A fatigue crack prediction method based on acoustic emission arrangement pattern
By using intermittent sampling and pattern feature extraction, combined with Pearson correlation coefficient and gradient descent method, the problem of difficult acoustic emission signal acquisition was solved, enabling fast and accurate prediction of fatigue crack propagation rate and reducing computational costs.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIHANG UNIV
- Filing Date
- 2023-10-11
- Publication Date
- 2026-05-29
AI Technical Summary
Existing technologies face difficulties in acquiring acoustic emission signals and suffer from low signal-to-noise ratios during fatigue processes. This results in complex and costly feature extraction processes based on deep learning, making it difficult to achieve efficient prediction of fatigue crack propagation rates.
Intermittent sampling was used to extract the arrangement pattern features of acoustic emission signals. Features were screened using Pearson correlation coefficient to establish a relationship model between crack propagation rate and arrangement pattern features. The gradient descent method was used to optimize the parameters and construct a crack propagation rate prediction model.
It achieves fast and accurate prediction of fatigue crack propagation rate in dynamic noise environment, reduces computing cost and improves prediction accuracy.
Smart Images
Figure CN117368330B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for predicting the fatigue crack propagation life of metal structures, and more particularly to a method for predicting the fatigue crack propagation life of metal structures based on acoustic emission signals. Background Technology
[0002] Fatigue failure is one of the main failure modes of engineering structures such as pressure vessels and aircraft structures. It accounts for over 80% of damage to automotive parts and approximately 60%–80% of material breakage in aerospace applications, posing a significant threat to all aspects of human life and production. Therefore, researching methods to predict the fatigue crack propagation rate of metallic materials is of paramount importance in mitigating these risks.
[0003] The detection and quantification of fatigue cracks are crucial for the safety and reliability of engineering structures. Traditionally, to avoid failure, non-destructive testing (NDT) techniques must be used for routine offline inspections of structures; however, this is a costly and time-consuming process. Therefore, structural health monitoring technology has been developed as an alternative to NDT techniques for online monitoring. The structural health monitoring process enables continuous or on-demand detection and diagnosis of damage, thereby facilitating predictive maintenance of structures.
[0004] Acoustic emission (AE) technology is a structural health monitoring technique that enables real-time detection of defect growth using highly sensitive sensors. AE is defined as the transmission of elastic waves within a material, originating from the rapid release of energy from internal sources such as plastic deformation and crack propagation. Different parametric features (i.e., count, peak amplitude, rise time, duration, energy, entropy, peak frequency, etc.) can be extracted from recorded AE waves and their spectra to characterize and diagnose the damage state of the material.
[0005] Current fatigue process studies based on acoustic emission signals all collect complete acoustic emission signals during the fatigue process. Due to the high sampling frequency of acoustic emission signals, recording the entire fatigue process is extremely difficult in practical engineering applications. Furthermore, because the fatigue process environment is complex, traditional time-frequency domain features have poor characterization capabilities, resulting in low signal-to-noise ratios for acoustic emission signals. This necessitates extensive filtering to ensure the accuracy of acoustic emission parameters, leading to a large sample size and lengthy deep learning time required for feature extraction based on deep learning. Moreover, the large volume of acquired acoustic emission signal data makes characterizing the fatigue process using deep learning models both difficult and costly.
[0006] Therefore, there is a need in the art for a method that can efficiently acquire and process signals and accurately predict the fatigue life of materials. Using intermittently sampled acoustic emission signals to extract dominant features and predict fatigue crack propagation rates is of great significance. To address the above problems, according to embodiments of the present invention, the arrangement pattern theory is simple in background, fast in computation, has few parameters, and is robust even in the presence of observational and dynamic noise. The fatigue process is characterized through arrangement pattern features, and a relationship model between crack propagation rate and these features is established. Summary of the Invention
[0007] To address the aforementioned problems in this field, an embodiment of the present invention provides a fatigue crack prediction method based on acoustic emission alignment patterns, the method comprising the following steps:
[0008] Step 1: Collect relevant data during the fatigue process. Collect acoustic emission signal data and relevant mechanical data during the fatigue process. Take the first 40-50% of the data for training and use it as training data. The remaining data is used for verification.
[0009] Step 2: Obtain the parameters required for extracting the permutation pattern features. Use the training data to obtain the permutation entropy of acoustic emission signals with different window sizes, dimension parameters, and time delay parameters. Find suitable feature parameters and extract the permutation pattern features.
[0010] Step 3: Screening arrangement pattern features, calculating the Pearson correlation coefficient between arrangement pattern features and crack propagation rate values, and screening arrangement pattern features based on the magnitude of the correlation;
[0011] Step 4: Establish a relationship model between crack propagation rate and arrangement pattern characteristics. Obtain the feature weights of each arrangement pattern through optimization algorithms and establish a relationship model between crack propagation rate and arrangement pattern characteristics. Predict the crack propagation rate of the material under different cycle counts based on the relationship model.
[0012] Step 5: Predict the crack length at different cycle counts. Input the verification data into the relationship model between crack propagation rate and arrangement pattern characteristics to obtain the crack propagation rate at different times. Then, obtain the predicted crack length at different times by integration.
[0013] In step one, a total of t sets of data are recorded during the fatigue test. Each set of data includes the current crack length at that moment, the cumulative number of cycles, and a set of acoustic emission signals at that moment. The crack length is converted using compliance, which is expressed as:
[0014] α = a / W
[0015] Where α represents the compliance, a represents the current crack length of the specimen, and W represents the specimen width. This compliance can be measured using a compliance gauge.
[0016] In an optional implementation, the crack propagation rate is calculated as follows:
[0017]
[0018] Among them, a i+1 -a i The cumulative number of cycles is represented by N. i Increase to N i+1 The corresponding crack increment during the process is used to calculate the slope of the straight line corresponding to the lengths of two adjacent cracks and the number of cycles. Where:
[0019]
[0020] In the formula, It represents the average crack length from time i to time i+1. Represented as The corresponding crack propagation rate.
[0021] In step two, considering the integrity of the signal, in an optional implementation, a complete fatigue loading process is used as the smallest unit of signal analysis. First, the signal sequence {x} of length N is analyzed. t} t＝1,...,N Phase space reconstruction is performed:
[0022]
[0023] Where m represents the dimension parameter, τ represents the time delay parameter, n = N - (m-1)τ represents the number of subsequences in the original phase space, and Y represents the original phase space. In this embodiment, an m-dimensional tuple (r0, r1, ..., rm-1) containing the numbers 0, 1, ..., m-1, with each number appearing only once, is used. m-1 ) represents the permutation pattern, and the set of all permutation patterns is represented as Π. m Π m R contains m! permutation patterns. m Represents the row vector y in the original phase space Y. i =[x i ,x i+τ ,…,x i+(m-1)τ Define π:R m →Π m , used to convert y i =[x i ,x i+τ ,…,x i+(m-1)τ ]∈R m Mapped to a unique permutation pattern π(y)i )=(r0,r1,…,r m-1 )∈Π m The mapping relationship needs to satisfy the following two conditions:
[0024] 1)
[0025] 2) If Then r j <r j+1 ;
[0026] The distribution of permutation patterns is defined as the set Π m The probability distribution of the permutation pattern, for the permutation pattern π j Its probability is defined as:
[0027]
[0028] Among them, I A(u) The indicator function for set A, used to calculate the number of specified permutations in a time series, is expressed as:
[0029]
[0030] Mode It means that when y i The corresponding permutation patterns u and π j If they are the same, the indicator function is recorded as 1; otherwise, it is recorded as 0. Indicates when y i The corresponding permutation pattern u exists in the set Π m When p, the indicator function is denoted as 1. τ (π j ) represents the permutation pattern π j The ratio of the number of occurrences to the cumulative number of occurrences of all permutations.
[0031] By calculating the time series in set Π m The probability of all permutations can be used to obtain the permutation distribution P(m,τ), which is a vector containing the probability of each permutation:
[0032] P(m,τ)=[p τ (π1) p τ (π2) … p τ (π m！ )]
[0033] This vector is used as the permutation pattern feature in this implementation. Since t sets of data were collected, t permutation pattern features corresponding to t time points can be obtained, forming a permutation pattern feature matrix:
[0034]
[0035] When selecting an appropriate input data size, the acoustic emission permutation entropy extracted under different parameters is used as a basis to ensure a small sample size while having a sufficiently large amount of information. The permutation entropy expression is:
[0036]
[0037] By calculating the permutation entropy under different feature parameters, appropriate permutation mode parameters are selected to ensure that the amount of data is as small as possible while the amount of information is large enough.
[0038] In step three, due to the large dimensionality of the permutation pattern features and the small number of samples collected during fatigue (e.g., 20-30), overfitting can occur when the number of features is close to or greater than the number of samples. This means the model performs well on the training set but has low accuracy and poor generalization ability during validation. To avoid overfitting and shorten training time, the Pearson correlation coefficient method is used to calculate the Pearson correlation coefficient between each permutation pattern in the permutation pattern vector and the crack propagation rate. The calculation method is as follows:
[0039]
[0040] r(π j ) represents the permutation pattern π j The Pearson correlation coefficient between crack propagation rate and crack growth rate. Calculate the Pearson correlation coefficient between m! permutations and crack growth rate, and retain the five permutations with the highest correlation coefficients as feature vectors for subsequent analysis. The selected feature vectors are denoted as E(m,τ), and expressed as:
[0041]
[0042] π M1 π M2 ...π M5 The above formula represents the five arrangements with the highest Pearson correlation coefficients, where m represents the dimension parameter and τ represents the time delay parameter.
[0043] In step five, during the crack propagation rate prediction process, the first 40%-50% of the sample data is used for training, and all sample points are used for validation analysis. It is assumed that the logarithmic crack propagation rate and the permutation pattern characteristics have a linear relationship, and a model is constructed, as shown below:
[0044]
[0045] Where β is the parameter vector, γ is the parameter, both of which are unknown model parameters, m represents the dimension parameter, and τ represents the time delay parameter.
[0046] The optimal solution for the parameters is found using the gradient descent method. The iterative process of the gradient descent method is expressed as follows:
[0047]
[0048] θ is the parameter to be optimized, and ρ is the learning rate set. This represents the derivative of a differentiable function J(θ) with parameter θ.
[0049] In an optional implementation, the iterative process includes the following steps:
[0050] 1. Given a continuously differentiable function J(θ) to be optimized, a learning rate ρ, and a set of initial values (true values);
[0051] 2. Calculate the gradient of the function to be optimized;
[0052] 3. Update and iterate;
[0053] 4. Recalculate the new gradient;
[0054] 5. Determine whether to stop iterating based on the loss function and convergence condition.
[0055] During this iteration, the loss function is constructed, with the following expression:
[0056]
[0057] According to relevant theories in fracture mechanics, the crack propagation rate and the strength stress factor have a linear relationship on a logarithmic coordinate axis, expressed as:
[0058]
[0059] In the formula, k and b are unknown parameters.
[0060] Therefore, the second part of the loss function incorporates the root mean square error between the slopes of the lines after least-squares fitting of the predicted and actual values to the strength stress factor on logarithmic coordinates. k1 and k2 represent the slopes of the lines after least-squares fitting of the predicted and actual crack propagation rates to the strength stress factor on logarithmic coordinates, respectively, expressed as:
[0061]
[0062]
[0063] in, x i =lg(ΔK) i ), where E i (m,τ) represents the vector formed by the i-th row of the characteristic matrix, expressed as:
[0064]
[0065] Where k1 and k2 are the slopes of the lines obtained by least-squares fitting of the predicted and actual values with the strength stress factor ΔK on logarithmic coordinates. The expression for the strength stress factor is:
[0066]
[0067] The unit conversions in the formula are as follows: ΔP is the difference between the maximum and minimum stress, W is the specimen width, B is the specimen thickness, and α is the compliance.
[0068] According to fracture mechanics theory, during the fatigue process of a material, the crack propagation rate and the strength stress factor have a linear relationship in logarithmic coordinates. When constructing the loss function, introducing the slope of the least squares estimate of the predicted value and the true value in logarithmic coordinates as the loss function can effectively improve the prediction accuracy and avoid overfitting of features.
[0069] The fatigue crack prediction method based on the arrangement pattern characteristics of acoustic emission signals provided by embodiments of the present invention has at least the following advantages: it requires few parameters, has a fast calculation speed, and is robust even in the presence of observational and dynamic noise. Because it directly extracts the shape features of the signal, it avoids complex noise reduction processing caused by excessive noise during the fatigue process. This provides a reliable reference for analyzing the fatigue process and formulating maintenance plans and decisions. Attached Figure Description
[0070] The foregoing features of the present invention can be more readily understood in conjunction with the accompanying drawings and the following detailed description, wherein:
[0071] Figure 1a A flowchart of a fatigue crack prediction method based on acoustic emission arrangement patterns according to an embodiment of the present invention is shown;
[0072] Figure 1b A flowchart of a fatigue crack prediction method based on acoustic emission arrangement patterns according to another embodiment of the present invention is shown;
[0073] Figure 2 A side-dimensional view of a compact tensile specimen used in an example of a fatigue crack prediction method based on acoustic emission arrangement patterns according to an embodiment of the present invention is shown.
[0074] Figure 3 The following is an example of a fatigue crack prediction method based on acoustic emission arrangement patterns according to an embodiment of the present invention, showing the crack lengths at different cycle numbers during an experiment.
[0075] Figure 4 An example of a fatigue crack prediction method based on acoustic emission arrangement patterns according to an embodiment of the present invention is shown, with 24 arrangement patterns embedded in dimension m=4.
[0076] Figure 5 This paper illustrates an example of a fatigue crack prediction method based on acoustic emission arrangement patterns according to an embodiment of the present invention, showing the arrangement entropy of the signal at different window sizes (300000*n) and different cycle numbers.
[0077] Figure 6 An example of a fatigue crack prediction method based on acoustic emission arrangement patterns according to an embodiment of the present invention is shown, illustrating the relationship between the actual and predicted crack propagation rates on a logarithmic coordinate axis, with their 95% confidence intervals marked.
[0078] Figure 7 The diagram illustrates an example of a fatigue crack prediction method based on acoustic emission arrangement patterns according to an embodiment of the present invention, showing the correspondence between predicted and actual crack length values at different cycle counts.
[0079] Figure 8 The diagram illustrates an example of the correspondence between predicted and actual crack length values when applying a fatigue crack prediction method based on acoustic emission arrangement patterns according to an embodiment of the present invention. Detailed Implementation
[0080] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey its scope to those skilled in the art. It should be noted that, unless otherwise stated, the technical or scientific terms used in this invention should be understood in their ordinary sense by those skilled in the art to which this invention pertains.
[0081] According to an embodiment of the present invention, a fatigue crack prediction method based on the arrangement pattern characteristics of acoustic emission signals is provided, which mainly includes five steps: acoustic emission signal and fatigue data acquisition, arrangement pattern parameter determination, feature screening, crack propagation rate calculation, and crack length calculation. Figure 1a A flowchart of a fatigue crack prediction method based on acoustic emission arrangement patterns according to an embodiment of the present invention is shown. Figure 1b A flowchart illustrating a fatigue crack prediction method based on acoustic emission alignment patterns according to another embodiment of the present invention is shown.
[0082] like Figures 1a-1b As shown, according to an embodiment of the present invention, a fatigue crack prediction method based on acoustic emission arrangement mode is provided, comprising the following steps:
[0083] Step 1: Collect relevant data during the fatigue process. Collect acoustic emission signal data and relevant mechanical data during the fatigue process. Take the first 40-50% of the data for training and use it as training data. The remaining data is used for verification.
[0084] Step 2: Obtain the parameters required for extracting the permutation pattern features. Use the training data to obtain the permutation entropy of acoustic emission signals with different window sizes, dimension parameters, and time delay parameters. Find suitable feature parameters and extract the permutation pattern features.
[0085] Step 3: Screening arrangement pattern features, calculating the Pearson correlation coefficient between arrangement pattern features and crack propagation rate values, and screening arrangement pattern features based on the magnitude of the correlation;
[0086] Step 4: Establish a relationship model between crack propagation rate and arrangement pattern characteristics. Obtain the feature weights of each arrangement pattern through optimization algorithms and establish a relationship model between crack propagation rate and arrangement pattern characteristics. Predict the crack propagation rate of the material under different cycle counts based on the relationship model.
[0087] Step 5: Predict the crack length at different cycle counts. Input the verification data into the relationship model between crack propagation rate and arrangement pattern characteristics to obtain the crack propagation rate at different times. Then, obtain the predicted crack length at different times by integration.
[0088] Optionally, in another embodiment, in step one, a total of t sets of data are recorded during the fatigue test. Each set of data includes the current crack length at that moment, the cumulative number of cycles, and a set of acoustic emission signals at that moment. The crack length is converted using compliance, which is expressed as:
[0089] α = a / W
[0090] Where α is the specimen compliance, a is the current crack length of the specimen, and W is the specimen width.
[0091] The crack propagation rate is calculated as follows:
[0092]
[0093] Where a i+1 -a i The cumulative number of cycles is represented by N. i Increase to N i+1The corresponding crack increment during the process is used to calculate the slope of the straight line corresponding to the lengths of two adjacent cracks and the number of cycles. Where:
[0094]
[0095] Let be the average crack length from time i to time i+1. Represented as The corresponding crack propagation rate.
[0096] Alternatively, in another embodiment, in step two, a complete fatigue loading process is used as the smallest unit of signal analysis. First, the signal sequence {x} of length N is analyzed. t} t＝1,...,N Phase space reconstruction is performed:
[0097]
[0098] Where m represents the dimension parameter, τ represents the time delay parameter, n = N - (m-1)τ represents the number of subsequences in the original phase space, Y represents the original phase space, and uses m-dimensional tuples (r0, r1, ..., r) containing the numbers 0, 1, ..., m-1, with each number appearing only once. m-1 ) represents the permutation pattern, and the set of all permutation patterns is represented as Π. m Π m It contains m! permutation patterns, R m Represents the row vector y in the original phase space Y. i =[x i ,x i+τ ,…,x i+(m-1)τ Define π:R m →Π m , used to convert y i =[x i ,x i+τ ,…,x i+(m-1)τ ]∈R m Mapped to a unique permutation pattern π(y) i )=(r0,r1,…,r m-1 )∈Π m This mapping relationship needs to satisfy the following two conditions:
[0099] 1)
[0100] 2) If Then r j <r j+1 ;
[0101] The distribution of permutation patterns is defined as the set Π mThe probability distribution of the permutation pattern, for the permutation pattern π j Its probability is defined as:
[0102]
[0103] Among them, I A(u) The indicator function for set A, used to calculate the number of specified permutations in a time series, is expressed as:
[0104]
[0105] Mode It means that when y i The corresponding permutation patterns u and π j If the values are the same, the indicator function is set to 1; otherwise, it is set to 0. Indicates when y i The corresponding permutation pattern u exists in the set Π m When p is denoted as 1, the indicator function is recorded as 1. τ (π j ) represents the permutation pattern π j The ratio of the number of occurrences to the cumulative number of occurrences of all permutations;
[0106] By calculating the time series in set Π m The probability of all permutations can be used to obtain the permutation distribution P(m,τ), which is a vector containing the probability of each permutation:
[0107] P(m,τ)=[p τ (π1) p τ (π2) … p τ (π m！ )]
[0108] Using this vector as the permutation pattern feature, and since t sets of data were collected, t permutation pattern features corresponding to t time points can be obtained, forming a permutation pattern feature matrix:
[0109]
[0110] When selecting an appropriate input data size, the acoustic emission permutation entropy extracted under different parameters is used as a basis to ensure a small sample size while having a sufficiently large amount of information. The permutation entropy expression is:
[0111]
[0112] Alternatively, in another embodiment, in step four, the Pearson coefficient method is used to calculate the Pearson correlation coefficient between each arrangement pattern in the arrangement pattern vector and the crack propagation rate, as follows:
[0113]
[0114] r(π j ) represents the permutation pattern π j The Pearson correlation coefficient between crack propagation rate and crack growth rate is calculated. For m! permutation patterns, the Pearson correlation coefficients between crack propagation rate and crack growth rate are calculated. The five permutation patterns with the highest correlation coefficients are retained as feature vectors for subsequent analysis. The selected feature vectors are denoted as E(m,τ) and expressed as:
[0115]
[0116] π M1 π M2 ...π M5 These represent the five arrangements with the highest Pearson correlation coefficients, where m represents the dimension parameter and τ represents the time delay parameter.
[0117] Alternatively, in another embodiment, in step five, during the crack propagation rate prediction process, the first 40%-50% of the sample data is used for training, and all sample points are used for validation analysis. It is assumed that the logarithmic crack propagation rate and the arrangement pattern characteristics have a linear relationship, and a model is constructed, as shown below:
[0118]
[0119] Where β is the parameter vector, γ is the parameter (both unknown model parameters), m represents the dimension parameter, and τ represents the time delay parameter.
[0120] The optimal solution for the parameters is found using the gradient descent method. The iterative process of the gradient descent method is expressed as follows:
[0121]
[0122] θ is the parameter to be optimized, and ρ is the learning rate set. This represents the derivative of a differentiable function J(θ) with parameter θ.
[0123] Alternatively, in another embodiment, step five of the iterative process further includes the following steps:
[0124] Given a continuously differentiable function J(θ) to be optimized, a learning rate ρ, and a set of initial values;
[0125] Calculate the gradient of the function to be optimized;
[0126] Update and iterate;
[0127] Recalculate the new gradient;
[0128] Determine whether to stop iteration based on the loss function and convergence condition;
[0129] In this iteration, the expression for the loss function is constructed as follows:
[0130]
[0131] Where β is the parameter vector and γ is the parameter;
[0132] According to relevant theories in fracture mechanics, the crack propagation rate and the strength stress factor have a linear relationship on a logarithmic coordinate axis, expressed as:
[0133]
[0134] Where ΔK is the strength stress factor of the specimen, and k and b are unknown parameters. Therefore, the second part of the loss function includes the root mean square error between the slopes of the lines after least square fitting of the predicted and actual values with the strength stress factor on logarithmic coordinates. k1 and k2 represent the slopes of the lines after least square fitting of the predicted and actual crack propagation rates with the strength stress factor on logarithmic coordinates, respectively, and are expressed as:
[0135]
[0136]
[0137] in, x i =lg(ΔK) i ), where E i (m,τ) represents the vector formed by the i-th row of the characteristic matrix, expressed as:
[0138]
[0139] Where k1 and k2 are the slopes of the lines obtained by least-squares fitting of the predicted and actual values with the strength stress factor ΔK on logarithmic coordinates. The expression for the strength stress factor is:
[0140]
[0141] The unit conversions in the formula are as follows: ΔP is the difference between the maximum and minimum stresses, W is the specimen width, and B is the specimen thickness.
[0142] Referring to the accompanying drawings, a compact tensile specimen is used as an example to illustrate a fatigue crack prediction method based on acoustic emission arrangement patterns according to an embodiment of the present invention. The specific implementation steps are as follows:
[0143] In this experiment, the fatigue process stress ratio was designed to be 0.1. Based on the performance of the fatigue testing machine, the loading frequency was adjusted to 10Hz, the average stress was 1.44KN, the stress amplitude was 1.18KN, and the equivalent zero mean stress was 7.5Mpa.
[0144] Step 1: Conduct fatigue tests according to the relevant fatigue test parameters. Acoustic emission signals are collected during the experiment using acoustic emission sensors and relevant mechanical sensors, and the mechanical data during this process is recorded. During the fatigue test, the crack length is calculated according to the compliance gauge; the compliance expression is:
[0145] α = a / W
[0146] Where α is the compliance, a is the current crack length of the specimen, W is the specimen width, and the compliance is measured by a compliance gauge.
[0147] The compact (CT) tensile standard specimen specified in the national standard was used in the test. The specimen dimensions are shown in the figure below. Figure 2 As shown, the specimen width W = 40 mm.
[0148] The crack length data and loading cycle data recorded in the experiment are as follows: Figure 3 As shown.
[0149] Based on the recorded loading cycle data and crack length data, the secant method in the national standard is used for calculation. The calculation method is as follows:
[0150]
[0151] The calculated crack propagation rate data is used as the true value of the crack propagation rate in that cycle.
[0152] Step Two: Based on research experience and considering computational costs, a dimensionality parameter m=4 was selected. The permutation pattern features with a dimensionality parameter of 4 are as follows: Figure 4 First, we compare and analyze the permutation entropy under different time delay parameters when inputting acoustic emission data of unit length, and then reconstruct the phase space of the input signal:
[0153]
[0154] At this point, the signal length N = 300000, and n = N - (m-1)τ = 299121. The set of all permutation patterns is represented by Π. m Π m It contains m! = 24 permutations. Define π: R m →Π m This is used to transform each row vector y in the original phase space Y. i =[x i ,x i+τ ,…,x i+(m-1)τ ]∈Rm Mapped to a unique permutation pattern π(y) i )=(r0,r1,…,r m-1 )∈Π m The mapping relationship must satisfy the following conditions:
[0155] 1)
[0156] 2) If Then r j <r j+1 ;
[0157] For set Π m The probability distribution of different permutation patterns is defined as follows:
[0158]
[0159] Among them, I A(u) The indicator function for set A, used to calculate the number of specified permutations in a time series, is expressed as:
[0160]
[0161] By calculating the time series in set Π m The probability of all permutations can be used to obtain the permutation distribution P(m,τ), which is a vector containing the probability of each permutation:
[0162] P(m,τ)=[p τ (π1)p τ (π2)…p τ (π m！ )]
[0163] In this example, the 24-dimensional eigenvector P(4,τ) can be calculated.
[0164] Based on the obtained permutation pattern feature vector, the permutation entropy is calculated. The formula for calculating the permutation entropy is:
[0165]
[0166] Due to the high-frequency nature of acoustic emission signals, within the effective range of the time delay parameter, a larger parameter setting results in a smaller calculated permutation entropy, such as... Figure 4 As shown, the time delay parameters m = 4 and τ = 293 are chosen respectively. Simultaneously, the arrangement entropy obtained by inputting acoustic emission signals of different lengths under these parameters is compared. The comparison shows that as the signal data volume increases (300000*n), the acoustic emission arrangement entropy does not change significantly, as shown... Figure 5As shown, therefore, in each sampled signal segment, a unit (containing a complete loading process, i.e., 0.1 seconds of acoustic emission signal data) is randomly selected as the input data. A 0.1-second segment (corresponding to a data size of 300,000) is extracted from each acoustic emission signal segment as a feature parameter, and the permutation pattern feature vector is calculated.
[0167] Step 3: Combine the calculated permutation pattern feature vector with the crack propagation rate ground truth value calculated in Step 1, and calculate the Pearson correlation coefficient between each permutation pattern in the feature vector and the crack propagation rate. The calculation formula is as follows:
[0168]
[0169] The calculation results are as follows Figure 5 As shown. The five patterns with the highest correlation coefficients are retained as the feature matrix for further analysis.
[0170] Step 5: Assuming a linear relationship between the logarithmic crack propagation rate and the arrangement pattern characteristics, a model is constructed, which is expressed as follows:
[0171]
[0172] Where β is the parameter vector, γ is the parameter, both of which are unknown model parameters, m represents the dimension parameter, and τ represents the time delay parameter.
[0173] The optimal solution for the parameters is found using the gradient descent method. The iterative process of the gradient descent method is expressed as follows:
[0174]
[0175] Where β is the parameter vector, γ is the parameter, and ρ is the learning rate. This represents the derivative of a differentiable function J(β,γ) with parameters β and γ.
[0176] Alternatively, adaptive gradient descent (AdaGrad) can be used for parameter optimization, with an initial learning rate ρ set to 0.1. The iterative process of adaptive gradient descent is as follows:
[0177]
[0178]
[0179] Where s is a constant to avoid a denominator of 0, β is the parameter vector, γ is the parameter, and ρ is the learning rate. This represents the derivative of a differentiable function J(β,γ) with parameters β and γ. In this example, the differentiable function is the loss function defined below. During iteration, the method adjusts the learning rate for different dimensions based on the gradient descent. In dimensions with large gradients, the descent speed is reduced; in dimensions with small gradients, the descent speed is increased.
[0180] The loss function for parameter optimization is defined as follows:
[0181]
[0182] The loss function consists of two parts. The first part calculates the root mean square error between the actual and predicted crack propagation rates. k1 and k2 are the slopes of the straight lines obtained by performing least-squares regression of the predicted and actual values with respect to the strength stress factor ΔK on a logarithmic coordinate axis. In this example, a compact tensile specimen is used, and its strength stress factor expression is:
[0183]
[0184] The unit conversions in the formula are as follows: ΔP is the difference between the maximum and minimum stresses, W is the specimen width, B is the specimen thickness, and α is the specimen compliance.
[0185] According to relevant theories in fracture mechanics, the crack propagation rate and the strength stress factor have a linear relationship on a logarithmic coordinate axis, expressed as:
[0186]
[0187] Where ΔK is the strength stress factor of the specimen, and k and b are unknown parameters. Therefore, the second part of the loss function incorporates the root mean square error between the slopes of the lines after least-squares fitting of the predicted and actual values with the strength stress factor on logarithmic coordinates. k1 and k2 represent the slopes of the lines after least-squares fitting of the predicted and actual crack propagation rates with the strength stress factor on logarithmic coordinates, respectively, expressed as:
[0188]
[0189]
[0190] in, x i =lg(ΔK) i The prediction results are as follows: Figure 6 As shown, most of the predicted values are within the 95% confidence interval.
[0191] Step five also includes: calculating the crack length prediction result based on the arrangement pattern features by integrating the crack propagation rate at each point, and comparing the predicted value with the actual value as follows: Figure 7 and Figure 8 As shown.
[0192] The method proposed in this invention achieves a goodness-of-fit of 0.81 between the predicted crack propagation rate and the actual crack length, and a goodness-of-fit of 0.97 between the crack length calculated from the crack propagation rate and the actual crack length. Therefore, the method provided according to the embodiments of this invention can achieve accurate assessment of fatigue crack length.
[0193] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.
[0194] It should be understood that the foregoing only illustrates some embodiments, and changes, modifications, additions, and / or variations can be made without departing from the scope and spirit of the disclosed embodiments. These embodiments are illustrative and not restrictive. Furthermore, the described embodiments relate to those currently considered most practical and preferred, and should be understood as not being limited to the disclosed embodiments, but rather intended to cover different modifications and equivalent arrangements included within the spirit and scope of those embodiments. Moreover, the various embodiments described above can be used in conjunction with other embodiments; for example, an aspect of one embodiment can be combined with an aspect of another embodiment to achieve yet another embodiment. Additionally, individual features or components of any given component can constitute another embodiment.
[0195] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.
Claims
1. A fatigue crack prediction method based on acoustic emission arrangement patterns, characterized in that... Includes the following steps: Step 1: Collect relevant data during the fatigue process. Collect acoustic emission signal data and relevant mechanical data during the fatigue process. Take the first 40-50% of the data for training and use it as training data. The remaining data is used for verification. Step 2: Obtain the parameters required for extracting the permutation pattern features. Use the training data to obtain the permutation entropy of acoustic emission signals with different window sizes, dimension parameters, and time delay parameters. Find suitable feature parameters and extract the permutation pattern features. Step 3: Screening arrangement pattern features, calculating the Pearson correlation coefficient between arrangement pattern features and crack propagation rate values, and screening arrangement pattern features based on the magnitude of the correlation; Step 4: Establish a relationship model between crack propagation rate and arrangement pattern characteristics. Obtain the feature weights of each arrangement pattern through optimization algorithms and establish a relationship model between crack propagation rate and arrangement pattern characteristics. Predict the crack propagation rate of the material under different cycle counts based on the relationship model. Step 5: Predict the crack length at different cycle counts. Input the verification data into the relationship model between crack propagation rate and arrangement pattern characteristics to obtain the crack propagation rate at different times. Then, obtain the predicted crack length at different times by integration.
2. The fatigue crack prediction method based on acoustic emission arrangement mode as described in claim 1, characterized in that: In step one, a total of t sets of data are recorded during the fatigue test. Each set of data includes the current crack length at that moment, the cumulative number of cycles, and a set of acoustic emission signals at that moment. The crack length is converted using compliance, which is expressed as: in, Here, 'a' represents the specimen compliance, 'a' represents the current crack length of the specimen, and 'W' represents the specimen width. The crack propagation rate is calculated as follows: in Indicates the cumulative cycle number from Increase to The corresponding crack increment during the process is used to calculate the slope of the straight line corresponding to the length of two adjacent cracks and the number of cycles, where: Let be the average crack length from time i to time i+1. Represented as The corresponding crack propagation rate.
3. The fatigue crack prediction method based on acoustic emission arrangement mode as described in claim 2, characterized in that: In step two, a complete fatigue loading process is used as the smallest unit of signal analysis. First, the signal sequence {x} of length N is analyzed. t } t=1, ..., N Phase space reconstruction is performed: Where m represents the dimension parameter, τ represents the time delay parameter, n = N - (m - 1)τ represents the number of subsequences in the original phase space, and Y represents the original phase space, using m-dimensional tuples (r0, r1, ..., r) containing numbers 0, 1, ..., m-1, with each number appearing only once. m-1 ) represents the permutation pattern, and the set of all permutation patterns is represented as Π. m Π m It contains m! permutation patterns, R m Represents the row vector y in the original phase space Y. i = [x i , x i+τ , …, x i+(m-1)τ Define π: R m →Π m , used to convert y i = [x i , x i+τ , …, x i+(m-1)τ ] ∈ R m Mapped to a unique permutation pattern π(y) i ) = (r0, r1, …, r m-1 )∈ Π m This mapping relationship needs to satisfy the following two conditions: 1) ; 2) If ,but ; The distribution of permutation patterns is defined as the set Π m The probability distribution of the permutation pattern, for the permutation pattern π j Its probability is defined as: Among them, I A(u) The indicator function for set A, used to calculate the number of specified permutations in a time series, is expressed as: Mode It means that when The corresponding permutation pattern u and If the values are the same, the indicator function is set to 1; otherwise, it is set to 0. Indicates when The corresponding permutation pattern u exists in set Π m When the indicator function is set to 1, Represents the permutation pattern π j The ratio of the number of occurrences to the cumulative number of occurrences of all permutations; By calculating the time series in set Π m The probability of all permutations can be used to obtain the permutation distribution P(m, τ), which is a vector containing the probability of each permutation: Using this vector as the permutation pattern feature, and since t sets of data were collected, t permutation pattern features corresponding to t time points can be obtained, forming a permutation pattern feature matrix: When selecting an appropriate input data size, the acoustic emission permutation entropy extracted under different parameters is used as a basis to ensure a small sample size while having a sufficiently large amount of information. The permutation entropy expression is:
4. The fatigue crack prediction method based on acoustic emission arrangement mode as described in claim 3, characterized in that: In step three, the Pearson coefficient method is used to calculate the Pearson correlation coefficient between each arrangement pattern in the arrangement pattern vector and the crack propagation rate, as follows: Indicates the arrangement pattern The Pearson correlation coefficient between m! permutations and crack propagation rate is calculated. The five permutations with the highest correlation coefficients are retained as feature vectors for subsequent analysis. These selected feature vectors are denoted as... , is represented as: , ... These represent the five arrangements with the highest Pearson correlation coefficients, where m represents the dimension parameter and τ represents the time delay parameter.
5. The fatigue crack prediction method based on acoustic emission arrangement mode as described in claim 4, characterized in that: In step five, during the crack propagation rate prediction process, the first 40%-50% of the sample data is used for training, and all sample points are used for validation analysis. It is assumed that the logarithmic crack propagation rate and the permutation pattern characteristics have a linear relationship, and a model is constructed, as shown below: in, For parameter vectors, Both are unknown model parameters, where m represents the dimension parameter and τ represents the time delay parameter. The optimal solution for the parameters is found using the gradient descent method. The iterative process of the gradient descent method is expressed as follows: θ is the parameter to be optimized. The learning rate is set. Represents a differentiable function With parameters The differential of time.
6. The fatigue crack prediction method based on acoustic emission arrangement mode as described in claim 5, characterized in that, In step five, the iterative process further includes the following steps: Given a continuously differentiable function to be optimized Learning rate and a set of initial values; Calculate the gradient of the function to be optimized; Update and iterate; Recalculate the new gradient; Determine whether to stop iteration based on the loss function and convergence condition; In this iteration, the expression for the loss function is constructed as follows: in, For parameter vectors, For parameters; According to relevant theories in fracture mechanics, the crack propagation rate and the strength stress factor have a linear relationship on a logarithmic coordinate axis, expressed as: in, Let be the strength stress factor of the specimen, and k and b be unknown parameters. Therefore, the second part of the loss function incorporates the root mean square error between the slopes of the lines after least-squares fitting of the predicted and true values with the strength stress factor on logarithmic coordinates. Let represent the slopes of the straight lines after least-squares fitting of the predicted and actual crack propagation rates onto the logarithmic coordinate axis with the strength stress factor, respectively. The expressions are as follows: in, , , ,in, The vector representing the i-th row of the characteristic matrix is denoted as: in, The predicted and actual values are respectively compared with the strength stress factor. By performing least-squares fitting on logarithmic coordinates, the slope of the straight line is obtained, and the expression for the intensity stress factor is: The unit conversions in the formula are as follows: , The maximum stress is the difference between the minimum stress and the maximum stress. W is the width of the specimen and B is the thickness of the specimen.