Method and system for predicting crack width of three-cantilever beam structure based on regression problem

Abstract

The invention belongs to the technical field of building monitoring, and discloses a three-cantilever beam structure crack width prediction method and system based on a regression problem, and the method comprises the following steps: obtaining simulation data sets of a three-cantilever beam identifier structure under different crack conditions; through multivariable visualization and correlation analysis, identifying the multicollinearity between the crack width data and the cantilever beam strain data, and deleting redundant variables to obtain an optimized data set; constructing a plurality of regression models, training and evaluating each regression model by using the optimized data set, and selecting an optimal regression model as a crack width prediction model according to an evaluation result; and the obtained cantilever beam strain data are input into the crack width prediction model, and corresponding crack width data are predicted through the crack width prediction model. According to the method, multi-dimensional information identification and event prediction of the micro gap of the structural body are effectively realized, and technical support is provided for building structure health monitoring and engineering implementation.

Description

Technical Field

[0001] The present invention relates to the technical field of building monitoring, and particularly to a method and system for predicting crack width of a three-cantilever beam structure based on a regression problem. Background Art

[0002] Buildings are important places or facilities for humans to live or engage in various survival activities, and their safety directly affects the survival and development of humans. Therefore, accurate health monitoring of buildings such as buildings and bridges is an important research direction in modern engineering. The main purpose of building structure health monitoring is to collect information of various different physical quantities by installing a variety of sensors on structures such as buildings, roads, and bridges, obtain the structural responses of buildings, roads, and bridges to factors such as human or environmental excitation, and further judge the degree of structural damage, so as to provide safety assessment and maintenance reference for the human living environment and provide a basis for predicting its future health trend. The core of structural health monitoring is information acquisition, analysis, and judgment. With the continuous improvement of humans' requirements for the safety of the living environment, sensing the structural health through sensors is becoming an effective means and measure and is widely used; at the same time, traditional structural health monitoring means and measurement methods that highly rely on manual work are gradually withdrawing from the historical stage, and intelligent sensors and massive data processing technologies based on artificial intelligence are quickly highlighting their advantages and will play an increasingly important role in the field of structural health monitoring.

[0003] The connotation of building structure health monitoring is all-encompassing, and cracks are one of the important monitoring objects. There are various crack monitoring methods such as sensors and fiber Bragg gratings. There are various modes of sensor monitoring, and among them, the strain gauge type is widely favored due to its simple structure. The existing method of pasting strain gauges on a double-cantilever beam structure can identify the width of existing cracks, but cannot predict the width of newly generated cracks. In addition, the existing single-dimensional identification method for double-cantilever beams has a large error when measuring the crack width that is not centered on the geometric center of the double-cantilever beam structure through traditional calibration techniques.

[0004] Therefore, how to provide a method and system for predicting crack width of a three-cantilever beam structure based on a regression problem is an urgent problem to be solved at present. Summary of the Invention

[0005] Embodiments of the present invention provide a method and system for predicting crack width of a three-cantilever beam structure based on a regression problem to solve the problems in the prior art.

[0006] To have a basic understanding of some aspects of the disclosed embodiments, a simple summary is given below. This summary part is not a general review, nor is it to identify key / important constituent elements or depict the protection scope of these embodiments. Its sole purpose is to present some concepts in a simple form as a preface to the subsequent detailed description.

[0007] According to the first aspect of the embodiments of the present invention, a method for predicting the crack width of a three-cantilever beam structure based on a regression problem is provided.

[0008] In one embodiment, the method for predicting the crack width of a three-cantilever beam structure based on a regression problem includes the following steps: Perform a static simulation on the three-cantilever beam identification structure using the finite element method, and obtain a simulation data set of the three-cantilever beam identification structure under different crack conditions; the simulation data set includes crack width data and cantilever beam strain data; According to the simulation data set, identify the multicollinearity between the crack width data and the cantilever beam strain data through multivariate visualization and correlation analysis, and delete redundant variables to obtain an optimized data set; Construct multiple regression models, train and evaluate each regression model using the optimized data set, and select the optimal regression model as the crack width prediction model according to the evaluation results; Obtain the cantilever beam strain data and input it into the crack width prediction model, and predict the corresponding crack width data through the crack width prediction model.

[0009] In one embodiment, the step of performing a static simulation on the three-cantilever beam identification structure using the finite element method and obtaining a simulation data set of the three-cantilever beam identification structure under different crack conditions includes the following steps: Construct a simulation measurement environment for the three-cantilever beam identification structure and the matching calibration structure, and determine the constraint conditions of the three-cantilever beam identification structure; Combine the preset simulation purpose to determine the boundary conditions of the three-cantilever beam identification structure and the matching calibration structure; Perform a static simulation in the finite element analysis software, and collect the strain data of the three-cantilever beam identification structure under different crack conditions to obtain a simulation data set.

[0010] In one embodiment, the step of performing a static simulation in the finite element analysis software, and collecting the strain data of the three-cantilever beam identification structure under different crack conditions to obtain a simulation data set includes the following steps: Create a three-dimensional geometric model of the three-cantilever beam identification structure and the matching calibration structure in the finite element analysis software, and perform mesh division processing on the geometric model; Based on the constraint conditions of the three-cantilever beam identification structure, apply a load to the three-cantilever beam identification structure, and obtain the strain data at the cantilever of the three-cantilever beam identification structure to obtain a simulation data set.

[0011] In one embodiment, the constraint condition of the three-cantilever beam identification structure is to fix the crack direction and change the crack width size.

[0012] In one embodiment, the load applied to the three-cantilever beam identification body structure is a forced displacement load.

[0013] In one embodiment, the steps of identifying the multicollinearity between the crack width data and the cantilever beam strain data according to the simulation data set through multivariate visualization and correlation analysis, and deleting redundant variables to obtain an optimized data set include the following: For the simulation data set, use visualization software to draw the corresponding relationship diagram between variables, observe the distribution relationship and trend between variables, and calculate the determination coefficient in combination with the multiple regression model; the variables include the response variable vector and the regression variables. Calculate the variance inflation factor of the regression variables according to the determination coefficient, and judge whether there is a multicollinearity problem between the regression variables based on a preset threshold. If so, delete the regression variables; otherwise, retain the regression variables. Integrate the deleted or retained regression variables with the response variable vector to obtain an optimized data set.

[0014] In one embodiment, the calculation formula for calculating the variance inflation factor of the regression variables according to the determination coefficient is: ; In the formula, represents the variance inflation factor of the regression variable j , represents the determination coefficient of the regression variable j .

[0015] In one embodiment, the steps of constructing multiple regression models, training and evaluating each regression model using the optimized data set, and selecting the optimal regression model as the crack width prediction model according to the evaluation results include the following: Based on a preset regression algorithm, construct multiple regression models, and divide the optimized data set into a training set and a test set. Use the training set to train the multiple regression models, and use the test set to evaluate the trained multiple regression models to obtain evaluation indicators. According to the values of the evaluation indicators, compare the performance of different regression models, and select the regression model with the best performance as the crack width prediction model.

[0016] In one embodiment, the evaluation indicators include mean square error, root mean square error, mean absolute error, and determination coefficient.

[0017] According to the second aspect of the embodiments of the present invention, a three-cantilever beam structure crack width prediction system based on a regression problem is provided.

[0018] In one embodiment, the three-cantilever beam structure crack width prediction system based on regression problems includes: A data acquisition module, configured to perform static simulation on the three-cantilever beam identification body structure by using the finite element method, and obtain a simulation data set of the three-cantilever beam identification body structure under different crack conditions; the simulation data set includes crack width data and cantilever beam strain data; A data optimization module, configured to identify the multicollinearity between the crack width data and the cantilever beam strain data according to the simulation data set through multivariate visualization and correlation analysis, and delete redundant variables to obtain an optimized data set; A model construction module, configured to construct multiple regression models, train and evaluate each regression model by using the optimized data set, and select the optimal regression model as the crack width prediction model according to the evaluation results; A width prediction module, configured to obtain the cantilever beam strain data and input it into the crack width prediction model, and predict the corresponding crack width data through the crack width prediction model.

[0019] According to the third aspect of the embodiments of the present invention, a computer device is provided.

[0020] In some embodiments, the computer device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps of the above method are implemented.

[0021] According to the fourth aspect of the embodiments of the present invention, a computer-readable storage medium is provided.

[0022] In one embodiment, a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0023] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects: Based on the application background of building structure health monitoring, starting from the cause tracing of concrete structure cracks, taking the single-dimensional identification of a double-cantilever beam as the research basis point, generalizing the concrete structure cracks into tiny gaps in the structure body, the present invention proposes a multi-dimensional identification method for a three-cantilever beam, and establishes a prediction model for the width of tiny gaps in the structure body based on regression problems from the perspective of machine learning, effectively realizing the multi-dimensional information identification and situation prediction of tiny gaps in the structure body, and will provide technical support for building structure health monitoring and engineering implementation.

[0024] It should be understood that the above general description and subsequent detailed description are only exemplary and explanatory, and cannot limit the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings here are incorporated into the specification and form a part of this specification, showing embodiments consistent with the present invention, and are used together with the specification to explain the principles of the present invention.

[0026] Figure 1 is a flowchart of a method for predicting crack width of a three-cantilever beam structure based on a regression problem shown according to an exemplary embodiment; Figure 2 is a schematic block diagram of a system for predicting crack width of a three-cantilever beam structure based on a regression problem shown according to an exemplary embodiment; Figure 3 is a schematic structural diagram of a computer device shown according to an exemplary embodiment; Figure 4 is a scatter plot of autoregressive residuals of regression variables of a three-cantilever beam multi-dimensional identification method in a method for predicting crack width of a three-cantilever beam structure based on a regression problem shown according to an exemplary embodiment; Figure 5 is a schematic diagram of the correlation between strain data and crack width in a method for predicting crack width of a three-cantilever beam structure based on a regression problem shown according to an exemplary embodiment; Figure 6 is of different regression models in a method for predicting crack width of a three-cantilever beam structure based on a regression problem shown according to an exemplary embodiment k line chart of evaluation indexes of k-fold cross-validation; Figure 7 is a line chart of the mean absolute error MAE and mean square error MSE of different regression models in a method for predicting crack width of a three-cantilever beam structure based on a regression problem shown according to an exemplary embodiment; Figure 8 is of the coefficient of determination of different regression models in a method for predicting crack width of a three-cantilever beam structure based on a regression problem shown according to an exemplary embodiment line chart. Detailed implementation manners

[0027] The following description and drawings fully disclose specific embodiments herein, enabling those skilled in the art to practice them. Parts and features of some embodiments may be included in or replace parts and features of other embodiments. The scope of the embodiments herein includes the entire scope of the claims and all available equivalents of the claims. In this document, terms such as "first", "second", etc. are only used to distinguish one element from another, without requiring or implying any actual relationship or order between these elements. In fact, the first element can also be called the second element, and vice versa. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, such that a structure, device or equipment comprising a series of elements not only includes those elements but also other elements not explicitly listed, or elements inherent to such structure, device or equipment. Without further limitation, an element defined by the statement "comprising one..." does not exclude the presence of additional identical elements in the structure, device or equipment comprising the said element. The embodiments herein are described in a progressive manner, with each embodiment highlighting the differences from other embodiments. For the same or similar parts among the embodiments, reference may be made to each other.

[0028] In this document, the orientation or positional relationships indicated by terms such as "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. are based on the orientation or positional relationships shown in the drawings, and are only for the convenience of describing this document and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation of the present invention. In the description herein, unless otherwise specified and defined, the terms "mounted", "connected" and "coupled" shall be understood in a broad sense. For example, it may be a mechanical connection or an electrical connection, or it may be the communication inside two elements. It may be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms may be understood according to specific circumstances.

[0029] In this document, unless otherwise stated, the term "plurality" means two or more.

[0030] In this document, the character " / " indicates that the objects before and after are in an "or" relationship. For example, A / B means: A or B.

[0031] In this document, the term "and / or" is an associative relationship describing an object, indicating that three relationships can exist. For example, A and / or B means: A or B, or, A and B these three relationships.

[0032] It should be understood that although the steps in the flowcharts are shown sequentially in the direction of the arrows, these steps are not necessarily executed sequentially in the order indicated by the arrows. Unless otherwise clearly stated in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, at least a part of the steps in the figure may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least a part of other steps or sub-steps or stages of other steps.

[0033] Each module in the device or system of the present application can be implemented in whole or in part by software, hardware, and their combination. The above-mentioned modules can be embedded in the processor of the computer device in hardware form or independent of it, or stored in the memory of the computer device in software form, so that the processor can call and execute the operations corresponding to the above-mentioned modules.

[0034] Without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0035] Figure 1 An embodiment of the method for predicting the crack width of a three-cantilever beam structure based on a regression problem of the present invention is shown.

[0036] In this alternative embodiment, the method for predicting the crack width of a three-cantilever beam structure based on a regression problem includes the following steps: Step S101, performing a static simulation on the three-cantilever beam identification body structure by using the finite element method, and obtaining a simulation data set of the three-cantilever beam identification body structure under different crack conditions; the simulation data set includes crack width data and cantilever beam strain data; Step S102, according to the simulation data set, through multivariate visualization and correlation analysis, identifying the multicollinearity between the crack width data and the cantilever beam strain data, and deleting redundant variables to obtain an optimized data set; Step S103, constructing multiple regression models, training and evaluating each regression model by using the optimized data set, and selecting the optimal regression model as the crack width prediction model according to the evaluation results; Step S104, obtaining the cantilever beam strain data and inputting it into the crack width prediction model, and predicting the corresponding crack width data through the crack width prediction model.

[0037] It should be noted that in order to accurately identify the width and direction information of the tiny gaps in the building structure, it is necessary to establish a crack prediction model based on the multi-dimensional identification method of a three-cantilever beam. Compared with the two-cantilever beam single-dimensional identification body, the measurement dimension of the three-cantilever beam multi-dimensional identification body increases, which also increases the sensor measurement point data, and the types of regression variables used as the input of the prediction model also increase. The static simulation variables of the three-cantilever beam multi-dimensional identification body include the strain of cantilever beam A , the strain of cantilever beam B , the strain of cantilever beam C , the crack width and the crack angle . The goal of establishing the prediction model of the three-cantilever beam multi-dimensional identification body is to accurately predict the width of new and old cracks , and using the strains of the cantilever beams, and the crack angle , where the crack angle is the crack direction .

[0038] In this alternative embodiment, the steps of performing static simulation on the structure of the three-cantilever beam identification body using the finite element method and obtaining the simulation data set of the three-cantilever beam identification body structure under different crack conditions are as follows: Construct the simulation measurement environment of the three-cantilever beam identification body structure and the matching calibration structure, and determine the constraint conditions of the three-cantilever beam identification body structure; Combined with the preset simulation purpose, determine the boundary conditions of the three-cantilever beam identification body structure and the matching calibration structure; Perform static simulation in the finite element analysis software, and collect the strain data of the three-cantilever beam identification body structure under different crack conditions to obtain the simulation data set.

[0039] Among them, the three-cantilever beam identification body structure is the main body of the mechanical structure of the three-cantilever beam multi-dimensional identification body. It is composed of a bottom plate, a spring steel sheet, a pressing block, a PCB bearing stud, an installation foot, etc. The simplified structure material of the three-cantilever beam identification body is ordinary carbon steel.

[0040] Among them, the matching calibration structure includes two calibration platforms symmetrically arranged and a calibration threaded hole array evenly distributed with the pitch of the simplified structure installation threaded holes as the diameter. The change in the crack direction is achieved by changing the matching relationship between the simplified structure installation holes and the calibration threaded hole array; the change in the crack width is achieved by changing the displacement between the calibration platforms. The change of the matching parameters and the displacement parameters during the simulation process is collectively referred to as the change of the test conditions. The simplified structure is constrained by matching with a certain symmetric thread of the calibration threaded hole array through the bottom foot installation threaded holes; the bottom corner planes of the simplified structure are respectively constrained by the contact surfaces with the calibration platforms; the calibration platforms are constrained by the contact surfaces. Once the constraint relationship is established, it means that there is a rigid connection in the matching during the simulation process, that is, there is no relative displacement.

[0041] In this alternative embodiment, the static simulation is carried out in the finite element analysis software, and the strain data of the three-cantilever beam identification body structure under different crack conditions are collected. The steps to obtain the simulation data set include: Create a three-dimensional geometric model of the three-cantilever beam identification body structure and the matching calibration structure in the finite element analysis software, and perform mesh division processing on the geometric model; Based on the constraint conditions of the three-cantilever beam identification body structure, apply a load to the three-cantilever beam identification body structure, and obtain the strain data at the upper cantilever of the three-cantilever beam identification body structure to obtain the simulation data set.

[0042] In this alternative embodiment, the constraint condition of the three-cantilever beam identification body structure is to fix the crack direction and change the crack width size.

[0043] In this alternative embodiment, the load applied to the three-cantilever beam identification body structure is a forced displacement load.

[0044] In this alternative embodiment, the steps to obtain the optimized data set by identifying the multicollinearity between the crack width data and the cantilever beam strain data through multivariate visualization and correlation analysis based on the simulation data set and deleting redundant variables include: For the simulation data set, use visualization software to draw the corresponding relationship diagram between variables, observe the distribution relationship and trend between variables, and calculate the determination coefficient in combination with the multiple regression model; the variables include the response variable vector and the regression variables; Calculate the variance inflation factor of the regression variables according to the determination coefficient, and judge whether there is a multicollinearity problem between the regression variables based on a preset threshold. If so, delete the regression variables, otherwise, retain the regression variables; Integrate the deleted or retained regression variables with the response variable vector to obtain the optimized data set.

[0045] In this alternative embodiment, the calculation formula for calculating the variance inflation factor of the regression variables according to the determination coefficient is: ; In the formula, represents the variance inflation factor of the regression variable j , represents the coefficient of determination of the regression variable j .

[0046] It should be noted that through variable visualization, it can be seen that there is a weak correlation among the three regression variables of the strain of the cantilever beam , and . However, as the crack angle increases or decreases, the change trends of the three regression variables are similar, and there is an obvious periodic delay between the similar change trends. To test and confirm whether there is a problem of multicollinearity among the regression variables, the variance inflation factors of the three regression variables of the strain of the cantilever beam , and are now examined. Taking the strain of cantilever beam A as the response variable, its autoregressive residual scatter plot is as shown in Figure 4 .

[0047] In addition, if the regression variables participating in the establishment of the prediction model are orthogonal, an inaccurate inference can be obtained, that is, the mutual influence among the regression variables is small and it is suitable for the prediction model. In most cases, the regression variables are not orthogonal, and the lack of orthogonality is not a serious problem restricting the quality of the prediction model; if there is a nearly linear relationship among the regression variables, there may be a problem of multicollinearity, which may lead to the prediction model being misled and giving wrong prediction conclusions.

[0048] To check the multicollinearity of the variable data, a multiple regression model is first introduced: ; In the formula, y is the response variable vector, X is the regression variable matrix, β is the coefficient vector, is the random error, where follows a normal distribution with a mean of 0 and a variance of . If there exists a set t 1 , t 2 ，t 3 ,....... t p that are not all zero and satisfy the equation: ; In the formula, p represents the upper limit of the summation operation ( j = 1~ p ), represents the regression coefficient.

[0049] Then the regression variables X can be considered to be linearly correlated. If the subset of X satisfies the above equation, the correlation coefficient matrix The rank of is less than p, and does not exist. Assume that this is approximately true for some subset of X, then There will be a linear correlation in the data, and it can be considered that there is a multicollinearity problem.

[0050] Variance inflation factor is usually used to test multicollinearity. For the correlation coefficient matrix, we have: ; The j-th diagonal element of the correlation coefficient matrix C It can be written as: ; In the formula, Yes The coefficient of determination obtained when regressing on the other (p-1) regressors. If the regressors are nearly orthogonal, then Smaller, is close to 1; if there is a nearly linear relationship between the regression variables, then Close to 1, On the contrary, it becomes larger. Since the variance of the j-th regression coefficient is ,in Can be seen as the slope Least Squares Estimation Variance Increased impact factor, thus As a variance inflation factor To test multicollinearity. According to the multicollinearity diagnostic criteria, if the variance inflation factor is less than 10, it can be considered that there is no multicollinearity problem between the regression variables, and the smaller the index, the better; on the contrary, if it is greater than 10, it indicates that there is a multicollinearity problem between the regression variables and the severity of the problem increases with the increase of the index.

[0051] In addition, there are several common methods to solve multicollinearity: (1) Increase the amount of data for regression variables: The biggest problem with multicollinearity is that it increases the slope. The least squares estimate of variance Increasing the amount of data for regression variables can reduce the variance of parameter estimates overall, thereby reducing the impact of multicollinearity; but on the other hand, the increase in data volume is limited by more practical factors, such as cost or the scope of the design model.

[0052] (2) Reducing the types of regression variables: When there are 3 or more types of regression variables, deleting one of the two regression variables with multicollinearity problems may solve the problems caused by multicollinearity. However, deleting variables will also result in the loss of variable information in the prediction model. Once important variables are removed, the quality of the prediction model will be immediately affected.

[0053] (3) Dimension reduction of regression variables: Dimension reduction of data refers to generating new regression variables through a certain operation using two or more original regression variables to replace the original regression variables. Dimension reduction of data requires minimizing information loss after the emergence of new variables and the elimination of original variables. A common method for data dimension reduction is principal component analysis.

[0054] (4) Adding penalty terms: For a linear regression model, it is a relatively common method to eliminate multicollinearity by adding penalty terms (regularization terms) to the loss function (cost function). For penalty terms, the L0 norm penalty term starts from non-zero parameters for restriction, that is, restricting the number of non-zero parameters within a certain range to achieve the purpose of restricting the model; the L1 norm penalty term requires the sum of parameter values to be restricted within a certain range, that is, the sum of parameters needs to be less than a certain value, and the L1 norm penalty is also called parameter sparsity penalty; the L2 norm penalty term adds a square term to avoid the problem of positive and negative cancellation, and the L2 norm penalty is also called weight decay penalty. Among the multiple regression algorithms selected in this paper, the LASSO regression uses the L1 norm penalty term; the Ridge regression uses the L2 norm penalty term.

[0055] (5) Head-in-the-sand policy: The essence of the head-in-the-sand policy is to ignore the problem of multicollinearity. If the prediction model is not affected by the multicollinearity of known data, the problem of multicollinearity can be ignored. The rationality of the head-in-the-sand policy also shows from another angle that the problem of multicollinearity among regression variables cannot be used as a necessary and sufficient condition for the inapplicability of the prediction model.

[0056] In this alternative embodiment, the steps of constructing multiple regression models, training and evaluating each regression model using the optimized data set, and selecting the optimal regression model as the crack width prediction model according to the evaluation results are as follows: Based on a preset regression algorithm, construct multiple regression models, and divide the optimized data set into a training set and a test set; Use the training set to train the multiple regression models, and use the test set to evaluate the trained multiple regression models to obtain evaluation indicators; According to the values of the evaluation indicators, compare the performances of different regression models, and select the regression model with the best performance as the crack width prediction model.

[0057] In this alternative embodiment, the evaluation indicators include mean squared error, root mean squared error, mean absolute error, and coefficient of determination.

[0058] It should be noted that according to the target variable attributes, the essence of width prediction is a regression problem. In the process of establishing, training, and evaluating the prediction model in the present invention, the prediction variable (strain data) data set will be divided into a training set and a test set to improve the generalization ability of the model. The data volume of the training set accounts for about 70% of the total data volume of the data set; the data volume of the test set accounts for about 30%.

[0059] Among them, regression analysis is to study the internal relationship between variables by building a regression model. The regression equation is an approximation of the actual variable functional relationship by the regression model. It reflects the mutual dependence and influence degree between variables. The actual functional relationship is usually based on physical, chemical, or other engineering theories. Therefore, the actual functional relationship is often called a mechanism model, while the regression equation is called an empirical model. Regression analysis is also the theoretical basis of machine learning and the core connotation of various data processing algorithms in machine learning. Establishing a multi-dimensional recognition and situation prediction model for micro-gaps in structures from the perspective of machine learning is the innovation basis of this article. Based on the regression-based variable correlation analysis, the present invention only considers two variables, aiming to reveal the relationship between the strain of the cantilever beam and the width of the micro-gap in the structure when the crack direction is known through a relatively complete regression analysis; Taking the strain of the cantilever beam as the independent variable and the crack width as the dependent variable, a scatter plot of the crack width versus the two independent variables can be given, as shown in Figure 5 ; the crack width shows a linear relationship with the strain of the cantilever beam respectively; now, from the perspective of regression, the correlation between the crack width and the strain of any single-sided cantilever beam is analyzed.

[0060] Now considering the correlation between the crack width and the strain of any single-sided cantilever beam, taking cantilever beam A as an example, let the strain of cantilever beam A be the independent variable x and the crack width be the dependent variable y, then the regression model is: ; The above formula is also called the overall regression model, where is the intercept, is the slope, which belongs to unknown constant terms; is the random error term, usually assumed to be uncorrelated, representing the noise term not covered by the linear relationship of the model, with a mean of 0 and a variance of .

[0061] For the evaluation index of the regression algorithm, there is the mean squared error (Mean Squared Error, MSE), Root Mean Squared Error, RMSE ), Mean Absolute Error, MAE ), and coefficient of determination R 2 (R Squared, R 2 ).

[0062] Mean squared error MSE : ; In the formula, m represents the upper limit of the cumulative operation ( i= 1 ~m ), i represents the counting pointer.

[0063] Mean squared error MSE For the test set, from the formula, the mean squared error MSE is the sum of squared residuals (sum of squared errors) averaged based on the total data volume of the dataset. Its essence is also the squared loss function. The mean squared error MSE gives the gap between the observed value and the predicted value . The smaller this indicator, the better.

[0064] Root Mean Squared Error RMSE : ; Root Mean Squared Error RMSE For the test set, it is obtained by taking the square root of the mean squared error MSE . The Root Mean Squared Error RMSE gives the gap between the observed value and the predicted value from the perspective of square root. The smaller this indicator, the better.

[0065] Mean Absolute Error MAE : ; The role of the coefficient of determination is to give the nature of the variability explained by the regression variable x. By the relationship between the total sum of squares of the model and the sum of squared residuals , that is , the value range of should be within . Thus the closer it is to 1, the more it indicates that most of the variability of the response variable y can be explained by the regression model: ; Coefficient of determination R 2 The value range is 0 ≤ R 2 ≤ 1. The closer the coefficient of determination R 2 is to 1, the stronger the explanatory power of the prediction model for the predicted value.

[0066] In addition, the crack width prediction model uses 15 regression algorithms including LASSO (Least Absolute Shrinkage and Selection Operator regression), Elastic Net regression, Ridge regression, Gradient Boosting regression, Light GBM (Light Gradient Boosted Machine) regression, XG Boost (Extreme Gradient Boosting regression), decision tree regression, linear regression, SVM (Support Vector Machine regression), KNN (K-Nearest Neighbor regression), random forest regression, Adaboost regression, GBRT (Gradient Boost Regression Tree regression), Bagging regression, and Extra Tree (extremely randomized tree regression).

[0067] By dividing the strain simulation data into a training set and a test set, the data volume of the training set accounts for about 70% of the total data volume of the data set; the data volume of the test set accounts for about 30%. Among them, the training set is used to train the model and complete model verification, and the test set is used to evaluate the prediction effect of the trained model.

[0068] Before model training, cross-validation can be performed on the training set. Cross-validation includes Holdout test, simple cross-validation, k k-fold cross-validation, and leave-one-out cross-validation, a total of 4 types. Considering factors such as the characteristics of the simulation data, the total data volume, and the verification accuracy, this paper uses k k-fold cross-validation.

[0069] k The process of k-fold cross-validation is to divide the training set into k k non-overlapping and equal-sized data sets. Among them, ( k k - 1) subsets are used to train the model, and the remaining subset is used to test the model. Repeatk Next, select the root mean square error RMSE The model with the smallest value. k The larger the value of [[[value]]], the smaller the statistical deviation, but the computational cost also increases accordingly. Therefore, the optimal value of 10 is selected in this paper to achieve a balance between computational cost and performance.

[0070] As Figure 6 shown, the root mean square errors of different regression models are given RMSE mean value and RMSE standard deviation line chart. The mean value of the root mean square error RMSE obtained by using the KNN regression algorithm is the smallest (RMSE mean ≈ 0.000mm, when only 3 significant digits are retained), and the standard deviation of the root mean square error RMSE is the smallest (RMSE standard deviation ≈ 0.000mm, when only 3 significant digits are retained).

[0071] As Figures 7 - 8 shown, the mean absolute error MAE, mean square error MSE and coefficient of determination of different regression models are given line chart. The mean square error MSE and mean absolute error MAE obtained by using the KNN regression algorithm are the smallest ( MSE ≈ 0.000mm, MAE ≈ 0.000mm, when only 3 significant digits are retained), and R 2 is closest to 1 ( R 2 ≈ 1.000, when only 3 significant digits are retained). Considering comprehensively RMSE the mean value, RMSE standard deviation, it is feasible to establish a three - cantilever beam structure width prediction model based on the KNN regression algorithm for regression problems, and the evaluation indicators can meet the error requirements of engineering practice for crack width measurement. In addition, the performance of the decision tree regression and Extra Tree regression algorithms is second only to that of the KNN regression and can be used as alternative solutions for establishing this prediction model.

[0072] Figure 2 An embodiment of the three - cantilever beam structure crack width prediction method based on regression problems of the present invention is shown.

[0073] In this alternative embodiment, a three - cantilever beam structure crack width prediction system based on regression problems includes: A data acquisition module 201, configured to perform a static simulation on the three - cantilever beam identification body structure by using the finite element method and obtain a simulation data set of the three - cantilever beam identification body structure under different crack conditions; the simulation data set includes crack width data and cantilever beam strain data; A data optimization module 202, configured to identify the multicollinearity between crack width data and cantilever beam strain data according to a simulation data set through multivariate visualization and correlation analysis, and delete redundant variables to obtain an optimized data set; A model construction module 203, configured to construct multiple regression models, train and evaluate each regression model by using the optimized data set, and select the optimal regression model as the crack width prediction model according to the evaluation results; A width prediction module 204, configured to obtain the cantilever beam strain data and input it into the crack width prediction model, and predict the corresponding crack width data through the crack width prediction model.

[0074] In one embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as Figure 3 shown. The computer device includes a processor, a memory, and a network interface connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store static information and dynamic information data. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, the steps in the above method embodiments are implemented.

[0075] Those skilled in the art can understand that Figure 3 the structure shown in

[0076] is only a block diagram of some structures related to the solution of the present invention, and does not constitute a limitation on the computer device to which the solution of the present invention is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.

[0077] In addition, the present invention further provides a computer device, including a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps in the above method embodiments are implemented.

[0078] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the various embodiments provided by the present invention can include at least one of non-volatile and volatile memories. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical memory, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0079] The present invention is not limited to the structures that have been described above and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present invention is only limited by the appended claims.

Claims

1. A crack width prediction method for a three-cantilever beam structure based on a regression problem, characterized in that, Including the following steps: Performing a static simulation on the three-cantilever beam identification body structure using the finite element method, and obtaining a simulation data set of the three-cantilever beam identification body structure under different crack conditions; the simulation data set includes crack width data and cantilever beam strain data; According to the simulation data set, through multivariate visualization and correlation analysis, identifying the multicollinearity between the crack width data and the cantilever beam strain data, and deleting redundant variables to obtain an optimized data set; Constructing multiple regression models, training and evaluating each regression model using the optimized data set, and selecting the optimal regression model as the crack width prediction model according to the evaluation results; Obtaining the cantilever beam strain data and inputting it into the crack width prediction model, and predicting the corresponding crack width data through the crack width prediction model.

2. The crack width prediction method for a three-cantilever beam structure based on a regression problem according to claim 1, characterized in that, The step of performing a static simulation on the three-cantilever beam identification body structure using the finite element method and obtaining a simulation data set of the three-cantilever beam identification body structure under different crack conditions includes the following steps: Constructing a simulation measurement environment for the three-cantilever beam identification body structure and the matching calibration structure, and determining the constraint conditions of the three-cantilever beam identification body structure; Combined with the preset simulation purpose, determining the boundary conditions of the three-cantilever beam identification body structure and the matching calibration structure; Performing a static simulation in the finite element analysis software, and collecting the strain data of the three-cantilever beam identification body structure under different crack conditions to obtain a simulation data set.

3. The method for predicting the crack width of a three-cantilever beam structure based on a regression problem according to claim 2, wherein The step of performing a static simulation in the finite element analysis software and collecting the strain data of the three-cantilever beam identification body structure under different crack conditions to obtain a simulation data set includes the following steps: Creating a three-dimensional geometric model of the three-cantilever beam identification body structure and the matching calibration structure in the finite element analysis software, and performing mesh division processing on the geometric model; Based on the constraint conditions of the three-cantilever beam identification body structure, applying a load to the three-cantilever beam identification body structure, and obtaining the strain data at the cantilever of the three-cantilever beam identification body structure to obtain a simulation data set.

4. The method for predicting the crack width of a three-cantilever beam structure based on a regression problem according to claim 3, wherein, The constraint condition of the three-cantilever beam identification body structure is to fix the crack direction and change the crack width size.

5. The method for predicting the crack width of a three-cantilever beam structure based on a regression problem according to claim 3, characterized in that, The load applied to the three-cantilever beam identification body structure is a forced displacement load.

6. The method for predicting the crack width of a three-cantilever beam structure based on a regression problem according to claim 5, characterized in that, The step of identifying the multicollinearity between the crack width data and the cantilever beam strain data according to the simulation data set, through multivariate visualization and correlation analysis, and deleting redundant variables to obtain an optimized data set includes the following steps: For the simulation data set, using visualization software to draw a corresponding relationship diagram between variables, observing the distribution relationship and trend between variables, and calculating the determination coefficient in combination with a multiple regression model; the variables include a response variable vector and regression variables; Calculating the variance inflation factor of the regression variables according to the determination coefficient, and judging whether there is a multicollinearity problem between the regression variables based on a preset threshold. If so, deleting the regression variables; otherwise, retaining the regression variables; Integrating the deleted or retained regression variables with the response variable vector to obtain an optimized data set.

7. The method for predicting the crack width of a three-cantilever beam structure based on a regression problem according to claim 6, characterized in that, The calculation formula for calculating the variance inflation factor of the regression variables according to the determination coefficient is: ； In the formula, represents the variance inflation factor of the regression variable j , and represents the coefficient of determination of the regression variable j .

8. The method for predicting the crack width of a three-cantilever beam structure based on a regression problem according to claim 1, wherein The steps of constructing multiple regression models, training and evaluating each regression model using an optimized dataset, and selecting the optimal regression model as the crack width prediction model based on the evaluation results are as follows: Based on a preset regression algorithm, construct multiple regression models, and divide the optimized dataset into a training set and a test set; Use the training set to train the multiple regression models, and use the test set to evaluate the trained multiple regression models to obtain evaluation metrics; According to the values of the evaluation metrics, compare the performance of different regression models, and select the regression model with the best performance as the crack width prediction model.

9. The method for predicting the crack width of a three-cantilever beam structure based on a regression problem according to claim 8, wherein, The evaluation metrics include mean squared error, root mean squared error, mean absolute error, and coefficient of determination.

10. A three-cantilever beam structure crack width prediction system based on regression problems, characterized in that, It includes: A data acquisition module, which is used to perform static simulation on the three-cantilever beam identification body structure using the finite element method, and obtain a simulation dataset of the three-cantilever beam identification body structure under different crack conditions; the simulation dataset includes crack width data and cantilever beam strain data; A data optimization module, which is used to identify the multicollinearity between the crack width data and the cantilever beam strain data through multivariate visualization and correlation analysis according to the simulation dataset, and delete redundant variables to obtain an optimized dataset; A model construction module, which is used to construct multiple regression models, train and evaluate each regression model using the optimized dataset, and select the optimal regression model as the crack width prediction model according to the evaluation results; A width prediction module, which is used to obtain the cantilever beam strain data and input it into the crack width prediction model, and predict the corresponding crack width data through the crack width prediction model.

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