A method for predicting the bearing capacity of concrete-filled steel tube arch

Abstract

The present invention relates to a method for predicting the bearing capacity of a steel tube concrete yielding arch frame, and belongs to the field of artificial intelligence and data processing technology. The method comprises the following steps: collecting stress data at key stress-bearing positions of a steel tube concrete arch frame entity structure; screening the stress data, and storing the screened data set in an HDF5 layered format; denoising the stored stress data using an adaptive normalization method and a wavelet threshold function; fusing time-domain and frequency-domain features of the denoised and normalized stress data through dynamic time segmentation and short-time Fourier transform; constructing a steel tube concrete yielding arch frame bearing capacity prediction model, inputting the fused feature vector into the model, training the model, and obtaining a trained model; inputting the collected data into the trained model after processing to obtain a bearing capacity prediction value, and triggering an early warning when the predicted value exceeds 90% of the design bearing capacity for three consecutive times. The present invention can improve the prediction ability of the model.

Description

Technical Field

[0001] The present invention belongs to the field of artificial intelligence and data processing technology, and in particular relates to a method for predicting the bearing capacity of a steel tube concrete yielding arch frame. Background Art

[0002] As a novel composite structural form combining high strength, high stiffness, and good ductility, steel tube concrete-yielding arch structures are widely used in complex load-bearing environments such as tunnel linings and long-span bridges. Their structural safety is highly dependent on accurate assessment of their bearing capacity. However, traditional bearing capacity prediction methods, which primarily rely on structural theoretical models or static test regression, are ill-suited to the real-world operating conditions of steel tube concrete arches under the combined effects of complex loads, material nonlinearity, and construction errors. Furthermore, raw stress data collected by strain gauges often suffer from nonstationarity, high noise interference, and scale variations. Conventional data processing methods are unable to effectively remove pulse interference or preserve key stress evolution features, resulting in a decline in model input quality. Furthermore, existing deep learning methods are mostly general-purpose and lack the constraints of material mechanics. The training process is prone to falling into physically meaningless local optima, severely limiting the reliability and interpretability of bearing capacity predictions. Therefore, a novel approach that integrates dynamic stress data preprocessing, physical property-driven modeling, and feature enhancement strategies is urgently needed to achieve high-precision predictions of the bearing capacity of steel tube concrete arches with guaranteed physical consistency.

[0003] Existing technical solutions still have the following problems: Most existing denoising technologies rely on fixed thresholds, which makes them have great deficiencies when processing data with large noise fluctuations or mutations, easily introduce distortion or false denoising, and cannot 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 stress oscillations under periodic loads, and cannot effectively capture the resonant frequency characteristics related to bearing capacity, limiting the comprehensiveness and accuracy of data analysis; current deep learning methods often ignore the principles of material mechanics and physical constraints in stress-bearing capacity prediction, resulting in the model being unable to effectively simulate the nonlinear behavior of the structure, and easily falling into local optimal solutions or prediction results that do not conform to physical laws; traditional gradient descent optimization algorithms are easily affected by noise when processing non-stationary stress data, resulting in overfitting in the gradient oscillation area or too slow convergence in the flat area, making efficient model training impossible. Summary of the Invention

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

[0005] To achieve the above-mentioned purpose, the present invention is implemented through the following technical solutions:

[0006] S1. Collect stress data at key stress-bearing locations of the concrete-filled steel tube arch structure;

[0007] S2. Set screening rules based on the principles of material mechanics to screen stress data and store the screened dataset in HDF5 hierarchical format;

[0008] S3. De-noising the stored stress data using an adaptive normalization method and a wavelet threshold function to obtain de-noised and normalized stress data;

[0009] S4. Perform time-domain and 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;

[0010] S5. Construct a prediction model for the bearing capacity of concrete-filled steel tube arches. The overall architecture of the model is a multi-layer, fully connected feedforward neural network that combines a physics-inspired initialization mechanism, a physics-constrained activation function, and a hybrid physics loss function. The fused feature vector is input into the model, and the model is trained to obtain a trained model.

[0011] S6. The collected data is processed in steps S3-S4 and 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 early warning is triggered.

[0012] Furthermore, step S1 specifically includes:

[0013] High-precision resistance strain gauges are embedded in key stress-bearing locations of the concrete-filled steel tube arch structure, and stress data is collected in a static acquisition mode. The data is stored in a time series format, including timestamps and microstrain values, and in CSV format.

[0014] Furthermore, step S2 specifically includes:

[0015] The data of the initial prestressing stage of loading is deleted, and the mutation points caused by sensor failure are eliminated based on the steel yield strength threshold. Combined with the load sensor synchronization data, the invalid sections with no load are removed, and finally a time series data set with validity flags is generated.

[0016] Furthermore, in step S3, adaptive normalization and wavelet denoising of stress data are performed, which specifically includes:

[0017] S31. Calculate the stress mean of the local time window: Based on the dynamic time window, accumulate the stress values ​​within the interval and calculate the local stress mean;

[0018] S32. Calculate the stress standard deviation in the local time window: Calculate the stress standard deviation based on the local stress mean;

[0019] S33. Calculate the normalized median value: Subtract the local mean from the original stress data and divide it by the local standard deviation to convert it into a standardized form to obtain the normalized median value;

[0020] S34. Calculate the adaptive threshold: Based on the statistical characteristics of the normalized median value, calculate the median of the absolute value sequence of the difference between the original stress and the local mean, and combine it with the noise scale factor and the normalization constant to obtain the adaptive threshold;

[0021] S35. Use the wavelet threshold function to complete denoising and normalization: Use the wavelet threshold function to process the normalized intermediate value, suppress the impulse noise through the soft threshold, and retain the true stress fluctuation characteristics at the same time to obtain the denoised and normalized stress data.

[0022] Furthermore, step S4 specifically includes:

[0023] S41. Dynamic time segmentation: Divide the time series data of each sample in the denoised and normalized stress data into segments of equal length and extract local time domain features;

[0024] S42. Calculate the time-domain statistical eigenvector: Based on the segmentation results, calculate the segment stress mean, segment stress standard deviation, and segment stress skewness, which respectively characterize the average stress level, fluctuation amplitude, and distribution asymmetry within the segment. The time-domain statistical eigenvector is obtained as the time-domain part of the fusion feature and is expressed as:

[0025] ,

[0026] in, Represents the time domain statistical feature vector of the i-th sample; represents the mean value of segmental stress; represents the standard deviation of segmental stress; represents the segmental stress deflection;

[0027] S43. Extract frequency domain energy eigenvector: The denoised and normalized stress data is processed by short-time Fourier transform to obtain a time-frequency matrix. The frequency domain energy within the effective frequency range is weighted and summed using a frequency weighting function to extract the frequency domain energy eigenvector as the frequency domain portion of the fusion feature, which is expressed as:

[0028] ,

[0029] in, 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 Stress data after denoising and normalization at all times; is the frequency weight function;

[0030] S44. Generate a fused feature vector: concatenate the time domain statistical feature vector and the frequency domain energy feature vector to form a fused feature vector.

[0031] Furthermore, step S5 specifically includes:

[0032] S51. Define the deep neural network architecture: the input layer dimension is equal to the feature dimension after the fusion of the time and frequency domains; the output layer is a single neuron; DropPath is used for structural regularization between layers; during the parameter initialization phase, the weight starting point is constructed by fusing the feature statistical mean with the physical scaling matrix, and combined with the correction terms generated by spectral decomposition to ensure that the initial parameter distribution conforms to the physical response space of the steel tube concrete arch;

[0033] S52. Initialize the deep neural network: Calculate initial weights based on the statistical properties of the feature data and physical priors to ensure that the model's starting point is close to the physically feasible region.

[0034] S53. Perform forward propagation of the deep neural network and calculate a custom activation function: During the forward propagation of the deep neural network, an activation function based on the physical properties of stress is used to simulate the saturation characteristics of stress data and the nonlinear changes when the stress value approaches the bearing capacity limit;

[0035] S54. Calculate the loss function: Calculate the loss function by combining the traditional mean square error loss with the physical violation penalty term through a hybrid loss function.

[0036] S55. Update parameters of deep neural networks: Parameter updates are achieved by calculating the dynamic first-order moment decay rate and the second-order moment decay rate, combining gradient information and adaptive adjustment of historical momentum;

[0037] S56. Perform DropPath regularization: During each forward propagation, a portion of the paths in the network are randomly discarded. The probability of discarding a path is dynamically adjusted based on the current number of iterations and the total number of iterations.

[0038] S57. Perform early stopping mechanism judgment: The early stopping mechanism continuously monitors the performance indicators on the validation set during the model training process. When the loss on the validation set no longer decreases significantly, the training will stop early.

[0039] Furthermore, step S52 specifically includes:

[0040] S521. Calculate the initialization weight matrix: Based on the feature mean vector and the physical guidance matrix, a scaling operation is performed to obtain the weight reference term. At the same time, combined with the adaptive correction term, the initialization weight matrix of the deep neural network is calculated, which is expressed as:

[0041] ,

[0042] in, Initialization weight matrix for deep neural network; is the physical guidance matrix; For the The fusion feature vector of samples; is the total number of training samples; is an adaptive correction term used to enhance the robustness to changes in feature distribution;

[0043] S522. Calculate the adaptive correction term: Generate the adaptive correction term by spectral decomposition of the characteristic covariance matrix, expressed as:

[0044]

[0045] in, is the adaptive coefficient; is the feature covariance matrix The eigenvector matrix of is the square root of the eigenvalue diagonal matrix; is the diagonal matrix of eigenvalues ​​of fusion features; feature covariance matrix Defined as: ; is the global mean vector of the fused features; Represents the matrix Perform a transpose operation.

[0046] Furthermore, step S53 specifically includes:

[0047] 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, and define For the The linear output vector of the layer represents the inactivated intermediate feature representation, which is obtained as follows: , is a positive integer, For the The weight matrix of the layer, For the The output vector of the layer, For the The bias vector of the layer;

[0048] S532. Computational Physics-Inspired Activation Function: Input the linear output into a physics-inspired adaptive activation function to simulate stress saturation characteristics and obtain the activated feature representation. Define For the The activation output vector of the layer represents the features after nonlinear transformation and serves as the basis for the input or output layer of the next layer; The activation function is used to The linear output vector of the layer is calculated; the activation function is defined to be calculated based on the physical properties of stress, expressed as:

[0049] ,

[0050] in, is the input scalar of the activation function, i.e. The linear output vector of the layer Each element of is processed independently; is the activation function; is a logarithmic function; is the saturation coefficient, simulating the gain attenuation after stress yielding; is the linear gain coefficient; is the threshold adjustment parameter.

[0051] Furthermore, step S54 specifically includes:

[0052] S541. Calculation of basic numerical error terms: Calculate the mean square error between the predicted bearing capacity and the actual bearing capacity , as the basic numerical precision term of the loss function;

[0053] S542. Calculate physical violation penalties: Define three sub-constraint penalties, one for negative bearing capacity prediction, one for non-monotonic increasing relationship between bearing capacity and mean stress, and one for convexity violation, expressed as:

[0054] ,

[0055] in, It is a penalty item for physical violations; is a non-negative constraint penalty term; is the monotonicity constraint penalty is the convexity constraint penalty;

[0056] S543. Synthetic total loss function: The basic numerical error term and the physical violation penalty term are weighted together to form the final total loss function, which is used for backpropagation gradient calculation and optimization of model parameters. It is expressed as:

[0057] ,

[0058] in, is the total loss function; is the physical constraint weight coefficient.

[0059] Furthermore, step S55 specifically includes:

[0060] S551. Calculate the dynamic first-order moment decay rate: Adaptively adjust the first-order moment decay rate based on the gradient norm to reduce history dependence when the gradient oscillates;

[0061] S552. Calculate the dynamic second-order moment decay rate: adjust the second-order moment decay rate based on the consistency of the gradient and the historical momentum direction to accelerate the convergence direction;

[0062] S553. Update first-order moment estimation: fuse the current gradient with the historical momentum, establish the exponential moving average of the gradient direction, and estimate the gradient direction;

[0063] S554. Update the second-order moment estimate: Fuse the current squared gradient with the historical magnitude to establish an exponential moving average of the squared gradient, and combine it with a dynamic decay rate to achieve adaptive acceleration in the convergence direction.

[0064] S555. Update model parameters: Update the model's trainable parameters based on the bias-corrected moment estimates. By dynamically adjusting the moment estimates, balance the stability in the oscillation zone with the convergence speed in the flat zone.

[0065] The advantages of the present invention are:

[0066] The present invention solves the problems of non-stationarity and high noise interference in traditional methods when processing steel tube concrete arch stress data by combining adaptive normalization and wavelet threshold denoising. Compared with conventional fixed threshold denoising technology, the present invention can dynamically adjust the normalization range and effectively remove impulse noise through the wavelet threshold function, retaining the true fluctuation characteristics of the stress signal and avoiding distortion in the yield stage of the strain data. Traditional stress data analysis usually ignores frequency domain information. The present invention enhances data expression capabilities by fusing time domain statistical features with frequency domain energy features. Through dynamic time segmentation and short-time Fourier transform, the resonant frequency characteristics of stress data can be captured, thereby providing a more accurate feature description for bearing capacity prediction and improving the prediction accuracy of the model. measurement capability and accuracy; the deep neural network architecture proposed in the present invention combines the physics-inspired initialization mechanism, the physics-constrained activation function and the hybrid physics loss function, which enhances the model's modeling ability of 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 vanishing or unstable convergence in the early stage of training, and better adapt to the physical characteristics of steel tube concrete arch frames; 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0068] Figure 1 is a flow chart of the steps of the method of the present invention;

[0069] Figure 2 This is a flow chart of the adaptive normalization and wavelet denoising of the present invention;

[0070] Figure 3 is the stress signal of the steel tube concrete arch under load;

[0071] Figure 4 Comparison of the processing effects between traditional fixed threshold denoising and this technology;

[0072] Figure 5 This is a flow chart of time domain-frequency domain feature fusion in the present invention;

[0073] Figure 6 is the prediction accuracy of the four feature extraction methods in the present invention;

[0074] Figure 7This is a flow chart of the training of the steel tube concrete yielding arch bearing capacity prediction model of the present invention;

[0075] Figure 8 The response characteristics of the common activation function and the function of the present invention in the stress saturation region;

[0076] Figure 9 is the prediction error distribution of different activation functions;

[0077] Figure 10 Flowchart of deep neural network parameter updates during model training;

[0078] Figure 11 Training convergence curves for different optimizers;

[0079] Figure 12 Comparison of physical violation penalty values ​​for different optimizers. DETAILED DESCRIPTION

[0080] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments derived by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0081] Example 1

[0082] In this embodiment, Figure 1 As shown, the present invention provides a method for predicting the bearing capacity of a steel tube concrete yielding arch frame, which specifically includes the following steps:

[0083] S1. Collect stress data at key stress-bearing locations of the concrete-filled steel tube arch structure.

[0084] Specifically, high-precision resistance strain gauges are embedded in key stress-bearing locations of the concrete-filled steel tube arch structure, such as the arch foot, arch crown, and quarter span. Stress data is collected in a static acquisition mode with a sampling frequency of 10 Hz to ensure that the gradual change of stress is captured.

[0085] Each sample is collected continuously for no less than 300 seconds, covering the entire process from arch loading to failure;

[0086] The data are stored in the form of time series, including timestamps (millisecond precision) and microstrain values ​​(με), and are stored in CSV format.

[0087] S2. Set screening rules based on the principles of material mechanics to screen stress data and store the filtered data set in HDF5 layered format.

[0088] Specifically, the data from the initial prestressing stage of loading is deleted because there is installation disturbance in this stage; based on the steel yield strength threshold, such as |ε|>1700με for Q345 steel, the mutation points caused by sensor failure are eliminated, and the strain difference between two adjacent points is >500με; combined with the synchronous data of the load sensor, invalid sections with no load (load <5kN) or overload (load >120% of the design value) are removed; the data retained after screening must meet the continuity requirement - the proportion of valid data in any 10-second window must be ≥95%, and finally a time series data set with a validity flag is generated.

[0089] S3. Adopt the adaptive normalization method and the wavelet threshold function to denoise the stored stress data and obtain the denoised and normalized stress data.

[0090] Specifically, the stress data collected by the strain gauges are characterized by non-stationarity, high noise interference, and large time scale differences. The noise comes from sensor drift and environmental vibration. For example, the stress amplitude of different arch samples ranges from MPa to MPa, conventional global minimum-maximum normalization easily leads to amplified noise effects;

[0091] The present invention solves the non-stationary and noise problems by dynamically adjusting the normalization range and suppressing noise, combining adaptive normalization with wavelet threshold denoising. Figure 2 The specific steps are as follows:

[0092] S31. Calculate the stress mean of the local time window: Based on the dynamic time window, the stress values ​​within the interval are accumulated and the local stress mean is calculated to capture the local trend and avoid global normalization distortion. It is expressed as:

[0093] ,

[0094] in, express The local stress mean at each moment is used to dynamically capture the local trend of stress data and solve the non-stationary problem; is the time window size, preferably set to 50 time points, which represents the length of the integration interval and controls the smoothness of local statistics; is a positive integer; for The raw stress value at time t represents the input data collected by the strain gauge.

[0095] It should be noted that The accumulation operation in the term represents the sum of the intervals The stress values ​​within the time window are summed to represent the accumulation within the time window.

[0096] S32. Calculate the stress standard deviation in the local time window: Based on the local stress mean, calculate the stress standard deviation to quantify the stress fluctuation amplitude, provide a basis for implementing adaptive normalization, and solve the scale difference problem of the data. It is expressed as:

[0097] ,

[0098] in, express The standard deviation of local stress at a given moment is used to quantify the amplitude of stress fluctuations and solve the problem of scale differences.

[0099] S33. Calculate the normalized median value: Subtract the local mean from the original stress data and divide it by the local standard deviation to convert it into a standardized form to obtain the normalized median value. This eliminates local trends and scale differences and is expressed as:

[0100] ,

[0101] in, express The normalized intermediate value at the moment represents the stress data after adaptive normalization; for The original stress value at the time.

[0102] S34. Calculate the adaptive threshold: Based on the statistical characteristics of the normalized median, the median of the absolute value sequence of the difference between the original stress and the local mean is calculated, and combined with the noise proportional coefficient and the normalization constant, the adaptive threshold is obtained to distinguish between noise and real signals and provide a critical value for soft threshold processing. It is expressed as:

[0103] ,

[0104] in, It is an adaptive threshold used to determine the critical value of noise and suppress high noise interference through soft threshold processing; is the noise proportional coefficient, adjust the threshold sensitivity, such as, ; is the median function, which calculates the median value of the sequence; It represents the absolute value sequence of the difference between the original stress and the local mean, and the noise level estimation is obtained by global calculation.

[0105] It should be noted that The denominator of the term is , which is converted into a normalization constant to calibrate the median absolute deviation.

[0106] S35. Use the wavelet threshold function to complete denoising and normalization: Use the wavelet threshold function to process the normalized intermediate value, suppress the impulse noise through the soft threshold, and retain the true stress fluctuation characteristics. The denoised and normalized stress data is obtained, which is expressed as:

[0107] ,

[0108] in, express The stress data after denoising and normalization at each moment represents the effective signal after processing; is the wavelet threshold function, which realizes the soft threshold processing of noise. The calculation method is expressed as: ; is a sign function. If its input is greater than 0, the sign function value is 1, otherwise, the sign function value is -1; To obtain the maximum value function, ensure that the output is non-negative; is the absolute value symbol.

[0109] S4. Perform time-domain-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.

[0110] Specifically, stress data implies time dependence and periodicity, such as stress oscillation caused by load cycles. Conventional methods ignore frequency domain information and cannot capture the resonant frequency characteristics related to bearing capacity;

[0111] The present invention uses dynamic time segmentation and short-time Fourier transform to fuse time domain statistics and frequency domain energy features to enhance data expression capabilities. Figure 5 The specific steps are as follows:

[0112] S41. Dynamic time segmentation: Divide the time series data of each sample in the denoised and normalized stress data into segments of equal length and extract local time domain features;

[0113] Define the number of segments as , used to control the granularity of feature extraction, preferably, .

[0114] S42. Calculate the time-domain statistical eigenvector: Based on the segmentation results, calculate the segment stress mean, segment stress standard deviation, and segment stress skewness, which respectively characterize the average stress level, fluctuation amplitude, and distribution asymmetry within the segment. The time-domain statistical eigenvector is obtained as the time-domain part of the fusion feature and is expressed as:

[0115] ,

[0116] in, Represents the time domain statistical feature vector of the i-th sample, which serves as the time domain part of the fusion feature; is the segment stress mean, which represents the average level of stress within the segment. The calculation method is expressed as ; is the segmented stress standard deviation, which represents the stress fluctuation amplitude, and the calculation method is expressed as ; is the segmented stress deflection, which describes the asymmetry of stress distribution and is calculated as ; represents the i-th sample Stress data after denoising and normalization at all times; is the total number of time points for a single sample; Indicates the current segment interval.

[0117] S43. Extract frequency domain energy eigenvector: The denoised and normalized stress data is processed by short-time Fourier transform to obtain a time-frequency matrix. The frequency domain energy within the effective frequency range is weighted and summed using a frequency weighting function to extract the frequency domain energy eigenvector. The resonant frequency feature is focused on as the frequency domain portion of the fusion feature, which is expressed as:

[0118] ,

[0119] in, Represents the frequency domain energy feature vector of the i-th sample, as the frequency domain part of the fusion feature, dimension ; is the frequency point number; is a positive integer; is the lower limit of the effective frequency range, such as, , indicating that the lower limit of the effective frequency range is 0.1Hz; is the upper limit of the effective frequency range, such as, , indicating that the upper limit of the effective frequency range is 10Hz; is the short-time Fourier transform function; represents the i-th sample Stress data after denoising and normalization at all times; The output of the term is a time-frequency matrix; is the frequency weight function, which enhances the dominant frequency contribution by Gaussian weighting. The calculation method is expressed as ; represents an exponential function with a natural constant as its base; is the dominant frequency of the sample, obtained by peak detection of the short-time Fourier transform function result; is the bandwidth parameter, which controls the weight decay rate, such as, .

[0120] It should be noted that The term represents the summation of all frequency points within the effective frequency range.

[0121] S44. Generate a fused feature vector: Concatenate the time domain statistical feature vector and the frequency domain energy feature vector to form a fused feature vector, which is expressed as:

[0122] ,

[0123] in, Represents the fusion feature vector of the i-th sample; Represents a vector concatenation operation.

[0124] S5. Construct a steel tube concrete yielding arch bearing capacity prediction model. The overall architecture of the model is a multi-layer fully connected feedforward neural network, which combines a physics-inspired initialization mechanism, a physical constraint activation function, and a hybrid physics loss function. The fused feature vector is input into the model, and the model is trained to obtain a trained model.

[0125] Specifically, if Figure 7 As shown, the steps are as follows:

[0126] S51. Define the deep neural network architecture: The overall architecture of the deep neural network used in the present invention is a multi-layer fully connected feedforward neural network, which combines a physics-inspired initialization mechanism, a physical constraint activation function, and a hybrid physical loss function to enhance the model's ability to model the laws of structural nonlinear mechanics;

[0127] In terms of specific structure, the dimension of the input layer is equal to the feature dimension after the fusion of time domain and frequency domain;

[0128] Optionally, 3 to 5 hidden layers can be set after the input layer, each layer containing 128-256 neurons, and the stress saturation physical activation function proposed in the present invention is used to simulate the nonlinear changes in the stress critical response area;

[0129] The output layer is a single neuron, corresponding to the predicted bearing capacity of the arch;

[0130] DropPath is used between layers for structural regularization to prevent overfitting;

[0131] During 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 steel tube concrete arch.

[0132] S52. Initializing the Deep Neural Network: The fused feature vector is highly sparse, and the load-bearing capacity prediction must conform to material mechanics constraints. Conventional deep neural networks use random initialization, but this ignores the physical relationship between stress and load-bearing capacity, which can easily lead to unstable gradients or convergence to nonphysical solutions in the early stages of training.

[0133] The present invention calculates initial weights based on the statistical properties of feature data and physical priors, ensuring that the starting point of the model is close to the physically feasible region.

[0134] Specifically, the initialization process of the deep neural network is as follows:

[0135] S521. Calculate the initialization weight matrix: Based on the feature mean vector and the physical guidance matrix, a scaling operation is performed to obtain the weight reference term. At the same time, an adaptive correction term is combined to enhance the robustness to changes in feature distribution, thereby calculating the initialization weight matrix of the deep neural network, which is expressed as:

[0136] ,

[0137] in, Initialization weight matrix for 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; For the The physical scaling factor of a feature is calculated as ; is the physical scaling factor of the first feature; is the physical scaling factor of the second feature; For the The physical scaling factor of each feature; represents a diagonal matrix; It is a reference elastic modulus that characterizes the physical properties of the material, for example, the value range is 30000-210000 MPa; For the The global standard deviation of the features is calculated as ; For the The first fusion feature vector dimensional eigenvalues; For fusion feature The global mean of the dimensional features; For the The fusion feature vector of samples; is the total number of training samples; It is an adaptive correction term that enhances the robustness to changes in feature distribution;

[0138] S522. Calculate the adaptive correction term: Generate the adaptive correction term by spectral decomposition of the feature covariance matrix to adaptively adjust the feature correlation. This solves the problem of being unable to handle the correlation differences between feature dimensions when relying solely on global statistics. It is expressed as:

[0139]

[0140] in: is the adaptive coefficient, which controls the amplitude of the correction term, such as, 0.05; is the feature covariance matrix The eigenvector matrix of is obtained by eigendecomposition and represents the main direction of the feature space; the eigencovariance matrix Defined as: ; is the global mean vector of the fusion feature, and the calculation method is expressed as ; is the square root of the eigenvalue diagonal matrix, representing the principal component scaling of the feature space, is the diagonal matrix of eigenvalues ​​of fusion features; Represents the matrix Perform transpose operation;

[0141] It should be noted that The term reflects the adaptive adjustment of feature correlation and ensures that the initialization weights adapt to the data distribution through spectral decomposition.

[0142] S53. Perform forward propagation of deep neural networks and calculate custom activation functions: The nonlinear relationship of stress data is complex. The gradient of the conventional ReLU activation function is zero in the negative region, which easily leads to gradient vanishing and fails to capture the critical nonlinear behavior of stress data. During the forward propagation of the deep neural network, an activation function based on the physical properties of stress is used to simulate the saturation characteristics of stress data and the nonlinear changes when the stress value approaches the bearing capacity limit. This avoids the problem that the traditional ReLU activation function cannot effectively capture the stress-bearing capacity relationship when dealing with extreme stress, thereby improving the stability and accuracy of the model.

[0143] Specifically, 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, and define For the The linear output vector of the layer represents the inactivated intermediate feature representation, which is obtained as follows: , is a positive integer, For the The weight matrix of the layer, For the The output vector of the layer, For the The bias vector of the layer;

[0144] S532. Computational Physics-Inspired Activation Function: Input the linear output into a physics-inspired adaptive activation function to simulate stress saturation characteristics and obtain the activated feature representation. Define For the The activation output vector of the layer represents the features after nonlinear transformation and serves as the basis for the input or output layer of the next layer; The activation function is used to The linear output vector of the layer is calculated; the activation function is defined to be calculated based on the physical characteristics of stress to solve the problem of insufficient critical nonlinear capture, which is expressed as:

[0145] ,

[0146] in, is the input scalar of the activation function, i.e. The linear output vector of the layer Each element of is processed independently; is the activation function; It is a logarithmic function, and the default base is 10; is the saturation coefficient, simulating the gain attenuation after stress yielding, e.g., 0.1; is the linear gain coefficient, which controls the amplitude of the linear region, such as, 0.2; is the threshold adjustment parameter, which adjusts the transition slope between the linear region and the saturation region, such as, 0.5;

[0147] It should be noted that The term models the saturation effect, i.e., activation decay at large inputs, and The term approximates a linear response, avoids the hard saturation of the ReLU activation function, and enhances the sensitivity to the critical point of carrying capacity.

[0148] S54. Loss function calculation: During deep learning model training, the predicted bearing capacity output by the forward propagation must satisfy material mechanics constraints, such as a non-negative bearing capacity and a monotonically increasing relationship with stress. Conventional mean square error loss only considers numerical differences and ignores physical feasibility, which can easily lead to model predictions violating basic laws.

[0149] The present invention combines the traditional mean square error loss with the physical violation penalty term through a hybrid loss function to perform loss function calculation; it can effectively avoid the model prediction results from violating the mechanical principles. The model can not only optimize the numerical error, but also ensure that the bearing capacity prediction results conform to physical rationality and engineering practice requirements, thereby improving the reliability and robustness of the prediction.

[0150] Specifically, S541. Calculate the basic numerical error term: Calculate the mean square error between the predicted bearing capacity and the actual bearing capacity, which is used as the basic numerical accuracy term of the loss function to measure the average square deviation between the predicted value and the actual value, expressed as:

[0151] ,

[0152] in, is the mean square error loss term, which represents the average square deviation between the predicted value and the true value; For the The predicted carrying capacity of samples is generated by the output layer of the deep neural network; For the The actual bearing capacity of each sample comes from experimental measurement data.

[0153] S542. Calculate physical violation penalties: Define three sub-constraint penalties, respectively penalizing negative bearing capacity predictions, non-monotonic increasing relationships between bearing capacity and mean stress, and convexity violations, to ensure that the prediction results conform to the physical priors. They are expressed as:

[0154] ,

[0155] in, is the physical violation penalty term, and the gradient calculation is achieved through automatic differentiation; is a non-negative constraint penalty term that penalizes negative bearing capacity predictions to ensure the physical rationality of the bearing capacity. The calculation method is expressed as: ,when 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 mean stress. The calculation method is expressed as: ,when When , it satisfies monotonically increasing trend and the penalty value is 0; when 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. The calculation method is expressed as: ; For the The partial derivative of the predicted bearing capacity of each sample with respect to the mean stress; For the The second-order partial derivative of the predicted bearing capacity of each sample with respect to the mean stress; For the The average stress of the sample is obtained by segment stress mean Calculation of the global mean; is the symbol of partial derivative;

[0156] S543. Synthetic total loss function: The basic numerical error term and the physical violation penalty term are weighted together to form the final total loss function, which is used for backpropagation gradient calculation and optimization of model parameters. It is expressed as:

[0157] ,

[0158] in, is the total loss function, used for back propagation gradient calculation; is the physical constraint weight coefficient, which adjusts the importance of physical laws, such as 0.8.

[0159] S55. Parameter Updates for Deep Neural Networks: During the backpropagation process of deep learning models, the gradient of the loss function is affected by stress data noise, exhibiting non-stationarity, such as alternation between local oscillations and plateaus. Conventional Adam optimizers use a fixed decay rate, which can lead to underfitting in plateaus and overshoot in oscillatory regions.

[0160] The present invention achieves parameter updating by calculating the dynamic first-order moment decay rate and second-order moment decay rate, combining gradient information and adaptive adjustment of historical momentum. It ensures that the model can balance stability and convergence speed during training, and the optimization process can more effectively cope with the non-stationarity of the data, thereby improving the training efficiency and final performance of the model.

[0161] Specifically, the parameter update process of the deep neural network, such as Figure 10 As shown:

[0162] S551. Calculate the dynamic first-order moment decay rate: Adaptively adjust the first-order moment decay rate based on the gradient norm to reduce history dependence when the gradient oscillates and avoid overshoot problems. It is expressed as:

[0163] ,

[0164] in, For the The dynamic first-order moment decay rate of the iteration controls the strength of the historical gradient memory; is the lower limit of the first-order moment decay rate, such as, ; is the upper limit of the first-order moment decay rate, such as, ; is the gradient norm scaling factor, which adjusts the sensitivity of the decay rate to the gradient amplitude, such as, ; For the The gradient norm of the total loss function of the iteration represents the gradient amplitude.

[0165] It should be noted that The term realizes that the attenuation rate decreases when the gradient amplitude increases, avoiding the overshoot problem in the gradient oscillation area.

[0166] S552. Calculate the dynamic second-order moment decay rate: Adjust the second-order moment decay rate based on the consistency of the gradient and the historical momentum direction to accelerate the convergence direction and solve the underfitting problem in the flat area. It is expressed as:

[0167] ,

[0168] in, For the The dynamic second-order moment decay rate of the iteration controls the memory strength of the square of the historical gradient; is the second-order moment base decay rate, such as, ; is the directional sensitivity coefficient, which adjusts the gain amplitude of directional consistency, such as, ; For the The total loss function gradient of the iteration; For the The first-order moment estimate vector for the iteration.

[0169] It should be noted that The term is used to quantify the consistency of the gradient and the historical momentum direction, and When the terms are in the same direction, the attenuation rate is increased, the current gradient weight is enhanced, and the under-fitting problem in the flat area is solved.

[0170] S553. Update the first-order moment estimate: fuse the current gradient with the historical momentum, establish the exponential moving average of the gradient direction, and estimate the gradient direction, which is expressed as:

[0171] ,

[0172] in, For the The first-order moment estimation vector of the iteration represents the exponential moving average of the gradient direction.

[0173] S554. Update the second-order moment estimate: The current squared gradient is integrated with the historical magnitude to establish an exponential moving average of the squared gradient. This is combined with a dynamic decay rate to achieve adaptive acceleration in the convergence direction, expressed as:

[0174] ,

[0175] in, For the The second-order moment estimation vector of the iteration, representing the exponential moving average of the squared gradient; For the The second-order moment estimation vector of the iteration; Indicates the The total loss function gradient vector of the iteration is squared element by element; this estimate is combined with the dynamic decay rate , achieving adaptive acceleration in the convergence direction.

[0176] S555. Update model parameters: Update the model trainable parameters based on the bias-corrected moment estimates. By dynamically adjusting the moment estimates, balance the stability in the oscillation region and the convergence speed in the flat region, expressed as:

[0177] ,

[0178] in, For the The model trainable parameters of the iteration; For the The model trainable parameters of the iteration; For the The learning rate of the iteration; It is a numerical stability term to prevent division by zero errors, such as .

[0179] It should be noted that Items are dynamically adjusted and Collaboratively solve the non-stationary gradient problem and balance the stability in the oscillation area and the convergence speed in the flat area.

[0180] S56. Perform DropPath regularization: During the training of a deep neural network, DropPath regularization is used to prevent the model from overfitting. The present invention enhances the generalization ability of the model by dynamically adjusting the probability of discarding paths. Specifically, DropPath regularization randomly discards a portion of the paths in the network, that is, the connections between certain neurons, during each forward propagation. The probability of discarding paths is dynamically adjusted according to the current number of iterations and the total number of iterations, and is expressed as:

[0181]

[0182] in, is the minimum value of the probability of discarding the path, such as, ; is the maximum value of the probability of discarding the path, such as, ; is the current iteration number; is the total number of iterations.

[0183] It should be noted that the dynamic adjustment mechanism enables the model to retain more path information in the early stages of training, facilitating rapid learning of the basic features of the data. As training progresses, the probability of discarding paths gradually increases, enhancing the generalization ability of the model.

[0184] S57. Perform early stopping mechanism judgment: The early stopping mechanism is used to ensure that the deep neural network training process does not lead to overfitting or resource waste due to excessive training iterations. The early stopping mechanism continuously monitors the performance indicators on the validation set during the model training process. When the loss on the validation set no longer decreases significantly, the training will be stopped early.

[0185] S6. The collected data is processed in steps S3-S4 and 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 early warning is triggered.

[0186] Specifically, online prediction is implemented for newly built arches. Specifically, strain gauges are installed at the same position of the arch to be tested and 300 seconds of raw stress data are collected;

[0187] Then, the collected data is processed in steps S3-S4 to obtain a fused feature vector;

[0188] Then, the trained deep neural network model is loaded and forward propagated to obtain the carrying capacity prediction value.

[0189] A sliding window mechanism is used for real-time prediction, and the input features are updated every 10 seconds. An early warning is triggered when the predicted values ​​exceed 90% of the design bearing capacity for three consecutive times.

[0190] Example 2

[0191] In this embodiment, the signal processing advantages of the combination of adaptive normalization and wavelet denoising technology are verified, such as Figure 3 As shown in the figure, by analyzing the real stress signal (black solid line) of the steel tube concrete arch under load, the characteristics of the original signal (gray curve) containing sensor noise and pulse interference are shown, such as Figure 4 As 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 strain 1500 microstrain, while this technology completely retains the characteristics of the bilinear constitutive relationship.

[0192] Example 3

[0193] In this embodiment, the contribution of the time-frequency domain feature fusion strategy to improving the bearing capacity prediction accuracy is analyzed. Figure 6As shown in the figure, the prediction accuracy of four feature extraction methods is compared in the form of a bar graph, using only time domain statistical features (mean, standard deviation, etc.), only frequency domain energy features, simple splicing 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 texture-filled cylinder intuitively shows its advantages, which proves the necessity of fusing time domain statistical characteristics and frequency domain dynamic response characteristics, and can fully capture the stress state of the arch frame.

[0194] Example 4

[0195] In this embodiment, the effectiveness of the physical inspiration activation function proposed in the present invention is evaluated, such as Figure 8 As shown in the figure, the response characteristics of common activation functions (rectifier linear unit ReLU, leaky rectifier 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 specially marked in the figure. It can be seen that the traditional function has the problem of hard saturation or insufficient linear response in the critical region, while the function of the present invention presents a smooth transition characteristic when approaching the yield strength, accurately simulating the nonlinear behavior of steel under extreme load, as shown in the figure. Figure 9 As shown in the figure, the prediction error distribution of different activation functions is displayed. The prediction error of the function of the present invention is significantly smaller and the distribution is more concentrated. Most of the prediction values ​​are lower than the engineering safety threshold (the red dotted line in the figure). The width of the violin shape in the error distribution graph represents the error distribution range. The violin body of the function of the present invention is narrower and the peak is higher, indicating that it has higher reliability and stability.

[0196] Example 5

[0197] In this embodiment, the advantages of the physical constraint optimizer of the present invention in terms of training efficiency and prediction are evaluated. Figure 11 As shown in Figure 2, the training convergence curves of different optimizers are shown. The optimizer of the present invention (green solid line) is superior to traditional optimizers (stochastic gradient descent, adaptive moment estimation, etc.) in terms of loss value reduction speed and stability, and can reach the engineering practical convergence threshold (gray dotted line) faster. Figure 12 As shown in the figure, the change of the physical violation penalty value is displayed. The method of the present invention (green solid line) always remains in the safe physical constraint area (green background), while the violation value of the traditional method is higher and fluctuates significantly. The safe physical constraint area specially marked in the figure ensures that the prediction results meet the three basic mechanical principles: non-negative bearing capacity, monotonically increasing relationship with stress, and correct curvature characteristics. It proves that the optimizer of the present invention ensures that the prediction results conform to the laws of material mechanics while ensuring the convergence speed by dynamically adjusting the learning mechanism.

[0198] Finally, it should be noted that the above descriptions are merely 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 aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for predicting the bearing capacity of a steel tube concrete yielding arch frame, characterized in that: The following steps are involved: S1. Collect stress data at key stress-bearing locations of the concrete-filled steel tube arch structure; S2. Filter stress data by setting filtering rules based on the principles of material mechanics and storing the filtered dataset in HDF5 layered format. Specifically, data from the initial prestressing phase of loading is deleted, and mutation points caused by sensor failure are eliminated based on the steel yield strength threshold. Invalid sections with no load are removed by combining synchronized data from load sensors, ultimately generating a time series dataset with validity flags. S3. De-noising the stored stress data using an adaptive normalization method and a wavelet threshold function to obtain de-noised and normalized stress data; S4. Perform time-domain and 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 prediction model for the bearing capacity of concrete-filled steel tube arches. The overall architecture of the model is a multi-layer, fully connected feedforward neural network that combines a physics-inspired initialization mechanism, a physics-constrained activation function, and a hybrid physics loss function. The fused feature vector is input into the model, and the model is trained to obtain a trained model. The construction process of the steel tube concrete yielding arch bearing capacity prediction model is as follows: S51. Define the deep neural network architecture: the input layer dimension is equal to the feature dimension after the fusion of the time domain and frequency domain; the output layer is a single neuron; DropPath is used for structural regularization between layers; During the parameter initialization phase, the weight starting point is constructed by fusing the feature statistical mean with 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 CFST arch. S52. Initialize the deep neural network: Calculate initial weights based on the statistical properties of the feature data and physical priors to ensure that the model's starting point is close to the physically feasible region. S53. Perform forward propagation of the deep neural network and calculate a custom activation function: During the forward propagation of the deep neural network, an activation function based on the physical properties of stress is used to simulate the saturation characteristics of stress data and the nonlinear changes when the stress value approaches the bearing capacity limit; S54. Calculate the loss function: Calculate the loss function by combining the traditional mean square error loss with the physical violation penalty term through a hybrid loss function. S55. Update parameters of deep neural networks: Parameter updates are achieved by calculating the dynamic first-order moment decay rate and the second-order moment decay rate, combining gradient information and adaptive adjustment of historical momentum; S56. Perform DropPath regularization: During each forward propagation, a portion of the paths in the network are randomly discarded. The probability of discarding a path is dynamically adjusted based on the current number of iterations and the total number of iterations. S57. Early stopping mechanism judgment: The early stopping mechanism continuously monitors the performance indicators on the validation set during the model training process. When the loss on the validation set no longer decreases significantly, training will be stopped early. S6. The collected data is processed in steps S3-S4 and 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 early warning is triggered.

2. The method for predicting the bearing capacity of a steel tube concrete yield arch according to claim 1, characterized in that: Step S1 specifically includes: High-precision resistance strain gauges are embedded in key stress-bearing locations of the concrete-filled steel tube arch structure, and stress data is collected in a static acquisition mode. The data is stored in a time series format, including timestamps and microstrain values, and in CSV format.

3. The method for predicting the bearing capacity of a steel tube concrete yield arch according to claim 2, characterized in that: In step S3, adaptive normalization and wavelet denoising of stress data are performed, which specifically includes: S31. Calculate the stress mean of the local time window: Based on the dynamic time window, accumulate the stress values ​​within the interval and calculate the local stress mean; S32. Calculate the stress standard deviation in the local time window: Calculate the stress standard deviation based on the local stress mean; S33. Calculate the normalized median value: Subtract the local mean from the original stress data and divide it by the local standard deviation to convert it into a standardized form to obtain the normalized median value; S34. Calculate the adaptive threshold: Based on the statistical characteristics of the normalized median value, calculate the median of the absolute value sequence of the difference between the original stress and the local mean, and combine it with the noise scale factor and the normalization constant to obtain the adaptive threshold; S35. Use the wavelet threshold function to complete denoising and normalization: Use the wavelet threshold function to process the normalized intermediate value, suppress the impulse noise through the soft threshold, and retain the true stress fluctuation characteristics at the same time to obtain the denoised and normalized stress data.

4. The method for predicting the bearing capacity of a steel tube concrete yield arch according to claim 3, characterized in that: Step S4 specifically includes: S41. Dynamic time segmentation: Divide the time series data of each sample in the denoised and normalized stress data into segments of equal length and extract local time domain features; S42. Calculate the time-domain statistical eigenvector: Based on the segmentation results, calculate the segment stress mean, segment stress standard deviation, and segment stress skewness, which respectively characterize the average stress level, fluctuation amplitude, and distribution asymmetry within the segment. The time-domain statistical eigenvector is obtained as the time-domain part of the fusion feature and is expressed as: ， in, Represents the time domain statistical feature vector of the i-th sample; represents the mean value of segmental stress; represents the standard deviation of segmental stress; represents the segmental stress deflection; S43. Extract frequency domain energy eigenvector: The denoised and normalized stress data is processed by short-time Fourier transform to obtain a time-frequency matrix. The frequency domain energy within the effective frequency range is weighted and summed using a frequency weighting function to extract the frequency domain energy eigenvector as the frequency domain portion of the fusion feature, which is expressed as: ， in, 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 Stress data after denoising and normalization at all times; is the frequency weight function; S44. Generate a fused feature vector: concatenate the time domain statistical feature vector and the frequency domain energy feature vector to form a fused feature vector.

5. The method for predicting the bearing capacity of a steel tube concrete yield arch according to claim 4, characterized in that: Step S52 specifically includes: S521. Calculate the initialization weight matrix: Based on the feature mean vector and the physical guidance matrix, a scaling operation is performed to obtain the weight reference term. At the same time, combined with the adaptive correction term, the initialization weight matrix of the deep neural network is calculated, which is expressed as: ， in, Initialization weight matrix for deep neural network; is the physical guidance matrix; For the The fusion feature vector of samples; is the total number of training samples; is an adaptive correction term used to enhance the robustness to changes in feature distribution; S522. Calculate the adaptive correction term: Generate the adaptive correction term by spectral decomposition of the characteristic covariance matrix, expressed as: in, is the adaptive coefficient; is the feature covariance matrix The eigenvector matrix of is the square root of the eigenvalue diagonal matrix; is the diagonal matrix of eigenvalues ​​of fusion features; feature covariance matrix Defined as: ; is the global mean vector of the fused features; Represents the matrix Perform a transpose operation.

6. A method for predicting the bearing capacity of a steel tube concrete yielding arch according to claim 5, characterized in that: 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, and define For the The linear output vector of the layer represents the inactivated intermediate feature representation, which is obtained as follows: , is a positive integer, For the The weight matrix of the layer, For the The output vector of the layer, For the The bias vector of the layer; S532. Computational Physics-Inspired Activation Function: Input the linear output into a physics-inspired adaptive activation function to simulate stress saturation characteristics and obtain the activated feature representation. Define For the The activation output vector of the layer represents the features after nonlinear transformation and serves as the basis for the input or output layer of the next layer; The activation function is used to The linear output vector of the layer is calculated; the activation function is defined to be calculated based on the physical properties of stress, expressed as: ， in, is the input scalar of the activation function, i.e. The linear output vector of the layer Each element of is processed independently; is the activation function; is a logarithmic function; is the saturation coefficient, simulating the gain attenuation after stress yielding; is the linear gain coefficient; is the threshold adjustment parameter.

7. The method for predicting the bearing capacity of a steel tube concrete yield arch according to claim 6, characterized in that: Step S54 specifically includes: S541. Calculation of basic numerical error terms: Calculate the mean square error between the predicted bearing capacity and the actual bearing capacity , as the basic numerical precision term of the loss function; S542. Calculate physical violation penalties: Define three sub-constraint penalties, one for negative bearing capacity prediction, one for non-monotonic increasing relationship between bearing capacity and mean stress, and one for convexity violation, expressed as: ， in, It is a penalty item for physical violations; is a non-negative constraint penalty term; is the monotonicity constraint penalty is the convexity constraint penalty; S543. Synthetic total loss function: The basic numerical error term and the physical violation penalty term are weighted together to form the final total loss function, which is used for backpropagation gradient calculation and optimization of model parameters. It is expressed as: ， in, is the total loss function; is the physical constraint weight coefficient.

8. The method for predicting the bearing capacity of a steel tube concrete yield arch according to claim 7, characterized in that: Step S55 specifically includes: S551. Calculate the dynamic first-order moment decay rate: Adaptively adjust the first-order moment decay rate based on the gradient norm to reduce history dependence when the gradient oscillates; S552. Calculate the dynamic second-order moment decay rate: adjust the second-order moment decay rate based on the consistency of the gradient and the historical momentum direction to accelerate the convergence direction; S553. Update first-order moment estimation: fuse the current gradient with the historical momentum, establish the exponential moving average of the gradient direction, and estimate the gradient direction; S554. Update the second-order moment estimate: Fuse the current squared gradient with the historical magnitude to establish an exponential moving average of the squared gradient, and combine it with a dynamic decay rate to achieve adaptive acceleration in the convergence direction. S555. Update model parameters: Update the model's trainable parameters based on the bias-corrected moment estimates. By dynamically adjusting the moment estimates, balance the stability in the oscillation zone with the convergence speed in the flat zone.

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