Data-driven fatigue life prediction method and related apparatus

Abstract

A data-driven fatigue life prediction method and related device, comprising: constructing two new information entropy damage characteristic values: energy singular spectrum entropy and power singular spectrum entropy; constructing a damage degree Gaussian mixture model (GMM), deriving a crack length prediction curve according to the principle of relative entropy (KL) distance evaluation of damage, and then building fatigue crack propagation curves of multiple same components to form a comprehensive propagation evolution model of damage and life of this type of component; and then establishing a Gaussian mixture model (GMM) of multiple same components at the same damage, and using the Gaussian mixture model (GMM) to predict the crack propagation and life evolution trend of the new component. The method can effectively predict the propagation of structural cracks, does not need to consider the structure form and bearing condition of the equipment, does not need to consider the failure mechanism, has strong nonlinear fitting capability, can effectively reduce the error accumulation of crack propagation prediction and the influence of various uncertainties in engineering application, and further improves the precision and efficiency of fatigue life prediction.

Description

Technical Field

[0001] This invention belongs to the field of fatigue life prediction technology, and specifically relates to a data-driven fatigue life prediction method and related apparatus. Background Technology

[0002] Fatigue cracking is one of the main causes of mechanical structure failure. The presence of cracks leads to stress concentration in the structure, and under the action of alternating stress over a long period of time, the cracks will continue to propagate, eventually causing structural fracture. Fatigue fracture seriously affects the safety of mechanical structures; common engineering structures (such as aircraft, vehicles, bridges, cranes, etc.) have all experienced safety problems due to fatigue. Structural Health Monitoring (SHM) is one of the core technologies of safety monitoring, and it is a multidisciplinary science and technology that ensures the safe operation of equipment structures. SHM technology, without damaging the structure's own performance and maintaining the structure's integrity, uses non-destructive testing methods to collect structural status information online, continuously, and in real time, and analyzes the monitoring signals to determine whether there is damage to the structure and the severity of the damage. Due to the advantages of Lamb wave detection technology, such as non-destructive testing, sensitivity to minor damage, and strong stability, Lamb wave-based SHM technology has become an important method for fatigue crack monitoring. With the proposal of the "Made in China 2025" plan and the continuous improvement of the manufacturing industry, the country is paying increasing attention to production safety and has listed improving the reliability and safety of major equipment as one of its strategic action plans. Therefore, research on structural fatigue crack monitoring and life prediction technology has significant practical implications and broad application prospects.

[0003] Structural health monitoring, fatigue damage analysis, and life prediction technologies can not only detect early fatigue crack damage in structures and equipment and prevent catastrophic accidents, but also effectively predict fatigue crack propagation and remaining service life. This allows for guidance on the regular maintenance of engineering structures and mechanical equipment, fundamentally addressing the drawbacks of insufficient or excessive maintenance. Monitoring and predicting fatigue cracks in structures is of great significance for improving structural reliability and ensuring the safe operation of equipment. The interaction between Lamb waves and crack defects causes wave scattering and mode conversion phenomena. Analyzing the scattered wave signals allows for quantitative assessment of crack damage. Due to the complexity of Lamb wave signals, complex signal processing methods are typically required for analysis, and it is difficult to simulate the propagation of Lamb waves in complex structures. However, this method offers high detection efficiency, reusability, and the ability to inspect surface and internal damage in large structures within a short time. It does not require transducer movement, making it a low-energy-consumption, high-damage-sensitivity, and highly efficient SHM method, and it enables online structural health monitoring. In recent years, with the rapid development of artificial intelligence technology, Lamb wave detection combined with data-driven algorithms has been extensively and deeply studied in crack propagation and life prediction, becoming a research hotspot both domestically and internationally. Therefore, we need to conduct in-depth research on fatigue crack monitoring and prediction technologies, employing effective technical means to monitor the health status of mechanical structures and achieve high-precision, high-efficiency prediction of crack propagation processes and fatigue life.

[0004] Currently, the diagnosis, life prediction, and management of structural equipment damage are important research directions in the field of PHM (Problem Mechanics). Previous research in this area has employed methods based on damage mechanics and damage propagation models, followed by prediction of remaining life using methods such as SN curves. However, methods based on damage mechanics and fatigue damage propagation analysis require assumptions about fatigue crack propagation conditions. Uncertainties related to materials, parameters, and the environment often have a significant impact on the prediction results. These factors greatly limit the effective implementation of structural life prediction.

[0005] The current mainstream crack propagation and life prediction methods are shown in the figure below. After acquiring the original signal, traditional damage feature values ​​are selected to describe the damage, such as correlation coefficient and phase difference. However, these feature values ​​often require manual selection of specific lambda modes to extract the correct damage feature values. In addition, traditional feature values ​​have high requirements for signal quality. However, in actual engineering applications, the operating environment of components is complex, often with many alternating loads, resulting in poor signal-to-noise ratio of the acquired signals, which leads to the inability of the acquired feature values ​​to accurately characterize the damage. After acquiring the feature values, traditional methods often use Paris rules, Walker models, Forman models, etc. These models require the acquisition of stress intensity factors and material parameter uncertainties, and require a large amount of prior information before they can be used. Therefore, this limits the widespread application of such crack life prediction models. Summary of the Invention

[0006] The purpose of this invention is to provide a data-driven fatigue life prediction method and related apparatus to solve the problem that the uncertainty of obtaining stress intensity factors and material parameters is required, and a large amount of prior information is needed to use the model, which limits the widespread application of such crack life prediction models.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] Data-driven fatigue life prediction methods include:

[0009] The raw signals of the acquisition components are collected, and information entropy damage feature values ​​are extracted from the raw signals to construct two new information entropy damage feature values: energy singular spectrum entropy and power singular spectrum entropy.

[0010] The Gaussian Mixture Model (GMM) for the damage degree is constructed by extracting the information entropy under the same damage state. The crack length prediction curve is derived based on the principle of evaluating damage by relative entropy KL distance. Then, fatigue crack propagation curves of multiple components of the same type are constructed to form a comprehensive propagation evolution model of damage and life of this type of component.

[0011] Then, Gaussian mixture models (GMMs) are established for multiple components of the same type at the same damage site. These GMMs are then used to predict the crack propagation and life evolution trends of the new components.

[0012] Furthermore, the raw signals from the acquired components are used to extract information entropy impairment feature values ​​from the raw signals:

[0013] The information entropy extraction process for non-stationary signals under time-varying temperature conditions is as follows: Each signal data acquired from the piezoelectric element PZT is a continuous time series x(t), which is decomposed by the EEMD algorithm; n IMF(t) components IMF1(t), IMF2(t), ..., IMF n (t), obtained through EEMD analysis; the reconstructed signal is obtained through SSA algorithm analysis of n IMF(t) components; the specific calculation process of EEMD and SSA algorithm is as follows: in the original signal y i Gaussian white noise n(t) is added multiple times to (t), i = 1, 2, 3, ..., N; the sum of the m-th Gaussian white noise signals is:

[0014] x(t)=x(t)+h×n m (t) (m≤N) (1)

[0015] In the above formula, n m(t) represents the white noise added for the m-th time, h is the amplitude coefficient of the noise, and N is the number of EMD decompositions and aggregations; EEMD decomposition xm(t) is performed on the signal, adding white noise to obtain n IMF components cm,i(t), i≤n, and residual component rm,n(t). When m<n, the above steps are repeated, adding different white noise signals each time, then the average value...

[0016]

[0017] It is the final intrinsic mode function; SSA is performed on the IMF component, transforming the one-dimensional signal sequence into an IMF. i (t) is transformed into a multidimensional sequence to obtain the trajectory matrix X:

[0018]

[0019] Calculate the singular values ​​of matrix X and decompose it to obtain m indices and their corresponding eigenvectors:

[0020]

[0021] Where p < m, α p =p. When p > t - m + 1, α p = t - p + 1. When m ≤ p ≤ t - m + 1, α p =m.

[0022] Through the above calculations, the component is reconstructed into a new time series, which replaces the component as the input for calculating the traditional information entropy, and two new information entropies are obtained: power singular spectral entropy PS and energy singular spectral entropy ES.

[0023] Furthermore, the entropy of the singular energy spectrum:

[0024] Energy singular spectral entropy represents the complexity of signal energy. Information from different frequency bands in the signal is contained in different IMF components. The algorithm's input is the IMF components of the new time series, and the output is the ES. The steps are as follows:

[0025] Calculate the energy of each reconstructed IMF component separately:

[0026]

[0027] Calculate the proportion of total energy consumed by each reconstructed IMF component:

[0028] p i =E i / E (6)

[0029] Calculate the ES of the signal:

[0030]

[0031] Furthermore, power heterospectral entropy:

[0032] Based on the calculation principle of ES, the IMF component was also reconstructed in time, and the new time series was used to replace the IMF component in the calculation of PS; the input of the algorithm is the IMF component of the new time series, and the output is PS; the steps are as follows:

[0033] The reconstructed power spectrum is estimated using the formula of the maximum entropy method, and the corresponding singular power spectrum is obtained:

[0034]

[0035] Where a0 and a m This is a solution to the Yule Walker equation:

[0036] Calculate the PS of the signal:

[0037]

[0038] Where α i It is the proportion of the power spectral density of the i-th reconstructed IMF component in the total PS.

[0039] Furthermore, the information entropy extracted under the same damage state is used to construct a Gaussian mixture model (GMM) for this damage level:

[0040] The specific steps for establishing the GMM under each damage state are shown below:

[0041] Let Dam = [A1, A2, A3, ... A q …A Q [ ] is a set of damage feature values ​​containing damage information extracted based on Lamb wave signals, consisting of Q sample signals A q Composition, where q = 1, 2, 3…Q; A q It is a D-dimensional sample, where the size of D is determined by the number of selected damage feature values. The distribution of the damage feature set Dam is fitted using a Gaussian Mixture Model (GMM), and its GMM probability density function expression is:

[0042]

[0043] Where k represents the number of Gaussian components, and each Gaussian distribution N(x|u) k ,∑ k ) is called a Gaussian component of GMM, N(x|u k ,∑ k The expression for ) is:

[0044]

[0045] In the above formula: n represents the number of components included; u k , ∑ k ω represents the mean and covariance matrix of the corresponding Gaussian distribution; k These are called the weighting coefficients of a single Gaussian distribution in the mixture model;

[0046]

[0047] Furthermore, the Gaussian mixture model is fitted using algorithms including K-means and EM; the damage feature value dataset is divided into K groups, and the entire process is as follows:

[0048] 5) Select K random points, called cluster centroids;

[0049] 6) For each data point in the dataset, associate it with the nearest centroid based on its distance from the K centroids, and cluster all points associated with the same centroid into one class;

[0050] 7) Calculate the average value for each group and move the center point associated with that group to the position of the average value;

[0051] 8) Repeat the steps until each cluster center satisfies formula (20), then stop the iteration;

[0052] In the K-means algorithm, the weight coefficient ω corresponding to each cluster is calculated according to formulas (21)(22)(23). k Mean u k Covariance

[0053] |Cte i+1 -Cte i |≤δ (20)

[0054]

[0055]

[0056]

[0057] The EM algorithm consists of two steps in each iteration:

[0058] 3) E-step: Calculate the expectation. Based on the initial parameters, calculate the probability that each data point j comes from the sub-model k according to formula (24).

[0059] 4) M-step: Find the maximum value and calculate the model parameters for the new iteration according to formulas (25)(26)(27).

[0060]

[0061]

[0062]

[0063]

[0064] The EM algorithm consists of an E-step for finding the expectation and an M-step for maximum likelihood estimation. The log-likelihood function of the GMM is:

[0065]

[0066] After substituting the initial values, the iteration is repeated alternately until the change in the log-likelihood function satisfies the set threshold ε. At this point, convergence is considered achieved, and the iterative calculation ends. The threshold expression is:

[0067] |L i+1 / L i |-1≤ε (29).

[0068] Furthermore, based on the principle of relative entropy KL distance for damage assessment, a crack length prediction curve is derived. Then, fatigue crack propagation curves of multiple identical components are constructed to form a comprehensive propagation evolution model of damage and lifespan for this type of component.

[0069] The information entropy of the component is measured when it is free of cracks. Then, a GMM for the healthy state is established. After that, a GMM for each damaged state is established. Then, according to the principle of Kullback-Leibler (KL) distance quantification based on the minimum matching of probability components, the difference between each damaged state and the healthy state is quantified. Finally, the damaged state is evaluated based on this.

[0070] The steps for damage assessment based on KL are as follows: First, for undamaged GMMφ 0 A Gaussian component The dynamic GMMφ at the nth monitoring time was quantified using KL distance. n one component The probability distribution distance between them is shown in the following formula:

[0071]

[0072] in: and for The mean and covariance matrices; and for The mean vector and covariance matrix; n is the number of monitoring times, n = 1, 2, 3, ... N; tr is the trace of the matrix; det represents the determinant of the matrix; D is the sample dimension;

[0073] The smaller the KL distance, the smaller the difference between the two components, and the better the ability to identify the damage GMMφ. n Neutral and undamaged GMMφ 0 Medium component Gaussian components with the smallest difference Final damage GMMφ n Compared to non-damaging GMMφ 0 The minimum matching KL distance is:

[0074]

[0075] in: and Components and The weights;

[0076] The greater the difference between the damaged GMM and the undamaged GMM, the larger the probability migration index KL value will be. The damage state in the structure can be evaluated by the migration trend of the KL value.

[0077] Similarly, the Mahalanobis distance, KL distance, and JS distance of the damaged GMM and the undamaged GMM are calculated using the same principle. These three distances are then superimposed according to different weighting coefficients to obtain the predicted crack length. The calculation process for the weighting coefficients is as follows:

[0078]

[0079] In the formula D KL Let D be the distance between K and L. JS Let D be the distance between JS and JS. M Let be the Mahalanobis distance, abc be the optimization parameters, l be the predicted crack length, L be the actual crack length, and ΔL be the prediction error, which is also the optimization objective, i.e., minimizing ΔL. The quantum-genetic optimization algorithm PSO is used for multi-parameter optimization to finally obtain the crack propagation prediction curve. Then, fatigue crack propagation curves of multiple components of the same type are constructed to form a comprehensive propagation evolution model of damage and life of this type of component. In addition, GMMs of multiple components of the same type at the same damage point are established, and the crack propagation and life evolution trend of the new component is predicted using the GMM.

[0080] Furthermore, a data-driven fatigue life prediction system includes:

[0081] The information entropy damage feature value establishment module is used to collect the original signal of the component, extract information entropy damage feature values ​​from the original signal, and construct two new information entropy damage feature values: energy singular spectrum entropy and power singular spectrum entropy.

[0082] The integrated extended evolution model component module is used to construct a Gaussian mixture model (GMM) for the damage degree by extracting information entropy under the same damage state. Based on the principle of evaluating damage by relative entropy KL distance, the crack length prediction curve is derived. Then, fatigue crack propagation curves of multiple components of the same type are built to form an integrated extended evolution model of damage and life of this type of component.

[0083] The trend evolution module is used to re-establish Gaussian mixture models (GMMs) for multiple similar components at the same damage site, and to use these GMMs to predict the crack propagation and life evolution trends of the new components.

[0084] Furthermore, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of a data-driven fatigue life prediction method.

[0085] Furthermore, a computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of a data-driven fatigue life prediction method.

[0086] Compared with the prior art, the present invention has the following technical effects:

[0087] This invention employs a structural health monitoring (SHM) method based on piezoelectric elements (PZT) and Lamb waves. This method boasts high detection efficiency, reusability, and the ability to inspect surface and internal damage in large structures within a short time. It eliminates the need for transducer movement, making it a low-energy-consumption, highly sensitive, and efficient SHM method. Furthermore, it enables online structural health monitoring, demonstrating excellent economic and engineering applicability. This invention proposes two novel information entropies: power singular spectrum entropy and energy singular spectrum entropy. These two entropy values ​​characterize damage information in Lamb wave signals. This allows for a clearer description of fault information, eliminating the need for manual selection of specific signal bands; instead, it utilizes the entire signal, encompassing more fault information. A Gross Model (GMM) of information entropy under the same damage state is established, and a quantum-genetic optimization algorithm is used to characterize the combined distances of different GMMs (including Mahalanobis distance, KL distance, and JS distance) into crack lengths, i.e., fatigue crack propagation curves. By constructing fatigue crack propagation curves for multiple identical components, a comprehensive propagation evolution model of damage and life for this type of component is formed. Furthermore, a Gross Model (GMM) for multiple identical components at the same damage location is established. Using this GMM, the crack propagation and life evolution trend of a new component can be predicted. This invention's method can effectively predict structural crack propagation without considering the equipment's structural form and load-bearing conditions, and it does not require consideration of failure mechanisms. It also possesses strong nonlinear fitting capabilities, effectively reducing the accumulation of errors in crack propagation prediction and the impact of various uncertainties in engineering applications, further improving the accuracy and efficiency of fatigue life prediction. Attached Figure Description

[0088] Figure 1 This is a flowchart of the present invention;

[0089] Figure 2 Flowcharts of EEMD and SSA algorithms;

[0090] Figure 3 Schematic diagram of KL-based damage assessment method;

[0091] Figure 4 Schematic diagram of KL-based damage assessment method;

[0092] Figure 5 A comprehensive predictive model for the extended evolution of crack damage and lifespan. Detailed Implementation

[0093] The present invention will be further described below with reference to the accompanying drawings:

[0094] Please see Figures 1 to 4 This invention discloses a data-driven fatigue life prediction method and related apparatus:

[0095] 1. Two novel information entropy damage features were constructed: energy singular spectral entropy and power singular spectral entropy. These can more clearly describe fault information, eliminating the need for manual selection of specific signal bands; instead, they utilize the entire signal, containing more fault information. Furthermore, after processing with EEMD and SSA, the fault characteristics can be represented even more clearly.

[0096] 2. Using KL to characterize crack length, the greater the difference between the damaged GMM and the undamaged GMM, the larger the probability migration index KL value will be. Therefore, the damage state in the structure can be evaluated by the migration trend of the KL value. This method does not need to consider the structural form and load-bearing conditions of the equipment, nor does it need to consider the failure mechanism, which can improve the accuracy and efficiency of crack prediction.

[0097] 3. Construct fatigue crack propagation curves for multiple identical components to form a fan-shaped crack propagation region, thus creating a comprehensive propagation evolution model of damage and life for this type of component. Then, construct a GMM at the same damage location. Using this GMM, the crack propagation and life evolution trend of the new component can be predicted. This data-driven method, which does not need to consider the failure mechanism and has a strong nonlinear fitting capability, is applied to fatigue life research, which can further improve the accuracy and efficiency of fatigue life prediction.

[0098] The specific process will be explained in detail below:

[0099] The calculation process for the two new information entropies mainly consists of two parts: EEMD and SSA. The average value of the IMF components obtained after decomposition is selected as the decomposed signal. The average value of the IMF components can eliminate additional noise effects and retain the useful signal mapped to the corresponding feature scale. Then, singular spectrum analysis is performed on these signals to obtain the reconstructed signal sequence. By replacing the original signal with the reconstructed time series, the energy singular spectrum entropy (ES) and power singular spectrum entropy can be calculated. The flowcharts for the EEMD and SSA algorithms are shown below. Figure 1 As shown.

[0100] The information entropy extraction process for non-stationary signals under time-varying temperature conditions is as follows: Each signal data acquired from PZT is a continuous time series x(t), which is decomposed by EEMD. There are n IMF(t) components: IMF1(t), IMF2(t), ..., IMF... n (t), obtained through EEMD analysis. The reconstructed signal is obtained through SSA analysis of n IMF(t) components. The specific calculation process of the EEMD and SSA algorithms is as follows: In the original signal y i Gaussian white noise n(t) is added multiple times to the sequence (t), i = 1, 2, 3, ..., N. The sum of the m-th Gaussian white noise signals is:

[0101] x(t)=x(t)+h×n m(t) (m≤N) (1)

[0102] In the above formula, nm(t) is the white noise added for the m-th time, h is the amplitude coefficient of the noise, and N is the number of EMD decompositions and aggregations, usually taken as 100. Performing EEMD decomposition on the signal xm(t) and adding white noise yields n IMF components cm,i(t), i≤n, and a residual component rm,n(t). When m<n, the above steps are repeated, adding a different white noise signal each time. Then the average value...

[0103]

[0104] This is the final intrinsic mode function. SSA is performed on the IMF component, with an appropriate window length selected. The one-dimensional signal sequence is then processed by the IMF. i (t) is transformed into a multidimensional sequence to obtain the trajectory matrix X:

[0105]

[0106] Calculate the singular values ​​of matrix X and decompose it to obtain m indices and their corresponding eigenvectors:

[0107]

[0108] Where p < m, α p =p. When p > t - m + 1, α p = t - p + 1. When m ≤ p ≤ t - m + 1, α p =m.

[0109] Through the above calculations, the component is reconstructed into a new time series, which can replace the component as input for calculating traditional information entropy, and two new information entropies, PS and ES, are obtained.

[0110] Energy Singular Spectrum Entropy

[0111] Energy singular spectral entropy can represent the complexity of signal energy. Information from different frequency bands in a signal is contained in different IMF components. The algorithm's input is the IMF components of the new time series, and the output is the ES. The steps are as follows:

[0112] Calculate the energy of each reconstructed IMF component separately:

[0113]

[0114] Calculate the proportion of total energy consumed by each reconstructed IMF component:

[0115] p i =E i / E (6)

[0116] Calculate the ES of the signal:

[0117]

[0118] Power heterogeneous entropy

[0119] Based on the computational principle of Elasticsearch (ES), the IMF component was also reconstructed in time, and the new time series was used to replace the IMF component in the PS calculation. The algorithm's input is the IMF component of the new time series, and the output is the PS. The steps are as follows:

[0120] The reconstructed power spectrum is estimated using the formula of the maximum entropy method, and the corresponding singular power spectrum is obtained:

[0121]

[0122] Where a0 and a m This is a solution to the Yule Walker equation:

[0123] Calculate the PS of the signal:

[0124]

[0125] Where α i It is the proportion of the power spectral density of the i-th reconstructed IMF component in the total PS.

[0126] Because the equipment operates in complex environments, the damage indicators reflected by the signals in the time and frequency domains are neither singular nor regular. The proposed ES and PS decompose the original signal using EEMD and SSA, transforming the original nonlinear and non-stationary signal into a new signal sequence with different characteristic scales. The proposed information entropy eigenvalues ​​and PS calculate the entire signal segment, preserving more complete fault information. Therefore, the ES and PS extracted in this paper can more clearly describe the fault information.

[0127] The GMM is established for each damage state as follows: Let Dam = [A1, A2, A3, ... Aq… AQ], which is the set of damage feature values ​​containing damage information extracted based on Lamb wave signals, consisting of Q sample signals Aq, where q = 1, 2, 3… Q. Aq is a D-dimensional sample, and the size of D is determined by the number of selected damage feature values. The distribution law of the damage feature set Dam is fitted using GMM, and its GMM probability density function expression is:

[0128]

[0129] Where k represents the number of Gaussian components, and each Gaussian distribution N(x|u) k ,∑ k) is called a Gaussian component of GMM, N(x|u k ,∑ k The expression for ) is:

[0130]

[0131] In the above formula: n represents the number of components included; u k , ∑ k ωk represents the mean and covariance matrix of the corresponding Gaussian distribution; ωk is called the weight coefficient of the corresponding single Gaussian distribution in the mixture model.

[0132]

[0133] The Gaussian mixture model is primarily determined by two parameters: variance and mean. Different learning mechanisms for the mean and variance directly impact the model's stability, accuracy, and convergence. Since we are modeling feature values ​​extracted from different lamb signals, we need to update the variance and mean parameters of the Gaussian mixture model. Therefore, this paper uses both K-means and EM algorithms for fitting. K-means is an unsupervised learning clustering algorithm that takes an unlabeled dataset and clusters the data into different groups. We divide the damage feature value dataset into K groups, and the entire process is as follows:

[0134] K random points are selected and called cluster centroids.

[0135] For each data point in the dataset, based on its distance from the K centroids, associate it with the nearest centroid, and cluster all points associated with the same centroid into one class;

[0136] Calculate the average value for each group, and move the center point associated with that group to the position of the average value;

[0137] Repeat the steps until each cluster center satisfies formula (20), at which point the iteration stops.

[0138] In the K-means algorithm, the weight coefficient ω corresponding to each cluster can be calculated according to formulas (21)(22)(23). k Mean u k Covariance

[0139] |Cte i+1 -Cte i |≤δ (20)

[0140]

[0141]

[0142]

[0143] The EM algorithm is an iterative algorithm, summarized and proposed by Dempster et al. in 1977, used for maximum likelihood estimation of parameters in probabilistic models containing hidden variables. Each iteration consists of two steps:

[0144] E-step: Calculate the expectation. Based on the initial parameters, calculate the probability that each data point j comes from sub-model k according to formula (24).

[0145] M-step: Find the maximum value, and calculate the model parameters for the new iteration according to formulas (25)(26)(27).

[0146]

[0147]

[0148]

[0149]

[0150] Therefore, it can be seen that the EM algorithm consists of the E-step of expectation calculation and the M-step of maximum likelihood estimation. The log-likelihood function of GMM is:

[0151]

[0152] After substituting the initial values, the iteration is repeated alternately until the change in the log-likelihood function satisfies the set threshold ε. At this point, convergence is considered achieved, and the iterative calculation ends. The threshold expression is:

[0153] |L i+1 / L i |-1≤ε (29)

[0154] First, the information entropy of the component is measured in a healthy state (i.e., without cracks). Then, a Generative Model (GMM) for the healthy state is established using the method described above. Next, a GMM is established for each damaged state (i.e., for each crack length). Following the principle of quantifying the migration change of the latter relative to the former using the Kullback-Leibler (KL) distance based on probability component minimum matching, this method establishes a comprehensive distance to quantify the difference between each damaged state and the healthy state. The final assessment of the damage state is illustrated in the following diagram:

[0155] The steps for damage assessment based on KL are as follows: First, for undamaged GMMφ 0 A Gaussian component The dynamic GMMφ at the nth monitoring time was quantified using KL distance. n A component The probability distribution distance between them is shown in the following formula:

[0156]

[0157] in: and for The mean and covariance matrices; and for The mean vector and covariance matrix are given; n is the number of monitoring times, n = 1, 2, 3, ... N; tr is the trace of the matrix; det represents the determinant of the matrix; D is the sample dimension.

[0158] The smaller the KL distance, the smaller the difference between the two components, thus the damage GMMφ can be identified. n Neutral and undamaged GMMφ 0 Medium component Gaussian components with the smallest difference Final damage GMMφ n Compared to non-damaging GMMφ 0 The minimum matching KL distance is:

[0159]

[0160] in: and Components and The weights.

[0161] The greater the difference between the damaged GMM and the undamaged GMM, the larger the probability migration index KL value will be. Therefore, the damage state in the structure can be evaluated by the migration trend of the KL value.

[0162] Similarly, the Mahalanobis distance, KL distance, and JS distance of the damaged GMM and the undamaged GMM are calculated using the same principle. These three distances are then superimposed according to different weighting coefficients to obtain the predicted crack length. The calculation process for the weighting coefficients is as follows:

[0163]

[0164] In the formula D KL Let D be the distance between K and L. JS Let D be the distance between JS and JS. MLet be the Mahalanobis distance, abc be the optimization parameters, l be the predicted crack length, L be the actual crack length, and ΔL be the prediction error, which is also the optimization objective: minimizing ΔL. A quantum-genetic optimization algorithm (PSO) is used for multi-parameter optimization, ultimately yielding the crack propagation prediction curve, as shown below. Figure 3 As shown in the diagram. Fatigue crack propagation curves of multiple identical components are then constructed to form a comprehensive damage and life evolution model for this type of component. Furthermore, a Gross Model (GMM) is established for multiple identical components at the same damage location. This GMM can be used to predict the crack propagation and life evolution trend of the new component. A schematic diagram is shown in the diagram. Figure 4 As shown.

[0165] A comprehensive prediction model for the propagation and evolution of crack damage and life, such as Figure 4 As shown, fatigue crack propagation curves of multiple identical components are first constructed to form... Figure 4 The image shows a fan-shaped region. When predicting the crack length of a new component, it's necessary to first measure the damage entropy characteristic value in the early stages of damage, i.e., the known measurement points in the figure. A Geometric Matrix (GMM) is constructed here, and the location of the measurement point and its cluster center is calculated. Then, after inferring the later crack length and the cluster center location of the predicted point in the GMM, the predicted crack length is derived, thus completing the prediction of the later crack propagation length of the new component.

[0166] In another embodiment of the present invention, a data-driven fatigue life prediction system is provided, which can be used to implement the above-described data-driven fatigue life prediction method. Specifically, the system includes:

[0167] The information entropy damage feature value establishment module is used to collect the original signal of the component, extract information entropy damage feature values ​​from the original signal, and construct two new information entropy damage feature values: energy singular spectrum entropy and power singular spectrum entropy.

[0168] The integrated extended evolution model component module is used to construct a Gaussian mixture model (GMM) for the damage degree by extracting information entropy under the same damage state. Based on the principle of evaluating damage by relative entropy KL distance, the crack length prediction curve is derived. Then, fatigue crack propagation curves of multiple components of the same type are built to form an integrated extended evolution model of damage and life of this type of component.

[0169] The trend evolution module is used to re-establish Gaussian mixture models (GMMs) for multiple similar components at the same damage site, and to use these GMMs to predict the crack propagation and life evolution trends of the new components.

[0170] The module division in this embodiment of the invention is illustrative and represents only one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional modules in the various embodiments of the invention can be integrated into a single processor, exist as separate physical entities, or be integrated into a single module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0171] In another embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions from the computer storage medium to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used in the operation of a data-driven fatigue life prediction method.

[0172] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the data-driven fatigue life prediction method in the above embodiments.

[0173] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0174] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0175] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0176] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0177] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A data-driven fatigue life prediction method, characterized in that, include: The raw signals from the acquisition components are collected, and information entropy damage features, including energy singular spectrum entropy and power singular spectrum entropy, are extracted from the raw signals. A Gaussian mixture model (GMM) is constructed by extracting information entropy from the same damage state. The crack length prediction curve is derived based on the principle of evaluating damage by relative entropy KL distance. Then, fatigue crack propagation curves of multiple components of the same type are constructed to form a comprehensive propagation evolution model of damage and life of this type of component. Then, Gaussian mixture models (GMMs) are established for multiple components of the same type at the same damage site. These GMMs are then used to predict the crack propagation and life evolution trends of the new components. Based on the principle of relative entropy KL distance for damage assessment, a crack length prediction curve is derived. Then, fatigue crack propagation curves of multiple identical components are constructed to form a comprehensive propagation evolution model of damage and life for this type of component. The information entropy of the component is measured when it is free of cracks. Then, a GMM for the healthy state is established. After that, a GMM for each damaged state is established. Then, according to the principle of Kullback-Leibler (KL) distance quantification based on the minimum matching of probability components, the difference between each damaged state and the healthy state is quantified. Finally, the damaged state is evaluated based on this. The steps for damage assessment based on KL are as follows: First, for undamaged GMMs... A Gaussian component The dynamic GMM at the nth monitoring time was quantified using KL distance. one component The probability distribution distance between them is shown in the following formula: in: and for The mean and covariance matrices; and for The mean vector and covariance matrix; n is the number of monitoring times. ;tr represents the trace of the matrix; det represents the determinant of the matrix; D is the sample dimension; The smaller the KL distance, the smaller the difference between the two components, and the better the identification of the damage GMM. Neutral and non-damaging GMM Medium component Gaussian components with the smallest difference Ultimately, GMM is damaged. Compared to non-destructive GMM The minimum matching KL distance is: in: and Components and The weights; The greater the difference between the damaged GMM and the undamaged GMM, the larger the probability migration index KL value will be. The damage state in the structure can be evaluated by the migration trend of the KL value. Similarly, the Mahalanobis distance, KL distance, and JS distance for damaged and undamaged GMMs are calculated using the same principle. These three distances are then superimposed according to different weighting coefficients to obtain the predicted crack length. The calculation process for the weighting coefficients is as follows: In the formula For KL distance, For JS distance, The Mahalanobis distance, abc To optimize parameters, l To predict the crack length, L is the actual crack length. The prediction error is also the optimization objective, i.e., minimizing the error. Multi-parameter optimization was performed using the quantum-genetic optimization algorithm PSO to obtain the crack propagation prediction curve. Then, fatigue crack propagation curves of multiple components of the same type were constructed to form a comprehensive propagation evolution model of damage and life of this type of component. In addition, GMMs of multiple components of the same type at the same damage site were established, and the crack propagation and life evolution trend of the new component were predicted using the GMM.

2. The data-driven fatigue life prediction method according to claim 1, characterized in that, The raw signal from the acquisition component is used to extract information entropy damage feature values ​​from the raw signal: The process of extracting information entropy from non-stationary signals under time-varying temperature conditions is as follows: Each signal data acquired from the piezoelectric element PZT is a continuous time series. ( ), which is decomposed by the EEMD algorithm; n Quantity , ,..., Obtained through EEMD analysis; the reconstructed signal is obtained through n... The SSA algorithm analysis of the components is obtained; the specific calculation process of EEMD and SSA algorithms is as follows: Gaussian white noise n(t) is added multiple times to the original signal, and the result is added to the m-th Gaussian white noise signal: （1） In the above formula ( ) is the white noise added for the m-th time, is the amplitude coefficient of noise, and N is the number of EEMD decomposition aggregations; white noise is added to the signal for EEMD decomposition to obtain n IMF components , ≤ and residual components ; when m<n, repeat the above steps and add different white noise signals each time, then the average value : （2） It is the final intrinsic mode function; SSA is performed on the IMF component, transforming a one-dimensional signal sequence Transform into a multidimensional sequence to obtain the trajectory matrix X: （3） Calculate the singular values ​​of matrix X and decompose it to obtain m indices and their corresponding eigenvectors: （4） Among them, when , ;when , ;when , ; Through the above calculations, the component is reconstructed into a new time series, which replaces the component as the input for calculating the traditional information entropy, and two new information entropies are obtained: power singular spectral entropy PS and energy singular spectral entropy ES.

3. The data-driven fatigue life prediction method according to claim 2, characterized in that, Entropy of the singular spectrum of energy: Energy singular spectral entropy represents the complexity of signal energy. Information from different frequency bands in the signal is contained in different IMF components. The algorithm's input is the IMF components of the new time series, and the output is the ES. The steps are as follows: Calculate the energy of each reconstructed IMF component separately: （5） Calculate the proportion of total energy consumed by each reconstructed IMF component: （6） Calculate the ES of the signal: （7）。 4. The data-driven fatigue life prediction method according to claim 3, characterized in that, Power singular spectral entropy: Based on the calculation principle of ES, the IMF component was also reconstructed in time, and the new time series was used to replace the IMF component in the calculation of PS; the input of the algorithm is the IMF component of the new time series, and the output is PS; the steps are as follows: The reconstructed power spectrum is estimated using the formula of the maximum entropy method, and the corresponding power singular spectrum is obtained: （8） in and This is a solution to the Yule Walker equation: ; Calculate the PS of the signal: （9） in It is the proportion of the power spectral density of the i-th reconstructed IMF component in the total PS.

5. The data-driven fatigue life prediction method according to claim 1, characterized in that, A Gaussian Mixture Model (GMM) for damage is constructed from the information entropy extracted under the same damage state. The specific steps for establishing the GMM under each damage state are shown below: Let Dam = [ A1, A2, A3, ... Aq… AQ [ ] is a set of damage feature values ​​containing damage information extracted based on Lamb wave signals, which is composed of... Q Sample signal Aq Composition, in which q =1,2,3… Q ; Aq It is a D-dimensional sample, where the size of D is determined by the number of selected damage feature values. The distribution of the damage feature set Dam is fitted using the Gaussian Mixture Model (GMM), and its GMM probability density function expression is: Where k represents the number of Gaussian components, each Gaussian distribution A Gaussian component known as a GMM. The expression is: In the above formula: n Indicates the number of components included; , These represent the mean and covariance matrices of the corresponding Gaussian distribution; ω k These are called the weighting coefficients of a single Gaussian distribution in the mixture model; 6. The data-driven fatigue life prediction method according to claim 5, characterized in that, The Gaussian mixture model is fitted using algorithms including K-means and EM; the damage feature value dataset is divided into K groups, and the entire process is as follows: 1) Select These random points are called cluster centroids; 2) For each data point in the dataset, sort by distance The distance to each center point is used to associate it with the nearest center point, and all points associated with the same center point are grouped into one class; 3) Calculate the average value for each group and move the center point associated with that group to the position of the average value; 4) Repeat the steps until each cluster center satisfies formula (20), then stop the iteration; In the K-means algorithm, the weight coefficients corresponding to each cluster are calculated according to formulas (21), (22), and (23). mean Covariance ; The EM algorithm consists of two steps in each iteration: 1) E-step: Calculate the expectation based on the initial parameters and the formula (24) for each data point. j The probability of originating from sub-model k; 2) M-step: Find the maximum value and calculate the model parameters for the new iteration according to formulas (25), (26), and (27); The EM algorithm consists of an E-step for finding the expectation and an M-step for maximum likelihood estimation. The log-likelihood function of the GMM is: After substituting the initial value, the iteration is repeated alternately until the change in the log-likelihood function satisfies the set threshold ε. At this point, convergence is considered achieved, and the iteration ends. The threshold expression is set as follows:

7. A data-driven fatigue life prediction system, characterized in that, include: The information entropy damage feature value establishment module is used to collect the original signals of the components and extract information entropy damage feature values ​​from the original signals, including energy singular spectrum entropy and power singular spectrum entropy. The integrated extended evolution model component module is used to construct a damage Gaussian mixture model (GMM) based on the information entropy extracted under the same damage state. The crack length prediction curve is derived based on the principle of relative entropy KL distance to evaluate damage. Then, fatigue crack propagation curves of multiple components of the same type are built to form an integrated extended evolution model of damage and life of this type of component. The trend evolution module is used to re-establish Gaussian mixture models (GMMs) for multiple similar components at the same damage site, and use these GMMs to predict the crack propagation and life evolution trends of the new components. Based on the principle of relative entropy KL distance for damage assessment, a crack length prediction curve is derived. Then, fatigue crack propagation curves of multiple identical components are constructed to form a comprehensive propagation evolution model of damage and life for this type of component. The information entropy of the component is measured when it is free of cracks. Then, a GMM for the healthy state is established. After that, a GMM for each damaged state is established. Then, according to the principle of Kullback-Leibler (KL) distance quantification based on the minimum matching of probability components, the difference between each damaged state and the healthy state is quantified. Finally, the damaged state is evaluated based on this. The steps for damage assessment based on KL are as follows: First, for undamaged GMMs... A Gaussian component The dynamic GMM at the nth monitoring time was quantified using KL distance. one component The probability distribution distance between them is shown in the following formula: in: and for The mean and covariance matrices; and for The mean vector and covariance matrix; n is the number of monitoring times. ;tr represents the trace of the matrix; det represents the determinant of the matrix; D is the sample dimension; The smaller the KL distance, the smaller the difference between the two components, and the better the identification of the damage GMM. Neutral and non-damaging GMM Medium component Gaussian components with the smallest difference Ultimately, GMM is damaged. Compared to non-destructive GMM The minimum matching KL distance is: in: and Components and The weights; The greater the difference between the damaged GMM and the undamaged GMM, the larger the probability migration index KL value will be. The damage state in the structure can be evaluated by the migration trend of the KL value. Similarly, the Mahalanobis distance, KL distance, and JS distance for damaged and undamaged GMMs are calculated using the same principle. These three distances are then superimposed according to different weighting coefficients to obtain the predicted crack length. The calculation process for the weighting coefficients is as follows: In the formula For KL distance, For JS distance, The Mahalanobis distance, abc To optimize parameters, l To predict the crack length, L is the actual crack length. The prediction error is also the optimization objective, i.e., minimizing the error. Multi-parameter optimization was performed using the quantum-genetic optimization algorithm PSO to obtain the crack propagation prediction curve. Then, fatigue crack propagation curves of multiple components of the same type were constructed to form a comprehensive propagation evolution model of damage and life of this type of component. In addition, GMMs of multiple components of the same type at the same damage site were established, and the crack propagation and life evolution trend of the new component were predicted using the GMM.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the data-driven fatigue life prediction method as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the data-driven fatigue life prediction method as described in any one of claims 1 to 6.

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