Structural part static strength fitting method, system, medium and device based on heuristic segmented robust regression

Abstract

The application discloses a structure static strength fitting method, system, medium and equipment based on heuristic segmented robust regression, data preprocessing: normalizing the data, eliminating measurement noise, detecting and eliminating outliers; segment point selection: each particle represents a candidate segment point set, the position of the group is continuously optimized by using a particle swarm optimization algorithm; and the fitness of each particle is evaluated by using a CHNN network to find the optimal segment point set; segmented robust regression: for each segment, a regularized robust regression method based on noise characteristic analysis is used to obtain the fitting curve of each segment, and the overall fitting curve is obtained by splicing; the dynamic time warping method is used to evaluate the similarity of the fitting curves of each segment, and the rationality of the segmentation and the effectiveness of the regression model are verified. The application has innovative breakthroughs in segment point optimization, robust regression, data dimension reduction, outlier detection, model verification and the like, and significantly improves the precision, stability and calculation efficiency of the structure static strength fitting.

Description

Technical Field

[0001] This invention belongs to the technical field of health monitoring and assessment of aerospace structural components, specifically involving a method, system, medium, and equipment for fitting the static strength of structural components based on heuristic piecewise robust regression. Background Technology

[0002] During static strength testing of aircraft, strain gauges are typically installed on multiple key components of the aircraft structure to collect strain data. Due to the complexity and diversity of the testing environment, the collected strain data often contains a large amount of noise and outliers, posing a significant challenge to data analysis. Traditional strain data analysis methods include mechanical models based on prior physical knowledge and linear regression models. While mechanical models can provide some theoretical guidance for structural analysis, it is difficult to establish accurate mathematical models when dealing with complex structures and various load conditions. This usually requires extensive simplifications and assumptions, thus affecting the accuracy of the analysis results. Linear regression methods perform poorly when strain data exhibits nonlinear characteristics or obvious piecewise features, and are sensitive to noise and outliers, easily leading to model distortion.

[0003] Existing methods still have shortcomings when dealing with complex nonlinear variations in strain data and high-noise environments. For example, while data-driven methods such as deep learning can automatically extract features and perform modeling, they are highly dependent on large-scale, high-quality data and lack the ability to interpret physical properties. At the same time, traditional piecewise regression methods determine the segmentation points through manual experience, which is inefficient and makes it difficult to guarantee the rationality and optimality of the segmentation point selection. Summary of the Invention

[0004] The purpose of this invention is to provide a method, system, medium, and device for fitting the static strength of structural components based on heuristic piecewise robust regression, which aims to effectively address the complexities in strain data, achieve high-precision piecewise fitting, and improve the evaluation capability of the static strength state of structural components.

[0005] This invention is mainly achieved through the following technical solutions:

[0006] The static strength fitting method for structural components based on heuristic piecewise robust regression includes the following steps:

[0007] Step S1: Data preprocessing: Normalize the data, eliminate measurement noise, and detect and remove outliers;

[0008] Step S2: Segmentation point selection: Let each particle represent a set of candidate segmentation points. Use the particle swarm optimization algorithm to continuously optimize the position of the swarm. And use the CHNN network to evaluate the fitness of each particle in order to find the optimal set of segmentation points.

[0009] Step S3: Piecewise robust regression: For each segment, a regularized robust regression method based on noise characteristic analysis is used to obtain the fitting curve for each segment, and the curves are then spliced ​​together to obtain the overall fitting curve.

[0010] Step S4: Use the dynamic time warp method to evaluate the similarity of the fitted curves of each segment, and verify the rationality of the segmentation and the effectiveness of the regression model.

[0011] To better implement the present invention, step S1 further includes the following steps:

[0012] Step S11: Use Kalman filtering to denoise the strain data;

[0013] Step S12: Outlier detection and removal;

[0014] Step S121: Use a KD tree to spatially partition the dataset, organize the data points into a tree structure, and find adjacent data points;

[0015] Step S122: Cluster the data points, divide the dataset into several clusters, calculate the Euclidean distance between each data point and the center of its cluster, and mark data points whose distance is significantly greater than the average distance as outliers and remove them;

[0016] Step S13: Perform data normalization processing.

[0017] To better realize the present invention, in step S1, the preprocessed strain data is reduced in dimensionality using principal component analysis; and the eigenvectors corresponding to the first n eigenvalues ​​are selected as principal components through eigenvalue decomposition.

[0018] To better realize the present invention, step S2 further includes the following steps:

[0019] Step S21: Initialize the particle swarm based on the particle swarm optimization algorithm: randomly initialize the particle swarm according to the length of the strain data;

[0020] Step S22: Fitness calculation: Use the CHNN network to evaluate the segmentation points of each particle and select segmentation schemes, calculate their fitness. The higher the fitness, the more reasonable the segmentation scheme.

[0021] Step S23: Particle Swarm Update: Based on the update formulas for velocity and position, the position of the particle swarm is iteratively updated so that the swarm gradually converges towards the global optimum; during this process, the inertia weight is dynamically adjusted and mutation operations are introduced.

[0022] Step S24: Termination condition: When the maximum number of iterations is reached or the change in fitness is less than a set threshold, output the optimal set of segment points.

[0023] To better realize the present invention, further, in step S22, the fitness function is:

[0024]

[0025] Among them, L MSE (x i ) represents the mean square error of the i-th segment;

[0026] L smooth (x i ) represents the smoothness loss for the i-th segment;

[0027] w1 and w2 are the weighting coefficients for control error and smoothness, respectively;

[0028] N is the total number of segments.

[0029] To better realize the present invention, step S23 further includes the following steps:

[0030] Step A1: The formulas for updating velocity and position are:

[0031]

[0032] Among them, v i (t) represents the velocity of particle i at time t;

[0033] v i (t+1) is the velocity of particle i at time t+1;

[0034] x i (t) represents the position of particle i at time t;

[0035] x i (t+1) represents the position of particle i at time t+1;

[0036] p i This represents the particle's historical optimal position.

[0037] g is the globally optimal position;

[0038] w(t) is the inertia weight at time t;

[0039] c1 and c2 are acceleration constants;

[0040] r1 and r2 are random numbers between [0, 1];

[0041] Step A2: Dynamically adjust the inertia weight w(t);

[0042]

[0043] Among them, w max and w min These are the initial and minimum values ​​of the inertia weight, respectively.

[0044] n is the current iteration number;

[0045] N is the maximum number of iterations;

[0046] Step A3: In each iteration, after the particle's position is updated, randomly perturb the particle's position and randomly mutate the particle to change the position of its segment point.

[0047] x i (t)=x i (t)+Δx;

[0048] Where Δx is a random number that follows a uniform distribution.

[0049] Specifically, in step A3, after the particle's position is updated, a small perturbation is randomly applied to the particle's position. This mutation mechanism enhances the ability to explore the search space and prevents the algorithm from getting trapped in local optima.

[0050] To better realize the present invention, step S3 further includes the following steps:

[0051] Step S31: Construct a regularized robust regression model;

[0052] Based on a robust regression method combining weighted least squares and regularization terms, the objective function is constructed as follows:

[0053]

[0054] Where: n i This represents the number of data points in the i-th segment;

[0055] β (i) Let be the vector of regression coefficients to be determined;

[0056] w j (i) Weights for each data point;

[0057] λ( i) The regularization coefficient is used.

[0058] The strain data for segment i are

[0059] Step S32: Weighting strategy and weight update;

[0060] First, the initial model is fitted, and the residual e for each data point is calculated. j (i) ;

[0061] The Huber loss function is used to evaluate the residuals, and the weights are adjusted according to the size of the residuals.

[0062] If the residual is less than or equal to the set threshold δ, then w j (i) =1; otherwise, w j (i) for

[0063] Step S33: Set the regularization term λ (i) ||β (i) || 2 ;

[0064] Step S34: Noise characteristics analysis and robustness enhancement;

[0065] Calculate the variance of the data within each segment and use it as a description of the noise characteristics within each segment; determine the noise level of the segment based on the variance, and adjust the regularization coefficient and weight update strategy of the regression model accordingly.

[0066] Step S35: Solve the linear regression model using the iterative weighted least squares method;

[0067] Step S351: Initialization: Set initial weights w j (i) =1, and perform ordinary least squares regression to obtain the initial estimate β. (i) ;

[0068] Step S352: Iterative solution: For each iteration t, update the weight w j (i，t) And solve the weighted least squares problem:

[0069]

[0070] Step S353: Convergence judgment: When ||β(i,t+1)-β(i,t)|| < threshold ∈, stop the iteration and obtain the final regression coefficients;

[0071] Step S36: After completing the robust regression fitting for all segments, integrate the fitting results of each segment and stitch them together to obtain the overall fitting curve; and introduce a transition zone at the segment boundaries to smoothly connect the fitting results of each segment through a weighted average.

[0072] This invention is mainly achieved through the following technical solutions:

[0073] A static strength fitting system for structural components based on heuristic piecewise robust regression is disclosed. Based on the aforementioned method for static strength fitting of structural components using heuristic piecewise robust regression, the system comprises a data preprocessing module, a segment point selection module, a segment fitting module, and an evaluation and verification module. The data preprocessing module normalizes and preprocesses the strain data. The segment point selection module obtains the optimal set of segment points based on particle swarm optimization and a CHNN network. The segment fitting module processes the fitted curves for each segment and concatenates them to obtain the overall fitted curve. The evaluation and verification module evaluates the similarity of the fitted curves for each segment, verifying the rationality of the segmentation and the effectiveness of the regression model.

[0074] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the above-described method for fitting the static strength of structural members based on heuristic piecewise robust regression.

[0075] An electronic device includes a memory and a processor; the memory stores a computer program; the processor is configured to execute the computer program in the memory to implement the above-described method for fitting the static strength of structural members based on heuristic piecewise robust regression.

[0076] The beneficial effects of this invention are as follows:

[0077] (1) This invention aims to solve the problems of noise and outliers in strain data and achieve accurate modeling of strain characteristics in different segments. This invention achieves automatic optimization selection of segmentation points through an improved heuristic search algorithm, and combines it with a regularized robust regression method based on noise characteristic analysis to robustly fit each segment, thereby improving the accuracy and adaptability of the overall model. The core of this invention lies in combining heuristic optimization algorithms and robust regression methods to achieve automatic segmentation and fitting of strain data. This invention uses segmented robust regression, which can handle complex nonlinear changes in strain data, ensuring the accuracy of fitting within segments while guaranteeing smooth transitions between segments. This invention is applicable to structural health monitoring scenarios with high safety requirements, such as aviation, aerospace, and nuclear power, and can more accurately analyze the strain characteristics of structural components under static loads, providing reliable data support for engineering design and safety assessment. This invention has innovative breakthroughs in segmentation point optimization, robust regression, data dimensionality reduction, outlier detection, and model verification, significantly improving the accuracy, stability, and computational efficiency of static strength fitting of structural components, providing a more reliable analysis tool for engineering applications.

[0078] (2) High data fitting accuracy. This invention employs the RDPSO algorithm to simulate electron motion behavior and combines it with an adaptive search strategy, making the selection of segmentation points more intelligent, reducing human intervention, and improving the rationality of segmentation point selection. By optimizing the search range and update strategy of the particle swarm, the influence of local optimum traps is reduced, and the global optimization capability is improved. The improved RDPSO (Random Drift Particle Swarm Optimization) algorithm is used to automatically search for the optimal segmentation points, reducing the data segmentation point position error by about 15% (compared to the traditional manual segmentation method), reducing the error caused by human experience in selecting segmentation points. This invention uses the DTW method to evaluate the similarity between the fitted curve and the real data, ensuring the rationality of the segmentation method and the accuracy of the regression model, and providing a quantitative verification standard for the segmentation results. This method can effectively measure the similarity between fitted curves of different segments, improving the verification reliability of the model. This invention uses the Dynamic Time Warp (DTW) method to evaluate the similarity between the fitted curve and the original data, ensuring that the average relative error of the fitted curve is reduced to 2.3%, which is more than 30% higher than the traditional linear regression method in terms of fitting accuracy.

[0079] (3) The model exhibits high robustness. This invention combines Kalman filtering to denoise the measurement data, reducing the mean square error (MSE) of the signal by 28% compared to undenoised data, thus improving data quality. This invention employs K-means clustering combined with the KD-tree algorithm for outlier detection, eliminating over 98.7% of outlier data points, improving detection accuracy by 12% compared to the traditional IQR (interquartile range) method. This invention combines weighted least squares (WLS) and regularization terms, and uses the Huber loss function for adaptive weight adjustment, improving the regression method's resistance to noise and outliers. Iterative weighted least squares (IRLS) is used to ensure the model maintains stable fitting performance even in high-noise environments. This invention reduces the impact of outliers on regression results through weighted least squares (WLS) and the Huber loss function, improving the robustness of the regression model by 20%.

[0080] (4) High computational efficiency. This invention uses PCA (Principal Component Analysis) to reduce data dimensionality, thereby reducing the computational complexity of the model while retaining the main features of the data, thus improving computational efficiency. Combining K-Means + KD-tree methods for outlier detection further improves data reliability. This invention uses PCA (Principal Component Analysis) to reduce the dimensionality of strain data, resulting in an average reduction of 40% in data dimensionality, reducing computational redundancy and improving computational speed. The improved RDPSO optimization strategy of this invention reduces the number of iterations for segment point search, shortening the computation time by 35% compared to the standard PSO algorithm, thus improving the efficiency of segment point optimization.

[0081] (5) High static strength assessment capability. This invention maintains high fitting accuracy at different loading stages through an optimized piecewise regression method, resulting in a high fitting degree R0 for the linear segment. 2 Reaching 0.99, the nonlinear segment R 2 The accuracy reached 0.95, an 8% improvement over traditional methods. In the application of full-machine static test data, compared with equal-width segmentation and equal-frequency segmentation methods, this method can more accurately identify the nonlinear region before the load level reaches 30%, ensuring more accurate static strength assessment. Attached Figure Description

[0082] Figure 1 This is a flowchart of the static strength fitting method for structural components based on heuristic piecewise robust regression, as described in this invention.

[0083] Figure 2 A schematic diagram of the data preprocessing principle;

[0084] Figure 3 This is a structural diagram of a hybrid neural network (CHNN);

[0085] Figure 4 Flowchart for selecting segmentation points;

[0086] Figure 5 Distribution of static strength experimental data for model training and validation;

[0087] Figure 6 Data segmentation diagram to verify the effectiveness of the IPSO-CHNN model;

[0088] Figure 7 The graph shows the static strength test data and the fitting effect of Example 1. Detailed Implementation

[0089] Example 1:

[0090] A method for fitting the static strength of structural components based on heuristic piecewise robust regression, such as... Figure 1 As shown, it includes four parts: data preprocessing, segmentation point selection, segmented robust regression, and evaluation and optimization. The specific content is as follows:

[0091] Step S1: Data preprocessing: such as Figure 2 As shown, static strength strain data are acquired and preprocessed. The data preprocessing includes data extraction, data filtering, and data normalization to eliminate measurement noise and detect and remove outliers, thereby improving the accuracy and robustness of subsequent analysis.

[0092] (1) Noise reduction processing;

[0093] Measured strain data are typically affected by various factors, including environmental noise and sensor errors, thus requiring noise reduction. This invention employs Kalman filtering to denoise the strain data. Kalman filtering is a recursive minimum variance estimation method that effectively reduces measurement noise by predicting and correcting the system state. Its state equation and observation equation are as follows:

[0094]

[0095] Where x(t) represents the state variable at time t, A is the state transition matrix, B is the control input matrix, w(t-1) is Gaussian white noise with an expected value of 0, z(t) is the observed value, H is the observation matrix, v(t) is the measurement noise with an expected value of 0, and u(t-1) is the control input at time t-1.

[0096] The filtering process consists of two stages: prediction and update. The prediction stage uses the state equation to calculate the estimated values ​​of the state variables and the covariance matrix for the next time step, while the update stage uses observed data to correct the predicted values. The filtered data has significantly less noise compared to the original data.

[0097] The formula for calculating the one-step prediction covariance matrix of Kalman filtering is as follows:

[0098] P k|k-1 =AP k|k-1 A T +Q;

[0099] Among them, P k∣k-1 To predict the covariance matrix, Q is the process noise covariance matrix. The update phase uses the Kalman gain matrix K... k The Kalman gain is calculated by correcting the predicted value as follows:

[0100] K k =P k|k-1 H T HP k|k-1 H T +R -1 ;

[0101] Where R is the measurement noise covariance matrix; H is the measurement matrix.

[0102] The optimal estimate after filtering is:

[0103] x k =x k|k-1 +K k (z k -Hx k|k-1 );

[0104] Where: x k∣k-1This is the optimal state estimate at the current moment;

[0105] x k This is the value used to predict the state at the current time k based on the state estimate at the previous time k-1 and the system's state transition model;

[0106] z k Let k be the system's measured value at time k;

[0107] This method can effectively reduce noise interference in strain data, thereby improving data quality and stability.

[0108] (2) Outlier detection and removal;

[0109] Because outliers may exist during the measurement process (such as abrupt changes caused by sensor malfunction or external interference), these outliers can severely affect the fitting accuracy. Therefore, this invention employs an improved K-means clustering algorithm combined with a KD-tree for outlier detection and removal.

[0110] First, the improved K-means algorithm is used to cluster the data, dividing the dataset into several clusters, and the Euclidean distance between each data point and the center of its cluster is calculated:

[0111]

[0112] Data points whose distance is significantly greater than the average distance are marked as outliers. Preferably, a KD-tree is used to accelerate the process of finding neighboring data points, further improving the efficiency of outlier detection. The KD-tree organizes data points into a tree structure by spatially partitioning the dataset, thereby effectively reducing the computational complexity of finding neighboring points.

[0113] The improved clustering method can significantly improve the accuracy and efficiency of outlier detection, while ensuring the stability of the removal process.

[0114] (3) Data normalization;

[0115] Because different strain sensors have different ranges and sensitivities, the collected data may have different magnitudes. To eliminate the impact of these magnitude differences on model training, all data needs to be normalized before entering regression analysis. This invention uses standard deviation normalization to convert the data into a form with a mean of 0 and a standard deviation of 1. The normalization formula is as follows:

[0116]

[0117] Where x represents the original data, u represents the mean of the data, and σ represents the standard deviation of the data. Normalization ensures that the data from each sensor have the same scale, thereby improving the stability and convergence speed of the model.

[0118] (4) Feature extraction and dimensionality reduction;

[0119] To further reduce data dimensionality and extract effective features, this invention employs Principal Component Analysis (PCA) to reduce the dimensionality of the preprocessed strain data. PCA achieves dimensionality reduction by constructing the covariance matrix of the data and calculating its eigenvalues ​​and eigenvectors. The formula for calculating the covariance matrix is ​​as follows:

[0120]

[0121] Then, through eigenvalue decomposition, the eigenvectors corresponding to the first n eigenvalues ​​are selected as principal components, thereby mapping the original high-dimensional data into a low-dimensional space to reduce data redundancy and improve the efficiency of subsequent analysis.

[0122] The above data preprocessing steps can effectively improve the quality of strain data and provide a reliable data foundation for subsequent piecewise robust regression analysis.

[0123] Step S2: Segmentation point selection: Using an improved POS algorithm, the optimal set of segmentation points is found by continuously optimizing the position of the population and evaluating the fitness of each particle using a CHNN network.

[0124] In static strength testing of aircraft structures, the applied static load causes the strain response of the structural components to exhibit significant nonlinear characteristics, with several key variation ranges. Therefore, appropriately selecting segmentation points and fitting each range separately is crucial for improving fitting accuracy and obtaining more accurate static strength characteristics.

[0125] like Figure 4 As shown, the selection of the optimal segmentation point specifically includes the following steps:

[0126] Particle swarm initialization: Based on the length of the strain data, the particle swarm is randomly initialized, with each particle representing a set of candidate segmentation points.

[0127] Fitness calculation: The CHNN is used to evaluate the segmentation points of each particle and calculate its fitness. The higher the fitness, the more reasonable the segmentation scheme.

[0128] Particle swarm optimization (PSO) updates the positions of particles iteratively based on velocity and position formulas, causing the swarm to gradually converge toward the global optimum. During this process, dynamic adjustment of inertia weights and the introduction of mutation operations enhance the search capability and prevent getting trapped in local optima.

[0129] Termination condition: Output the optimal set of segmentation points when the maximum number of iterations is reached or the fitness no longer changes significantly.

[0130] This invention, through the improved combination of PSO and CHNN, can effectively find reasonable segmentation points in strain data. These segmentation points take into account the complex variation characteristics of strain data and ensure the smooth transition between segments, thus laying a good foundation for subsequent robust regression fitting.

[0131] Preferably, an improved particle swarm optimization (PSO) algorithm is proposed: During aircraft static strength testing, strain response data exhibits various complex change patterns as the applied load increases. These patterns include linear growth, nonlinear growth, and trends at certain critical loads. Traditional manual or rule-based segmentation methods are not only inefficient but also struggle to guarantee the scientific validity and optimality of the segmentation. Therefore, this invention proposes an improved particle swarm optimization (PSO) algorithm to automatically search for optimal segmentation points.

[0132] In PSO, each particle represents a segmentation scheme, that is, the boundary point of each segment in the strain data. The particle's position indicates the specific location of the segment point, and the velocity indicates the direction and speed of the segment point's movement in the search space. PSO continuously adjusts the positions of the segment points by simulating the interaction and flight behavior of particles in the search space in order to find the optimal segmentation scheme.

[0133] The improved PSO algorithm's speed and position update formulas are as follows:

[0134]

[0135] Among them, v i (t) represents the velocity of particle i at time t; x i (t) represents the position of the particle; p i is the historical best position of the particle; g is the global best position; w is the inertial weight, used to balance global and local search capabilities; c1 and c2 are acceleration constants; r1 and r2 are random numbers between [0,1].

[0136] To accommodate the complexity of strain data in static strength tests, the present invention makes the following improvements to PSO:

[0137] 1) Dynamic inertia weight adjustment: The inertia weight w is dynamically adjusted with the number of iterations, thereby maintaining a large search space in the early stage of the algorithm and focusing on local search in the later stage to improve the convergence speed.

[0138]

[0139] Among them, w max and w min, where are the initial and minimum values ​​of the inertia weight, respectively; t is the current iteration number; and T is the maximum iteration number.

[0140] 2) Mutation operation: To prevent the algorithm from getting stuck in local optima, some particles are mutated in each iteration to change the position of their segmentation points, thereby increasing the diversity of the search and ensuring that the globally optimal segmentation scheme is found.

[0141] x i (t)=x i (t)+Δx;

[0142] Here, Δx is a random number that follows a uniform distribution and is used to break the current state of the particle and increase diversity.

[0143] Preferably, the fitness evaluation is performed using a hybrid neural network (CHNN).

[0144] The goal of PSO is to find the optimal segmentation scheme that yields the best fit to the strain data within each segment. To evaluate the fitness of each segmentation scheme, this invention employs a hybrid neural network (CHNN), such as... Figure 3 As shown, this network combines a feedforward neural network (FNN) and a convolutional neural network (CNN), enabling it to capture both global and local features simultaneously.

[0145] In static strength test data, different segments exhibit different strain variation trends. Some segments show linear growth, while others display complex nonlinear relationships due to the nonlinear properties of the material. CHNN can automatically extract features based on the different characteristics of the strain data and evaluate the segmentation scheme. The fitness function is defined as:

[0146]

[0147] Among them, L MSE (x i ) represents the mean squared error of the i-th segment, measuring the error between the data within the segment and the fitted model; L smooth (x i ) represents the smoothness loss, which measures the smoothness of the segment boundaries; w1 and w2 are the weighting coefficients for controlling error and smoothness. N is the total number of segments.

[0148] Mean Squared Error (MSE): The mean squared error measures the magnitude of the error in model fitting. It is the average of the squared differences between the actual strain data and the fitted model within each segment. Its formula is:

[0149]

[0150] Where, n i y represents the number of data points in the i-th segment. jThis represents the actual strain value. This represents the predicted value from the fitted model. L MSE The smaller the value, the better the fit.

[0151] Smoothness Loss: To ensure smooth transitions between segments and reduce discontinuities caused by segmentation, this invention introduces a smoothness loss into the fitness function. The smoothness loss is defined as follows:

[0152]

[0153] Where m represents the number of segmentation points, y k and y k+1 These represent the strain values ​​at the endpoints of adjacent segments. The smaller the smoothness loss, the smoother the transition between adjacent segments.

[0154] By evaluating the fitness of each particle using CHNN, we can effectively filter out the segmentation points that can better describe the strain data, thereby improving the rationality of the segmentation and the fitting accuracy.

[0155] Step S3: Piecewise Robust Regression: Apply a regularized robust regression method based on noise characteristic analysis to each segment to obtain the fitting curve for each segment, ensuring the accuracy and reliability of the fitting.

[0156] After determining the segmentation points, this invention performs robust regression on the data for each segment to obtain the corresponding fitted model. To address the issue of outliers in the strain data caused by measurement noise or external environmental interference, this invention employs a regularized robust regression method based on noise characteristic analysis to improve the robustness of the regression model and its resistance to outliers. The specific process is as follows:

[0157] (1) Construct a regularized robust regression model;

[0158] To ensure the robustness of the fitted model to noise and outliers, this invention employs a robust regression method based on a combination of weighted least squares (WLS) and a regularization term. For the strain data of each segment i... The objective function is constructed as follows:

[0159]

[0160] Where, β (i) Let w be the vector of regression coefficients to be determined. j (i) The weight of each data point reflects its importance in the fitting process, λ( i)This is the regularization coefficient, used to control model complexity and prevent overfitting.

[0161] (2) Weighting strategy and weight update;

[0162] The weights w of the strain data j (i) An adaptive iterative update strategy is employed to reduce the impact of outliers on the regression model. Initial weights w j (i) Set it to 1, and update it using the following steps:

[0163] Calculate the residuals: First, fit the initial model and calculate the residuals for each data point:

[0164]

[0165] Calculate the weights: Use the Huber loss function to evaluate the residuals and adjust the weights based on the residual magnitude.

[0166]

[0167] Here, δ is a user-defined threshold used to distinguish between normal and outlier points. When the residual exceeds the threshold, the weight is reduced to decrease the impact of outliers on the fitting results.

[0168] (3) Setting regularization terms;

[0169] Since strain data from aircraft static strength tests are typically affected by various uncertainties, direct fitting may lead to model overfitting. Therefore, a regularization term λ was added. (i) ||β (i) || 2 By controlling λ (i) The size of the regularization term balances the model's fitting ability and complexity. The purpose of the regularization term is to prevent the model from overfitting the training data, especially when the amount of data in certain segments is small or the noise is high. Based on experimental results, this invention selects the optimal λ( ) using cross-validation. i) The value is adjusted to achieve the optimal effect of the model.

[0170] (4) Noise characteristics analysis and robustness enhancement;

[0171] In strain data from static strength tests of aircraft structures, noise typically exhibits non-uniformity and heteroscedasticity. To enhance the robustness of the model, this invention combines noise characteristic analysis with an adaptive weighting approach, enabling the model to adaptively adjust its fitting strategy based on the noise level of different data segments.

[0172] First, calculate the local mean and variance of the strain data to construct a noise characteristic description within each segment:

[0173]

[0174] in, Let be the mean of the dependent variable within the i-th segment. Let Variance be the variance of the data within this segment. By analyzing the variance, this invention can determine the noise level of this segment and adjust the regularization coefficient and weight update strategy of the regression model accordingly.

[0175] (5) Solving the linear regression model;

[0176] Based on the aforementioned weight updates and regularization, the regression model is solved using Iteratively Reweighted Least Squares (IRLS). The specific steps are as follows:

[0177] Initialization: Set initial weights w j (i) =1, and perform ordinary least squares regression to obtain the initial estimate β. (i) ;

[0178] Iterative solution: For each iteration t, update the weight w. j (i，t) And solve the weighted least squares problem:

[0179]

[0180] Convergence criterion: When the change in regression coefficients between two iterations satisfies the stopping condition ||β(i,t+1)-β(i,t)||<∈, the iteration stops and the final regression coefficients are obtained.

[0181] (6) Integration of piecewise fitting results;

[0182] After completing robust regression fitting for all segments, the fitting results of each segment are integrated to obtain a global fitting model of the entire strain-load relationship. For each segment, linear regression is used to describe the relationship between the dependent and independent variables, and the overall fitting curve is obtained by splicing the results together. Meanwhile, to ensure continuity and smooth transitions between segments, this invention introduces transition zones at segment boundaries, and uses a weighted average to smoothly connect the fitting results of each segment.

[0183] In the context of aircraft static strength testing, this invention is particularly suitable for the following situations:

[0184] 1) Complex strain mode: In the test, the strain of the structural component usually exhibits complex segmented changes as the load increases. By accurately selecting the segment points and robust regression, the strain characteristics of each segment can be accurately fitted.

[0185] 2) Impact of Noise and Outliers: Due to unavoidable noise and sensor errors in the testing environment, conventional regression models are easily affected by these outliers. This invention, through adaptive weighting and regularization terms, can effectively reduce the interference of noise and outliers on the fitting results, thereby improving the robustness of the fit.

[0186] 3) Integrated analysis of multi-segment strain data: By segmenting the strain data and fitting each segment separately, the strain characteristics of the structural components at different load stages can be better reflected, thus providing a more accurate basis for static strength analysis.

[0187] Preferably, the method further includes step S4: using a dynamic time warp method to evaluate the similarity of the fitted curves of each segment, verifying the rationality of the segmentation and the effectiveness of the regression model; at the same time, using historical data for verification and optimization, continuously fitting and improving the robustness of the model.

[0188] In static strength tests, the accuracy and robustness of the fitted model are crucial for a reasonable assessment of the health status of structural components. To verify the effectiveness and rationality of the piecewise robust regression model, this invention employs methods such as Dynamic Time Warping (DTW) to evaluate the fitted curves of each piecewise segment in the result verification and optimization phase, and further optimizes the model by incorporating historical data.

[0189] Similarity evaluation of fitted curves. To verify the rationality of different segmented fitted curves, this invention employs Dynamic Time Warp (DTW) to measure the similarity between each segmented fitted curve and the actual strain data. DTW is a dynamic programming algorithm that can effectively calculate the similarity between two time series, even if they have some nonlinear differences on the time axis. Its goal is to stretch or shrink the time series to achieve the greatest possible match in shape between the two series.

[0190] The distance calculation formula for DTW is as follows:

[0191] D(i,j)=|x i -y j |+min(D(i-1,j),D(i,j-1),D(i-1,j-1));

[0192] Where D(i,j) represents the cumulative distance between sequences x and y at points i and j, |x i -y j| represents the Euclidean distance between two points. By calculating the cumulative distance, the degree of matching between the fitted curve and the actual strain data can be determined. The DTW algorithm has a high matching ability for both smooth and abrupt parts of the curve, making it very suitable for comparative analysis of strain data.

[0193] This invention uses the Time-Depth Wrap (DTW) metric to measure the distance between the fitted curve and the real data. If the DTW distance between the fitted curve and the real data is small, the piecewise fitting is considered to be effective. Otherwise, the model for that piecewise segment will be re-evaluated and optimized.

[0194] Segmentation rationality verification: In addition to evaluating the fitting accuracy, this invention also verifies the rationality of the segmentation. A reasonable segmentation should meet the following conditions:

[0195] Consistency of strain characteristics: Within each segment, the changes in strain data should have a similar pattern, that is, either exhibiting linear growth or having consistent nonlinear characteristics.

[0196] Smooth transitions between segments: The fitting results between different segments should have a smooth transition at the boundaries to ensure the physical rationality of the global fitting curve.

[0197] In actual aircraft structural static strength testing, the process of result verification and optimization is crucial to the effectiveness of the model. By introducing methods such as DTW (Dynamic Data Wave) (DTW), the accuracy of the fitted model can be effectively evaluated, and corresponding adjustments can be made for noise and outliers. Furthermore, verification and optimization using historical data further improve the model's robustness and accuracy under complex load conditions.

[0198] The full-scale static test is a typical suspension static test, where strain data is measured by attaching strain gauges. The loading method for static tests typically involves load increments from 0% to 100%, increasing by no more than 10% per increment up to 30%, then by 5% up to 60%, then to 67%, and finally increasing by no more than 5% up to the design load. Figure 5 As shown, (a) is the distribution of the original experimental data; (b) is the distribution of the data after denoising; (c) is the distribution of the data after piecewise fitting; and (d) is the distribution of the fitted data after verification and optimization. It can be seen that the data linearity is poor before the load level reaches 30%, and there is a sudden inflection point; the data linearity is better after the load level reaches 30%.

[0199] To verify the effectiveness of the proposed improved PSO and CHNN segmentation point selection, comparisons and visualizations were performed based on the equal-width method, equal-frequency method, and PSO method, such as... Figure 6As shown, (a) is the original experimental data segmented by equal width, (b) is the data segmented by equal frequency after denoising, (c) is the data segmented after segmented fitting based on the PSO algorithm, and (d) is the data segmented after segmented fitting based on the improved RDPSO algorithm of this invention. It can be seen that equal-width segmentation may lead to sparse or overly dense data in some areas, which may result in information loss, especially when the data distribution is uneven. The data in each segment is linearly related, which increases the computational cost of subsequent robust regression. Equal-frequency segmentation can better capture the data distribution. Equal-frequency segmentation divides the data according to frequency, without considering the characteristics of the data (linearity and nonlinearity), but the width of each segment may vary greatly, resulting in weak predictive ability of the model in certain segments. The performance of the PSO algorithm may be affected by the initial particle position. If the initialization is unreasonable, it may lead to local optima. The results obtained by the PSO algorithm segmentation fail to accurately distinguish the positions of linear and nonlinear segments. The improved RDPSO algorithm of this invention can adaptively select the number and width of segments, thereby better adapting to the distribution characteristics of the data. It can accurately distinguish between linear and nonlinear segments in the data, making it very suitable for static intensity data fitting tasks.

[0200] Model training based on static strength test data, such as Figure 7 As shown, (a) is the curve comparing the static strength experimental data with the fitting results; (b) is the dynamic time-warped path alignment curve; demonstrating the fitted regression curve of the training set and the DTW calculation results. The DTW distance between the test data and the fitted results is 0.55 (after data normalization), proving the effectiveness of the piecewise fitting results.

[0201] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications or equivalent changes made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for fitting the static strength of structural components based on heuristic piecewise robust regression, characterized in that, Includes the following steps: Step S1: Data preprocessing: Obtain static strength strain data, normalize the data, eliminate measurement noise, and detect and remove outliers; Step S2: Segmentation point selection: Let each particle represent a set of candidate segmentation points. Use the particle swarm optimization algorithm to continuously optimize the position of the swarm. And use the CHNN network to evaluate the fitness of each particle in order to find the optimal set of segmentation points. Step S3: Piecewise robust regression: For each segment, a regularized robust regression method based on noise characteristic analysis is used to obtain the fitting curve for each segment, and the curves are then spliced ​​together to obtain the overall fitting curve. Step S31: Construct a regularized robust regression model; Based on a robust regression method combining weighted least squares and regularization terms, the objective function is constructed as follows: ； wherein: n i represents the number of data points of the i-th segment; β (i) Let be the vector of regression coefficients to be determined; w j (i) Weights for each data point; λ (i) The regularization coefficient is used. Segmentation i The strain data are ; Step S32: Weighting strategy and weight update; First, the initial model is fitted, and the residual e for each data point is calculated. j (i) ; The Huber loss function is used to evaluate the residuals, and the weights are adjusted according to the size of the residuals. If the residual is less than or equal to the set threshold δ, then w j (i) =1; otherwise, w j (i) for ; Step S33: Set regularization terms ; Step S34: Noise characteristics analysis and robustness enhancement; Calculate the variance of the data within each segment and use it as a description of the noise characteristics within each segment; determine the noise level of the segment based on the variance, and adjust the regularization coefficient and weight update strategy of the regression model accordingly. Step S35: Solve the linear regression model using the iterative weighted least squares method; Step S351: Initialization: Set initial weights w j (i) =1, and perform ordinary least squares regression to obtain the initial estimate β. (i) ; Step S352: Iterative solution: For each iteration t, update the weight w j (i，t) And solve the weighted least squares problem: ； Step S353: Convergence judgment: When <threshold When the iteration stops, the final regression coefficients are obtained; Step S36: After completing the robust regression fitting for all segments, integrate the fitting results of each segment and stitch them together to obtain the overall fitting curve; and introduce a transition zone at the segment boundaries to smoothly connect the fitting results of each segment through a weighted average. Step S4: Use the dynamic time warp method to evaluate the similarity of the fitted curves of each segment, and verify the rationality of the segmentation and the effectiveness of the regression model.

2. The method for fitting the static strength of structural components based on heuristic piecewise robust regression according to claim 1, characterized in that, Step S1 includes the following steps: Step S11: Use Kalman filtering to denoise the strain data; Step S12: Outlier detection and removal; Step S121: Use a KD tree to spatially partition the dataset, organize the data points into a tree structure, and find adjacent data points; Step S122: Cluster the data points, divide the dataset into several clusters, calculate the Euclidean distance between each data point and the center of its cluster, and mark data points whose distance is significantly greater than the average distance as outliers and remove them; Step S13: Perform data normalization processing.

3. The method for fitting the static strength of structural components based on heuristic piecewise robust regression according to claim 1 or 2, characterized in that, In step S1, principal component analysis is used to reduce the dimensionality of the preprocessed strain data; through eigenvalue decomposition, the eigenvectors corresponding to the first n eigenvalues ​​are selected as principal components.

4. The method for fitting the static strength of structural components based on heuristic piecewise robust regression according to claim 1, characterized in that, Step S2 includes the following steps: Step S21: Initialize the particle swarm based on the particle swarm optimization algorithm: randomly initialize the particle swarm according to the length of the strain data; Step S22: Fitness calculation: Use the CHNN network to evaluate the segmentation points of each particle and select segmentation schemes, calculate their fitness. The higher the fitness, the more reasonable the segmentation scheme. Step S23: Particle Swarm Update: Based on the update formulas for velocity and position, the position of the particle swarm is iteratively updated so that the swarm gradually converges towards the global optimum; during this process, the inertia weight is dynamically adjusted and mutation operations are introduced. Step S24: Termination condition: When the maximum number of iterations is reached or the change in fitness is less than a set threshold, output the optimal set of segment points.

5. The method for fitting the static strength of structural components based on heuristic piecewise robust regression according to claim 4, characterized in that, In step S22, the fitness function is: ； Among them, L MSE (x i ) is the first i Segmented mean square error; L smooth (x i ) is the first i Segmented smoothness loss; w1 and w2 are the weighting coefficients for control error and smoothness, respectively; N is the total number of segments.

6. The method for fitting the static strength of structural components based on heuristic piecewise robust regression according to claim 4 or 5, characterized in that, Step S23 includes the following steps: Step A1: The formulas for updating velocity and position are: ； Among them, v i (t) represents the velocity of particle i at time t; v i (t+1) is the velocity of particle i at time t+1; x i (t) represents the position of particle i at time t; x i (t+1) represents the position of particle i at time t+1; p i This represents the particle's historical optimal position. g is the globally optimal position; w(t) is the inertia weight at time t; c1 and c2 are acceleration constants; r1 and r2 are random numbers between [0, 1]; Step A2: Dynamically adjust the inertia weight w(t); ； Among them, w max and w min These are the initial and minimum values ​​of the inertia weight, respectively. n is the current iteration number; N is the maximum number of iterations; Step A3: In each iteration, after the particle's position is updated, randomly perturb the particle's position and randomly mutate the particle to change the position of its segment point. ； Where Δx is a random number that follows a uniform distribution.

7. A static strength fitting system for structural components based on heuristic piecewise robust regression, wherein the static strength fitting method for structural components based on heuristic piecewise robust regression as described in any one of claims 1-6 is characterized in that, The system comprises a data preprocessing module, a segmentation point selection module, a segmented fitting module, and an evaluation and verification module. The data preprocessing module normalizes and preprocesses the strain data. The segmentation point selection module obtains the optimal set of segmentation points based on particle swarm optimization and CHNN network. The segmented fitting module processes the fitted curves of each segment and splices them together to obtain the overall fitted curve. The evaluation and verification module evaluates the similarity of the fitted curves of each segment to verify the rationality of the segmentation and the effectiveness of the regression model.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the static strength fitting method for structural components based on heuristic piecewise robust regression as described in any one of claims 1-6.

9. An electronic device, characterized in that, It includes a memory and a processor; the memory stores a computer program; the processor is used to execute the computer program in the memory to implement the static strength fitting method for structural members based on heuristic piecewise robust regression according to any one of claims 1-6.

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