A Phenomenological Method for Hysteresis Curve Parameter Recognition in Machine Vision

Abstract

This invention relates to the fields of structural engineering experimental data processing and machine learning technology, and discloses a hysteresis curve parameter recognition method based on machine vision phenomenology. It obtains initial estimates of hysteresis model parameters using traditional parameter recognition methods. These initial estimates serve as a benchmark for applying physical constraints to perform adaptive intelligent sampling in the parameter space, generating multiple parameter combinations. The force-displacement curves corresponding to each parameter combination are converted into standard grayscale images. A Siamese convolutional neural network model is constructed and trained to learn the mapping relationship between image similarity and curve fitting goodness. The similarity between the generated image and the original experimental image is evaluated using the trained model, and the parameter combination corresponding to the highest score is selected. Further multi-layer physical rationality verification is then performed to select the optimal hysteresis model parameters. This invention integrates the physical basis of traditional methods with the visual shape recognition capabilities of CNNs, significantly improving parameter recognition accuracy and robustness while ensuring that the recognition results conform to physical laws.

Description

Technical Field

[0001] This invention relates to the fields of structural engineering test data processing and machine learning technology, and in particular to a hysteresis curve parameter identification method based on machine vision phenomenology, which is applicable to the identification of hysteresis parameters of structural components such as reinforced concrete components, seismic isolation bearings, and metal dampers. Background Technology

[0002] In the field of structural engineering, hysteresis curves are the core tool for describing the mechanical properties of materials or components under cyclic loading. Accurately identifying the parameters of the hysteresis model is of vital importance for structural seismic analysis, performance evaluation, and numerical simulation.

[0003] Current traditional methods for identifying hysteresis curve parameters have many technical shortcomings: methods based on physical mechanisms require prior knowledge of the material's constitutive relationship, making it difficult to establish accurate mathematical models for complex hysteresis behaviors; methods based on empirical formulas have limited accuracy and cannot adapt to the hysteresis characteristics of different materials and under different loading conditions; traditional optimization methods are sensitive to initial values ​​and are prone to getting trapped in local optima, leading to biased identification results; at the same time, existing methods cannot simultaneously take into account multiple key characteristics of the hysteresis curve, such as pinching effect, strength degradation, and stiffness degradation, resulting in insufficient comprehensiveness in identification.

[0004] In recent years, machine learning methods have shown application potential in the field of parameter identification. However, pure machine learning methods lack physical constraints, and the parameters obtained from training often do not conform to the basic laws of materials mechanics, making them unsuitable for direct application in engineering practice. Therefore, there is an urgent need to develop a hysteresis curve parameter identification method that can guarantee both the accuracy and robustness of parameter identification, as well as ensure that the identification results conform to physical laws. Summary of the Invention

[0005] The purpose of this invention is to provide a hysteresis curve parameter recognition method based on machine vision phenomenology, which solves the technical problems of insufficient accuracy, easy getting trapped in local optima, lack of physical constraints, and the fact that the results of pure machine learning methods do not conform to physical laws, and achieves high-precision and physically compliant intelligent recognition of hysteresis curve parameters.

[0006] To achieve the above-mentioned objectives, the present invention employs the following technical solution:

[0007] A hysteresis curve parameter recognition method based on machine vision phenomenology, characterized by the following steps: S1: Obtaining initial estimates of hysteresis model parameters using traditional parameter recognition methods, wherein the hysteresis model parameters include 6 positive skeleton point parameters, 6 negative skeleton point parameters, and 5 hysteresis parameters, totaling 17; S2: Using the initial estimates as a benchmark, performing intelligent sampling in the parameter space using an adaptive sampling strategy, applying physical constraints during the sampling process, and generating multiple parameter combinations that conform to physical rationality; S3: For each parameter combination, calculating the corresponding force-displacement curve using the hysteresis model, and converting the force-displacement curve into a standard image format; S4: Constructing... A convolutional neural network model is constructed, using the original experimental hysteresis curve image and the hysteresis curve image generated in step S3 as inputs, and outputting a similarity score between the two. The convolutional neural network model is trained to learn the mapping relationship between image similarity and curve fitting goodness; S5: The original experimental hysteresis curve image and all generated hysteresis curve images are input into the trained convolutional neural network model to obtain a similarity score between each generated image and the original image. The parameter combination corresponding to the generated image with the highest score is selected as the candidate optimal hysteresis model parameters; S6: The physical rationality of the selected candidate optimal parameter combination is verified. After verification, it is determined as the final optimal hysteresis model parameters.

[0008] Optionally, the traditional parameter identification method in step S1 includes: extracting skeleton curves from experimental data, extracting positive skeleton curves through local maxima with positive displacement, and extracting negative skeleton curves through local minima with negative displacement; identifying feature points of the skeleton curves, including yield points, peak points, and limit points; determining the optimal feature point coordinates based on the principle of area equivalence, determining the limit point coordinates for skeleton curves with softened sections through area equivalence, and determining the feature point positions for skeleton curves without softened sections through a preset ratio; and optimizing the hysteresis parameters using the constrained least squares method to obtain initial estimates of 17 hysteresis model parameters.

[0009] Optionally, the optimization of hysteresis parameters using the constrained least squares method includes: using the sum of squared residuals between experimental data and model prediction data as the objective function, and solving the constrained nonlinear least squares problem using the Levenberg-Marquardt algorithm, with the hysteresis parameter constraints being 0 ≤ pinchX ≤ 1, 0 ≤ pinchY ≤ 1, damage1 ≥ 0, damage2 ≥ 0, and 0 ≤ beta ≤ 1.

[0010] Optionally, the adaptive sampling strategy in step S2 includes: using large-scale exploratory sampling in the early stage and small-scale fine sampling in the later stage, with the sampling interval being ±30% of the initial estimated value; applying triple physical constraints during the sampling process, including skeleton curve monotonicity constraint, hysteresis parameter range constraint, and energy dissipation consistency constraint, and filtering unreasonable parameter combinations in real time; dynamically adjusting the sampling density according to the goodness of fit, and increasing the number of samples if the highest goodness of fit R² < 0.8, until the preset goodness of fit threshold or the maximum number of samples is reached.

[0011] Optionally, the energy dissipation consistency constraint is that the relative error between the energy dissipation calculated by the model and the experimental energy dissipation does not exceed 15%, and the goodness-of-fit threshold is R. 2 ≥ 0.95.

[0012] Optionally, in step S3, converting the force-displacement curve into a standard image format specifically includes: converting the force-displacement curve into a standard-sized grayscale image and unifying the image resolution; automatically adjusting the coordinate range and increasing the boundary margin by 10% to ensure the curve is displayed completely; removing the coordinate axes, scales, labels, and borders, retaining only the pure curve shape information.

[0013] Optionally, the convolutional neural network model in step S4 adopts a Siamese network architecture, including: two feature extraction sub-networks with identical structures and shared weights, which process the original experimental hysteresis curve image and the generated hysteresis curve image respectively; wherein, each feature extraction sub-network contains 4 convolutional blocks, each convolutional block is a Conv2D-BatchNorm-ReLU-MaxPooling structure, and the output of the last convolutional block is flattened into a 512-dimensional feature vector; image similarity is evaluated by calculating the Euclidean distance between the two feature vectors, and the Euclidean distance is converted into a similarity score of 0-100; the coefficient of determination R² corresponding to the curve fitting goodness is used as the true similarity label, the mean squared error is used as the loss function, and the Adam optimizer is used to train the network.

[0014] Optionally, step S5, selecting candidate optimal hysteresis model parameters, includes: sorting the similarity scores of all generated images in descending order, selecting the parameter combination corresponding to the image with the highest score; verifying whether the difference between the highest score and the second highest score is greater than a preset threshold, checking whether the highest score is significantly higher than the second highest score, and ensuring the reliability of the selection; and outputting the candidate optimal parameter combination and the corresponding similarity score, and the top K high-scoring parameter combinations.

[0015] Optionally, the physical rationality verification in step S6 includes: basic constraint verification: checking whether all parameters are within a reasonable range and whether the skeleton point parameters meet the monotonicity constraint; curve quality verification: recalculating the hysteresis curve using candidate optimal parameters to verify whether the curve is continuous and uninterrupted, whether the shape is reasonable, and whether the key features are clear; whether the yield point is clear and variable, whether the peak point position is reasonable, and whether the pinching effect is appropriate; verification result processing: if the verification passes, it is determined as the final optimal parameter; if it fails, the parameter is fine-tuned within the constraint range, or the parameter with the second highest score that meets the constraint is selected; if multiple high-scoring parameters do not meet the constraint, the process returns to step S2 for resampling.

[0016] Optionally, the method is applicable to the identification of hysteresis curve parameters of reinforced concrete components, seismic isolation bearings, and metal dampers under cyclic loading, wherein the hysteresis model is the Hysteretic material model in OpenSees.

[0017] Compared with existing technologies, the hysteresis curve parameter recognition method based on machine vision phenomenology provided by this invention has at least the following beneficial effects:

[0018] High recognition accuracy and strong robustness: It integrates the physical basis of traditional structural engineering parameter recognition methods with the visual shape recognition capability of convolutional neural networks. It not only solves the problem that traditional methods are prone to getting trapped in local optima and cannot take multiple features into account, but also achieves high-precision shape matching of hysteresis curves through machine vision. It has good fault tolerance for noise and outliers in experimental data.

[0019] Physical constraints are embedded throughout the entire process, and the results conform to engineering principles: Physical constraints are integrated into the entire process of initial parameter optimization, parameter space sampling, and final parameter verification. This filters out unreasonable parameters from the source, avoids the problem that the results of pure machine learning methods do not conform to the laws of material mechanics, and ensures that the identified parameters can be directly applied to engineering practice.

[0020] High degree of automation and good engineering adaptability: It realizes the fully automated processing from test data to optimal parameters without a lot of manual intervention; it is clearly applicable to three types of core structural components: reinforced concrete components, seismic isolation bearings, and metal dampers, and provides quantitative operation standards and algorithms, which can be directly referenced and implemented by engineering technicians;

[0021] High generalization and reusability: After the model is trained, it can be quickly applied to new test data of the same type of components without redesigning the model architecture; both parameter space sampling and model training take into account the differences in hysteresis characteristics under different loading conditions, and can maintain high recognition accuracy in different test scenarios.

[0022] The results are highly reliable: Candidate parameters are selected by ranking them by similarity scores, and score difference verification and multi-layer physical rationality verification are set up. The layer-by-layer screening ensures that the optimal parameters in the final output not only fit the experimental curves highly, but also have a solid physical basis, providing reliable parameter support for structural seismic analysis and numerical simulation. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a schematic diagram of the hysteresis curve parameter recognition method of machine vision phenomenology according to an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of conventional parameter identification in an embodiment of the present invention;

[0026] Figure 3 This is a schematic diagram of the parameter space sampling strategy according to an embodiment of the present invention;

[0027] Figure 4 This is a schematic diagram of the hysteresis curve image generation process according to an embodiment of the present invention;

[0028] Figure 5 This is a schematic diagram of the CNN model architecture according to an embodiment of the present invention;

[0029] Figure 6 This is a schematic diagram illustrating the physical constraint verification of an embodiment of the present invention;

[0030] Figure 7 This is a schematic diagram comparing the conventional method and the present invention in an embodiment of the present invention. Detailed Implementation

[0031] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the basic embodiments disclosed below.

[0032] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0033] The hysteresis curve parameter identification method based on machine vision phenomenology of this invention is applicable to the identification of hysteresis curve parameters of reinforced concrete components, seismic isolation bearings, and metal dampers under cyclic loading. It can significantly improve the accuracy and robustness of hysteresis curve parameter identification, and embeds physical constraints throughout the process to ensure that the results conform to the laws of material mechanics.

[0034] This embodiment uses hysteresis test data of reinforced concrete columns under cyclic loading as the research object, and employs the method of this invention to identify hysteresis curve parameters, such as... Figure 1 As shown, it includes the following steps:

[0035] Step S1, Initial identification of traditional parameters: Obtain initial estimates of the hysteresis model parameters using traditional parameter identification methods.

[0036] In one alternative implementation, refer to Figure 2 The diagram shown illustrates a traditional parameter identification process, which includes the following steps:

[0037] S11, read the displacement-force data from the hysteresis test of the reinforced concrete column, extract the positive and negative skeleton curves. The positive skeleton curve is extracted through local maxima where the displacement is positive, and the negative skeleton curve is extracted through local minima where the displacement is negative. Specifically,

[0038] For the displacement-force data point sequence {(Xi, Fi)}_{i=1}∈N collected in the experiment:

[0039] ;

[0040] .

[0041] S12, Identify the feature points of the skeleton curve, including yield point, peak point, and limit point: Identify the three types of feature points of the skeleton curve: yield point, peak point, and limit point. Determine the optimal feature point coordinates based on the principle of area equivalence. For skeleton curves with softening segments, optimize the limit point coordinates through area equivalence. For skeleton curves without softening segments, determine the feature point positions using a preset ratio (yield point is 30% of peak point). Specifically,

[0042] (1) Selection of initial feature points

[0043] Peak point (Xp, Fp): ;

[0044] Yield point (X_{y0}, F_{y0}): Take the first obvious inflection point;

[0045] Limit point (X_{u0}, F_{u0}): Take the last data point.

[0046] (2) Determining the yield point using the principle of product equivalence

[0047] For the skeleton curve segment from the origin (0, 0) to the peak point (Xp, Fp):

[0048] Actual area under the curve: ;

[0049] Area under the curve in the ideal elastoplastic model (yield point is $(x_y, F_y)$): ;

[0050] Area equivalence conditions: ;

[0051] This requires that 0 < Xy < Xp and 0 < Fy < Fp;

[0052] This optimization problem can be solved within a reasonable range using the golden section search method.

[0053] (3) Determination of the limit points of the skeleton curve with softened segment

[0054] For the softened segment from the peak point (Xp, Fp) to the end point (Xu, Fu):

[0055] Actual area under the curve: ;

[0056] Ideal softening model (linear descent) area: ;

[0057] Area equivalence condition (used to optimize the coordinates of the limit point (Xu, Fu)): Where Xu > Xp and Fu < Fp must be satisfied.

[0058] (4) Method for determining the proportion of characteristic points of skeleton curves without softening segment

[0059] When the skeleton curve has no obvious softening segment, the preset ratio method is used:

[0060] Yield point: ,in The value is usually 0.3;

[0061] Limit point (equivalent to peak point): .

[0062] S13 uses the sum of squared residuals between experimental data and model prediction data as the objective function, and employs the Levenberg-Marquardt algorithm to solve a constrained nonlinear least squares problem. This optimization yields initial estimates for 17 hysteresis model parameters, including 6 positive skeleton point parameters (Fy_pos, xy_pos, Fd_pos, xd_pos, Fu_pos, xu_pos), 6 negative skeleton point parameters (Fy_neg, xy_neg, Fd_neg, xd_neg, Fu_neg, xu_neg), and 5 hysteresis parameters (pinchX, pinchY, damage1, damage2, beta). Specifically,

[0063] Suppose there are M hysteresis parameters p = [p1, p2, ..., pM]^T (M=5 in the code, including pinchX, pinchY, damage1, damage2, and beta);

[0064] (1) Objective function

[0065] Minimize the sum of squared residuals between the experimental data and the model predictions: ,in Calculations were performed using the Hysteretic material model in OpenSees.

[0066] (2) Constraints

[0067] Parameter physical range constraints:

[0068] (3) Optimization solution

[0069] The Levenberg-Marquardt algorithm is used to solve constrained nonlinear least squares problems. This algorithm combines the advantages of gradient descent and Gauss-Newton methods. The iterative formula is as follows:

[0070]

[0071] in: It is the residual vector. Regarding the parameters, Jacobian matrix, I is the damping factor, which is adaptively adjusted during iteration. I is the identity matrix.

[0072] (4) Initial value setting

[0073] Set reasonable initial values ​​based on experience: Regarding the convergence condition of the algorithm, the optimization process terminates when any of the following conditions are met:

[0074] The relative change in residuals is less than the tolerance. : ;

[0075] The parameter variation is less than the tolerance. : ;

[0076] The maximum number of iterations has been reached. Through the above steps, initial estimates of the hysteresis model parameters are obtained.

[0077] Step S2, parameter space sampling: Based on the initial estimate obtained in step S1, an adaptive sampling strategy is used to perform intelligent sampling in the parameter space. During the sampling process, physical constraints are applied to ensure the physical rationality of the parameter combination, and multiple parameter combinations that conform to physical rationality are generated.

[0078] In one alternative implementation, refer to Figure 3 The illustrated parameter space sampling strategy includes the following steps:

[0079] S21, Establish parameter space and baseline values.

[0080] Let the initial parameter vector obtained in step S1 be... It contains 17 parameters, which, in order, are: forward skeleton point parameters: Negative skeleton point parameters: Hysteresis parameters: Based on the initial estimates of these 17 parameters, a 17-dimensional parameter space is established.

[0081] S22, Adaptive Sampling Strategy

[0082] An adaptive sampling strategy is employed for intelligent sampling, based on random perturbations of the initial value. The sampling interval is set to ±30% of the initial estimated value, with large-scale exploratory sampling performed initially and small-scale fine-tuning performed later. Specifically,

[0083] (1) Sampling range setting

[0084] For the Parameters Its sampling interval is: ;in The coefficient of change is usually taken as... (30% variation range).

[0085] The specific method for generating new parameter values ​​is as follows: ;in Indicates the interval A random number that is uniformly distributed within the range.

[0086] (2) Sampling quantity control

[0087] Initial Exploration Sampling: Generation Group parameter combinations (such as) );

[0088] Adjust based on fit quality: If the highest goodness of fit is achieved... Then increase the number of samples to ;

[0089] Repeat sampling until the preset quality requirement or the maximum number of samplings is reached.

[0090] S23, Physical constraint application mechanism

[0091] During the sampling process, three physical constraints are applied in real time to ensure the physical rationality of parameter combinations: First, the monotonicity constraint of the skeleton curve: positive displacement increases monotonically, positive force increases first and then decreases, negative displacement increases monotonically by absolute value, and negative force increases first and then decreases by absolute value; second, the hysteresis parameter range constraint: 0≤pinchX≤1, 0≤pinchY≤1, damage1≥0, damage2≥0, 0≤beta≤1; third, the energy dissipation consistency constraint: the relative error between model energy consumption and experimental energy consumption does not exceed 15%, and unreasonable parameter combinations are filtered in real time. Specifically,

[0092] (1) Monotonicity constraint of skeleton curve

[0093] Normal force parameter constraints: and ;

[0094] Positive displacement parameter constraints: ;

[0095] Negative force parameter constraints (in absolute value): and ;

[0096] Negative displacement parameter constraints (in absolute value): ;

[0097] If the parameters do not meet the above constraints, then the constraints are met by swapping adjacent parameter values.

[0098] (2) Hysteresis parameter range constraint

[0099]

[0100] Parameters that are out of range are truncated and adjusted to the minimum or maximum allowed value.

[0101] (3) Consistency constraint of energy dissipation

[0102] For each parameter combination Calculate the energy consumption of its model. Energy consumption of the experiment : ;

[0103] relative error The calculation formula is: ;Require ,in Usually taken .

[0104] S24, Sampling process control

[0105] The sampling density is dynamically adjusted based on the goodness of fit. If the highest goodness of fit R² < 0.8, the number of samples is doubled until the goodness of fit threshold R² ≥ 0.95 or the preset maximum number of samples is reached, ultimately generating multiple parameter combinations that conform to physical rationality. Specifically,

[0106] (1) Iteration termination condition

[0107] Reaching the preset number of samples (e.g.) );

[0108] Highest goodness of fit Reaching the threshold (e.g.) );

[0109] Parameter space convergence (parameter variation range is less than the initial value) ).

[0110] (2) Quality assessment

[0111] Evaluate the fit quality for each sampling point:

[0112] Computational model predictive power With test force The correlation coefficient,

[0113] Calculate the root mean square error: ;

[0114] Calculate the coefficient of determination: ;

[0115] in, The average value of the test force data is calculated using the following formula:

[0116] (3) Parameter combination screening

[0117] Remove parameter combinations that do not meet physical constraints, sort by goodness of fit, and retain the top ones. Groups (e.g.) ), save parameter combinations and corresponding quality indicators.

[0118] Step S3, Hysteresis Curve Image Generation: For each parameter combination, the corresponding force-displacement curve (hysteresis curve) is calculated using the hysteresis model, and the force-displacement curve is converted into a standard image format. Here, the hysteresis model is the Hysteretic hysteresis model in OpenSees.

[0119] In one alternative implementation, refer to Figure 4 The diagram shown illustrates the process of generating the hysteresis curve image, which includes the following steps:

[0120] S31, Hysteresis Response Calculation

[0121] For each parameter combination generated in step S2 Substituting the values ​​into the Hysteretic material model, the force response is calculated based on the experimental displacement sequence, yielding the force-displacement curve. Specifically,

[0122] (1) Definition of material model

[0123] The Hysteretic material model uses 17 parameters, in the following order:

[0124] ;

[0125] (2) Calculation process

[0126] Input: Displacement sequence (Originated from experimental data);

[0127] Process: For each displacement point Call the material model to calculate the corresponding force response. ;

[0128] Output: Force sequence .

[0129] The force response is calculated based on the displacement sequence of the experiment, and the force-displacement curve is obtained.

[0130] S32, Image Generation and Standardization

[0131] The calculated force-displacement curves are converted into grayscale images in a standard image format, and the image resolution, coordinate axis range, and coordinate axes and labels are removed. Specifically,

[0132] (1) Image specification settings

[0133] Image size: 6 inches × 6 inches, 224 × 224 pixels, uniform resolution of 100 dpi, color mode of RGB (transparent background), original experimental curve: red dashed line, line width 1.5, transparency 0.7, generated curve: blue solid line, line width 2, transparency 0.8.

[0134] (2) Coordinate axis processing

[0135] Completely remove coordinate axes, ticks, labels, and borders, retaining only the pure curve shape information to avoid redundant information interfering with model training.

[0136] (3) Automatic Coordinate Range Adjustment Algorithm

[0137] Automatically calculates the maximum and minimum values ​​of displacement and force for all curves, adds a 10% boundary margin to determine the coordinate range, and ensures that the curves are displayed completely.

[0138] Minimum displacement: ,

[0139] Maximum displacement: ,

[0140] Minimum force: ,

[0141] Maximum force: ,

[0142] Increase Boundary margin, determining the coordinate range:

[0143] Displacement range: ,

[0144] Force range: .

[0145] S33, Image File Management

[0146] (1) File naming conventions

[0147] Image file: comparison_curve_set_{serial number:03d}.png

[0148] Parameter file: random_parameter_sets_N.txt, where This represents the number of parameter groups.

[0149] (2) Parameter storage format

[0150] The file header contains parameter names, each line corresponds to a set of parameters, and parameter values ​​are separated by spaces.

[0151] (3) Quality inspection and abnormality handling

[0152] Check if the generated force response is a valid value (not NaN, not infinite), check if the image file was saved successfully, handle calculation errors, record error information, and skip the parameter combination.

[0153] S34, Dataset Organization

[0154] (1) Construction of training dataset

[0155] Input: Hysteresis curve image (normalized PNG format); Output: corresponding 17 parameter values;

[0156] Dataset size: Determined based on the number of samples (e.g., 50 groups, 100 groups, 2000 groups, etc.).

[0157] (2) Dataset partitioning

[0158] Training set: Image-parameter pairs, validation set: Image-parameter pairs, test set: Image-parameter pairs.

[0159] Through the above steps, the hysteresis curves corresponding to each parameter combination are converted into a standardized image format, providing a high-quality dataset for subsequent CNN model training. This process is fully automated, capable of processing a large number of parameter combinations at once, ensuring that the generated images have a consistent format and quality, facilitating subsequent machine learning model training.

[0160] Step S4, CNN model training and image similarity evaluation: Construct a convolutional neural network model based on the Siamese network architecture, using the original experimental hysteresis curve image and the hysteresis curve image generated in step S3 as input, and output the similarity score between the two. Train the convolutional neural network model to learn the mapping relationship between image similarity and curve fitting goodness.

[0161] In one alternative implementation, refer to Figure 5 The diagram shown illustrates the CNN model architecture, and the steps include:

[0162] S41, CNN Model Construction

[0163] A convolutional neural network model based on a Siamese network architecture is constructed to evaluate the similarity between the original experimental hysteresis curve image and the generated hysteresis curve image. Specifically,

[0164] (1) Twin network architecture

[0165] A Siamese network structure is adopted, which contains two identical feature extraction subnetworks (sharing weights) to process the original experimental images and the generated images, respectively;

[0166] Input layer: Receives two 224×224×1 grayscale images;

[0167] Feature extraction network: Each sub-network contains 4 convolutional blocks, each convolutional block is "Conv2D-BatchNorm-ReLU-MaxPooling";

[0168] Feature vector: The feature map output by the last convolutional block is flattened into a 512-dimensional feature vector.

[0169] (2) Similarity calculation module

[0170] Distance calculation: Calculate the Euclidean distance between two feature vectors. ,

[0171] Similarity score: Converts distance into a similarity score (0-100 points). ,in Temperature is a parameter that controls the range of score distribution.

[0172] The original experimental hysteresis curve image and the generated hysteresis curve image are respectively input into two feature extraction sub-networks. The Euclidean distance between the two 512-dimensional feature vectors is calculated, and the Euclidean distance d is converted into a similarity score.

[0173] S42, Training Data Preparation

[0174] Using the coefficient of determination R² between the generated curve and the experimental curve as the true similarity label (true score is 100×R²), positive sample pairs, negative sample pairs, and hard sample pairs are constructed. Mean squared error is used as the loss function, and the Adam optimizer (learning rate 1×10⁻⁻⁶) is employed. 4 The training model involves random rotation, translation, and scaling of the input image for data augmentation, coupled with an early stopping strategy to prevent overfitting, enabling the model to learn the mapping relationship between image similarity and curve fit goodness. Specifically,

[0175] (1) Construction of training samples

[0176] Positive sample pair: The original experimental image and itself, with a similarity score of 100;

[0177] Negative sample pairs: the original experimental image and other random images, with similarity labels of 0-20;

[0178] Difficult sample pairs: Original experimental images and similar but not identical images, with a similarity score of 60-90.

[0179] (2) Tag generation

[0180] Use curve fit goodness as the true similarity label: ,in The coefficient of determination is the ratio between the generated curve and the experimental curve.

[0181] S43, Model Training

[0182] (1) Loss function

[0183] Using the mean squared error loss function: ,in This refers to the batch size.

[0184] (2) Training process

[0185] Optimizer: Adam optimizer, learning rate Batch size: 32; Training cycle: 100, with early stopping strategy; Data augmentation: Randomly rotate, translate, and scale the input image.

[0186] S44, Model Evaluation

[0187] Evaluation indicators include

[0188] Rating prediction error: ;

[0189] Ranking accuracy: Top-1 accuracy (whether the highest score corresponds to the best fit);

[0190] Correlation coefficient: Pearson correlation coefficient between predicted score and actual score.

[0191] Step S5, Optimal Parameter Identification and Output: Input the original experimental hysteresis curve image and all hysteresis curve images generated in step S3 into the trained convolutional neural network model to obtain the similarity score between each generated image and the original image, and select the parameter combination corresponding to the generated image with the highest score as the candidate optimal hysteresis model parameters.

[0192] In one alternative implementation, the step includes:

[0193] S51, Batch Image Processing

[0194] The original experimental hysteresis curve image is converted to a standard image format according to the method in step S3, and then preprocessed by grayscale conversion and normalization. Specifically,

[0195] (1) Image loading and preprocessing

[0196] Load all image files generated in step S3 (e.g., 50 images), and perform the same preprocessing on each image as during training: including resizing (224×224 pixels), grayscale conversion, and normalization (scaling pixel values ​​to the range [0,1]).

[0197] (2) Processing of raw experimental images

[0198] The original experimental hysteresis curves were converted into a standard image format, and the same preprocessing procedure was applied to generate input images in the same format as the training data.

[0199] S52, CNN model inference

[0200] The preprocessed original test images and all generated hysteresis curve images are batch-input into the trained convolutional neural network model. The model outputs a similarity score between each generated image and the original image. Specifically,

[0201] (1) Model loading and configuration

[0202] Load the weights of the trained CNN model and set the model to inference mode (disable random operations such as Dropout).

[0203] (2) Batch similarity assessment

[0204] For the Amplitude generated image : Constructing input pairs: original experimental images and generating images CNN forward propagation calculates similarity score Record the score and the corresponding parameter index.

[0205] S53, Ranking and Optimal Selection

[0206] All similarity scores are sorted in descending order, and the parameter combination corresponding to the image with the highest score is selected as the candidate optimal hysteresis model parameters; specifically,

[0207] (1) Ranking of scores

[0208] Sort the scores of all generated images in descending order: ,in This represents the total number of images generated.

[0209] (2) Optimal parameter selection

[0210] Select the image with the highest rating: Obtain the parameter combination corresponding to the image. ;

[0211] Verify the reliability of the ratings: Check whether the highest rating is significantly higher than the second highest rating. .

[0212] S54, Parameter Output

[0213] Verify that the difference between the highest and second-highest scores is greater than 5 points to ensure the reliability of parameter selection. Simultaneously, output the parameter combinations and score distribution statistics for the top K highest scores. Specifically,

[0214] (1) Parameter format

[0215] Output the optimal parameter combination, containing 17 parameters:

[0216] .

[0217] (2) Scoring Report

[0218] Simultaneously output: Highest similarity score: The top K highest-scoring parameter combinations (e.g., K=5) are used to calculate the score distribution statistics: mean, standard deviation, and median.

[0219] Step S6, Physical rationality verification: The physical rationality of the candidate optimal parameter combination selected in step S5 is verified to ensure that the parameters meet the basic constraints of material mechanics. After the verification is passed, it is determined as the final optimal hysteresis model parameter.

[0220] In one alternative implementation, refer to Figure 6 The illustrated diagram shows the physical constraint verification process, which includes the following steps:

[0221] S61, Basic Constraint Verification

[0222] Check that each parameter is within a reasonable range, including: positive force and displacement parameters are greater than 0, negative force and displacement parameters are less than 0, and hysteresis parameters meet range constraints; simultaneously check that the skeleton point parameters meet monotonicity constraints to ensure there are no logical contradictions. Specifically,

[0223] (1) Parameter range verification

[0224] Normal force parameters: ,

[0225] Positive displacement parameters: ,

[0226] Negative force parameters: ,

[0227] Negative displacement parameters: ,

[0228] Hysteresis parameters: .

[0229] (2) Monotonicity verification

[0230] Check whether the skeleton point parameters satisfy monotonicity, including:

[0231] Positive displacement monotonically increases: ,

[0232] The positive force first increases and then decreases: ,

[0233] Negative displacement decreases monotonically (in absolute value): ,

[0234] Negative forces decrease first and then increase (in absolute value): .

[0235] S62, Curve Quality Verification

[0236] The hysteresis curve is recalculated using the candidate optimal parameters and substituted back into the hysteresis model. This verifies whether the curve is continuous and uninterrupted, without abnormal oscillations, whether the curve shape conforms to the hysteresis characteristics of the component, whether key features such as the yield point and peak point are clearly identifiable, and whether the pinching effect is appropriate. Specifically,

[0237] (1) Curve integrity check

[0238] Recalculate the hysteresis curve using the optimal parameters and check: whether the curve is continuous and uninterrupted, whether the curve shape is reasonable (without abnormal oscillations), and whether the curve covers the displacement range of the test data.

[0239] (2) Key feature verification

[0240] Whether the yield point is clearly identifiable, whether the peak point is reasonably positioned, and whether the pinching effect is moderate (not excessively pinched or excessively saturated).

[0241] S63, Verification Result Processing

[0242] If the candidate optimal parameter combination satisfies both the basic constraint verification and the curve quality verification, it is determined as the final optimal hysteresis model parameter. If the verification fails, the outlier parameters are slightly adjusted within the physical constraints, and then re-verified. If the verification still fails after adjustment, the parameter combination with the second highest score that meets the physical constraints is selected. If multiple high-scoring parameter combinations fail to meet the constraints, the process returns to step S2 to resample the parameter space until the optimal parameters that meet physical rationality are obtained. Specifically,

[0243] (1) Verification passed the standard

[0244] The recognition result is considered physically reasonable when the following conditions are met: all parameters are within a reasonable range, the skeleton point parameters satisfy the monotonicity constraint, the recalculated curve shape is reasonable, and there are no obvious abnormalities.

[0245] (2) Verification failed.

[0246] If any validation fails:

[0247] Parameter fine-tuning: Making small adjustments to abnormal parameters within the constraints;

[0248] Suboptimal choice: If the optimal parameter does not satisfy the physical constraints, consider choosing the parameter with the second highest score that satisfies the constraints;

[0249] Resampling: If multiple high-scoring parameters do not meet the constraints, return to step S2 for resampling.

[0250] (3) Verification report

[0251] Generate a physical rationality verification report, including: verification results (pass / fail), parameter adjustment records (if any), the final confirmed optimal parameter combination, and the verified curve image.

[0252] S64, final output

[0253] After physical validity verification, the final confirmed optimal hysteresis model parameters are output, including:

[0254] The specific values ​​of the 17 parameters, the corresponding similarity scores, the physical verification results, and the recalculated hysteresis curve image.

[0255] Reference Figure 7 The diagram showing the comparison between the traditional method and the present invention demonstrates that the above steps ensure that the identified parameters are not only highly similar to the experimental curves, but also conform to the basic laws of materials mechanics, thus meeting the reliability requirements of engineering applications.

[0256] The hysteresis curve parameter recognition method based on machine vision phenomenology of the present invention combines the physical basis of traditional methods with the shape recognition capability of CNN, significantly improving the parameter recognition accuracy; it has good fault tolerance for noisy data and outliers; it ensures that the recognition results conform to the laws of material mechanics through physical constraints; it can adapt to hysteresis curves of different types of materials and loading conditions; it can be quickly applied to new experimental data after one training; and it is suitable for hysteresis parameter recognition of reinforced concrete components, seismic isolation bearings, and metal dampers.

[0257] It should be noted that, depending on the implementation needs, the steps described in the embodiments of the present invention can be broken down into more steps, or two or more steps or parts of steps can be combined into new steps to achieve the purpose of the embodiments of the present invention.

[0258] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for identifying hysteresis curve parameters based on machine vision phenomenology, characterized in that, Includes the following steps: S1: Initial estimates of the hysteresis model parameters are obtained through traditional parameter identification methods. The hysteresis model parameters include 6 positive skeleton point parameters, 6 negative skeleton point parameters, and 5 hysteresis parameters, for a total of 17. S2: Based on the initial estimated value, an adaptive sampling strategy is used to perform intelligent sampling in the parameter space. Physical constraints are applied during the sampling process to generate multiple parameter combinations that conform to physical rationality. S3: For each parameter combination, calculate the corresponding force-displacement curve using the hysteresis model, and convert the force-displacement curve into a standard image format; S4: Construct a convolutional neural network model, using the original experimental hysteresis curve image and the hysteresis curve image generated in step S3 as input, outputting the similarity score between the two, and training the convolutional neural network model to learn the mapping relationship between image similarity and curve fitting goodness of fit; S5: Input the original experimental hysteresis curve image and all generated hysteresis curve images into the trained convolutional neural network model to obtain the similarity score between each generated image and the original image, and select the parameter combination corresponding to the generated image with the highest score as the candidate optimal hysteresis model parameters. S6: Verify the physical rationality of the selected candidate optimal parameter combinations. Once the verification is passed, the final optimal hysteresis model parameters are determined.

2. The hysteresis curve parameter recognition method based on machine vision phenomenology according to claim 1, characterized in that, The traditional parameter identification method in step S1 includes: Skeleton curves are extracted from the experimental data. Positive skeleton curves are extracted by local maxima with positive displacement, and negative skeleton curves are extracted by local minima with negative displacement. Identify the characteristic points of the skeleton curve, including the yield point, peak point, and limit point; The optimal feature point coordinates are determined based on the principle of area equivalence. For skeleton curves with softened sections, the coordinates of the limit points are determined by area equivalence. For skeleton curves without softened sections, the position of the feature points is determined by a preset ratio. The constrained least squares method was used to optimize the hysteresis parameters, and the initial estimates of 17 hysteresis model parameters were obtained.

3. The hysteresis curve parameter recognition method based on machine vision phenomenology according to claim 2, characterized in that, The optimization of hysteresis parameters using constrained least squares method includes: Using the sum of squared residuals between experimental data and model prediction data as the objective function, the Levenberg-Marquardt algorithm is used to solve the constrained nonlinear least squares problem. The hysteresis parameters are constrained as follows: 0 ≤ pinchX ≤ 1, 0 ≤ pinchY ≤ 1, damage1 ≥ 0, damage2 ≥ 0, and 0 ≤ beta ≤ 1.

4. The hysteresis curve parameter recognition method based on machine vision phenomenology according to claim 1, characterized in that, The adaptive sampling strategy in step S2 includes: In the early stage, a large-scale exploratory sampling method was used, and in the later stage, a small-scale fine sampling method was used. The sampling range was ±30% of the initial estimated value. During the sampling process, three physical constraints are applied, including the monotonicity constraint of the skeleton curve, the range constraint of the hysteresis parameter, and the consistency constraint of energy dissipation, and unreasonable parameter combinations are filtered in real time. The sampling density is dynamically adjusted based on the goodness of fit. If the highest goodness of fit R² < 0.8, the number of samples is increased until the preset goodness of fit threshold or the maximum number of samples is reached.

5. The hysteresis curve parameter recognition method based on machine vision phenomenology according to claim 4, characterized in that, The energy dissipation consistency constraint is that the relative error between the energy dissipation calculated by the model and the experimental energy dissipation does not exceed 15%, and the goodness-of-fit threshold is R. 2 ≥ 0.

95.

6. The hysteresis curve parameter recognition method based on machine vision phenomenology according to claim 1, characterized in that, Step S3, which converts the force-displacement curve into a standard image format, specifically includes: Convert the force-displacement curve into a standard-sized grayscale image and unify the image resolution; Automatically adjust the coordinate range and increase the boundary margin by 10% to ensure the curve is displayed completely; Remove axes, ticks, labels, and borders, retaining only the pure curve shape information.

7. The hysteresis curve parameter recognition method based on machine vision phenomenology according to claim 1, characterized in that, The convolutional neural network model in step S4 adopts a Siamese network architecture, including: It contains two feature extraction sub-networks with identical structures and shared weights, which process the original experimental hysteresis curve image and the generated hysteresis curve image respectively; each feature extraction sub-network contains 4 convolutional blocks, each of which is a Conv2D-BatchNorm-ReLU-MaxPooling structure, and the output of the last convolutional block is flattened into a 512-dimensional feature vector. Image similarity is evaluated by calculating the Euclidean distance between two feature vectors and converting the Euclidean distance into a similarity score of 0-100. The coefficient of determination R² corresponding to the curve fitting goodness of fit is used as the true similarity label, the mean squared error is used as the loss function, and the Adam optimizer is used to train the network.

8. The hysteresis curve parameter recognition method based on machine vision phenomenology according to claim 1, characterized in that, The selection of candidate optimal hysteresis model parameters in step S5 includes: Sort all generated images in descending order of similarity scores and select the parameter combination corresponding to the image with the highest score; Verify whether the difference between the highest and second-highest scores is greater than a preset threshold, and check whether the highest score is significantly higher than the second-highest score to ensure the reliability of the selection; Output the candidate optimal parameter combinations and their corresponding similarity scores, as well as the top K high-scoring parameter combinations.

9. The hysteresis curve parameter recognition method based on machine vision phenomenology according to claim 1, characterized in that, The physical rationality verification in step S6 includes: Basic constraint verification: Check whether all parameters are within a reasonable range and whether the skeleton point parameters satisfy the monotonicity constraint; Curve quality verification: Recalculate the hysteresis curve using candidate optimal parameters to verify whether the curve is continuous and uninterrupted, whether the shape is reasonable, and whether the key features are clear; whether the yield point is clear and variable, whether the peak point position is reasonable, and whether the pinching effect is appropriate. Verification result processing: If the verification passes, it is determined as the final optimal parameter; if it fails, the parameter is fine-tuned within the constraint range, or the parameter with the second highest score that meets the constraint is selected. If multiple high-scoring parameters do not meet the constraint, the process returns to step S2 for resampling.

10. The hysteresis curve parameter recognition method based on machine vision phenomenology according to any one of claims 1-9, characterized in that, The method is applicable to the identification of hysteresis curve parameters of reinforced concrete components, seismic isolation bearings, and metal dampers under cyclic loading. The hysteresis model is the Hysteretic material model in OpenSees.

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