Method for predicting bearing capacity of concrete-filled steel tube yielding lagging jack

Abstract

The invention relates to a method for predicting the bearing capacity of a concrete-filled steel tube yielding lagging jack, and belongs to the technical field of artificial intelligence and data processing. The method comprises the following steps: acquiring stress data at a key stress position of a concrete filled steel tube arch solid structure; stress data screening is carried out, and a screened data set is stored in an HDF5 hierarchical format; denoising the stored stress data by adopting a self-adaptive normalization method and a wavelet threshold function; time domain-frequency domain feature fusion is carried out on the stress data after denoising normalization through dynamic time segmentation and short-time Fourier transform; constructing a concrete-filled steel tube yielding arch bearing capacity prediction model, inputting the fusion feature vector into the model, and training the model to obtain a trained model; and processing the collected data, inputting the processed data into the trained model to obtain a predicted value of the bearing capacity, and triggering early warning when the predicted value exceeds 90% of the designed bearing capacity for three continuous times. The prediction capability of the model can be improved.

Description

Technical Field

[0001] The invention belongs to the technical field of artificial intelligence and data processing, and particularly relates to a method for predicting the bearing capacity of a concrete-filled steel tubular yielding arch frame. Background Art

[0002] As a new type of composite structure combining high strength, high stiffness and good ductility, the concrete-filled steel tubular yielding arch frame structure is widely used in stress complex environments such as tunnel lining and long-span bridges. Its structural safety highly depends on the accurate assessment of the bearing capacity. However, traditional bearing capacity prediction methods mainly rely on structural theoretical models or static test regression, and it is difficult to adapt to the actual working state of the concrete-filled steel tubular arch frame under the combined action of complex loads, material nonlinearity and construction errors. In addition, the original stress data collected by strain gauges generally have problems such as non-stationarity, high noise interference and scale differences. Conventional data processing methods cannot effectively remove pulse interference or retain key stress evolution characteristics, resulting in a decline in the quality of model input. At the same time, most existing deep learning methods are general-purpose structures, lacking the constraints of material mechanics laws, and the training process is prone to fall into local optima without physical meaning, seriously restricting the reliability and interpretability of bearing capacity prediction. Therefore, there is an urgent need for a new method that integrates dynamic preprocessing of stress data, physics-driven modeling and feature enhancement strategies to achieve high-precision prediction of the bearing capacity of the concrete-filled steel tubular arch frame and ensure physical consistency.

[0003] The existing technical solutions still have the following problems: Most existing denoising techniques rely on fixed thresholds, making them have great deficiencies in dealing with data with large noise fluctuations or mutations, being prone to introduce distortion or mis-denoising, and unable to adapt to the dynamic changes of different stress signals. Traditional stress analysis methods are mostly limited to the extraction of time-domain features, ignoring the frequency-domain information of stress data, especially the stress oscillation under periodic loads, and unable to effectively capture the resonance frequency characteristics related to the bearing capacity, restricting the comprehensiveness and accuracy of data analysis. In current deep learning methods for stress-bearing capacity prediction, the principles of material mechanics and physical constraints are often ignored, resulting in the model being unable to effectively simulate the nonlinear behavior of the structure, being prone to falling into local optimal solutions or prediction results that do not conform to physical laws. Traditional gradient descent optimization algorithms are prone to being affected by noise when dealing with non-stationary stress data, resulting in overfitting in the gradient oscillation area or too slow convergence speed in the flat area, and unable to achieve efficient model training. Summary of the Invention

[0004] In order to solve the above problems, the invention provides a method for predicting the bearing capacity of a concrete-filled steel tubular yielding arch frame.

[0005] To achieve the above object, the invention is realized through the following technical solutions: S1. Collect stress data at the key stress-bearing positions of the concrete-filled steel tube arch frame entity structure; S2. Set screening rules based on the principles of material mechanics, perform stress data screening, and store the screened data set in the HDF5 hierarchical format; S3. Denoise the stored stress data using the adaptive normalization method and the wavelet threshold function to obtain the denoised and normalized stress data; S4. Perform time-domain to frequency-domain feature fusion on the denoised and normalized stress data through dynamic time segmentation and short-time Fourier transform to obtain the fusion feature vector; S5. Construct a bearing capacity prediction model for the concrete-filled steel tube yielding arch frame. The overall architecture of the model is a multi-layer fully connected feedforward neural network, combined with a physics-inspired initialization mechanism, a physical constraint activation function, and a hybrid physical loss function; input the fusion feature vector into the model and train the model to obtain a trained model; S6. Input the collected data after being processed in steps S3 - S4 into the trained model to obtain the bearing capacity prediction value. When the prediction value exceeds 90% of the design bearing capacity for three consecutive times, an early warning is triggered.

[0006] Further, step S1 specifically includes: At the key stress-bearing positions of the concrete-filled steel tube arch frame entity structure, embed high-precision resistance strain gauges and collect stress data using the static acquisition mode; the data is stored in the form of a time series, including time stamps and microstrain values, and is stored in the CSV format.

[0007] Further, step S2 specifically includes: Delete the data in the initial preloading stage, and eliminate the mutation points caused by sensor failures based on the steel yield strength threshold; combine the synchronous data of the load sensors and remove the invalid sections under no load to finally generate a time series data set with a validity flag bit.

[0008] Further, in step S3, perform adaptive normalization and wavelet denoising of the stress data, specifically including: S31. Calculate the stress mean of the local time window: Based on the dynamic time window, perform an accumulation operation on the stress values within the interval to calculate the local stress mean; S32. Calculate the stress standard deviation of the local time window: Based on the local stress mean, calculate the stress standard deviation; S33. Calculate the normalized intermediate value: Subtract the local mean from the original stress data and divide by the local standard deviation to convert it into a standardized form to obtain the normalized intermediate value; S34. Calculate the adaptive threshold: Based on the statistical characteristics of the normalized median, calculate the median of the absolute value sequence of the difference between the original stress and the local mean, and combine the noise ratio coefficient and the normalization constant to obtain the adaptive threshold; S35. Use the wavelet threshold function to complete denoising normalization: Use the wavelet threshold function to process the normalized median, suppress impulse noise through soft thresholding, and at the same time retain the true stress fluctuation characteristics to obtain the denoised and normalized stress data.

[0009] Further, step S4 specifically includes: S41. Dynamic time segmentation: Divide the time series data of each sample in the denoised and normalized stress data into equal-length segments, and extract local time-domain features; S42. Calculate the time-domain statistical feature vector: Based on the segmentation result, calculate the segmented stress mean, segmented stress standard deviation, and segmented stress skewness, which respectively characterize the average level, fluctuation amplitude, and asymmetry of the distribution of stress within the segment, to obtain the time-domain statistical feature vector, which is the time-domain part of the fusion feature, expressed as: , where, represents the time-domain statistical feature vector of the i-th sample; represents the segmented stress mean; represents the segmented stress standard deviation; represents the segmented stress skewness; S43. Extract the frequency-domain energy feature vector: Process the denoised and normalized stress data through short-time Fourier transform to obtain a time-frequency matrix, and then combine the frequency weight function to perform weighted summation on the frequency-domain energy within the effective frequency range to extract the frequency-domain energy feature vector, which is the frequency-domain part of the fusion feature, expressed as: , where, represents the frequency-domain energy feature vector of the i-th sample; is a positive integer; is the lower limit of the effective frequency range; is the upper limit of the effective frequency range; is the short-time Fourier transform function; represents the denoised and normalized stress data of the i-th sample at time; is the frequency weight function; S44. Generate the fusion feature vector: Concatenate the time-domain statistical feature vector and the frequency-domain energy feature vector to form the fusion feature vector.

[0010] Further, step S5 specifically includes: S51. Define the deep neural network architecture: The dimension of the input layer is equal to the feature dimension after the fusion of the time domain and the frequency domain; the output layer is a single neuron; DropPath is used for structural regularization between layers; in the parameter initialization stage, the weight starting point is constructed by fusing the feature statistical mean and the physical scaling matrix, and combined with the correction term generated by spectral decomposition to ensure that the initial parameter distribution conforms to the physical response space of the concrete-filled steel tubular arch frame; S52. Initialize the deep neural network: Calculate the initial weights based on the statistical characteristics of the feature data and physical priors to ensure that the starting point of the model is close to the physically feasible region; S53. Perform the forward propagation of the deep neural network and calculate the custom activation function: In the forward propagation process of the deep neural network, an activation function based on the physical characteristics of stress is used to simulate the saturation characteristics of stress data and the non-linear change when the stress value approaches the bearing capacity limit; S54. Calculate the loss function: Calculate the loss function by combining the traditional mean squared error loss and the physical violation penalty term through a mixed loss function; S55. Update the parameters of the deep neural network: Achieve parameter update by calculating the dynamic first-order moment decay rate and the second-order moment decay rate, combined with the adaptive adjustment of gradient information and historical momentum; S56. Perform DropPath regularization: In each forward propagation, randomly discard a part of the paths in the network, and the probability of discarding the paths is dynamically adjusted according to the current iteration number and the total iteration number; S57. Judge the early stopping mechanism: The early stopping mechanism continuously monitors during the model training process according to the performance index on the validation set. When the loss on the validation set no longer decreases significantly, the training will stop in advance.

[0011] Further, step S52 specifically includes: S521. Calculate the initial weight matrix: Perform a scaling operation based on the feature mean vector and the physical guidance matrix to obtain the weight reference term. At the same time, combine the adaptive correction term to calculate the initial weight matrix of the deep neural network, expressed as: , where, is the initial weight matrix of the deep neural network; is the physical guidance matrix; is the th fused feature vector of the sample; is the total number of training samples; is the adaptive correction term, which is used to enhance the robustness to the change of feature distribution; S522. Calculate the adaptive correction term: Generate the adaptive correction term through the spectral decomposition of the feature covariance matrix, expressed as: Among them, is the adaptive coefficient; is the eigenvector matrix of the feature covariance matrix ; is the square root of the eigenvalue diagonal matrix; is the eigenvalue diagonal matrix of the fused feature; the feature covariance matrix is defined as: ; is the global mean vector of the fused feature; represents the transpose operation on the matrix ;

[0012] Furthermore, step S53 specifically includes: S531. Calculate the hidden layer linear transformation: For each hidden layer, calculate the linear combination of the weight matrix and the output of the previous layer as the input of the activation function. Define as the linear output vector of the -th layer, representing the unactivated intermediate feature representation, and its obtaining method is expressed as: ; is a positive integer, is the weight matrix of the -th layer, is the output vector of the -th layer, is the bias vector of the -th layer; S532. Calculate the physically inspired activation function: Input the linear output into the physically inspired adaptive activation function to simulate the stress saturation characteristic, and obtain the activated feature representation. Define as the activation output vector of the -th layer, representing the feature after the non-linear transformation, as the basis for the next layer input or the output layer; is calculated by the activation function for the linear output vector of the -th layer; Define the activation function to be calculated based on the stress physical characteristics, expressed as: ; Among them, is the input scalar of the activation function, that is, each element of the linear output vector of the -th layer is processed independently; is the activation function; is the logarithmic function; is the saturation coefficient, simulating the gain attenuation after stress yield; is the linear gain coefficient; is the threshold adjustment parameter.

[0013] Further, step S54 specifically includes: S541. Calculate the basic numerical error term: Calculate the mean square error between the predicted bearing capacity and the true bearing capacity , as the basic numerical accuracy term of the loss function; S542. Calculate the physical violation penalty term: Define three sub-constraint penalties, which are respectively for negative bearing capacity prediction, non-monotonic increasing relationship between bearing capacity and mean stress, and convexity violation, expressed as: , where, is the physical violation penalty term; is the non-negative constraint penalty term; is the monotonicity constraint penalty term is the convexity constraint penalty term; S543. Synthesize the total loss function: Combine the basic numerical error term and the physical violation penalty term with weights to form the final total loss function for backpropagation gradient calculation and optimize the model parameters, expressed as: , where, is the total loss function; is the physical constraint weight coefficient.

[0014] Further, step S55 specifically includes: S551. Calculate the dynamic first-moment decay rate: Adaptively adjust the first-moment decay rate according to the gradient norm, and reduce the historical dependence when the gradient oscillates; S552. Calculate the dynamic second-moment decay rate: Adjust the second-moment decay rate according to the consistency between the gradient and the historical momentum direction to accelerate the convergence direction; S553. Update the first-moment estimate: Integrate the current gradient and the historical momentum to establish an exponential moving average of the gradient direction and estimate the gradient direction; S554. Update the second-moment estimate: Integrate the current gradient square and the historical magnitude to establish an exponential moving average of the gradient square, and combine the dynamic decay rate to achieve adaptive acceleration of the convergence direction; S555. Update the model parameters: Update the trainable parameters of the model based on the bias-corrected moment estimate, and balance the stability in the oscillation region and the convergence speed in the flat region through the dynamically adjusted moment estimate.

[0015] The advantages of the present invention are: By combining adaptive normalization and wavelet threshold denoising, the present invention solves the problems of non-stationarity and high noise interference that occur in the traditional method when processing the stress data of concrete-filled steel tubular arches. Compared with the conventional fixed threshold denoising technique, the present invention can dynamically adjust the normalization range, effectively remove impulse noise through the wavelet threshold function, retain the true fluctuation characteristics of the stress signal, and avoid distortion in the yield stage of the strain data. Traditional stress data analysis usually ignores the frequency domain information. By fusing the time-domain statistical features and frequency domain energy features, the present invention enhances the data expression ability. Through dynamic time segmentation and short-time Fourier transform, it can capture the resonance frequency characteristics of the stress data, thus providing a more accurate feature description for bearing capacity prediction and improving the prediction ability and accuracy of the model. The deep neural network architecture proposed by the present invention combines a physics-inspired initialization mechanism, a physics-constrained activation function, and a hybrid physics loss function, enhancing the model's ability to model the nonlinear mechanical laws of the structure. Through the physics-guided weight initialization and activation function design, the network can effectively avoid the problems of gradient disappearance or unstable convergence in the initial stage of training and better adapt to the physical characteristics of the concrete-filled steel tubular arch. The present invention proposes a dynamic first-order moment and second-order moment decay rate algorithm based on adaptive adjustment of data non-stationarity, which solves the limitations of the traditional Adam optimizer on non-stationary data. By dynamically adjusting the first-order and second-order moment decay rates, it can effectively avoid gradient oscillation or underfitting problems and improve the stability and convergence efficiency of model training. Description of the Drawings

[0016] The drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation to the present invention.

[0017] Figure 1 It is a flowchart of the steps of the method of the present invention; Figure 2 It is a flowchart of the adaptive normalization and wavelet denoising of the present invention; Figure 3 It is the stress signal of the concrete-filled steel tubular arch under the action of load; Figure 4 It is a comparison of the processing effects between the traditional fixed threshold denoising and the present technology; Figure 5 It is a flowchart of the time-domain - frequency-domain feature fusion in the present invention; Figure 6 It is the prediction accuracy of four feature extraction methods in the present invention; Figure 7 It is a flowchart of the training of the bearing capacity prediction model of the concrete-filled steel tubular yielding arch of the present invention; Figure 8 It is the response characteristics of common activation functions and the function of the present invention in the stress saturation region; Figure 9 The prediction error distributions for different activation functions; Figure 10 The flowchart of the parameter update of the deep neural network during the model training process; Figure 11 The training convergence curves for different optimizers; Figure 12 The comparison of the physical violation penalty values for different optimizers. Detailed implementation manners

[0018] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0019] Embodiment 1 In this embodiment, as Figure 1 shown, the present invention provides a method for predicting the bearing capacity of a concrete-filled steel tube yielding arch, and the specific steps include: S1. Collect stress data at the key stress positions of the concrete-filled steel tube arch entity structure.

[0020] Specifically, at the key stress positions of the concrete-filled steel tube arch entity structure, such as the arch feet, the arch crown, the 1 / 4 span and other parts, high-precision resistance strain gauges are embedded, and the stress data is collected in a static acquisition mode. The sampling frequency is set to 10 Hz to ensure capturing the slow stress change process; The continuous acquisition duration of each sample is not less than 300 seconds, covering the whole process from the loading to the failure of the arch; The data is stored in the form of a time series, including the time stamp (millisecond precision) and the microstrain value (με), and is stored in the CSV format.

[0021] S2. Set screening rules based on the principles of material mechanics, perform stress data screening, and store the screened data set in the HDF5 hierarchical format.

[0022] Specifically, delete the data in the preloading stage at the initial stage of loading because there are installation disturbances in this stage; according to the yield strength threshold of the steel, such as for Q345 steel, |ε| > 1700 με, eliminate the mutation points caused by sensor failures, and the strain difference between adjacent two points > 500 με; in combination with the synchronous data of the load sensor, remove the invalid sections of no-load (load < 5 kN) or over-load (load > 120% of the design value); the data retained after screening needs to meet the continuity requirement - the proportion of valid data in any 10-second window ≥ 95%, and finally generate a time series data set with a validity flag bit.

[0023] S3. Denoise the stored stress data using the adaptive normalization method and the wavelet threshold function to obtain the denoised and normalized stress data.

[0024] Specifically, the stress data collected by the strain gauge is characterized by non-stationarity, high noise interference, and large time-scale differences. The noise originates from sensor drift and environmental vibration. For example, the stress amplitude ranges of different arch frame samples are from MPa to MPa. Conventional global minimum-maximum normalization is likely to amplify the influence of noise; The present invention solves the non-stationarity and noise problems by dynamically adjusting the normalization range and suppressing noise, combining adaptive normalization and wavelet threshold denoising. As Figure 2 shown, the specific steps are as follows: S31. Calculate the stress mean of the local time window: Based on the dynamic time window, perform an accumulation operation on the stress values within the interval to calculate the local stress mean, thereby capturing the local trend and avoiding global normalization distortion, expressed as: , where, represents the local stress mean at time, which is used to dynamically capture the local trend of the stress data and solve the non-stationarity problem; is the time window size. Preferably, it is set to 50 time points, which represents the length of the integration interval and controls the smoothness of the local statistics; is a positive integer; is the original stress value at

[0025] It should be noted that the accumulation operation in the term represents the summation of the stress values within the interval

[0026] S32. Calculate the stress standard deviation of the local time window: Based on the local stress mean, calculate the stress standard deviation to quantify the fluctuation amplitude of the stress, providing a basis for realizing adaptive normalization and solving the problem of data scale differences, expressed as: , where, represents the local stress standard deviation at time, which is used to quantify the stress fluctuation amplitude and solve the scale difference problem.

[0027] S33. Calculate the normalization intermediate value: Subtract the local mean from the original stress data and then divide by the local standard deviation to convert it into a standardized form to obtain the normalization intermediate value; eliminate the local trend and scale differences, expressed as: , wherein, represents the normalized intermediate value at time , characterizing the stress data after adaptive normalization; is the original stress value at time

[0028] S34. Calculate the adaptive threshold: Based on the statistical characteristics of the normalized intermediate value, by calculating the median of the absolute value sequence of the difference between the original stress and the local mean, and combining the noise ratio coefficient and the normalization constant, an adaptive threshold is obtained for distinguishing noise from the true signal, providing a critical value for soft threshold processing, expressed as: , wherein, is the adaptive threshold, the critical value for determining noise, suppressing high-noise interference through soft threshold processing; is the noise ratio coefficient, adjusting the threshold sensitivity, e.g., ; is the median function, calculating the median value of the sequence; represents the absolute value sequence of the difference between the original stress and the local mean, obtaining an estimate of the noise level through global calculation.

[0029] It should be noted that the denominator of the term is

[0030] S35. Complete denoising normalization using the wavelet threshold function: Use the wavelet threshold function to process the normalized intermediate value, suppress impulse noise through soft threshold, and at the same time retain the true stress fluctuation characteristics, obtaining the denoised and normalized stress data, expressed as: , wherein, represents the denoised and normalized stress data at time , characterizing the processed effective signal; is the wavelet threshold function, implementing soft threshold processing of noise, ; is the sign function, if its input is greater than 0, the sign function value is 1, otherwise, the sign function value is -1; is the maximum value function, ensuring non-negative output; is the absolute value symbol.

[0031] S4. Perform time-domain to frequency-domain feature fusion on the denoised and normalized stress data through dynamic time warping and short-time Fourier transform to obtain a fused feature vector.

[0032] Specifically, stress data implies time dependence and periodicity, such as stress oscillations caused by load cycles. Conventional methods ignore frequency-domain information and cannot capture resonance frequency characteristics related to bearing capacity. In the present invention, through dynamic time warping and short-time Fourier transform, time-domain statistics and frequency-domain energy characteristics are fused to enhance the data representation ability. As Figure 5 shown, the specific steps are as follows: S41. Dynamic time warping: Divide the time-series data of each sample in the denoised and normalized stress data into equal-length segments, and extract local time-domain features. Define the number of segments as to control the granularity of feature extraction. Preferably, .

[0033] S42. Calculate the time-domain statistical feature vector: Based on the segmentation result, calculate the segmented stress mean, segmented stress standard deviation, and segmented stress skewness, which respectively represent the average level, fluctuation amplitude, and asymmetry of the distribution of stress within the segment, to obtain the time-domain statistical feature vector, which is used as the time-domain part of the fused feature and is expressed as: , where represents the time-domain statistical feature vector of the i-th sample and serves as the time-domain part of the fused feature; is the segmented stress mean, representing the average level of stress within the segment, and its calculation method is expressed as ; is the segmented stress standard deviation, representing the stress fluctuation amplitude, and its calculation method is expressed as ; is the segmented stress skewness, describing the asymmetry of the stress distribution, and its calculation method is expressed as ; represents the denoised and normalized stress data of the i-th sample at time; is the total number of time points of a single sample; represents the current segmentation interval.

[0034] S43. Extract the frequency-domain energy feature vector: Process the denoised and normalized stress data through short-time Fourier transform to obtain a time-frequency matrix, and then combine it with a frequency weight function to perform weighted summation of the frequency-domain energy within the effective frequency range to extract the frequency-domain energy feature vector, focusing on the resonance frequency characteristics, which is used as the frequency-domain part of the fused feature and is expressed as: , where represents the frequency-domain energy feature vector of the i-th sample, which is the frequency-domain part of the fusion feature, with a dimension of ; is the number of frequency points; is a positive integer; is the lower limit of the effective frequency range. For example, , indicating that the lower limit of the effective frequency range is 0.1 Hz; is the upper limit of the effective frequency range. For example, , indicating that the upper limit of the effective frequency range is 10 Hz; is the short-time Fourier transform function; represents the i-th sample the stress data after denoising and normalization at time the output of the is the frequency weight function, which enhances the contribution of the dominant frequency through Gaussian weighting, and the calculation method is expressed as ; represents the exponential function with the natural constant as the base; is the dominant frequency of the sample, which is obtained by peak detection of the result of the short-time Fourier transform function; is the bandwidth parameter, which controls the weight decay rate. For example, .

[0035] It should be noted that the

[0036] S44. Generate the fusion feature vector: Concatenate the time-domain statistical feature vector and the frequency-domain energy feature vector to form the fusion feature vector, which is expressed as: , where represents the fusion feature vector of the i-th sample; represents the vector concatenation operation.

[0037] S5. Construct a bearing capacity prediction model for concrete-filled steel tube yielding arches. The overall architecture of the model is a multi-layer fully connected feedforward neural network, combined with a physics-inspired initialization mechanism, a physics-constrained activation function, and a hybrid physics loss function; Input the fusion feature vector into the model and train the model to obtain a trained model.

[0038] Specifically, as Figure 7 shown, the steps are as follows: S51. Define the deep neural network architecture: The overall architecture of the deep neural network adopted in the present invention is a multi-layer fully connected feedforward neural network, combined with a physics-inspired initialization mechanism, a physics-constrained activation function, and a hybrid physics loss function to enhance the model's ability to model the nonlinear mechanical laws of the structure; Specifically in terms of the structure, the dimension of the input layer is equal to the feature dimension after the fusion of the time domain and the frequency domain; Optionally, 3 to 5 hidden layers can be set after the input layer, each layer contains 128 - 256 neurons, and the stress saturation physical activation function proposed by the present invention is adopted to simulate the non-linear change in the stress critical response region; The output layer is a single neuron corresponding to the predicted bearing capacity of the arch frame; DropPath is used for structural regularization between layers to prevent overfitting; In the parameter initialization stage, the weight starting point is constructed by fusing the feature statistical mean and the physical scaling matrix, and combined with the correction term generated by spectral decomposition to ensure that the initial parameter distribution conforms to the physical response space of the concrete-filled steel tube arch frame.

[0039] S52. Initialize the deep neural network: The fused feature vector has high-dimensional sparsity, and the bearing capacity prediction needs to conform to the material mechanics constraints. Conventional deep neural networks use random initialization, but ignore the physical relationship between stress and bearing capacity, which easily leads to unstable gradients or convergence to non-physical solutions in the initial stage of training; The present invention calculates the initial weights based on the statistical characteristics and physical priors of the feature data to ensure that the starting point of the model is close to the physically feasible region.

[0040] Specifically, the initialization process of the deep neural network is as follows: S521. Calculate the initialization weight matrix: Based on the feature mean vector and the physical guidance matrix, perform a scaling operation to obtain the weight reference term, and at the same time combine the adaptive correction term to enhance the robustness to the change of the feature distribution, so as to calculate the initialization weight matrix of the deep neural network, expressed as: , where, is the initialization weight matrix of the deep neural network; is the physical guidance matrix, and the calculation method is expressed as ; is the input feature dimension of the deep neural network; is the th physical scaling coefficient of the feature, and the calculation method is expressed as ; is the physical scaling coefficient of the first feature; is the physical scaling coefficient of the second feature; is the th physical scaling coefficient of the feature; represents a diagonal matrix; is the reference elastic modulus, which characterizes the physical properties of the material. For example, the value range is 30000 - 210000 MPa; is the The global standard deviation of a feature, calculated as ; is the -th eigenvalue of the -th dimensional feature of the fused feature vector; is the global mean of the -th dimensional feature of the fused feature; is the -th fused feature vector of the sample; is the total number of training samples; is the adaptive correction term, enhancing the robustness to changes in feature distribution; S522. Calculate the adaptive correction term: Through the spectral decomposition of the feature covariance matrix, generate the adaptive correction term to adaptively adjust the feature correlation and solve the problem that the difference in feature dimension correlation cannot be handled when only relying on global statistics, expressed as: where: is the adaptive coefficient, controlling the amplitude of the correction term, e.g., 0.05; is the eigenvector matrix of the feature covariance matrix , obtained through eigen-decomposition, representing the main direction of the feature space; the feature covariance matrix is defined as: ; is the global mean vector of the fused feature, calculated as ; is the square root of the eigenvalue diagonal matrix, representing the scaling of the main components of the feature space, is the eigenvalue diagonal matrix of the fused feature; represents the transpose operation on the matrix ; It should be noted that the term reflects the adaptive adjustment of feature correlation and ensures that the initial weights adapt to the data distribution through spectral decomposition.

[0041] S53. Perform the forward propagation of the deep neural network and calculate the custom activation function: The nonlinear relationship of stress data is complex. The conventional ReLU activation function has a zero gradient in the negative region, which easily leads to gradient disappearance and cannot capture the critical nonlinear behavior of stress data. During the forward propagation of the deep neural network, an activation function based on the physical characteristics of stress is adopted to simulate the saturation characteristics of stress data and the nonlinear change when the stress value approaches the bearing capacity limit, avoiding the problem that the traditional ReLU activation function cannot effectively capture the stress-bearing capacity relationship when dealing with ultimate stress, thereby improving the stability and accuracy of the model.

[0042] Specifically, S531. Calculate the linear transformation of the hidden layer: For each hidden layer, calculate the linear combination of the weight matrix and the output of the previous layer as the input to the activation function, and define as the linear output vector of the -th layer, representing the unactivated intermediate feature representation, and its obtaining method is expressed as: , where is a positive integer, is the weight matrix of the -th layer, is the output vector of the -th layer, is the bias vector of the -th layer; S532. Calculate the physically inspired activation function: Input the linear output into the physically inspired adaptive activation function to simulate the stress saturation characteristic, and obtain the activated feature representation, and define as the activation output vector of the -th layer, representing the features after the non-linear transformation, as the basis for the next layer or the output layer; is calculated by the activation function for the linear output vector of the -th layer; It is defined that the activation function is calculated based on the physical characteristics of stress to solve the problem of insufficient capture of critical non-linearity, and is expressed as: where is the input scalar of the activation function, that is, each element of the linear output vector of the -th layer is processed independently; is the activation function; is the logarithmic function, and the default base is 10; is the saturation coefficient, simulating the gain attenuation after stress yield, for example, 0.1; is the linear gain coefficient, controlling the amplitude of the linear region, for example, 0.2; is the threshold adjustment parameter, adjusting the transition slope between the linear region and the saturation region, for example, 0.5; It should be noted that the term reflects the modeling of the saturation effect, that is, the activation attenuation at large inputs, and the term approximates the linear response, avoiding the hard saturation of the ReLU activation function and enhancing the sensitivity to the bearing capacity critical point.

[0043] S54. Calculate the loss function: During the training process of the deep learning model, the predicted bearing capacity output by the forward propagation needs to satisfy the constraints of material mechanics, such as non - negative bearing capacity, monotonic increasing relationship with stress, etc. The conventional mean square error loss only considers the numerical difference and ignores the physical feasibility, which easily leads to the model prediction violating the basic laws; In the present invention, the traditional mean square error loss is combined with the physical violation penalty term through a hybrid loss function to calculate the loss function; it can effectively prevent the model prediction result from violating the mechanical principle. The model can not only optimize the numerical error, but also ensure that the bearing capacity prediction result conforms to the physical rationality and engineering practice requirements, improving the reliability and robustness of the prediction.

[0044] Specifically, S541. Calculate the basic numerical error term: Calculate the mean square error between the predicted bearing capacity and the true bearing capacity as the basic numerical accuracy term of the loss function, which is used to measure the average square deviation between the predicted value and the true value, expressed as: , where, is the mean square error loss term, representing the average square deviation between the predicted value and the true value; is the predicted bearing capacity of the th sample, generated by the output layer of the deep neural network; is the true bearing capacity of the th sample, from the experimental measurement data.

[0045] S542. Calculate the physical violation penalty term: Define three sub - constraint penalties, which respectively penalize the negative bearing capacity prediction, the non - monotonic increasing relationship between the bearing capacity and the average stress, and the convexity violation, to ensure that the prediction result conforms to the physical prior, expressed as: , where, is the physical violation penalty term, and the gradient calculation is realized through automatic differentiation; is the non - negative constraint penalty term, which penalizes the negative bearing capacity prediction to ensure the physical rationality of the bearing capacity. The calculation method is expressed as: , when , the penalty value is 0; when , the penalty value is ; is the monotonicity constraint penalty term, which penalizes the non - monotonic increasing relationship between the bearing capacity and the average stress. The calculation method is expressed as: , when , it satisfies the monotonic increasing, and the penalty value is 0; when , the penalty value is ; is the convexity constraint penalty term. The actual bearing capacity - stress curve is concave. The convexity constraint penalty term is used to penalize convexity violations, and its calculation method is expressed as: ; is the partial derivative of the predicted bearing capacity of the th sample with respect to the mean stress; is the second - order partial derivative of the predicted bearing capacity of the th sample with respect to the mean stress; is the mean stress of the th sample, calculated through the global mean of the piece - wise stress means ; is the sign of the partial derivative; S543. Composite total loss function: The basic numerical error term and the physical violation penalty term are weighted and combined to form the final total loss function, which is used for backpropagation gradient calculation to optimize the model parameters, and is expressed as: , where, is the total loss function, used for backpropagation gradient calculation; is the physical constraint weight coefficient, which adjusts the importance of physical laws. For example, 0.8.

[0046] S55. Update the parameters of the deep neural network: During the backpropagation process of the deep learning model, the gradient of the loss function is affected by stress data noise and shows non - stationarity, such as alternating between local oscillations and flat regions. The conventional Adam optimizer uses a fixed decay rate, which is prone to under - fitting in flat regions and over - shooting in oscillation regions; The present invention realizes parameter update by calculating the dynamic first - moment decay rate and the second - moment decay rate, and combining the adaptive adjustment of gradient information and historical momentum; ensuring that the model can balance stability and convergence speed during training, and the optimization process can more effectively cope with data non - stationarity, improving the training efficiency and final performance of the model.

[0047] Specifically, the parameter update process of the deep neural network is as shown in Figure 10 : S551. Calculate the dynamic first - moment decay rate: The first - moment decay rate is adaptively adjusted according to the gradient norm. When the gradient oscillates, the historical dependence is reduced to avoid over - shooting problems, and is expressed as: , where, is the dynamic first - moment decay rate of the th iteration, which controls the historical gradient memory strength; is the lower limit of the first - moment decay rate. For example, ; is the upper limit of the first - moment decay rate. For example, ; is the gradient norm scaling factor, which adjusts the sensitivity of the decay rate to the gradient magnitude. For example, ; is the gradient norm of the total loss function at the -th iteration, representing the gradient magnitude.

[0048] It should be noted that the term realizes that the decay rate decreases when the gradient magnitude increases, avoiding the overshoot problem in the gradient oscillation region.

[0049] S552. Calculate the dynamic second moment decay rate: Adjust the second moment decay rate according to the consistency between the gradient and the historical momentum direction to accelerate the convergence direction and solve the underfitting problem in the flat region, expressed as: , where is the dynamic second moment decay rate at the -th iteration, controlling the memory strength of the historical gradient square; is the second moment base decay rate, for example, ; is the direction sensitivity coefficient, adjusting the gain amplitude of the direction consistency. For example, ; is the gradient of the total loss function at the -th iteration; is the first moment estimation vector at the -th iteration.

[0050] It should be noted that the term is used to quantify the consistency between the gradient and the historical momentum direction, and the term increases the decay rate in the same direction, enhancing the current gradient weight and solving the underfitting problem in the flat region.

[0051] S553. Update the first moment estimation: Combine the current gradient and the historical momentum to establish an exponential moving average of the gradient direction to estimate the gradient direction, expressed as: , where is the first moment estimation vector at the -th iteration, representing the exponential moving average of the gradient direction.

[0052] S554. Update the second moment estimation: Combine the current gradient square and the historical magnitude to establish an exponential moving average of the gradient square, and realize the adaptive acceleration of the convergence direction in combination with the dynamic decay rate, expressed as: , where is the second moment estimation at the The second-moment estimation vector of the current iteration, which represents the exponential moving average of the squared gradient; is the second-moment estimation vector of the th iteration; represents taking the square of each element of the gradient vector of the total loss function for the th iteration; This estimation combines the dynamic decay rate to achieve adaptive acceleration in the convergence direction.

[0053] S555. Update model parameters: Update the trainable parameters of the model based on the bias-corrected moment estimation. By dynamically adjusting the moment estimation, balance the stability in the oscillation region and the convergence speed in the flat region, which is expressed as: , where is the trainable parameter of the model for the th iteration; is the trainable parameter of the model for the th iteration; is the learning rate for the th iteration; is a numerical stability term to prevent division-by-zero errors, e.g., .

[0054] It should be noted that the and terms jointly solve the non-stationary gradient problem by dynamically adjusting

[0055] S56. Perform DropPath regularization: During the training of a deep neural network, DropPath regularization is adopted to prevent the model from overfitting. In the present invention, the generalization ability of the model is enhanced by dynamically adjusting the probability of the dropped path. Specifically, in each forward propagation, DropPath regularization randomly drops a part of the paths in the network, that is, the connections between some neurons. The probability of the dropped path is dynamically adjusted according to the current iteration number and the total iteration number, which is expressed as: where is the minimum value of the probability of the dropped path, e.g., ; is the maximum value of the probability of the dropped path, e.g., ; is the current iteration number; is the total iteration number.

[0056] It should be noted that the dynamic adjustment mechanism enables the model to retain more path information in the initial stage of training, facilitating the rapid learning of the basic features of the data. As the training progresses, the probability of discarding paths is gradually increased to enhance the generalization ability of the model.

[0057] S57. Perform early stopping mechanism judgment: Through early stopping mechanism judgment, it is ensured that overfitting or resource waste will not occur due to excessive training iterations during the training process of the deep neural network; the early stopping mechanism continuously monitors during the model training process based on the performance metrics on the validation set. When the loss on the validation set no longer decreases significantly, the training will stop in advance.

[0058] S6. After the data collected is processed through steps S3 - S4, it is input into the trained model to obtain the bearing capacity prediction value. When the prediction value exceeds 90% of the design bearing capacity for three consecutive times, an alarm is triggered.

[0059] Specifically, online prediction is implemented for the newly built arch frame. Specifically, strain gauges are installed at the same position of the arch frame to be measured, and 300 - second raw stress data is collected; Then, the collected data is processed through steps S3 - S4 to obtain the fused feature vector; Then, the trained deep neural network model is loaded, and the bearing capacity prediction value is obtained through forward propagation.

[0060] During real - time prediction, a sliding window mechanism is adopted, and the input features are updated every 10 seconds. When the prediction value exceeds 90% of the design bearing capacity for three consecutive times, an alarm is triggered.

[0061] Embodiment 2 In this embodiment, the signal processing advantages of the combination technology of adaptive normalization and wavelet denoising are verified, as Figure 3 shown. By analyzing the true stress signal (black solid line) of the concrete - filled steel tubular arch frame under load, the characteristics of the original signal (gray curve) containing sensor noise and pulse interference are shown, as Figure 4 shown. By comparing the processing effects of traditional fixed - threshold denoising (blue curve) and this technology (red curve), it can be seen that the traditional method has stress - platform distortion in the yield stage above 1500 micro - strain in strain, while this technology completely retains the characteristics of the bilinear constitutive relationship.

[0062] Embodiment 3 In this embodiment, the contribution of the time - domain to frequency - domain feature fusion strategy to improving the bearing capacity prediction accuracy is analyzed, as Figure 6As shown, the prediction accuracies of four feature extraction methods are compared using a bar chart, namely, only using time-domain statistical features (such as mean, standard deviation, etc.), only using frequency-domain energy features, simple concatenated features, and the fusion method of the present invention. The accuracy of the method of the present invention is significantly higher than that of other methods. The textured columns intuitively show its advantages, proving the necessity of fusing time-domain statistical characteristics and frequency-domain dynamic response features, and can comprehensively capture the stress state of the arch frame.

[0063] Example 4 In this embodiment, the effectiveness of the physically inspired activation function proposed by the present invention is evaluated, as Figure 8 shown, the response characteristics of common activation functions (Rectified Linear Unit ReLU, Leaky Rectified Linear Unit Leaky ReLU, Exponential Linear Unit ELU) and the function of the present invention in the stress saturation region are compared. The high stress saturation region is specifically marked in the figure. It can be seen that traditional functions have problems of hard saturation or insufficient linear response in the critical region, while the function of the present invention shows a smooth transition characteristic when approaching the yield strength, accurately simulating the nonlinear behavior of steel under ultimate load, as Figure 9 shown, the prediction error distributions of different activation functions are presented. The prediction error of the function of the present invention is significantly smaller and more concentrated. Most of the predicted values are lower than the engineering safety threshold (the red dashed line in the figure). The width of the violin shape in the error distribution diagram represents the error distribution range. The violin body of the function of the present invention is narrower and the peak is higher, indicating higher reliability and stability.

[0064] Example 5 In this embodiment, the advantages of the physical constraint optimizer of the present invention in terms of training efficiency and prediction are evaluated, as Figure 11 shown, for the training convergence curves of different optimizers, the optimizer of the present invention (green solid line) is superior to traditional optimizers (such as Stochastic Gradient Descent, Adaptive Moment Estimation, etc.) in both the speed of loss value decrease and stability, and can reach the engineering practical convergence threshold (gray dashed line) faster, as Figure 12 shown, presenting the change of the physical violation penalty value. The method of the present invention (green solid line) always remains within the safe physical constraint region (green background), while the violation values of traditional methods are higher and fluctuate significantly. The specifically marked safe physical constraint region in the figure ensures that the prediction results meet the three basic mechanical principles, non-negative bearing capacity, monotonic increasing relationship with stress, and correct curvature characteristics, proving that the optimizer of the present invention ensures that the prediction results conform to the laws of material mechanics while guaranteeing the convergence speed through dynamic adjustment of the learning mechanism.

[0065] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for predicting the bearing capacity of a concrete-filled steel tube yielding arch support, characterized in that, It includes the following steps: S1. Collect stress data at the key stress-bearing positions of the concrete-filled steel tube arch frame entity structure; S2. Set screening rules based on the principles of material mechanics, conduct stress data screening, and store the screened data set in the HDF5 hierarchical format; S3. Denoise the stored stress data using the adaptive normalization method and the wavelet threshold function to obtain the denoised and normalized stress data; S4. Perform time-domain to frequency-domain feature fusion on the denoised and normalized stress data through dynamic time segmentation and short-time Fourier transform to obtain a fused feature vector; S5. Construct a bearing capacity prediction model for the concrete-filled steel tube yielding arch frame. The overall architecture of the model is a multi-layer fully connected feedforward neural network, combined with a physics-inspired initialization mechanism, a physical constraint activation function, and a hybrid physical loss function; input the fused feature vector into the model and train the model to obtain a trained model; S6. Input the collected data after being processed in steps S3 - S4 into the trained model to obtain the bearing capacity prediction value. When the prediction value exceeds 90% of the design bearing capacity for three consecutive times, an early warning is triggered.

2. The bearing capacity prediction method of a concrete-filled steel tube yielding arch frame according to claim 1, characterized in that Step S1 specifically includes: At the key stress-bearing positions of the concrete-filled steel tube arch frame entity structure, embed high-precision resistance strain gauges and collect stress data in the static acquisition mode; the data is stored in the form of a time series, including time stamps and microstrain values, and is stored in the CSV format.

3. A method for predicting the bearing capacity of a concrete-filled steel tubular yielding arch support according to claim 2, characterized in that, Step S2 specifically includes: Delete the data in the initial preloading stage of loading, eliminate the mutation points caused by sensor failures based on the steel yield strength threshold; combine the synchronous data of the load sensors and remove the invalid sections of no-load to finally generate a time series data set with a validity flag bit.

4. A method for predicting the bearing capacity of a concrete-filled steel tube yielding arch support according to claim 3, characterized in that, In step S3, the adaptive normalization and wavelet denoising of the stress data are specifically as follows: S31. Calculate the stress mean of the local time window: Based on the dynamic time window, perform an accumulation operation on the stress values within the interval to calculate the local stress mean; S32. Calculate the stress standard deviation of the local time window: Based on the local stress mean, calculate the stress standard deviation; S33. Calculate the normalized intermediate value: Subtract the local mean from the original stress data and divide by the local standard deviation to convert it into a standardized form to obtain the normalized intermediate value; S34. Calculate the adaptive threshold: Based on the statistical characteristics of the normalized intermediate value, calculate the median of the absolute value sequence of the difference between the original stress and the local mean, and combine the noise ratio coefficient and the normalization constant to obtain the adaptive threshold; S35. Complete denoising and normalization using the wavelet threshold function: Use the wavelet threshold function to process the normalized intermediate value, suppress impulse noise through soft thresholding, and at the same time retain the true stress fluctuation characteristics to obtain the denoised and normalized stress data.

5. A method for predicting the bearing capacity of a concrete-filled steel tube yielding arch frame according to claim 4, characterized in that, In step S4, it specifically includes: S41. Dynamic time segmentation: Divide the time series data of each sample in the denoised and normalized stress data into equal-length segments and extract local time-domain features; S42. Calculate the time-domain statistical feature vector: Based on the segmentation results, calculate the mean of the segmented stress, the standard deviation of the segmented stress, and the skewness of the segmented stress, which respectively characterize the average level, the fluctuation amplitude, and the asymmetry of the distribution of the stress within the segment, to obtain the time-domain statistical feature vector, which is used as the time-domain part of the fusion feature and is expressed as: ， Among them, represents the time-domain statistical feature vector of the i-th sample; represents the segmented stress mean; represents the segmented stress standard deviation; represents the segmented stress skewness; S43. Extract the frequency-domain energy feature vector: Process the denoised and normalized stress data through short-time Fourier transform to obtain a time-frequency matrix, and then combine the frequency weight function to perform weighted summation on the frequency-domain energy within the effective frequency range to extract the frequency-domain energy feature vector, which is used as the frequency-domain part of the fusion feature and is expressed as: ， Among them, represents the frequency-domain energy feature vector of the i-th sample; is a positive integer; is the lower limit of the effective frequency range; is the upper limit of the effective frequency range; is the short-time Fourier transform function; represents the i-th sample the stress data after denoising and normalization at time t; is the frequency weight function; S44. Generate the fusion feature vector: Concatenate the time-domain statistical feature vector and the frequency-domain energy feature vector to form the fusion feature vector.

6. A method for predicting the bearing capacity of a concrete-filled steel tube yielding arch support according to claim 5, characterized in that, Specifically included in step S5 are: S51. Define the deep neural network architecture: The dimension of the input layer is equal to the feature dimension after the time-domain and frequency-domain fusion; the output layer is a single neuron; DropPath is used for structural regularization between layers; in the parameter initialization stage, construct the weight starting point through the fusion feature statistical mean and the physical scaling matrix, and combine the correction term generated by spectral decomposition to ensure that the initial parameter distribution conforms to the physical response space of the concrete-filled steel tubular arch frame; S52. Initialize the deep neural network: Calculate the initial weights based on the statistical characteristics of the feature data and physical priors to ensure that the starting point of the model is close to the physically feasible region; S53. Perform the forward propagation of the deep neural network and calculate the custom activation function: In the forward propagation process of the deep neural network, use the activation function based on the physical characteristics of the stress to simulate the saturation characteristics of the stress data and the nonlinear change when the stress value is close to the bearing capacity limit; S54. Calculate the loss function: Combine the traditional mean squared error loss and the physical violation penalty term through the hybrid loss function to calculate the loss function; S55. Update the parameters of the deep neural network: Realize parameter update by calculating the dynamic first-order moment decay rate and the second-order moment decay rate, and combining the gradient information and the adaptive adjustment of the historical momentum; S56. Perform DropPath regularization: Randomly discard a part of the paths in the network during each forward propagation, and the probability of discarding the paths is dynamically adjusted according to the current iteration number and the total iteration number; S57. Perform the early stopping mechanism judgment: The early stopping mechanism continuously monitors during the model training process according to the performance index on the validation set, and when the loss on the validation set no longer decreases significantly, the training will stop in advance.

7. A method for predicting the bearing capacity of a concrete-filled steel tube yielding arch support according to claim 6, characterized in that, Specifically included in step S52 are: S521. Calculate the initialization weight matrix: Perform a scaling operation based on the feature mean vector and the physical guidance matrix to obtain the weight reference term, and at the same time combine the adaptive correction term to calculate the initialization weight matrix of the deep neural network, which is expressed as: ， Among them, is the initial weight matrix of the deep neural network; is the physics-guided matrix; is the fused feature vector of the th sample; is the total number of training samples; is the adaptive correction term used to enhance the robustness to changes in the feature distribution; S522. Calculate the adaptive correction term: Generate the adaptive correction term through the spectral decomposition of the feature covariance matrix, which is expressed as: Among them, is the adaptive coefficient; is the eigenvector matrix of the feature covariance matrix ; is the square root of the eigenvalue diagonal matrix; is the eigenvalue diagonal matrix of the fused feature; the feature covariance matrix is defined as: ; is the global mean vector of the fused feature; represents the transpose operation on the matrix .

8. A method for predicting the bearing capacity of a concrete-filled steel tube yielding arch support according to claim 7, characterized in that, Specifically included in step S53 are: S531. Calculate the linear transformation of the hidden layer: For each hidden layer, calculate the linear combination of the weight matrix and the output of the previous layer as the input to the activation function, and define as the linear output vector of the -th layer, representing the unactivated intermediate feature representation, and its obtaining method is expressed as: , is a positive integer, is the weight matrix of the -th layer, is the output vector of the -th layer, is the bias vector of the -th layer; S532. Computationally Physics-Inspired Activation Function: The linear output is input into a physics-inspired adaptive activation function to simulate the stress saturation characteristic, and the activated feature representation is obtained. Define as the activation output vector of the -th layer, which characterizes the features after the non-linear transformation and serves as the basis for the input of the next layer or the output layer; It is calculated by the activation function for the linear output vector of the -th layer; Define that the activation function is calculated based on the physical characteristics of stress, expressed as: ， Among them, is the input scalar of the activation function, that is, the linear output vector of the layer is processed independently for each element; is the activation function; is the logarithmic function; is the saturation coefficient, simulating the gain attenuation after stress yielding; is the linear gain coefficient; is the threshold adjustment parameter.

9. A method for predicting the bearing capacity of a concrete-filled steel tube yielding arch support according to claim 8, characterized in that, Specifically included in step S54 are: S541. Calculate the basic numerical error term: Calculate the mean square error between the predicted bearing capacity and the true bearing capacity , as the basic numerical accuracy term of the loss function; S542. Calculate the physical violation penalty term: Define three sub-constraint penalties, which are used to penalize the negative bearing capacity prediction, the non-monotonic increasing relationship between the bearing capacity and the mean stress, and the convexity violation respectively, expressed as: ， Among them, is the physical violation penalty term; is the non - negative constraint penalty term; is the monotonicity constraint penalty term is the convexity constraint penalty term; S543. Synthesize the total loss function: Combine the basic numerical error term and the physical violation penalty term with weights to form the final total loss function, which is used for backpropagation gradient calculation to optimize the model parameters, expressed as: ， Among them, is the total loss function; is the physical constraint weight coefficient.

10. A method for predicting the bearing capacity of a concrete-filled steel tube yielding arch frame according to claim 9, characterized in that, Specifically included in step S55 are: S551. Calculate the dynamic first-moment decay rate: Adaptively adjust the first-moment decay rate according to the gradient norm, and reduce the historical dependence during gradient oscillation; S552. Calculate the dynamic second-moment decay rate: Adjust the second-moment decay rate according to the consistency between the gradient and the historical momentum direction to accelerate the convergence direction; S553. Update the first-moment estimate: Combine the current gradient and the historical momentum to establish an exponential moving average of the gradient direction to estimate the gradient direction; S554. Update the second-moment estimate: Combine the current gradient square and the historical magnitude to establish an exponential moving average of the gradient square, and realize the adaptive acceleration of the convergence direction in combination with the dynamic decay rate; S555. Update the model parameters: Update the trainable parameters of the model based on the bias-corrected moment estimate, and balance the stability in the oscillation region and the convergence speed in the flat region through the dynamically adjusted moment estimate.

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