time-domain signal energy as crack propagation occurs; Frequency domain energy impairment factor: reflects the change in the energy of the frequency domain signal.

[0027] PCA (Principal Component Analysis): A feature fusion and dimensionality reduction method that extracts high-variance principal components by calculating feature vectors and contribution rates, thereby removing redundancy and enhancing sensitive features.

[0028] ST-GPR (Single-task Gaussian Process Regression): A nonparametric modeling method based on Bayesian theory that performs regression prediction on data from a single task, providing the prediction mean and range of uncertainty.

[0029] MT-GPR (Multi-task Gaussian Process Regression): An extension of ST-GPR, it can model multiple related tasks simultaneously. By sharing hyperparameters or joint kernel functions, it improves modeling accuracy and generalization ability, and is particularly suitable for crack prediction under small sample conditions.

[0030] Confidence Interval (CI): An interval of prediction uncertainty given by probability statistics. It is usually expressed with a 95% confidence level, indicating the range of confidence of the predicted value within this interval.

[0031] Crack propagation refers to the process by which microcracks in a material or structure gradually develop and extend under service loads, and is one of the main causes of structural failure.

[0032] Fused Damage Index: A comprehensive damage feature after PCA weighted fusion, which can more stably and monotonically characterize the crack propagation trend, improving the accuracy and robustness of the prediction model. Example

[0033] Reference Figure 1 This embodiment provides a material crack prediction method that incorporates damage factors, the method comprising the following steps: Acquire the ultrasonic guided wave signal of the composite material structure under test in its current state; The ultrasonic guided wave signal is preprocessed to extract various damage factors in the time domain and frequency domain, respectively; The multiple damage factors under different paths and frequencies are weighted and fused according to principal component analysis to obtain a comprehensive damage factor. A multi-task Gaussian process regression model is constructed, wherein the multi-task Gaussian process regression model adopts a joint kernel function, which includes an input kernel for characterizing the similarity of input features and a task kernel for characterizing the similarity between tasks; The comprehensive damage factor is input into the multi-task Gaussian process regression model, and the predicted crack length and its confidence interval of the composite material structure under test are output according to the multi-task Gaussian process regression model.

[0034] It should be noted that in the field of structural health monitoring of rail transit, the existing ultrasonic guided wave detection method has failed to achieve systematic integration of multi-path and multi-frequency signal characteristics, resulting in a single-dimensional defect in the damage feature extraction process. At the same time, the traditional Gaussian process regression model, under small sample conditions, lacks a task correlation modeling mechanism and cannot effectively adapt to cross-regional working condition changes. Moreover, the prediction results only provide point estimates and lack probabilistic uncertainty characterization, which fundamentally restricts the engineering reference value of crack length prediction. The above directly weakens the reliability of structural safety assessment and makes it difficult for the monitoring system to cope with the dual challenges brought about by signal feature distribution drift and data scarcity in actual working conditions.

[0035] Based on the above problems, this embodiment first acquires the ultrasonic guided wave signal of the composite material structure under test in its current state. It utilizes the wide coverage characteristics of ultrasonic guided waves to achieve multi-path detection, providing comprehensive structural response data for subsequent analysis. This solves the limitation of traditional methods in real-time monitoring of large areas. After filtering and denoising preprocessing, multiple damage factors in the time and frequency domains of the ultrasonic guided wave signal are extracted. By synchronously analyzing the dynamic characteristics and energy distribution of the signal, damage information is captured from two dimensions, avoiding the insufficient sensitivity of a single feature to complex crack morphology. Furthermore, it enhances the feature robustness for the differentiated responses of multi-frequency signals.

[0036] Furthermore, based on principal component analysis, multiple damage factors under different paths and frequencies are weighted and fused. The specific process includes standardizing the data matrix, calculating the covariance matrix, performing eigenvalue decomposition to obtain eigenvalues ​​and eigenvectors, selecting principal components based on the cumulative contribution rate and constructing a projection matrix, and finally projecting the data onto the principal component space to obtain the principal component score. The principal component scores are then weighted and fused based on the variance contribution rate, thereby eliminating redundant correlations between multi-path and multi-frequency factors, highlighting the contribution of key damage features, and enabling the comprehensive damage factor to adapt to feature-dominant changes in small sample scenarios.

[0037] It should also be noted that the comprehensive damage factor significantly improves the representation efficiency of cross-condition data. Specifically, the constructed multi-task Gaussian process regression model adopts a joint kernel function, which is composed of the Hadamard product of the input kernel matrix and the task kernel matrix. The input kernel is used to represent the similarity of input features, and the task kernel is used to represent the similarity between tasks. The task kernel is constructed based on the cosine similarity between principal components. The similarity of the fused features between tasks is represented by calculating the dot product of the principal component components of different tasks and dividing it by the product of the moduli of their respective principal component components. This design enables the model to mine shared patterns between tasks using limited samples.

[0038] In this embodiment, after the comprehensive damage factor is input into the model, the predicted crack length and its confidence interval are output. Specifically, the predicted value is calculated using the posterior mean formula, the predicted variance is calculated using the posterior variance formula, and the 95% confidence interval is determined based on the predicted variance, thereby quantifying the prediction uncertainty within a probabilistic framework. This effectively solves the problem of lacking integration with multi-path and multi-frequency guided wave signals in material crack prediction, providing comprehensive structural response data through multi-path detection. Addressing the issue of poor adaptability to small samples and cross-regional operating conditions, the design of a principal component analysis weighted fusion and a multi-task Gaussian process regression model improves the model's generalization ability under limited samples. By synchronously outputting the predicted crack length and its confidence interval, the prediction uncertainty is quantified, providing a reliable risk assessment basis for engineering decisions and overcoming the shortcomings of existing methods that only provide point estimates and lack uncertainty characterization. By deploying a piezoelectric sensor array on the structural surface to acquire guided wave signals under multi-path and multi-frequency conditions, damage factor features in the time and frequency domains are extracted, and feature fusion is achieved based on principal component analysis (PCA). Subsequently, a multi-task Gaussian process regression model is used to predict crack propagation and quantify uncertainty, thereby achieving high-precision, small-sample, cross-regional prediction of cracks in rail transit structures.

[0039] Example 2

[0040] In this embodiment, the multiple damage factors include: time-domain amplitude damage factor, frequency-domain amplitude damage factor, time-domain energy damage factor, and frequency-domain energy damage factor; The time-domain amplitude impairment factor is obtained by calculating the maximum absolute value of the difference between the time-domain reference signal and the time-domain signal in the current state, and dividing it by the maximum absolute value of the time-domain reference signal. The frequency domain amplitude impairment factor is obtained by calculating the maximum absolute value of the difference between the frequency domain reference signal and the frequency domain signal in the current state, and dividing it by the maximum absolute value of the frequency domain reference signal. The time-domain energy damage factor is obtained by calculating the square integral of the difference between the time-domain reference signal and the time-domain signal in the current state, and dividing it by the square integral of the time-domain reference signal. The frequency domain energy impairment factor is obtained by calculating the square integral of the difference between the frequency domain reference signal and the frequency domain signal in the current state, and then dividing it by the square integral of the frequency domain reference signal.

[0041] Understandably, to comprehensively acquire health status information of the composite material structure under test, this embodiment first deploys a piezoelectric sensor (PZT) array on the structure surface. The sensor array forms multiple excitation-reception channels. For example, when sensor A is used as the excitation source, sensors B, C, and D act as receivers, forming paths AB, AC, and AD, respectively. This multi-path design can cover a large area, ensuring that the crack, regardless of its location, will cause signal distortion on at least one path. Considering that cracks of different lengths have different sensitivities to guided waves of different wavelengths, this embodiment uses five-cycle Hanning window modulated sine waves with different center frequencies (e.g., 50kHz, 100kHz, 200kHz, etc.) as excitation signals. Through multi-frequency scanning, blind spots at a single frequency can be effectively avoided.

[0042] In some preferred embodiments, the acquired raw guided wave signals often contain environmental noise and electromagnetic interference, requiring the following preprocessing: Denoising: Use wavelet thresholding or bandpass filters to filter out environmental noise; Normalization: Eliminates the impact of differences in sensor coupling efficiency; Envelope Extraction and Frequency Domain Conversion: The envelope of the time-domain signal is extracted using the Hilbert transform, and the time-domain signal is converted into a frequency-domain signal using the Fast Fourier Transform (FFT).

[0043] It is also understandable that the time-domain amplitude impairment factor satisfies the expression: In the formula, The time-domain reference signal represents the structural health status; The difference between the two represents the time-domain signal under the current damage state, which is the scattering signal of the crack damage in the time domain.

[0044] For the time-domain amplitude impairment factor, the following expression is satisfied: In the formula, A frequency domain reference signal representing a structurally healthy state; The difference between the two represents the frequency domain signal under the current damage state, and is the scattering signal caused by the damage in the frequency domain.

[0045] For the time-domain amplitude impairment factor, the following expression is satisfied: In the formula, The time-domain reference signal represents the structural health status; The difference between the two represents the time-domain signal under the current damage state, which is the scattering signal of the crack damage in the time domain.

[0046] For the time-domain amplitude impairment factor, the following expression is satisfied: ; In the formula, A frequency domain reference signal representing a structurally healthy state; The difference between the two represents the frequency domain signal under the current damage state, and is the scattering signal caused by the damage in the frequency domain.

[0047] Example 3: In this embodiment, the weighted fusion of multiple damage factors under different paths and frequencies based on principal component analysis includes the following steps: Multiple damage factors of different paths and frequencies under several sample lengths are extracted, a data matrix is ​​constructed, and the data matrix is ​​standardized. Calculate the covariance matrix of the standardized data matrix, and perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalue matrix and eigenvector matrix; Based on the magnitude of the cumulative contribution rate, select the first few principal components and construct a projection matrix composed of the corresponding eigenvectors; The standardized data is projected onto the principal component space to obtain the principal component scores.

[0048] Understandably, the above steps involve extracting multiple damage factors with different sample lengths, paths, and frequencies, constructing a data matrix, and standardizing the data to ensure comparison at a uniform scale. Then, the covariance matrix of the standardized data is calculated and eigenvalue decomposition is performed. Based on the intrinsic correlation between damage factors, the data structure is revealed, and eigenvalues ​​and eigenvectors are obtained. Next, the top principal components are selected based on the cumulative contribution rate to construct a projection matrix, achieving dimensionality compression to retain key information and eliminate noise and weakly correlated factors. Finally, the standardized data is projected onto the principal component space to obtain principal component scores. These scores serve as the basis for weighted fusion, representing decorrelation and importance-ranked feature representations. This systematically optimizes the fusion process of multi-path, multi-frequency damage factors, effectively addressing the problems of high-dimensional data sensitivity to noise and poor adaptability to small samples.

[0049] In this embodiment, after obtaining the principal component scores, the principal component scores are weighted and fused using the variance contribution rate of the principal components as weights to obtain the comprehensive damage factor.

[0050] Understandably, the above steps establish a direct correlation between the importance of principal components and the fusion weights by using the variance contribution rate of the principal components as weights to weight the principal component scores. Since the variance contribution rate quantifies the degree of contribution of each principal component to data variation, using it as a weight ensures that principal components with high contribution rates are given a larger proportion during the fusion process, thus prioritizing the retention of feature components that significantly affect the damage state. This process effectively suppresses noise interference that may be contained in principal components with low contribution rates and avoids the problem of equal weighting of features across dimensions caused by simple averaging. On this basis, the weighted fusion operation achieves optimized integration of multi-dimensional damage information, enabling the comprehensive damage factor to more accurately characterize the actual damage state of the material. Especially under small sample conditions, it significantly enhances the model's robustness to noise, providing a highly reliable input basis for subsequent crack length prediction.

[0051] It is also understandable that, for damage signals of the same length but different paths and excitation frequencies, PCA analysis is used to calculate the principal component contribution rate of different damage factors for each path and under different frequency conditions. The top three original damage factors with the largest contribution rates are then weighted and fused into a single comprehensive damage factor. This comprehensive factor exhibits stronger monotonicity and can more stably characterize crack propagation. The above can be specifically divided into the following steps: Sub-step 1, extraction Different paths and frequencies for each sample length. Each damage factor is used to construct a data matrix. The data matrix satisfies: ;in, Indicates the first The first sample One damage factor; Sub-step 2, data standardization. Because PCA is sensitive to data scale, it is necessary to standardize the data. Standardize to satisfy the expression: ; in, and yes Column (i.e., the extracted first column) The mean and standard deviation of each damage factor.

[0052] Sub-step 3: Calculate the covariance matrix, which is the standardized data matrix. covariance matrix The covariance matrix satisfies the expression: ; Sub-step 4, eigenvalue decomposition, For covariance matrix Perform eigenvalue decomposition: ;in: It is a diagonal matrix, where the diagonal elements are eigenvalues. , It is an eigenvector matrix, each column It corresponds eigenvectors.

[0053] Sub-step 5: Select principal components, choosing the top ones based on the cumulative contribution rate of eigenvalues. Principal components: Projection matrix It consists of K eigenvectors: ; Sub-step 6: Calculate the principal component scores and standardize the data. Projecting onto the principal component space yields the principal component scores. ; Sub-step 7, weighted fusion Using the variance of the principal components as weights, the principal component scores in step 6 are weighted and fused to obtain the comprehensive damage factor. : ; where weight For the first The variance contribution rate of each principal component is: Among them, weight For the first The variance contribution rate of each principal component: ; The final fusion damage factor is: .

[0054] Example 4: In this embodiment, the joint kernel function is composed of the Hadamard product of the input kernel and the task kernel.

[0055] Understandably, when constructing a multi-task Gaussian process regression model, the input kernel matrix is ​​first calculated to characterize the similarity of the comprehensive damage factor as an input feature, while the task kernel matrix is ​​simultaneously calculated to characterize the correlation between different prediction tasks (such as crack length prediction under different waveguide paths or frequencies). Subsequently, the input kernel matrix and the task kernel matrix are element-wise combined through the Hadamard product to form a joint kernel function, which is used to define the covariance structure during model training. This mechanism allows the high-dimensional similarity information of the input features and the dynamic correlation characteristics between tasks to be preserved synchronously. Thus, in the prediction stage, when the comprehensive damage factor is input into the model, the joint kernel function can guide the model to accurately model the nonlinear mapping relationship between the damage factor and the crack length, and provide a reliable basis for posterior variance calculation, ultimately outputting the predicted crack length value and its confidence interval.

[0056] In this embodiment, the task kernel is constructed based on the cosine similarity between principal components. The specific process includes: calculating the dot product of the principal component components of different tasks and dividing it by the product of the moduli of their respective principal component components to characterize the similarity of the fused features between different tasks.

[0057] Understandably, based on the above steps, by combining the construction of the task kernel matrix with principal component analysis, the task kernel matrix is ​​constructed according to the cosine similarity between principal components, ensuring that the similarity measurement focuses on the main variation direction of the data rather than the original noise. By calculating the dot product of the principal component components of different tasks and dividing by the product of the moduli of their respective principal component components, the mathematical expression of cosine similarity is realized. This process uses the dot product to capture the consistency of feature directions, and at the same time, normalization is performed through the product of moduli, eliminating the interference of feature scale differences on similarity calculation. This construction method enables the task kernel matrix to adaptively represent the geometric relationship of different tasks in the dimensionality-reduced feature space. Especially in small sample scenarios, the principal component components, as a condensed representation of the key features of the data, significantly improve the robustness of task similarity estimation.

[0058] It is also understandable that, due to the anisotropy of composite materials, even under the same experimental conditions, the response data of different monitoring areas or structures may exhibit similar but not entirely consistent distributions. These data often show some correlation, but traditional single-task Gaussian process regression (ST-GPR) models often treat each monitoring path or structure as an isolated task, making it difficult to effectively utilize the potential information correlations between different tasks. Furthermore, the irreversible damage caused by real damage to the structure easily leads to performance degradation and insufficient generalization ability of the model under data scarcity. Based on this, in the MT-GPR provided by this invention, it is assumed that... There are 3 tasks, each containing several samples, and the input data is defined as follows: The corresponding output labels are , of which Each sample belongs to the task .

[0059] The core idea of ​​MT-GPR lies in constructing a joint kernel function. This joint kernel is used to simultaneously represent input feature similarity and task similarity; it consists of an input kernel. With the mission core The Hadamard (elemental) product is composed of: ; in, Represents the Hadmard product; Given the input kernel matrix and ; For the task kernel matrix and , It is an identity matrix.

[0060] The input kernel used in this embodiment is the squared exponential kernel (RBF): ; in, The variance of the output amplitude; The feature length scale is used to control the degree to which the input distance affects the similarity.

[0061] Task kernel function To model the similarity relationships between tasks, the task kernel selected in this embodiment is constructed based on the cosine similarity between PCA principal components, denoted as: ; in, For the task Principal component components; For the task With the task The principal component angle can be used to measure the similarity of fusion features between different tasks, so as to achieve more reasonable inter-task collaboration.

[0062] Let the test set input be The prediction formula for multi-task Gaussian process regression is as follows: ; ; in, The posterior mean is... For posterior variance, This represents the joint kernel matrix between the test samples and the training samples. This represents the joint kernel matrix of the test sample itself.

[0063] Example 5: In this embodiment, the step of outputting the predicted crack length and its confidence interval of the composite material structure under test based on the multi-task Gaussian process regression model includes the following steps: The crack length prediction is calculated based on the posterior mean formula of multi-task Gaussian process regression. The prediction variance is calculated based on the posterior variance formula of multi-task Gaussian process regression, and a 95% confidence interval is determined based on the prediction variance as the range of uncertainty of the prediction result.

[0064] Understandably, the above steps first calculate the predicted crack length using the posterior mean formula. This step, based on a Bayesian inference framework of multi-task Gaussian process regression, integrates the posterior distribution information of input features and inter-task correlations, ensuring that the predicted value reflects the true trend of structural damage under small sample conditions. Subsequently, the prediction variance is calculated using the posterior variance formula. This formula not only considers the noise impact of the input data but also incorporates the multi-task similarity represented by the task kernel function, thus comprehensively quantifying the uncertainty of the prediction. Finally, the prediction variance is converted into a 95% confidence interval, directly providing a reliability range. This mechanism enables the prediction to not only output point estimates but also systematically define the uncertainty boundary, effectively solving the problem of insufficient prediction reliability assessment.

[0065] Example 6: As attached Figure 2 As shown, this embodiment provides a prediction system, the system comprising: A data acquisition module is used to acquire the ultrasonic guided wave signal of the composite material structure under test in its current state. The feature extraction module is used to preprocess the ultrasonic guided wave signal and extract multiple damage factors in the time domain and frequency domain, respectively. The feature fusion module is used to perform weighted fusion of the multiple damage factors under different paths and frequencies according to the principal component analysis method to obtain a comprehensive damage factor. The prediction and evaluation module is used to construct a multi-task Gaussian process regression model. The multi-task Gaussian process regression model adopts a joint kernel function, which includes an input kernel for characterizing the similarity of input features and a task kernel for characterizing the similarity between tasks. The prediction and evaluation module is also used to input the comprehensive damage factor into the multi-task Gaussian process regression model, and output the predicted crack length of the composite material structure under test and its confidence interval according to the multi-task Gaussian process regression model.

[0066] It should be noted that by combining the extraction of time-domain and frequency-domain damage factors from multi-path and multi-band ultrasonic guided wave signals with principal component analysis and weighted fusion, and by adopting the joint kernel function design of a multi-task Gaussian process regression model, the problems of poor real-time performance, insufficient quantitative prediction accuracy, poor adaptability to small sample data, and inability to provide prediction intervals in existing crack prediction methods for composite material structures in rail transit are effectively solved, thus achieving the effect of improving prediction accuracy and reliability of engineering decisions.

[0067] Specifically, the data acquisition module achieves multi-path propagation characteristic coverage through a piezoelectric sensor array, ensuring the integrity of damage response data; the feature extraction module completes the decoupling of time-domain and frequency-domain features, comprehensively capturing the signal dynamic characteristics and energy distribution changes caused by crack propagation; the feature fusion module automatically allocates weights based on the variance contribution rate of the feature covariance matrix, eliminating redundant interference from multi-source features and enhancing adaptability in small-sample scenarios; the prediction and evaluation module constructs a joint kernel function through the Hadamard product of the input kernel and the task kernel, utilizes principal component cosine similarity to quantify the implicit correlation between tasks, significantly improving the generalization performance across regional working conditions, and outputs predicted values ​​and confidence intervals based on the Gaussian process posterior distribution, providing probabilistic decision-making basis for structural safety assessment. Through the above technical solutions, the system overcomes the shortcomings of traditional visual inspection and ultrasonic C-scan methods such as low efficiency and poor real-time performance, avoids the nonlinear shift problem of damage response caused by single-frequency guided wave signals under environmental changes, and effectively addresses the challenge of decreased model generalization ability caused by small-sample training data, enabling crack prediction results to have both high accuracy and uncertainty quantification capabilities.

[0068] In summary, the sorting and prediction processing logic of this invention can be divided into the following steps: Data acquisition and preprocessing: Based on the material properties and geometric characteristics of the structure under test, a sensor network covering the target area is constructed. To improve the portability, stability and design flexibility of the monitoring system, an intelligent interlayer with embedded PZT sensors is deployed on the surface of the structure to excite and receive Lamb wave signals carrying structural change information. The acquired data needs to be standardized and denoised before entering the model to ensure the accuracy and consistency of subsequent analysis.

[0069] Damage Factor Extraction: When a structure is damaged, its guided wave signal will change in terms of phase, energy, and amplitude. In order to effectively characterize the correlation between these changes and crack propagation length and reduce subsequent modeling costs, four typical damage factors are selected as inputs to the MT-GPR model: time-domain amplitude damage factor, frequency-domain amplitude damage factor, time-domain energy damage factor, and frequency-domain energy damage factor.

[0070] Damage Factor Fusion: Since each monitoring area contains multiple propagation paths, and different crack lengths have different sensitivities to excitation frequencies, damage factors exhibit information redundancy and differences across paths and frequencies. To enhance the damage-sensitive characteristics while suppressing the interference of irrelevant factors on the model, principal component analysis (PCA) is used to weightedly fuse multidimensional damage factors, resulting in a more comprehensive damage characteristic with stronger characterization capabilities.

[0071] Crack length prediction: Considering the influence of anisotropy in composite materials, even in the same specimen, the signals in different monitoring areas still differ. Therefore, the fusion damage factor of different areas is regarded as multiple related tasks and input into a multi-task Gaussian process regression model for joint modeling. This model can mine shared features between tasks, which not only improves the prediction accuracy and model generalization ability, but also effectively reduces the number of training samples required to train the model in the target area, thereby reducing the modeling cost and improving the feasibility of the model in practical applications.

[0072] Based on the above, this invention obtains ultrasonic guided wave signals under multiple paths and frequencies by arranging piezoelectric sheets on the surface of composite material structures in rail transit, and extracts damage factors such as time-domain amplitude, frequency-domain amplitude, time-domain energy and frequency-domain energy, and then performs feature fusion using the PCA method.

[0073] This allows the integrated damage factor to exhibit monotonic variation during crack propagation, enabling online real-time characterization of crack evolution without relying on manual inspection. Experimental results show that the fused damage factor curve has a high correlation with crack length growth, effectively improving the sensitivity of crack monitoring.

[0074] This invention addresses the shortcomings of existing methods that rely on large amounts of experimental data by introducing Multi-Task Gaussian Process Regression (MT-GPR). By utilizing the shared information of correlations between different monitoring paths, frequencies, or specimens, this approach achieves better prediction results with a smaller sample size compared to ordinary single-task Gaussian process regression models, demonstrating its better stability and applicability in small sample environments.

[0075] This invention utilizes the MT-GPR multi-task learning framework to jointly model the crack evolution process of different structures or different monitoring areas, and improves the generalization ability by sharing hyperparameters and kernel functions. It proves that it has strong transfer learning ability in multi-condition and multi-structure scenarios, and can be widely applied in actual rail transit structures.

[0076] This invention provides a predicted mean and a 95% confidence interval within the framework of a Gaussian process, enabling the prediction results to not only include point estimation but also credibility assessment capabilities. Based on the physical interpretation of the guided wave signal damage factor, this enhances the reference value of the prediction results in engineering applications.

[0077] In summary, the technical solution proposed in this invention can achieve real-time characterization, high-precision prediction, small-sample adaptability, cross-regional generalization ability, and reliable uncertainty quantification in the prediction of cracks in composite material structures of rail transit, effectively solving the shortcomings of existing technologies.

[0078] Example 7: Based on the same inventive concept as the foregoing embodiments, this embodiment provides a computer device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method.

[0079] Example 8: Based on the same inventive concept as the foregoing embodiments, this embodiment provides a computer-readable storage medium storing a computer program, and a processor executes the computer program to implement the above-described method.

[0080] In some embodiments, the computer-readable storage medium may be a memory such as FRAM, ROM, PROM, EPROM, EEPROM, flash memory, magnetic surface memory, optical disk, or CD-ROM; or it may be a device including one or any combination of the above-mentioned memories. The computer may be a variety of computing devices, including smart terminals and servers.

[0081] In some embodiments, executable instructions may take the form of a program, software, software module, script, or code, written in any form of programming language (including compiled or interpreted languages, or declarative or procedural languages), and may be deployed in any form, including as a standalone program or as a module, component, subroutine, or other unit suitable for use in a computing environment.

[0082] As an example, executable instructions may, but do not necessarily, correspond to files in a file system. They may be stored as part of a file that holds other programs or data, for example, in one or more scripts in a Hyper Text Markup Language (HTML) document, in a single file dedicated to the program in question, or in multiple collaborating files (e.g., a file that stores one or more modules, subroutines, or code sections).

[0083] As an example, executable instructions can be deployed to execute on a single computing device, or on multiple computing devices located in one location, or on multiple computing devices distributed across multiple locations and interconnected via a communication network.

[0084] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0085] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0086] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as read-only memory / random access memory, magnetic disk, optical disk) and includes several instructions to cause a multimedia terminal device (which may be a mobile phone, computer, television receiver, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0087] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A material crack prediction method incorporating damage factors, characterized in that, The method includes the following steps: Acquire the ultrasonic guided wave signal of the composite material structure under test in its current state; The ultrasonic guided wave signal is preprocessed to extract various damage factors in the time domain and frequency domain, respectively; The multiple damage factors under different paths and frequencies are weighted and fused using principal component analysis to obtain a comprehensive damage factor. A multi-task Gaussian process regression model is constructed, wherein the multi-task Gaussian process regression model adopts a joint kernel function, which includes an input kernel for characterizing the similarity of input features and a task kernel for characterizing the similarity between tasks; The comprehensive damage factor is input into the multi-task Gaussian process regression model, and the predicted crack length and its confidence interval of the composite material structure under test are output according to the multi-task Gaussian process regression model.

2. The material crack prediction method with fused damage factors as described in claim 1, characterized in that, The various damage factors include: time-domain amplitude damage factor, frequency-domain amplitude damage factor, time-domain energy damage factor, and frequency-domain energy damage factor; The time-domain amplitude impairment factor is obtained by calculating the maximum absolute value of the difference between the time-domain reference signal and the time-domain signal in the current state, and dividing it by the maximum absolute value of the time-domain reference signal. The frequency domain amplitude impairment factor is obtained by calculating the maximum absolute value of the difference between the frequency domain reference signal and the frequency domain signal in the current state, and dividing it by the maximum absolute value of the frequency domain reference signal. The time-domain energy damage factor is obtained by calculating the square integral of the difference between the time-domain reference signal and the time-domain signal in the current state, and dividing it by the square integral of the time-domain reference signal. The frequency domain energy impairment factor is obtained by calculating the square integral of the difference between the frequency domain reference signal and the frequency domain signal in the current state, and then dividing it by the square integral of the frequency domain reference signal.

3. The material crack prediction method with fused damage factors as described in claim 1, characterized in that, The weighted fusion of multiple damage factors under different paths and frequencies based on principal component analysis includes the following steps: Multiple damage factors of different paths and frequencies under several sample lengths are extracted, a data matrix is ​​constructed, and the data matrix is ​​standardized. Calculate the covariance matrix of the standardized data matrix, and perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalue matrix and eigenvector matrix; Based on the magnitude of the cumulative contribution rate, select the first few principal components and construct a projection matrix composed of the corresponding eigenvectors; The standardized data is projected onto the principal component space to obtain the principal component scores.

4. The material crack prediction method with fused damage factors as described in claim 3, characterized in that, After obtaining the principal component scores, the principal component scores are weighted and fused using the variance contribution rate of the principal components as weights to obtain the comprehensive damage factor.

5. The material crack prediction method with fused damage factors as described in claim 1, characterized in that, The joint kernel function is composed of the Hadamard product of the input kernel and the task kernel.

6. The material crack prediction method with fused damage factors as described in claim 5, characterized in that, The task kernel is constructed based on the cosine similarity between principal components. The specific process includes: calculating the dot product of the principal component components of different tasks and dividing it by the product of the moduli of their respective principal component components to characterize the similarity of the fused features between different tasks.

7. The material crack prediction method with fused damage factors as described in claim 1, characterized in that, The process of outputting the predicted crack length and its confidence interval of the composite material structure under test based on the multi-task Gaussian process regression model includes the following steps: The crack length prediction is calculated based on the posterior mean formula of multi-task Gaussian process regression. The prediction variance is calculated based on the posterior variance formula of multi-task Gaussian process regression, and a 95% confidence interval is determined based on the prediction variance as the range of uncertainty of the prediction result.

8. A prediction system, characterized in that, The system includes: A data acquisition module is used to acquire the ultrasonic guided wave signal of the composite material structure under test in its current state. The feature extraction module is used to preprocess the ultrasonic guided wave signal and extract multiple damage factors in the time domain and frequency domain, respectively. The feature fusion module is used to perform weighted fusion of the multiple damage factors under different paths and frequencies according to the principal component analysis method to obtain a comprehensive damage factor. The prediction and evaluation module is used to construct a multi-task Gaussian process regression model. The multi-task Gaussian process regression model adopts a joint kernel function, which includes an input kernel for characterizing the similarity of input features and a task kernel for characterizing the similarity between tasks. The prediction and evaluation module is also used to input the comprehensive damage factor into the multi-task Gaussian process regression model, and output the predicted crack length of the composite material structure under test and its confidence interval according to the multi-task Gaussian process regression model.

9. A computer device, characterized in that, The computer device includes a memory and a processor, wherein the memory stores a computer program and the processor executes the computer program to implement the method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, and the processor executes the computer program to implement the method as described in any one of claims 1-7.

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