Earthquake sand liquefaction prediction method, system and equipment based on deep learning and medium

Abstract

The invention relates to an earthquake sand liquefaction prediction method, system and device based on deep learning and a medium. According to the method, historical site parameters are standardized, a deep neural network is constructed, and an initial pore pressure ratio predicted value is obtained through forward propagation; sequentially calculating physical constraint loss to ensure that the prediction does not violate the effective stress non-negative and pore pressure ratio upper limit principle, calculating monotonicity constraint loss to force the model to learn the correct trend that the liquefaction probability is not reduced when the seismic oscillation intensity is enhanced and the liquefaction probability is not increased when the soil anti-liquefaction index is enhanced, and calculating data fitting loss; and carrying out weighted fusion on the three types of loss to form a total loss function, and iteratively optimizing model parameters through back propagation to obtain a prediction model of the embedded soil mechanics principle. Therefore, while the precision of the prediction model is ensured, wrong prediction violating basic physical rules under extreme working conditions is avoided, and the reliability, generalization and engineering credibility of the model under unknown or complex scenes are improved.

Description

Technical Field

[0001] This invention belongs to the field of artificial intelligence, and in particular relates to a method, system, device and medium for predicting earthquake sand liquefaction based on deep learning. Background Technology

[0002] In the fields of earthquake engineering and geotechnical engineering, accurately predicting the likelihood of soil liquefaction triggered by earthquakes is a crucial step in assessing site seismic safety and conducting seismic design. For a long time, the engineering community has primarily relied on empirical formulas or probabilistic statistical models based on simplified assumptions for liquefaction assessment. While these methods have some reference value under conventional conditions, their ability to characterize complex nonlinear relationships is limited, and they struggle to comprehensively consider diverse soil layer characteristics and variable seismic motion parameters. Consequently, the accuracy and reliability of predictions under boundary conditions or special soil conditions are often unsatisfactory.

[0003] In recent years, data-driven methods, represented by deep learning, have offered new insights into this challenge. They can automatically extract high-dimensional features and complex patterns from vast amounts of historical case data, demonstrating fitting capabilities that surpass traditional methods. However, existing deep learning prediction models are essentially "black box" tools. Their training process relies entirely on the numerical correlation between input features and output labels, neglecting widely validated fundamental physical principles of soil mechanics and engineering common sense. This purely data-driven paradigm has a fundamental flaw: when the model is applied to "extreme conditions" outside the training data distribution, such as scenarios with extremely high seismic intensity and extremely low soil resistance, its prediction results are prone to significantly violating physical laws, such as predicting negative effective stress or a pore water pressure ratio greater than 1, which is impossible in physical reality. Furthermore, the model may fail to internalize the established monotonic relationships between key parameters; for example, the probability of liquefaction should increase with increasing seismic intensity, while the probability of liquefaction should decrease with increasing soil density. These unreasonable predictions not only directly lead to engineering misjudgments, but also seriously weaken the model's generalization ability and engineering credibility in high-intensity areas, new regions, or data-sparse scenarios, thus limiting its application value in actual engineering decision-making.

[0004] Therefore, there is an urgent need for a new prediction method that can organically integrate domain physics knowledge into a data-driven framework, so as to ensure that the output results strictly conform to physical laws and engineering logic while maintaining the model's strong learning ability, thereby constructing a next-generation intelligent prediction model for sand liquefaction that combines high accuracy, strong robustness and high reliability. Summary of the Invention

[0005] Therefore, it is necessary to provide a method, system, equipment, and medium for predicting earthquake sand liquefaction based on deep learning to address the aforementioned technical problems.

[0006] Firstly, this application provides a deep learning-based method for predicting earthquake-induced sand liquefaction, including:

[0007] S1. Standardize the site parameters of historical earthquake sand liquefaction cases to generate a standardized training dataset; the site parameters include soil layer parameters and ground motion parameters.

[0008] S2. Based on the feature dimensions in the training dataset, a deep neural network prediction model is constructed using the samples in the training dataset as input and the predicted pore water pressure ratio as output. The samples in the training dataset are then input into the deep neural network prediction model for forward propagation to generate the initial predicted pore water pressure ratio.

[0009] S3. Calculate the physical constraint loss value based on the initial predicted pore water pressure ratio and the corresponding initial effective stress value in the training dataset;

[0010] S4. Calculate the monotonicity constraint loss value based on the changing trends of key sample features in the training dataset and the corresponding changing trends of the initial predicted pore water pressure ratio.

[0011] S5. Calculate the data fitting loss value based on the initial predicted pore water pressure ratio and the actual pore water pressure ratio in the training dataset.

[0012] S6. Perform a weighted summation of the data fitting loss value, physical constraint loss value, and monotonic constraint loss value to generate the total loss function value;

[0013] S7. Based on the total loss function value, update the parameters of the deep neural network prediction model through the backpropagation algorithm, and iteratively train the deep neural network prediction model to obtain the pre-trained pore water pressure ratio prediction model.

[0014] S8. Input the standardized site parameters of the site to be predicted into the pore water pressure ratio prediction model and output the predicted pore water pressure ratio; perform sand liquefaction discrimination based on the predicted pore water pressure ratio to obtain the earthquake sand liquefaction prediction results.

[0015] Secondly, this application also provides a deep learning-based earthquake sand liquefaction prediction system for implementing the method described in the first aspect, the system comprising:

[0016] The site data standardization module is used to standardize the site parameters of historical earthquake sand liquefaction cases and generate a standardized training dataset; the site parameters include soil layer parameters and seismic motion parameters.

[0017] The deep model initialization module is used to construct a deep neural network prediction model based on the feature dimensions in the training dataset, taking samples from the training dataset as input and the predicted pore water pressure ratio as output; the samples from the training dataset are input into the deep neural network prediction model for forward propagation to generate the initial predicted pore water pressure ratio value.

[0018] The physical constraint loss calculation module is used to calculate the physical constraint loss value based on the initial predicted pore water pressure ratio and the corresponding initial effective stress value in the training dataset.

[0019] The monotonicity constraint loss calculation module is used to calculate the monotonicity constraint loss value based on the changing trends of key sample features in the training dataset and the corresponding changing trends of the initial predicted pore water pressure ratio.

[0020] The data fitting loss calculation module is used to calculate the data fitting loss value based on the initial predicted pore water pressure ratio and the actual pore water pressure ratio in the training dataset.

[0021] The loss function aggregation module is used to perform a weighted summation of the data fitting loss value, physical constraint loss value, and monotonic constraint loss value to generate the total loss function value;

[0022] The model training iteration module is used to update the parameters of the deep neural network prediction model based on the total loss function value through the backpropagation algorithm, and to iteratively train the deep neural network prediction model to obtain a pre-trained pore water pressure ratio prediction model.

[0023] The liquefaction prediction output module is used to input standardized site parameters of the site to be predicted into the pore water pressure ratio prediction model and output the predicted pore water pressure ratio; based on the predicted pore water pressure ratio, sand liquefaction is judged to obtain the earthquake sand liquefaction prediction result.

[0024] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement a deep learning-based earthquake sand liquefaction prediction method as described in the first aspect.

[0025] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a deep learning-based method for predicting seismic sand liquefaction as described in the first aspect.

[0026] The aforementioned deep learning-based method, system, equipment, and medium for predicting earthquake sand liquefaction involves standardizing historical liquefaction site parameters and constructing a deep neural network model. Initial predicted pore pressure ratios are obtained through forward propagation. Based on this, the following losses are calculated sequentially: physical constraint loss to ensure the prediction does not violate the non-negativity of effective stress and the upper limit of pore pressure ratio; monotonicity constraint loss to force the model to correctly learn the influence trends of seismic intensity and anti-liquefaction strength parameters; and data fitting loss to measure prediction accuracy. These three types of losses are then weighted and fused into a total loss. The model parameters are iteratively optimized through backpropagation, ultimately resulting in a prediction model that incorporates fundamental principles of soil mechanics and engineering logic. This approach explicitly integrates physical and monotonic constraints into the model training objective, transforming the model from pure data fitting to learning guided by physical laws. This fundamentally avoids absurd outputs that violate soil mechanics axioms under extreme conditions while maintaining prediction accuracy. It significantly improves the model's prediction reliability, generalization ability, and engineering decision-making credibility in complex scenarios such as sparse data or high intensity. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 A flowchart illustrating a deep learning-based method for predicting earthquake sand liquefaction provided by this invention.

[0029] Figure 2 This is a schematic diagram of the process for calculating the monotonicity constraint loss value in an optional embodiment of the present invention;

[0030] Figure 3 This is a schematic diagram of the structure of a deep learning-based earthquake sand liquefaction prediction system provided by the present invention. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0032] refer to Figure 1 The document presents a flowchart illustrating a deep learning-based method for predicting seismic sand liquefaction, which includes the following steps:

[0033] S1. Standardize the site parameters of historical earthquake sand liquefaction cases to generate a standardized training dataset; the site parameters include soil layer parameters and ground motion parameters.

[0034] Specifically, the selection criteria for historical earthquake sand liquefaction cases should first be clarified. Cases with complete site parameter records and clear liquefaction determination results should be selected. Case sources can include measured data from typical domestic and international earthquake disaster investigation reports, geotechnical engineering test databases, and publicly available academic literature to ensure the representativeness of the cases and the reliability of the data. The soil layer parameters specifically include the relative density, effective unit weight, clay content, soil layer thickness, groundwater level depth, and initial effective stress of saturated sand; the seismic motion parameters specifically include peak ground acceleration, seismic motion duration, and characteristic period of the seismic response spectrum.

[0035] Before standardization, data preprocessing is required. For outliers in the site parameters, the 3σ criterion is used for identification and handling: the mean and standard deviation of each parameter are calculated, and data exceeding the mean plus or minus three standard deviations are identified as outliers. For parameters with a very low outlier rate, the corresponding samples are directly removed; for parameters with a moderate outlier rate, the median replacement method is used to correct for outliers, avoiding interference from a single outlier on the overall dataset distribution. For missing values, if the missing rate is extremely low, linear interpolation is used for imputation; if the missing rate is moderate, K-nearest neighbor interpolation is used, calculating the Euclidean distance between missing samples and other complete samples, selecting the mean of the corresponding parameters of the nearest samples for imputation, with the K value determined through cross-validation; if the missing rate is too high, the sample is removed to ensure the integrity of the dataset.

[0036] The standardization process employs the Z-score standardization method. Its core principle is to convert each parameter into a standard normal distribution with a mean of 0 and a standard deviation of 1, thereby eliminating the impact of differences in the dimensions of different parameters on model training and ensuring that each feature contributes equally to the model training process. The specific calculation process is as follows:

[0037]

[0038] in, This represents the original value of the j-th site parameter for the i-th sample. represent The standardized values This represents the mean of the j-th parameter across all historical cases. This represents the standard deviation of the j-th parameter.

[0039] During the calculation, first iterate through all historical case samples and solve for each parameter separately. and Then, the parameter values ​​of each sample are substituted into the above formula to complete the standardization transformation. After standardization, the processed dataset is randomly shuffled and divided into training, validation, and test sets according to the proportions. The training set is used for model parameter learning, the validation set is used for hyperparameter tuning during training, and the test set is used for final model performance evaluation, ultimately generating a standardized training dataset that meets the training requirements of deep neural networks.

[0040] S2. Based on the feature dimensions in the training dataset, a deep neural network prediction model is constructed using the samples in the training dataset as input and the predicted pore water pressure ratio as output. The samples in the training dataset are then input into the deep neural network prediction model for forward propagation to generate the initial predicted pore water pressure ratio.

[0041] Specifically, the feature dimension of the training dataset is first determined. The feature dimension equals the total number of standardized site parameters. The number of neurons in the input layer of the deep neural network prediction model is thus determined, maintaining consistency with the feature dimension. The model output layer is a single neuron, corresponding to the predicted pore water pressure ratio. The pore water pressure ratio is a core indicator in sand liquefaction assessment, defined as the ratio of the maximum pore water pressure in sand during an earthquake to the initial effective stress. Its value ranges from 0 to 1. Therefore, a linear activation function is used in the output layer to ensure the continuity and physical rationality of the output results.

[0042] The hidden layers of the deep neural network prediction model adopt a multilayer perceptron structure. The number of hidden layers is determined through hyperparameter optimization, as is the number of neurons in each layer. The activation function for the hidden layers is a rectified linear unit, and its expression is:

[0043]

[0044] in, Represents the linear output value of the hidden layer. This represents the output value after activation. This function effectively alleviates the vanishing gradient problem and is computationally efficient, making it suitable for training large-scale datasets. To further improve the model's generalization ability, a Dropout layer is added after each hidden layer to randomly drop some neurons and prevent the model from overfitting the training data. The model's weights are initialized using the He normal initialization method, and the bias term is initialized to 0 to ensure a uniform gradient distribution in the initial stage of model training.

[0045] After the model is built, samples from the standardized training dataset are input into the model for forward propagation calculations to generate initial predicted pore water pressure ratios. The specific process of forward propagation is as follows:

[0046] The first step is for the input layer to receive the standardized sample feature vectors. The weight matrix of the first hidden layer Perform matrix multiplication and then add bias terms. A linear output is obtained. The calculation process is as follows:

[0047]

[0048] in, Represents the sample feature vector of the input layer. The weight matrix represents the first hidden layer and is used to characterize the strength of the association between the input features and the neurons in the first hidden layer. This represents the bias term of the first hidden layer, used to adjust the baseline value of the linear output. This represents the linear output of the first hidden layer.

[0049] The second step is to Input the modified linear unit activation function to obtain the output of the first hidden layer. The calculation process is as follows:

[0050]

[0051] in, This represents the output of the first hidden layer after activation, which will be used as the input of the second hidden layer.

[0052] The third step is to Weight matrix of the second hidden layer Multiply and add bias terms The output of the second hidden layer is obtained after the activation of the modified linear unit. The calculation logic is the same as that of the first hidden layer, as shown in the formula below:

[0053]

[0054]

[0055] in, This represents the weight matrix of the second hidden layer. This represents the bias term of the second hidden layer. This represents the linear output of the second hidden layer. This represents the output result after the second hidden layer is activated.

[0056] Fourth step, repeat the above process. Weight matrix of the third hidden layer Bias terms And obtained after modifying the activation of the linear unit The calculation process is as follows:

[0057]

[0058]

[0059] in, The weight matrix represents the third hidden layer. This represents the bias term of the third hidden layer. This represents the linear output of the third hidden layer. This represents the output result after the third hidden layer is activated.

[0060] Fifth step, With the output layer weight matrix Multiply and add bias terms The initial predicted pore water pressure ratio is obtained through a linear activation function. The calculation process is as follows:

[0061]

[0062] in, The weight matrix represents the output layer. Represents the bias term of the output layer. This represents the initial predicted pore water pressure ratio.

[0063] S3. Calculate the physical constraint loss value based on the initial predicted pore water pressure ratio and the corresponding initial effective stress value in the training dataset.

[0064] Specifically, the core of physical constraint loss design is to ensure that the initial predicted pore water pressure ratio strictly conforms to the basic physical laws of soil mechanics, avoiding predictions that contradict reality. According to soil mechanics principles, the pore water pressure ratio is equal to the ratio of the maximum pore water pressure generated during an earthquake to the initial effective stress. The maximum value of the maximum pore water pressure cannot exceed the initial effective stress; otherwise, the effective stress of the sand will become negative, violating the soil equilibrium condition. Therefore, the physical range of the pore water pressure ratio must be between 0 and 1, which is the core basis of physical constraints.

[0065] Before calculating the physical constraint loss value, the initial effective stress normalized value corresponding to each sample is extracted from the training dataset, and then restored to the actual initial effective stress value through the inverse normalization process. The inverse normalization formula is as follows:

[0066]

[0067] in, The standardized value representing the initial effective stress parameter; The standard deviation of the initial effective stress parameter, The mean value of the initial effective stress parameter is represented by both of them, which are standardized parameters calculated in step S1. This represents the actual initial effective stress value after reduction.

[0068] Simultaneously, the initial predicted pore water pressure ratio is restored to the actual predicted value through the same inverse normalization process to ensure the dimensional consistency of the parameters during the calculation. The inverse normalization formula for the initial predicted pore water pressure ratio is:

[0069]

[0070] in, The standardized value representing the initial predicted pore water pressure ratio; This represents the standard deviation of the true pore water pressure ratio in the training dataset. , representing the mean of the true pore water pressure ratio in the training dataset, both are standardized parameters calculated in step S1; This represents the initial predicted pore water pressure after reduction compared to the actual value.

[0071] The physical constraint loss function uses a piecewise L2 loss function, which penalizes the portion of the restored initial predicted pore water pressure that exceeds the physical range of 0 to 1 compared to the actual value. The specific expression is as follows:

[0072]

[0073] in, This represents the physical constraint loss value, and N represents the number of samples in the training dataset. This represents the summation operation over all training samples. This means that when the initial predicted pore water pressure after reduction is greater than the actual value by 1, the penalty term is the square of the difference between the actual value and 1; when the actual value is less than or equal to 1, this penalty term is 0. This means that when the initial predicted pore water pressure after reduction is less than 0 compared to the actual value, the penalty term is the square of the opposite of the actual value; when the actual value is greater than or equal to 0, this penalty term is 0.

[0074] The specific calculation process is as follows: First, iterate through each sample in the training dataset to obtain the standardized value of the initial predicted pore water pressure ratio and the standardized value of the initial effective stress. Then, perform inverse standardization using the corresponding formulas to obtain the restored initial predicted pore water pressure ratio and the actual initial effective stress value. Second, judge the restored initial predicted pore water pressure ratio for each sample and calculate the penalty terms for exceeding the upper and lower limits. Then, sum the penalty terms for all samples and divide by the number of samples N to obtain the average physical constraint loss value. The magnitude of this loss value directly reflects the degree to which the initial prediction result violates physical laws. The larger the loss value, the more prediction values ​​that do not conform to physical reality exist. In subsequent model parameter updates, it is necessary to focus on adjusting the parameters corresponding to these samples to force the model to output prediction results that conform to the principles of soil mechanics.

[0075] S4. Calculate the monotonicity constraint loss value based on the changing trends of key sample features in the training dataset and the corresponding changing trends of the initial predicted pore water pressure ratio.

[0076] Specifically, the core purpose of monotonicity constraints is to ensure that the model internalizes the inherent monotonic relationships between key site parameters and the pore water pressure ratio, relationships that have been verified by soil mechanics theory and extensive engineering practice. For example, as peak ground acceleration increases, the disturbance effect of earthquakes on sand intensifies, and the pore water pressure ratio should monotonically increase; as the relative density of sand increases, soil particles are more densely packed, enhancing liquefaction resistance, and the pore water pressure ratio should monotonically decrease; as the depth of groundwater increases, effective stress increases, and the pore water pressure ratio should monotonically decrease. Therefore, monotonicity constraint losses are constructed based on these key sample characteristics to penalize instances where the model's predictions violate the aforementioned monotonic relationships.

[0077] First, core key features are selected from the site parameters of the training dataset. Other key features can be added later according to actual engineering needs. For each key feature, a monotonicity judgment criterion is constructed using adjacent sample pairs: the samples in the training dataset are sorted from smallest to largest according to a certain key feature value to generate an ordered sample sequence; then, two adjacent samples in the sequence are selected as sample pairs, where the key feature value of the first sample is less than that of the second sample, and the initial predicted pore water pressure of the two samples is the restored value compared to the actual value.

[0078] Based on the monotonic relationship between key features and pore water pressure ratio, a monotonicity judgment criterion is set: for positively correlated features, the actual value of the initial predicted pore water pressure ratio after restoration of the later sample should be greater than or equal to the corresponding value of the earlier sample; for negatively correlated features, the actual value of the initial predicted pore water pressure ratio after restoration of the later sample should be less than or equal to the corresponding value of the earlier sample. The monotonicity constraint loss function adopts a variant of the hinge loss function, calculating a penalty term for all adjacent sample pairs of each key feature. The specific expression is as follows:

[0079]

[0080] in, represents the monotonicity constraint loss value, K represents the number of key features selected, and M represents the total number of neighboring sample pairs of all key features. The number of neighboring sample pairs representing the k-th key feature. This represents the summation operation over all adjacent sample pairs of all key features; The sign function takes a value of 1 for positively correlated features and -1 for negatively correlated features. The initial predicted pore water pressure ratio after restoration to the actual value represents the (i+1)th sample in the ordered sequence of the k-th key feature. The initial predicted pore water pressure ratio after restoration to the actual value represents the i-th sample in the ordered sequence of the k-th key feature. This indicates that a penalty is applied when the value inside the parentheses is positive, and the penalty is zero when the value is negative.

[0081] The specific calculation process is as follows: First, sort the samples corresponding to each key feature to generate multiple ordered sample sequences, and calculate the number of adjacent sample pairs in each sequence. Second, traverse all adjacent sample pairs for each key feature, determine the value of the sign function based on the feature type, calculate the difference between the initial predicted pore water pressure of the next sample and the actual value, and multiply it by the value of the sign function. If the product is negative, it indicates a violation of the monotonic relationship, and its square is calculated as a penalty term; otherwise, the penalty term is 0. Third, sum all penalty terms for all key features and divide by the product of the number of key features and the total number of adjacent sample pairs to obtain the average monotonicity constraint loss value. The value of this loss value ranges from 0 to positive infinity. When the model prediction result completely conforms to the monotonic relationship of all key features, the loss value is 0; the greater the degree of violation, the greater the loss value. This loss term forces the model to learn and abide by these inherent engineering logic relationships during training, improving the interpretability and generalization ability of the model.

[0082] S5. Calculate the data fitting loss value based on the initial predicted pore water pressure ratio and the actual pore water pressure ratio in the training dataset.

[0083] Specifically, the core function of the data fitting loss is to measure the deviation between the initially predicted pore water pressure ratio and the actual pore water pressure ratio in the training dataset. This ensures that the model can accurately learn the statistical correlation between site parameters and pore water pressure ratios in historical cases, and is a fundamental loss term for training deep neural network models. The actual pore water pressure ratios in the training dataset are derived from measured data in historical earthquake sand liquefaction cases. For cases without direct measured data, simplified calculation methods from relevant seismic design codes are used to derive the values, ensuring the accuracy and reliability of the actual values.

[0084] Considering that the pore water pressure ratio is a continuous variable and that the training dataset may contain a small number of extreme values, the mean squared error loss function is chosen for data fitting. This loss function provides a continuous penalty for prediction bias, is easy to calculate, and its gradient is readily solvable. The specific expression is as follows:

[0085]

[0086] in, This represents the data fitting loss value, and N represents the number of samples in the training dataset. The standardized value representing the initial predicted pore water pressure ratio. This represents the standardized value of the actual pore water pressure ratio in the training dataset. Both values ​​have been standardized simultaneously to maintain dimensional consistency. This represents the summation operation over all training samples.

[0087] The specific calculation process is as follows: First, obtain the initial predicted values ​​of all training samples from the output layer of the deep neural network to form a predicted value vector; second, extract the corresponding true values ​​from the training dataset to form a true value vector, ensuring that the sample order of the two vectors is consistent; third, calculate the difference between corresponding elements in the two vectors and square each difference to obtain a deviation squared vector; fourth, sum all elements in the deviation squared vector and divide by the number of samples N to obtain the data fitting loss value. The value of this loss value ranges from 0 to positive infinity. The smaller the loss value, the higher the degree of fit between the model's prediction results and the real data, and the better the model's learning effect on historical cases; conversely, it indicates that the model has not yet fully learned the relationship between site parameters and pore water pressure ratio, and further adjustment of model parameters is needed.

[0088] To avoid the model overfitting noise in the training data, an early stopping mechanism can be used when calculating the data fitting loss value. This involves simultaneously monitoring the data fitting loss value during training and the fitting loss value on the validation set. When the validation set loss value no longer decreases for several consecutive training rounds, training is stopped to ensure the model's generalization ability.

[0089] S6. Perform a weighted summation of the data fitting loss value, physical constraint loss value, and monotonic constraint loss value to generate the total loss function value.

[0090] Specifically, the core of the overall loss function design is to balance the relationship between data fitting accuracy, conformity to physical laws, and monotonicity of engineering logic. By introducing weight coefficients to perform a weighted sum of the three loss terms, the model can simultaneously optimize multiple objectives during training, avoiding the problems of overfitting with insufficient constraints or vice versa. The selection of weight coefficients needs to be determined based on actual engineering needs and model training results. A grid search method is used to optimize the weight combination to ensure that the overall loss function can effectively guide the model towards optimization towards high accuracy, strong robustness, and high reliability.

[0091] Let the weighting coefficients of the data fitting loss value be... The weighting coefficient for the physical constraint loss value is The weighting coefficient of the monotonicity constraint loss value is The expression for the total loss function is:

[0092]

[0093] in, Represents the total loss function value. This represents the data fitting loss value. Represents the physical constraint loss value. Represents the monotonicity constraint loss value. , , All three are constants greater than 0, and their sum is 1. This constraint ensures the normalization of the weight coefficients and avoids a certain loss term from excessively dominating the total loss due to an excessively large absolute value of the weight.

[0094] The specific process for determining the weight coefficients is as follows: First, based on engineering experience, an initial weight combination range is set. Considering that data fitting is the foundation of the model, a higher initial weight range is assigned to the data fitting loss value; physical constraints are the core of ensuring model reliability, so a moderate initial weight range is assigned to the physical constraint loss value; monotonicity constraints help improve model interpretability, so a lower initial weight range is assigned to the monotonicity constraint loss value. Then, several weight combinations are evenly selected within the above range, and the model is trained using each weight combination. The comprehensive performance index of the model on the validation set is recorded. The comprehensive performance index is obtained by weighting the fitting accuracy, physical conformity rate, and monotonicity conformity rate in a certain proportion. The physical conformity rate is the proportion of samples whose predicted values ​​satisfy the range of 0 to 1, and the monotonicity conformity rate is the proportion of sample pairs that satisfy the monotonic relationship of key features. Finally, the weight combination with the highest comprehensive performance index is selected as the final weight coefficient.

[0095] The calculation process for the total loss function is as follows: Substitute the data fitting loss value obtained in step S5, the physical constraint loss value obtained in step S3, and the monotonicity constraint loss value obtained in step S4 into the formula for calculating the total loss function. Then, sum these values ​​using determined weighting coefficients to obtain the total loss function value for each training epoch. The total loss function value is the core basis for updating model parameters. During training, by continuously minimizing the total loss function value, the model improves data fitting accuracy while strictly adhering to physical laws and engineering logic, ultimately achieving a balance between high-precision prediction and high-reliability output.

[0096] S7. Based on the total loss function value, update the parameters of the deep neural network prediction model through the backpropagation algorithm, and iteratively train the deep neural network prediction model to obtain the pre-trained pore water pressure ratio prediction model.

[0097] Specifically, the core principle of the backpropagation algorithm is to calculate the gradient of the loss function with respect to the weights and biases of each layer of the model based on the total loss function value using the chain rule, and then use a gradient descent-type optimizer to update the model parameters, thereby minimizing the total loss function. This training uses the Adam optimizer, which combines the advantages of momentum gradient descent and adaptive learning rate, effectively improving training stability and convergence speed, and avoiding getting trapped in local optima.

[0098] First, set the hyperparameters for model training: the learning rate adopts a dynamic adjustment strategy to achieve rapid convergence in the early stages of training and fine-tune the parameters in the later stages; the training batch size is determined based on the GPU memory capacity to ensure that the samples in each training batch can be fully loaded into the memory, thereby improving training efficiency; set the maximum number of training epochs and enable the early stopping mechanism to avoid overtraining.

[0099] The specific training process is as follows: First, input the standardized training dataset into the model in batches to complete the forward propagation calculation, obtain the initial predicted values, and generate the total loss function value. Second, calculate the gradient of the total loss function value with respect to the parameters of each layer of the model based on the backpropagation algorithm. Taking the gradient calculation of the output layer weights as an example, according to the chain rule, the gradient of the total loss function value with respect to the output layer weights is equal to the product of the partial derivative of the total loss function value with respect to the initial predicted pore water pressure ratio and the partial derivative of the initial predicted pore water pressure ratio with respect to the output layer weights. The partial derivative of the initial predicted pore water pressure ratio with respect to the output layer weights is the output of the last hidden layer during the forward propagation process. The partial derivative of the total loss function value with respect to the initial predicted pore water pressure ratio can be solved by the partial derivative of the total loss function with respect to the initial predicted pore water pressure ratio. This process is repeated to solve the gradient of each layer parameter sequentially. Third, input the calculated gradients into the Adam optimizer and update the model parameters according to the following formula:

[0100]

[0101] in, This represents the parameter value in the t-th training round. The parameter value represents the (t-1)th training epoch. Represents the current learning rate. The first-moment estimate, representing the gradient of the parameters, is used to characterize the cumulative trend of the gradient. The second-moment estimate representing the parameter gradient is used to characterize the cumulative trend of the squared parameter gradient. This represents a tiny constant to prevent the denominator from being zero. The fourth step involves repeating the forward propagation, gradient calculation, and parameter update process until the maximum number of training epochs is reached or the early stopping mechanism is triggered.

[0102] During training, the total loss values ​​of the training and validation sets are monitored in real time. If the loss value of the training set continues to decrease while the loss value of the validation set increases, it indicates that the model is overfitting, and the Dropout layer parameters need to be adjusted or a regularization term added. If the loss values ​​of both the training and validation sets decrease slowly, it indicates that the learning rate is set improperly, and the learning rate needs to be adjusted. After training is completed, the model parameters with the best overall performance on the validation set are saved to obtain the pre-trained pore water pressure ratio prediction model.

[0103] S8. Input the standardized site parameters of the site to be predicted into the pore water pressure ratio prediction model and output the predicted pore water pressure ratio; perform sand liquefaction discrimination based on the predicted pore water pressure ratio to obtain the earthquake sand liquefaction prediction results.

[0104] Specifically, the first step is to conduct an on-site investigation of the site to be assessed to obtain complete site parameters. The investigation process must comply with the requirements of the geotechnical engineering investigation specifications. Sand samples can be obtained through borehole sampling, and relative density tests can be used to determine relative density, ring sampler methods to determine effective unit weight, and sieve analysis to determine clay content. Groundwater level depth can be determined through water level observation wells. Seismic safety assessments of the site can be used to determine seismic parameters such as peak ground acceleration, seismic duration, and characteristic period of the seismic response spectrum. Static cone penetration tests can be used to determine soil layer thickness and initial effective stress, ensuring that the accuracy of all site parameter measurements meets engineering requirements.

[0105] The site parameters to be predicted are standardized using the same method as in step S1. Specifically, the mean and standard deviation of each parameter calculated in step S1 are used for standardization transformation to ensure that the standardization benchmark of the data to be predicted is consistent with that of the training dataset, thus avoiding prediction bias due to differences in the standardization benchmark. If a parameter of the site to be predicted has a missing value, it is supplemented using the K-nearest neighbor interpolation method in step S1. The K value used for interpolation is consistent with that used in the preprocessing of the training dataset.

[0106] The standardized site parameters to be predicted are input into the pre-trained pore water pressure ratio prediction model. The standardized value of the predicted pore water pressure ratio is calculated through forward propagation. Then, the actual predicted value is restored through the inverse standardization process. The inverse standardization formula is as follows:

[0107]

[0108] in, The standardized value representing the predicted pore water pressure ratio; This represents the standard deviation of the true pore water pressure ratio in the training dataset. , representing the mean of the true pore water pressure ratio in the training dataset, both are standardized parameters calculated in step S1; This represents the predicted pore water pressure after reduction compared to the actual value.

[0109] The liquefaction of sand was determined using the threshold method in the seismic design code for buildings, with the threshold determined based on the seismic fortification intensity of the site to be predicted. The predicted pore water pressure ratio was compared with the actual value to the threshold value corresponding to the fortification intensity: if the actual predicted value was greater than or equal to the threshold value, it was determined that sand liquefaction would occur at the site under seismic loading; if the actual predicted value was less than the threshold value, it was determined that sand liquefaction would not occur.

[0110] To improve the reliability of prediction results, an ensemble prediction strategy can be adopted: a pre-trained model is combined with multiple deep neural network models with different structures to form an ensemble model. Multiple predicted values ​​are obtained by inputting the site parameters to be predicted, and the average of these predicted values ​​is taken as the final prediction result, followed by liquefaction discrimination. The final output of the seismic sand liquefaction prediction result can include the predicted pore water pressure ratio to the actual value, the discrimination threshold, the liquefaction discrimination conclusion, and the prediction credibility. The credibility is calculated by the proportion of models with consistent discrimination conclusions in the ensemble model, providing a comprehensive and reliable technical basis for seismic design and site safety assessment.

[0111] The aforementioned deep learning-based method for predicting earthquake-induced sand liquefaction standardizes historical liquefaction site parameters and constructs a deep neural network model. Initial predicted pore pressure ratios are obtained through forward propagation. Based on this, the method sequentially calculates the physical constraint loss to ensure the prediction does not violate the non-negativity of effective stress and the upper limit of pore pressure ratio; the monotonicity constraint loss to force the model to correctly learn the influence trends of seismic intensity and anti-liquefaction strength parameters; and the data fitting loss to measure prediction accuracy. These three types of losses are then weighted and fused into a total loss. The model parameters are iteratively optimized through backpropagation, ultimately resulting in a prediction model that embeds fundamental principles of soil mechanics and engineering logic. This approach explicitly integrates physical and monotonic constraints into the model training objective, transforming the model from pure data fitting to learning guided by physical laws. This ensures prediction accuracy while fundamentally avoiding absurd outputs that violate soil mechanics axioms under extreme conditions, significantly improving the model's prediction reliability, generalization ability, and engineering decision-making credibility in complex scenarios such as sparse data or high-intensity seismic events.

[0112] In one optional embodiment, the physical constraint loss value is calculated based on the initial predicted pore water pressure ratio and the corresponding initial effective stress value in the training dataset, including the following steps:

[0113] S11. Based on the ratio of the initial effective stress value to the initial predicted pore water pressure of each sample in the training dataset, calculate the predicted effective stress value for each sample; the formula for calculating the predicted effective stress value is as follows:

[0114]

[0115] in, This represents the initial effective stress value of sample i. This represents the initial predicted pore water pressure ratio for sample i. This represents the predicted effective stress value for sample i.

[0116] Specifically, according to the core principles of soil mechanics, there is a clear quantitative correlation between the effective stress and pore water pressure ratio in sand under seismic loading; that is, the effective stress decreases as the pore water pressure increases. This step derives the predicted effective stress value by comparing the initial effective stress value with the initial predicted pore water pressure ratio, providing a direct basis for determining the non-negative constraint of the effective stress. The formula for calculating the predicted effective stress value is as follows: ,in The initial effective stress value of sample i in the training dataset is derived from the preprocessed standardized training dataset. If it is necessary to determine the physical meaning, the mean and standard deviation of the initial effective stress parameter in the preprocessing step can be used for inverse standardization to ensure the accuracy of the dimensions. The initial predicted pore water pressure ratio representing sample i, i.e. the initial prediction result output by the forward propagation of the deep neural network, can also be reduced to the actual physical value through inverse normalization. The predicted effective stress value represents sample i, and its physical meaning is the magnitude of the effective stress in the soil layer corresponding to that sample under earthquake action as predicted by the model.

[0117] The specific calculation process is as follows: First, extract the initial effective stress values ​​of all samples in the current training batch from the standardized training dataset. Simultaneously, the initial predicted pore water pressure ratio for the corresponding sample is extracted from the model output. First, strictly ensure that the sample numbers correspond one-to-one to avoid data misalignment; second, perform the operation sequentially for each sample, first calculating 1 and... The difference, then compare this difference with... Multiplying them together yields the predicted effective stress value for a single sample. Finally, all samples Organize the data into vector form for subsequent calculation of constraint penalty terms. Note that if standardized numerical calculations are used, it is necessary to ensure... and The standardization benchmarks must be consistent; if the judgment is based on physical meaning, inverse standardization must be completed simultaneously to ensure the physical rationality of the calculation results.

[0118] S12. Based on the predicted effective stress value, construct an effective stress non-negativity constraint penalty term; wherein, when the predicted effective stress value is less than 0, the effective stress non-negativity constraint penalty term incurs a penalty; the expression for the effective stress non-negativity constraint penalty term is:

[0119]

[0120] in, The effective stress non-negativity constraint penalty term represents the effective stress non-negativity constraint loss component; N represents the number of samples in the current training batch. This represents the squared penalty imposed on the negative effective stress prediction of sample i.

[0121] Specifically, according to the soil mechanics equilibrium condition, the effective stress of sand is the core mechanical index for maintaining soil stability, and its value must be greater than or equal to 0. If the effective stress is negative, it indicates that the pore water pressure has exceeded the initial effective stress, and the soil particles will lose effective support, which contradicts actual physical phenomena. Therefore, a non-negative constraint penalty term for effective stress is constructed to apply a targeted penalty to the negative effective stress prediction results, forcing the model to learn a mapping relationship that conforms to this physical law. The expression for the non-negative constraint penalty term for effective stress is: ,in The effective stress non-negative constraint penalty term (i.e., the effective stress non-negative constraint loss component) has a value range from 0 to positive infinity. The larger the value, the more unreasonable predictions of negative effective stress are in the current training batch, and the higher the penalty intensity. N is the number of samples in the current training batch. It is calculated by averaging the number of samples in the batch, which can eliminate the influence of the number of samples on the magnitude of the loss value and ensure the comparability of loss values ​​in different training batches. Let i be the predicted effective stress value for sample i; For the maximum value function, only when Time output (Absolute value of negative effective stress), when The output is 0, which enables accurate penalty for negative effective stress prediction; the squaring operation can enhance the penalty for larger negative effective stress predictions and guide the model to prioritize the output of non-negative effective stress values.

[0122] The specific construction and calculation steps are as follows: First, obtain the predicted effective stress values ​​of all samples in the current training batch obtained in step S11. The second step is to process the vector element by element, using a maximum value function to determine the optimal value. The first step is to determine the absolute value of the non-negative stress constraint penalty for each sample. The second step is to calculate the absolute value of the penalty for each sample, and set it to 0 if it is negative. The third step is to square each processed result to obtain the effective stress non-negative constraint penalty component for a single sample. The fourth step is to sum the penalty components of all samples to obtain the total effective stress non-negative constraint penalty value for the current training batch. The fifth step is to divide the total penalty value by the batch sample size N to obtain the average effective stress non-negative constraint penalty term. During the calculation process, it is necessary to ensure that the sample data within the batch is complete. If there is any missing data, it must be supplemented according to the missing value handling rules in the preprocessing steps before calculation to avoid the penalty term being biased due to missing data.

[0123] S13. Based on the initial predicted pore water pressure ratio, construct an upper limit constraint penalty term for the pore pressure ratio; wherein, when the initial predicted pore water pressure ratio is greater than 1, the upper limit constraint penalty term applies a penalty; the expression for the upper limit constraint penalty term for the pore pressure ratio is:

[0124]

[0125] in, This is the penalty term for the upper limit constraint of the porosity-pressure ratio, representing the loss component of the upper limit constraint of the porosity-pressure ratio. This represents the squared penalty imposed on sample i for exceeding the upper limit of pore water pressure compared to the prediction.

[0126] Specifically, the pore water pressure ratio is defined as the ratio of the maximum pore water pressure in sand during an earthquake to the initial effective stress. Physically, the maximum pore water pressure cannot exceed the initial effective stress; therefore, the upper limit of the pore water pressure ratio is 1. If the model predicts a value greater than 1, it violates the physical definition and real-world laws. Therefore, a penalty term for the upper limit constraint of the pore pressure ratio needs to be constructed to penalize predictions exceeding the upper limit, guiding the model to output a pore water pressure ratio that conforms to the physical definition. The expression for the upper limit constraint penalty term is as follows: ,in This is the penalty term for the upper limit constraint of pore pressure ratio (i.e., the loss component of the upper limit constraint of pore pressure ratio), with a value range from 0 to positive infinity. The larger the value, the more pore water pressure ratios exceeding the upper limit are predicted in the current training batch, and the higher the penalty intensity. N is the number of samples in the current training batch, which is consistent with N in step S12 to ensure that the calculation basis of the two constraint components is consistent. The initial predicted pore water pressure ratio for sample i can be either the standardized value or the actual value after inverse standardization, as long as it is consistent with the comparison benchmark of 1. For the maximum value function, only when Time output (Difference exceeding the upper limit), when The output is 0, which implements targeted penalty for predictions that exceed the upper limit; the squaring operation can enhance the penalty for predictions that exceed the upper limit by a large amount, prompting the model to prioritize outputting pore water pressure ratios ≤1.

[0127] The specific construction and calculation steps are as follows: First, extract the initial predicted pore water pressure ratio of all samples in the current training batch. The samples correspond one-to-one with those in step S12; the second step is to judge each sample individually. The first step is to check if the value exceeds 1. If it does, calculate the difference between the upper limit and the lower limit; otherwise, set it to 0. The second step is to square each processed result to obtain the penalty component of the upper limit constraint for the pore pressure ratio of a single sample. The third step is to sum the penalty components of all samples to obtain the total penalty value of the upper limit constraint for the pore pressure ratio of the current training batch. The fourth step is to divide the total penalty value by the number of samples N to obtain the average upper limit constraint penalty term for the pore pressure ratio. It should be noted that if When using standardized values, it is necessary to first confirm the original physical value corresponding to 1 after standardization to avoid deviation of the comparison benchmark due to standardization. It is recommended to use the actual pore water pressure ratio after inverse standardization for calculation to ensure that it meets the upper limit requirements of the physical definition.

[0128] S14. Weighted summation of the effective stress non-negative constraint loss component and the pore pressure ratio upper limit constraint loss component is performed to generate the physical constraint loss value; the formula for calculating the physical constraint loss value is:

[0129]

[0130] in, This represents the physical constraint loss value. The first hyperparameter for controlling the penalty strength of the effective stress non-negative constraint loss component is... The second hyperparameter is used to control the penalty strength of the loss component of the upper limit constraint of the pore pressure ratio.

[0131] Specifically, the effective stress non-negativity constraint and the pore pressure ratio upper limit constraint are two core dimensions ensuring the physical rationality of the model's predictions. They constrain the model output from the perspectives of mechanical equilibrium and index definition, respectively. Since the importance of these two constraints may vary depending on the engineering scenario and dataset characteristics, they need to be weighted and summed to form the total physical constraint loss value. The penalty strength of the two constraint components is then adjusted using hyperparameters to achieve an optimal balance of constraint effects, ensuring that the model avoids unreasonable predictions without affecting its learning from normal data. The formula for calculating the physical constraint loss value is as follows: ,in The physical constraint loss value is the weighted sum of the effective stress non-negative constraint loss component and the pore pressure ratio upper limit constraint loss component, providing an important basis for subsequent model parameter updates; The first hyperparameter controls the penalty strength for the non-negative constraint loss component of effective stress. It is a constant with a value greater than 0. The larger the value, the more severe the penalty for negative effective stress prediction. The second hyperparameter controls the penalty strength of the loss component of the upper limit constraint on the pore pressure ratio. It is also a constant greater than 0. The larger the value, the more severe the penalty for the prediction of the pore water pressure ratio exceeding the upper limit. The effective stress non-negative constraint loss component obtained in step S12, This is the upper limit constraint loss component of the pore pressure ratio obtained in step S13.

[0132] The specific calculation is divided into two stages: hyperparameter determination and weighted summation. The first stage is hyperparameter determination. and The determination of the effective stress is based on a combination of engineering experience and hyperparameter optimization methods. According to engineering experience, the non-negativity of the effective stress is a core prerequisite for soil stability, and its importance is usually higher than the upper limit constraint of the pore pressure ratio. Therefore, it can be initially set as [value missing]. The value range is [0.5, 0.8]. The value range is [0.2, 0.5], and satisfies... To ensure the normalization of penalty intensity, a grid search method was then used to uniformly select multiple hyperparameter combinations within a set range. These combinations were then substituted into the model for training. The constraint effect was evaluated by the physical compliance rate of the validation set (the proportion of samples where the predicted effective stress is non-negative and the pore water pressure ratio is ≤1). The combination with the highest physical compliance rate was selected as the final hyperparameter. The second stage involved a weighted summation calculation, which determined the... and Multiplying them yields the effective stress non-negative constraint weighted penalty value. and Multiplying the two values ​​yields the weighted penalty value for the upper limit constraint of the pore pressure ratio. Adding the two values ​​together gives the physical constraint loss value for the current training batch. .

[0133] The physical constraint loss value This value directly reflects the degree to which the model's predictions match the physical laws of soil mechanics. A smaller value indicates that the predictions are more consistent with physical reality, while a larger value suggests that the predictions violate physical laws. During model training... Together with the data fitting loss value and the monotonicity constraint loss value, they participate in the construction of the total loss function, guiding the model to strictly abide by physical laws while learning the correlation of historical data, significantly improving the reliability and engineering applicability of the model.

[0134] refer to Figure 2 In one optional embodiment, the monotonicity constraint loss value is calculated based on the changing trends of key sample features in the training dataset and the corresponding changing trends of the initial predicted pore water pressure ratio, including the following steps:

[0135] S21. Construct a first sample pair set within the current training batch. Each sample pair in the first sample pair set contains the first sample... Second Sample The first sample Compared with the second sample The peak ground acceleration characteristic values ​​are different for the second sample, while all other characteristic values ​​are the same. The peak ground acceleration characteristic value is greater than that of the first sample. The peak ground acceleration characteristic value.

[0136] Specifically, peak ground acceleration (PGA) is a core seismic parameter affecting sand liquefaction. It exhibits a clear positive monotonic correlation with the pore water pressure ratio (PPR), meaning that the greater the PPA, the stronger the earthquake's disturbance effect on the sand, the more significant the increase in pore water pressure, and the higher the PPR ratio. This step constructs a set of sample pairs that differ only in PPA and have identical other characteristics. This isolates the influence of a single feature, ensuring that subsequent constraint penalties only regulate the monotonic relationship between PPA and the PPR, avoiding interference from other features.

[0137] The specific construction process is as follows: First, extract all samples in the current training batch, clarify the feature dimensions of the samples, and filter out complete samples containing peak ground acceleration (excluding samples missing peak ground acceleration); second, based on the feature vector of the sample, traverse all samples and group samples with identical feature values ​​(excluding peak ground acceleration) into several feature matching groups; then, within each feature matching group, sort the peak ground acceleration feature values ​​from smallest to largest, and sequentially select two adjacent samples to form a sample pair, where the first sample is designated as the first sample a, and the second sample as the second sample b (ensuring that the peak ground acceleration feature value of the second sample b is greater than that of the first sample a); finally, integrate all qualified sample pairs to form the first sample pair set. If a feature matching group contains only one sample and cannot form a sample pair, then the samples in that group will not participate in the construction of the first sample pair set; if the number of samples in a group is greater than two, multiple adjacent sample pairs can be formed to ensure that the sample pairs cover the complete range of feature value variation.

[0138] S22, Based on the first sample The initial predicted pore water pressure ratio and the second sample The initial predicted pore water pressure ratio is used to construct a monotonically undiminished constraint penalty term for peak ground acceleration; where, when the first sample The initial predicted pore water pressure ratio is greater than that of the second sample. When calculating the initial predicted pore water pressure ratio, a penalty term for the monotonically undecreasing peak ground acceleration constraint is applied; the expression for the monotonically undecreasing peak ground acceleration constraint penalty term is:

[0139]

[0140] in, The peak ground acceleration monotonicity constraint penalty term represents the loss component of the peak ground acceleration monotonicity constraint. Denotes the first set of sample pairs. This indicates the number of sample pairs in the first sample pair set. and They represent the first sample respectively. Second Sample The initial predicted pore water pressure ratio, This represents the squared penalty imposed on a prediction that violates the monotonically non-decreasing relation.

[0141] Specifically, based on the positive correlation between peak ground acceleration and pore water pressure ratio, a monotonically non-decreasing constraint penalty term needs to be constructed to penalize prediction results that violate this relationship, thus forcing the model to output prediction values ​​that conform to engineering logic.

[0142] In the expression for the peak ground acceleration monotonically non-decreasing constraint penalty term, This is the penalty term for the peak ground acceleration monotonically nondecreasing constraint, which is the loss component of the peak ground acceleration monotony constraint. Its value ranges from 0 to positive infinity. The larger the value, the more predictions in the current training batch violate the peak ground acceleration monotonically nondecreasing relationship, and the stronger the penalty. This represents the first set of sample pairs, which contains all sample pairs that differ only in peak ground acceleration; This represents the number of sample pairs in the first sample pair set. The average number of sample pairs is used to calculate the loss value, which can eliminate the influence of the number of sample pairs on the magnitude of the loss value and ensure the comparability of loss values ​​between different training batches. and These represent the initial predicted pore water pressure ratios of the first sample a and the second sample b, respectively, which are the prediction results output by the model forward propagation. For the maximum value function, only when When (violating the monotonically non-decreasing relation), output the difference between the two. When the condition is monotonically non-decreasing, the output is 0, which implements a targeted penalty for the prediction of violation of the relationship; the squaring operation can enhance the penalty for predictions of greater violation, guiding the model to prioritize learning the mapping rules that conform to the monotonically constant relationship.

[0143] The specific construction and calculation steps are as follows: First, obtain the first set of sample pairs. and the corresponding number of sample pairs Simultaneously, the initial predicted pore water pressure ratio of the first sample a and the second sample b in each sample pair within the set is extracted. and The second step is to iterate through each sample pair and calculate... and The first step is to calculate the difference; the second step is to process the difference using a maximum value function to filter out the differences that violate the monotonic relationship (i.e., the positive differences); the third step is to square the processed differences to obtain the peak ground acceleration monotonicity constraint penalty component for each sample pair; the fifth step is to sum the penalty components of all sample pairs to obtain the total peak ground acceleration constraint penalty value for the current training batch; the sixth step is to divide the total penalty value by the number of sample pairs. The monotonically non-decreasing constraint term for the mean peak ground acceleration is obtained. .

[0144] S23. Construct a second set of sample pairs within the current training batch. Each sample pair in the second set contains a third sample pair. and the fourth sample The third sample Compared with the fourth sample The standard penetration test (SPT) hit count eigenvalues ​​are different for the fourth sample, while all other eigenvalues ​​are the same. The standard penetration hit count eigenvalue is greater than that of the third sample. The standard penetration number characteristic value.

[0145] Specifically, the Standard Penetration Test (SPT) blow count is a core soil layer parameter reflecting the compaction and liquefaction resistance of sand. It exhibits a clear negative monotonic correlation with the pore water pressure ratio; that is, the higher the SPT blow count, the denser the sand particles, the stronger the liquefaction resistance, the slower the pore water pressure rises, and the lower the pore water pressure ratio. This step employs a sample pair construction logic similar to S21. By constructing a second set of sample pairs that differ only in SPT blow count while maintaining identical characteristics in all other aspects, the single influence of the SPT blow count is isolated, laying the foundation for subsequently constructing targeted constraint penalty terms.

[0146] The specific construction process is as follows: First, extract complete samples containing the standard penetration count (SPC) from the current training batch, and remove samples with missing SPC. Second, based on all feature values ​​except for the SPC, group samples with identical feature values ​​together to form several SPC matching groups. Then, within each matching group, sort the SPC feature values ​​from smallest to largest, and sequentially select two adjacent samples to form a sample pair, where the first sample is the third sample c, and the second sample is the fourth sample d (ensuring that the SPC feature value of the fourth sample d is greater than that of the third sample c). Finally, integrate all qualified sample pairs to form a second sample pair set. If a matching group contains only one sample, it will not participate in the set construction; if the number of samples in a group is greater than two, multiple adjacent sample pairs can be formed to ensure coverage of the complete variation range of the SPC and improve the comprehensiveness of the constraints.

[0147] S24, Based on third samples The initial predicted pore water pressure ratio and the fourth sample The initial predicted pore water pressure ratio is used to construct a standard penetration test (SPT) blow count monotonically non-increasing constraint penalty term; where, when the fourth sample The initial predicted pore water pressure ratio is greater than that of the third sample. When calculating the initial predicted pore water pressure ratio, a penalty term for the standard penetration test (SPT) blow count monotonically increasing constraint is applied; the expression for the standard penetration test (SPT) blow count monotonically increasing constraint penalty term is:

[0148]

[0149] in, The standard penetration test (SPT) hit count monotonically non-increasing constraint penalty term represents the loss component of the standard penetration test (SPT) hit count monotony constraint. For the second set of sample pairs, This indicates the number of sample pairs in the second sample pair set. and Representing the third sample and the fourth sample The initial predicted pore water pressure ratio, This represents the squared penalty imposed on a prediction that violates the monotonically non-increasing relation.

[0150] Specifically, based on the negative correlation between standard penetration test blows and pore water pressure ratio, a monotonically non-increasing constraint penalty term needs to be constructed to penalize prediction results that violate this relationship, thereby guiding the model to learn a mapping relationship that conforms to the anti-liquefaction mechanism.

[0151] In the expression for the standard penetration test (SPT) blow count monotonically non-increasing constraint penalty term, This is the penalty term for the standard pass hit count (SPT) monotonically non-increasing constraint, which is the loss component of the standard pass hit count monotony constraint. Its value ranges from 0 to positive infinity. The larger the value, the more predictions in the current training batch violate the standard pass hit count monotonically non-increasing relationship, and the stronger the penalty. This represents the second set of sample pairs, which contains all sample pairs that differ only in the number of standard penetration shots. This represents the number of sample pairs in the second sample pair set, and... They serve the same purpose: to normalize penalty values ​​and ensure comparability between different batches. and These represent the initial predicted pore water pressure ratios for the third sample c and the fourth sample d, respectively. For the maximum value function, only when When (violating the monotonically non-increasing relation), output the difference between the two. When the condition is monotonically non-increasing, output 0 to implement targeted punishment; the squaring operation can enhance the punishment for predictions of greater violations and improve the constraint effect.

[0152] The specific construction and calculation steps are as follows: First, obtain the second sample pair set. and the number of sample pairs Extract the initial predicted pore water pressure ratio of the third sample c and the fourth sample d in each sample pair. and The second step is to iterate through each sample pair and calculate... and The first step is to find the difference; the second step is to filter out the differences that violate the monotonic relationship (i.e., the positive differences) using the maximum value function; the third step is to square the filtered differences to obtain the standard penetration hit count monotonicity constraint penalty component for each sample pair; the fifth step is to sum the penalty components of all sample pairs to obtain the total standard penetration hit count constraint penalty value for the current training batch; the sixth step is to divide the total penalty value by the number of sample pairs. The average standard penetration number is obtained as a monotonically non-increasing constraint penalty term. .

[0153] S25. The monotonic constraint loss components of peak ground acceleration and standard penetration test (SPT) blow count are weighted and summed to generate the monotonic constraint loss value. The formula for calculating the monotonic constraint loss value is as follows:

[0154]

[0155] in, This represents the loss value due to the monotonicity constraint. The third hyperparameter is used to control the penalty intensity of the peak ground acceleration monotonicity constraint loss component. The fourth hyperparameter is used to control the penalty strength of the loss component under the standard penetration test (SPT) blow count monotonicity constraint.

[0156] Specifically, the peak ground acceleration monotonicity constraint and the standard penetration test (SPT) blow count monotonicity constraint ensure the engineering logic of the model's predictions from two core dimensions: ground motion and soil characteristics. The importance of these constraints to the model may vary depending on the characteristics of the training dataset and the engineering application scenario. The two constraint loss components are merged into a total monotonicity constraint loss value through weighted summation. The penalty intensity of the two components can be flexibly adjusted through hyperparameters to achieve an optimal balance of constraint effects, ensuring that the model follows the two types of monotonic relationships without affecting the learning of the core correlation patterns in the data.

[0157] In the formula for calculating the monotonicity constraint loss value, The monotonicity constraint loss value represents the weighted sum of the two feature constraint loss components, providing an important basis for updating model parameters. The third hyperparameter controls the penalty strength for the peak ground acceleration monotonicity constraint loss component. It is a constant with a value greater than 0. The larger the value, the more severe the penalty for the model to violate the peak ground acceleration monotonicity prediction. The fourth hyperparameter controls the penalty strength of the loss component for the standard penetration hit count monotonicity constraint. It is also a constant greater than 0. The larger the value, the more severe the penalty for the model to violate the standard penetration hit count monotonicity prediction. The peak ground acceleration monotonicity constraint loss component obtained in step S22. The loss component is the standard penetration blow count monotonicity constraint obtained in step S24.

[0158] The specific calculation process is divided into two stages: hyperparameter determination and weighted summation. The first stage is hyperparameter determination. and The determination of the parameters is based on a combination of engineering experience and hyperparameter optimization methods. Based on engineering experience, peak ground acceleration and standard penetration test (SPT) blow count are both key factors affecting sand liquefaction. Initially, the weights of both can be set to a range of [0.4, 0.6], and satisfy the following conditions: To ensure the normalization of penalty intensity, a grid search method was then used to uniformly select multiple hyperparameter combinations within a set range. These combinations were then substituted into the model for training. The constraint effect of each combination was evaluated by the monotonicity compliance rate of the validation set (i.e., the proportion of sample pairs that conform to the two monotonic relationships). The combination with the highest monotonicity compliance rate was selected as the final constraint. and The second stage is a weighted summation calculation, which will determine the... and Multiplying yields the weighted penalty value for the peak ground acceleration constraint. and Multiplying the two values ​​yields the weighted penalty for the standard penetration hit count constraint. Adding the two weighted penalty values ​​together gives the monotonicity constraint loss value for the current training batch. .

[0159] The monotonic constraint loss value This value directly reflects the degree of fit between the model's prediction results and the monotonic relationship of the core features; the smaller the value, the more the prediction results conform to engineering logic and the anti-liquefaction mechanism. During model training... Together with the data fitting loss value and the physical constraint loss value, they participate in the construction of the total loss function, guiding the model to accurately fit historical data while strictly following inherent engineering rules, significantly improving the model's interpretability, reliability, and engineering applicability.

[0160] In one alternative embodiment, constructing a first set of sample pairs within the current training batch includes the following steps:

[0161] S31. Randomly select a sample from the current training batch as the first basic sample, copy all the features of the first basic sample, and generate the first virtual copy sample.

[0162] Specifically, the core objective of this step is to construct a consistent basic framework through sample replication, laying the foundation for subsequent perturbation processing targeting only the peak ground acceleration feature. Randomly selecting the first basic sample ensures the diversity of sample pairs and avoids constraint bias caused by selecting specific samples in a concentrated manner; replicating all features ensures that the first virtual copy sample is completely consistent with the first basic sample in all features except the target feature (peak ground acceleration), thereby achieving isolated control over the influence of the single feature of peak ground acceleration.

[0163] The specific operation process is as follows: First, determine the sample range of the current training batch and clarify the feature dimensions of the samples (including peak ground acceleration, standard penetration hit count, and all other core features); then, use uniform random sampling to select one sample from the training batch as the first basic sample, ensuring that each sample has an equal probability of being selected; finally, call the sample copying interface to completely copy all feature values ​​of the first basic sample (including numerical features, classification features, etc.), generate the first virtual copy sample that is completely consistent with the features of the first basic sample, and establish the basic framework of the sample pair.

[0164] S32. Apply a first positive random perturbation increment to the peak ground acceleration feature value of the first virtual copy sample to generate a first perturbation copy sample; wherein, the peak ground acceleration feature value of the first perturbation copy sample is equal to the peak ground acceleration feature value of the first base sample plus the first positive random perturbation increment.

[0165] Specifically, based on the positively correlated monotonic relationship between peak ground acceleration and pore water pressure ratio, it is necessary to ensure that there is a difference in peak ground acceleration between the two samples in a sample pair, where "the base sample < the perturbed sample". Therefore, this difference is constructed by applying a positive random perturbation increment. The setting of the positive random perturbation increment must take into account both physical rationality and constraint effectiveness. It must ensure that the perturbed eigenvalues ​​conform to the actual engineering range, while also ensuring that the difference is significant enough to trigger effective monotonicity constraint learning.

[0166] The specific operation process is as follows: First, determine the range of the first positive random perturbation increment. This range needs to be determined based on the actual engineering distribution of peak ground acceleration (for example, if the range of peak ground acceleration in the training data is 0.1g-0.8g, the range of the first positive random perturbation increment can be set to 0.05g-0.2g) to avoid the perturbation value exceeding the reasonable physical range. Second, select one specific increment value from the set range as the first positive random perturbation increment using a random sampling method (such as uniform distribution sampling or normal distribution sampling). Third, calculate the peak ground acceleration feature value of the replica sample after the first perturbation, which is the sum of the peak ground acceleration feature value of the first base sample and the first positive random perturbation increment. Fourth, update the peak ground acceleration feature value of the first virtual replica sample to the calculated perturbation value, while keeping all other feature values ​​unchanged, and generate the first perturbation replica sample.

[0167] S33. Combine the first basic sample and the first perturbated copy sample into a sample pair and add it to the new set.

[0168] Specifically, this step completes the construction and collection of single sample pairs. The composition of the sample pairs must strictly follow the rule of "first basic sample (smaller peak ground acceleration) + first perturbation-triggered copy sample (larger peak ground acceleration)" to ensure that the calculation logic of the subsequent monotonically non-decreasing constraint penalty term holds true. The new set serves as a temporary storage container for the first sample pair set, used to gradually accumulate batch-generated sample pairs.

[0169] The specific operation process is as follows: First, define an empty new set (the initial number of sample pairs is 0); then, take the first basic sample selected in S31 as the first element of the sample pair, and take the first perturbed copy sample generated in S32 as the second element of the sample pair to form an ordered sample pair (ensure that the order of elements cannot be reversed to avoid affecting the subsequent monotonicity judgment); finally, add the ordered sample pair to the new set to complete the storage of a single sample pair.

[0170] S34. Repeat steps S31 to S33 until the number of generated sample pairs reaches the preset first quantity threshold, and obtain the constructed first sample pair set.

[0171] Specifically, by generating sample pairs in batches, the size of the first sample pair set can be ensured to meet the requirements of monotonicity constraint training, avoiding insufficient constraint strength due to an insufficient number of sample pairs. The setting of the preset first quantity threshold needs to be determined in combination with factors such as training batch size and model training requirements to balance training efficiency and constraint effect.

[0172] Specific operation and threshold setting instructions: Step 1: Preset a first quantity threshold. This threshold can be determined based on experience or cross-validation results (for example, if the current training batch has 100 samples, the first quantity threshold can be set to 200 to ensure sufficient sample pairs to cover the feature distribution of different base samples). Step 2: Execute steps S31-S33 repeatedly, generating one new sample pair and adding it to the new set each time, while simultaneously counting the number of sample pairs in the new set in real time. Step 3: Stop the loop when the number of sample pairs in the new set reaches the preset first quantity threshold. At this point, the new set is the completed first sample pair set, which can be directly used for calculating the peak ground acceleration monotonically non-decreasing constraint penalty term. If samples are selected repeatedly during the loop, no special handling is required; repeated selection can further strengthen the constraint learning of the corresponding feature interval and improve the model's generalization ability.

[0173] Similarly, constructing a second set of sample pairs within the current training batch includes the following steps:

[0174] S41. Randomly select a sample from the current training batch as the second basic sample, copy all the features of the second basic sample, and generate the second virtual copy sample.

[0175] Specifically, the logic of this step is consistent with S31. The core objective is to construct the basic framework for perturbing the standard penetration test (SPT) feature by randomly selecting a base sample and replicating its features. Randomly selecting a second base sample ensures the diversity of sample pairs, and replicating all features ensures that the second virtual copy sample is completely consistent with the second base sample in all features except for the SPT, thus achieving isolated control over the influence of the single feature of the SPT.

[0176] The specific operation process is as follows: within the sample range of the current training batch, select one sample as the second basic sample using uniform random sampling; completely copy all feature values ​​of the second basic sample to generate a second virtual copy sample that is completely consistent with the features of the second basic sample, providing a basic template for subsequent feature perturbation.

[0177] S42. Apply a second positive random perturbation increment to the standard penetration number (SPT) feature value of the second virtual copy sample to generate a second perturbation copy sample; wherein, the SPT feature value of the second perturbation copy sample is equal to the SPT feature value of the second base sample plus the second positive random perturbation increment.

[0178] Specifically, based on the negatively correlated monotonic relationship between standard penetration test (SPT) blows and pore water pressure ratio, it is necessary to ensure that there is a difference in SPT blows between the two samples in a sample pair, where "the base sample < the perturbed sample". Therefore, this difference is constructed by applying a positive random perturbation increment. The setting of the second positive random perturbation increment needs to be combined with the actual engineering distribution of SPT blows to ensure that the perturbed eigenvalues ​​conform to physical meaning, while ensuring that the difference is significant enough to achieve effective monotonicity constraints.

[0179] The specific operation process is as follows: First, determine the range of the second positive random perturbation increment, based on the actual distribution of standard penetration hits in the training data (for example, if the range of standard penetration hits in the training data is 5-30 hits, the range of the second positive random perturbation increment can be set to 2-8 hits); Second, randomly select one increment value from the set range as the second positive random perturbation increment; Third, calculate the standard penetration hits feature value of the second perturbation copy sample, which is the sum of the standard penetration hits feature value of the second base sample and the second positive random perturbation increment; Fourth, update the standard penetration hits feature value of the second virtual copy sample to the perturbation value, while keeping other feature values ​​unchanged, and generate the second perturbation copy sample.

[0180] S43. Combine the second basic sample with the second perturbated copy sample to form a sample pair and add it to the new set.

[0181] Specifically, this step completes the construction and collection of standard penetration test (SPT) hit count feature sample pairs. The sample pairs must follow the rule of "second basic sample (smaller SPT hit count) + second perturbated copy sample (larger SPT hit count)" to ensure that the calculation logic of the subsequent monotonically non-increasing constraint penalty term holds true. The new set here is a temporary storage container for the second sample pair set and is independent of the new set in S33.

[0182] The specific operation process is as follows: Define an empty new set; take the second basic sample selected in S41 as the first element of the sample pair, and the second perturbed copy sample generated in S42 as the second element to form an ordered sample pair; add the sample pair to the new set to complete the storage of a single standard penetration hit count feature sample pair.

[0183] S44. Repeat steps S41 to S43 until the number of generated sample pairs reaches the preset second quantity threshold, and obtain the constructed second sample pair set.

[0184] Specifically, by generating sample pairs in batches, the size of the second sample pair set is ensured to meet the constraints of the training. The preset second quantity threshold can be set with reference to the logic of the first quantity threshold, and adjusted in conjunction with the distribution characteristics of the standard penetration hit count feature to ensure that it matches the size of the first sample pair set and balances the constraint weights of the two features.

[0185] The specific operation process is as follows: First, preset a second quantity threshold (for example, if the first quantity threshold is 200, the second quantity threshold can also be set to 200 to ensure that the number of constraint sample pairs for the two features is balanced); Second, execute steps S41-S43 in a loop, generating one sample pair and adding it to the new set each time, and counting the number of sample pairs in real time; Third, when the number of sample pairs reaches the second quantity threshold, stop the loop. The new set at this time is the completed second sample pair set, which can be used for the calculation of the standard penetration test (SPT) click count monotonically non-increasing constraint penalty term.

[0186] The core advantages of this implementation method are: by generating virtual samples and random perturbation, it overcomes the limitation of insufficient feature matching samples in the original training data, and can flexibly construct a sufficient number of effective sample pairs; the setting of positive random perturbation increment ensures that the difference between sample pairs meets the requirement of monotonic relationship, without relying on the feature distribution of the original data; the batch generation logic improves the efficiency of sample pair construction, and the random selection of basic samples can enhance the diversity of sample pairs, making the monotonicity constraint more generalizable, and ultimately improving the engineering logic and reliability of model prediction.

[0187] In one optional embodiment, sand liquefaction is determined based on the predicted pore water pressure ratio to obtain the earthquake sand liquefaction prediction result, including the following steps:

[0188] S51. Compare the predicted pore water pressure ratio with the preset critical pore water pressure ratio threshold for liquefaction to obtain the comparison result.

[0189] Specifically, the predicted pore water pressure ratio reflects the relative magnitude of pore water pressure at the site under seismic action, while the critical pore water pressure ratio threshold for liquefaction is the key dividing point for distinguishing whether sandy soil has liquefied. Its value directly determines the accuracy of the judgment result and needs to be determined based on soil mechanics theory, engineering specifications, and a large amount of measured data.

[0190] The specific operation process is as follows: First, obtain the predicted pore water pressure ratio of the site to be predicted from the model output. This predicted value needs to be inversely standardized (if the pore water pressure ratio was standardized during model training) to restore it to a value with actual physical meaning, ensuring that it is consistent with the dimensions of the critical threshold. Second, determine the preset critical liquefaction pore water pressure ratio threshold. This threshold can be adjusted by referring to relevant engineering standards and combining the specific geological conditions of the site to be predicted, such as soil layer type, density, and groundwater depth. Third, use a numerical comparison algorithm to compare the restored predicted pore water pressure ratio with the preset critical threshold and record the comparison result (i.e., predicted value ≥ threshold or predicted value < threshold).

[0191] S52. Based on the comparison results, if the predicted pore water pressure ratio is greater than or equal to the critical pore water pressure ratio threshold for liquefaction, then it is determined that liquefaction has occurred at the site to be predicted.

[0192] Specifically, according to the soil liquefaction mechanism, when the pore water pressure ratio reaches or exceeds the critical threshold, the effective stress between sand particles approaches zero, the soil loses its shear strength, and liquefaction failure occurs. This step, based on this core mechanism, clarifies the liquefaction judgment rules when the predicted value reaches the critical state, ensuring that the judgment results conform to engineering reality. When the comparison result is "predicted pore water pressure ratio ≥ liquefaction critical pore water pressure ratio threshold," it indicates that under the target earthquake, the increase in pore water pressure at the site to be predicted is sufficient to cause the loss of effective stress in the sand, and the soil cannot maintain its own stability; therefore, liquefaction is directly determined to have occurred at the site. Key data must be recorded simultaneously during the judgment process, including the specific value of the predicted pore water pressure ratio, the preset critical threshold, and the core geological parameters of the site to be predicted (such as soil layer name, standard penetration test blow count, etc.), providing complete data support for subsequent result verification.

[0193] S53. Based on the comparison results, if the predicted pore water pressure ratio is less than the critical pore water pressure ratio threshold for liquefaction, then it is determined that liquefaction will not occur at the site to be predicted.

[0194] Specifically, when the predicted pore water pressure ratio does not reach the critical threshold, there is still sufficient effective stress between sand particles to maintain the shear strength and stability of the soil, preventing liquefaction failure. This step clarifies the non-liquefaction judgment rule when the critical state is not reached, complementing S52 and covering all possible comparison results. When the comparison result is "predicted pore water pressure ratio < liquefaction critical pore water pressure ratio threshold," it indicates that under the target earthquake, the increase in pore water pressure at the site to be predicted is limited and insufficient to cause loss of effective stress; the soil still possesses stable bearing capacity, therefore, the site is determined not to liquefy. The judgment basis must also be recorded, including the predicted value, critical threshold, and site geological parameters, to ensure the traceability of the judgment process.

[0195] The core advantages of this implementation method are: the judgment logic is simple and intuitive, achieving accurate discrimination based on clear quantitative comparisons and reducing errors from subjective human judgment; the critical threshold can be flexibly adjusted in combination with engineering specifications and actual site conditions to adapt to the discrimination needs of different geological scenarios; key data are recorded simultaneously during the judgment process to ensure the verifiability and reliability of the results. The final output of the earthquake sand liquefaction prediction result should include a clear conclusion of "liquefaction occurred" or "liquefaction did not occur," as well as corresponding core data such as the predicted pore water pressure ratio and critical threshold, providing direct and effective technical support for seismic design and site risk assessment.

[0196] The aforementioned deep learning-based method for predicting earthquake-induced sand liquefaction standardizes historical liquefaction site parameters and constructs a deep neural network model. Initial predicted pore pressure ratios are obtained through forward propagation. Based on this, the method sequentially calculates the physical constraint loss to ensure the prediction does not violate the non-negativity of effective stress and the upper limit of pore pressure ratio; the monotonicity constraint loss to force the model to correctly learn the influence trends of seismic intensity and anti-liquefaction strength parameters; and the data fitting loss to measure prediction accuracy. These three types of losses are then weighted and fused into a total loss. The model parameters are iteratively optimized through backpropagation, ultimately resulting in a prediction model that embeds fundamental principles of soil mechanics and engineering logic. This approach explicitly integrates physical and monotonic constraints into the model training objective, transforming the model from pure data fitting to learning guided by physical laws. This ensures prediction accuracy while fundamentally avoiding absurd outputs that violate soil mechanics axioms under extreme conditions, significantly improving the model's prediction reliability, generalization ability, and engineering decision-making credibility in complex scenarios such as sparse data or high-intensity seismic events.

[0197] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0198] Based on the same inventive concept, this application also provides a system for implementing the deep learning-based earthquake sand liquefaction prediction method described above. The solution provided by this system is similar to the implementation scheme described in the above method. Therefore, the specific limitations of one or more deep learning-based earthquake sand liquefaction prediction system embodiments provided below can be found in the limitations of the deep learning-based earthquake sand liquefaction prediction method described above, and will not be repeated here.

[0199] In one exemplary embodiment, such as Figure 3 As shown, a deep learning-based earthquake sand liquefaction prediction system 30 is provided to implement the methods in the above embodiments. The system includes:

[0200] The site data standardization module 31 is used to standardize the site parameters of historical earthquake sand liquefaction cases and generate a standardized training dataset; the site parameters include soil layer parameters and ground motion parameters.

[0201] The deep model initialization module 32 is used to construct a deep neural network prediction model based on the feature dimensions in the training dataset, with the samples in the training dataset as input and the predicted pore water pressure ratio as output; the samples in the training dataset are input into the deep neural network prediction model for forward propagation to generate the initial predicted pore water pressure ratio.

[0202] The physical constraint loss calculation module 33 is used to calculate the physical constraint loss value based on the initial predicted pore water pressure ratio and the corresponding initial effective stress value in the training dataset.

[0203] The monotonicity constraint loss calculation module 34 is used to calculate the monotonicity constraint loss value based on the changing trends of key sample features in the training dataset and the corresponding changing trends of the initial predicted pore water pressure ratio.

[0204] The data fitting loss calculation module 35 is used to calculate the data fitting loss value based on the initial predicted pore water pressure ratio and the actual pore water pressure ratio in the training dataset.

[0205] The loss function aggregation module 36 is used to perform a weighted summation of the data fitting loss value, the physical constraint loss value, and the monotonic constraint loss value to generate the total loss function value.

[0206] The model training iteration module 37 is used to update the parameters of the deep neural network prediction model based on the total loss function value through the backpropagation algorithm, and to iteratively train the deep neural network prediction model to obtain a pre-trained pore water pressure ratio prediction model.

[0207] The liquefaction prediction output module 38 is used to input the standardized site parameters of the site to be predicted into the pore water pressure ratio prediction model and output the predicted pore water pressure ratio; based on the predicted pore water pressure ratio, the sand liquefaction is judged, and the earthquake sand liquefaction prediction result is obtained.

[0208] Embodiments of this application also provide a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the aforementioned method embodiments.

[0209] Embodiments of this application also provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the above-described method embodiments.

[0210] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The components described as separate parts may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this disclosure according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0211] The above-described embodiments are merely illustrative of several implementation methods of the embodiments of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the embodiments of this application, and these modifications and improvements all fall within the protection scope of the embodiments of this application.

Claims

1. A deep learning-based method for predicting seismic sand liquefaction, characterized in that, The method includes: S1. Standardize the site parameters of historical earthquake sand liquefaction cases to generate a standardized training dataset; wherein, the site parameters include soil layer parameters and seismic motion parameters. S2. Based on the feature dimensions in the training dataset, a deep neural network prediction model is constructed using the samples in the training dataset as input and the predicted pore water pressure ratio as output; the samples in the training dataset are input into the deep neural network prediction model for forward propagation to generate an initial predicted pore water pressure ratio value. S3. Calculate the physical constraint loss value based on the initial predicted pore water pressure ratio and the corresponding initial effective stress value in the training dataset; S4. Calculate the monotonicity constraint loss value based on the changing trends of key sample features in the training dataset and the corresponding changing trends of the initial predicted pore water pressure ratio. S5. Calculate the data fitting loss value based on the initial predicted pore water pressure ratio and the actual pore water pressure ratio in the training dataset. S6. The data fitting loss value, the physical constraint loss value, and the monotonic constraint loss value are weighted and summed to generate the total loss function value; S7. Based on the total loss function value, update the parameters of the deep neural network prediction model through the backpropagation algorithm, and iteratively train the deep neural network prediction model to obtain a pre-trained pore water pressure ratio prediction model. S8. Input the standardized site parameters of the site to be predicted into the pore water pressure ratio prediction model and output the predicted pore water pressure ratio; perform sand liquefaction discrimination based on the predicted pore water pressure ratio to obtain the earthquake sand liquefaction prediction result.

2. The method according to claim 1, characterized in that, The step of calculating the physical constraint loss value based on the initial predicted pore water pressure ratio and the corresponding initial effective stress value in the training dataset includes: S11. Based on the ratio of the initial effective stress value to the initial predicted pore water pressure of each sample in the training dataset, calculate the predicted effective stress value for each sample; the formula for calculating the predicted effective stress value is as follows: in, This represents the initial effective stress value of sample i. This represents the initial predicted pore water pressure ratio for sample i. The predicted effective stress value represents sample i; S12. Based on the predicted effective stress value, construct an effective stress non-negative constraint penalty term; wherein, when the predicted effective stress value is less than 0, the effective stress non-negative constraint penalty term incurs a penalty; the expression of the effective stress non-negative constraint penalty term is: in, Let be the effective stress non-negativity constraint penalty term, representing the effective stress non-negativity constraint loss component; N represents the number of samples in the current training batch. This represents the squared penalty imposed on the negative effective stress prediction of sample i; S13. Based on the initial predicted pore water pressure ratio, construct a pore pressure ratio upper limit constraint penalty term; wherein, when the initial predicted pore water pressure ratio is greater than 1, the pore pressure ratio upper limit constraint penalty term incurs a penalty; the expression for the pore pressure ratio upper limit constraint penalty term is: in, The penalty term for the upper limit constraint of the pore pressure ratio represents the loss component of the upper limit constraint of the pore pressure ratio; This represents the squared penalty imposed on sample i for exceeding the upper limit of pore water pressure ratio prediction; S14. The effective stress non-negative constraint loss component and the pore pressure ratio upper limit constraint loss component are weighted and summed to generate the physical constraint loss value; the formula for calculating the physical constraint loss value is: in, This represents the physical constraint loss value. The first hyperparameter for controlling the penalty intensity of the effective stress non-negative constraint loss component is... This is a second hyperparameter for controlling the penalty strength of the upper limit constraint loss component of the pore pressure ratio.

3. The method according to claim 1, characterized in that, The step of calculating the monotonic constraint loss value based on the changing trends of key sample features in the training dataset and the corresponding changing trends of the initial predicted pore water pressure ratio includes: S21. Construct a first sample pair set within the current training batch, wherein each sample pair in the first sample pair set contains a first sample. Second Sample The first sample With the second sample The peak ground acceleration characteristic values ​​are different for the second sample, while all other characteristic values ​​are the same. The peak ground acceleration characteristic value is greater than that of the first sample. The peak ground acceleration characteristic value; S22, Based on the first sample The initial predicted pore water pressure ratio and the second sample The initial predicted pore water pressure ratio is used to construct a monotonically non-decreasing constraint penalty term for peak ground acceleration; wherein, when the first sample The initial predicted pore water pressure ratio is greater than that of the second sample. When calculating the initial predicted pore water pressure ratio, the peak ground acceleration monotonically non-decreasing constraint penalty term incurs a penalty; the expression for the peak ground acceleration monotonically non-decreasing constraint penalty term is: in, The peak ground acceleration monotonically non-decreasing constraint penalty term represents the peak ground acceleration monotony constraint loss component; Denotes the first set of sample pairs. This indicates the number of sample pairs in the first sample pair set. and Representing the first sample and the second sample The initial predicted pore water pressure ratio, This represents the squared penalty imposed on predictions that violate the monotonically non-decreasing relation; S23. Construct a second set of sample pairs within the current training batch, where each sample pair in the second set contains a third sample pair. and the fourth sample The third sample With the fourth sample The standard penetration number feature value is different for the fourth sample, while all other feature values ​​are the same. The standard penetration hit count eigenvalue is greater than that of the third sample. Standard penetration blow count eigenvalue; S24, Based on the third sample The initial predicted pore water pressure ratio and the fourth sample The initial predicted pore water pressure ratio is used to construct a standard penetration test (SPT) blow count monotonically non-increasing constraint penalty term; wherein, when the fourth sample The initial predicted pore water pressure ratio is greater than that of the third sample. When calculating the initial predicted pore water pressure ratio, the standard penetration test (SPT) blow count monotonically non-increasing constraint penalty term incurs a penalty; the expression for the standard penetration test (SPT) blow count monotonically non-increasing constraint penalty term is: in, The standard penetration test (SPT) hit count monotonically non-increasing constraint penalty term represents the loss component of the standard penetration test (SPT) hit count monotony constraint. For the second set of sample pairs, This indicates the number of sample pairs in the second sample pair set. and The third sample represents respectively and the fourth sample The initial predicted pore water pressure ratio, This represents the squared penalty imposed on predictions that violate the monotonically non-increasing relation; S25. The monotonic constraint loss component of the peak ground acceleration and the monotonic constraint loss component of the standard penetration test (SPT) blow count are weighted and summed to generate the monotonic constraint loss value; the formula for calculating the monotonic constraint loss value is: in, This represents the monotonicity constraint loss value. The third hyperparameter is used to control the penalty intensity of the peak ground acceleration monotonicity constraint loss component. A fourth hyperparameter is used to control the penalty strength of the loss component under the standard penetration test (SPT) blow count monotonicity constraint.

4. The method according to claim 3, characterized in that, The construction of the first sample pair set within the current training batch includes: S31. Randomly select a sample from the current training batch as the first basic sample, copy all the features of the first basic sample, and generate the first virtual copy sample; S32. Apply a first positive random perturbation increment to the peak ground acceleration feature value of the first virtual replica sample to generate a first perturbation replica sample; wherein, the peak ground acceleration feature value of the first perturbation replica sample is equal to the peak ground acceleration feature value of the first base sample plus the first positive random perturbation increment. S33. Combine the first basic sample with the first perturbated copy sample to form a sample pair and add it to a new set; S34. Repeat steps S31 to S33 until the number of generated sample pairs reaches a preset first quantity threshold, and obtain the constructed first sample pair set. The construction of the second set of sample pairs within the current training batch includes: S41. Randomly select a sample from the current training batch as the second basic sample, copy all the features of the second basic sample, and generate a second virtual copy sample; S42. Apply a second positive random perturbation increment to the standard penetration number (SPT) feature value of the second virtual copy sample to generate a second perturbated copy sample; wherein, the SPT feature value of the second perturbated copy sample is equal to the SPT feature value of the second base sample plus the second positive random perturbation increment. S43. Combine the second basic sample and the second perturbated copy sample into a sample pair and add it to the new set; S44. Repeat steps S41 to S43 until the number of generated sample pairs reaches the preset second quantity threshold, and obtain the constructed second sample pair set.

5. The method according to any one of claims 1 to 4, characterized in that, The step of determining sand liquefaction based on the predicted pore water pressure ratio to obtain earthquake sand liquefaction prediction results includes: S51. Compare the predicted pore water pressure ratio with the preset critical liquefaction pore water pressure ratio threshold to obtain the comparison result; S52. Based on the comparison results, if the predicted pore water pressure ratio is greater than or equal to the liquefaction critical pore water pressure ratio threshold, then it is determined that the site to be predicted has liquefied. S53. Based on the comparison results, if the predicted pore water pressure ratio is less than the critical liquefaction pore water pressure ratio threshold, then it is determined that the site to be predicted will not liquefy.

6. A deep learning-based earthquake sand liquefaction prediction system, used to implement the method according to any one of claims 1 to 5, characterized in that, The system includes: The site data standardization module is used to standardize the site parameters of historical earthquake sand liquefaction cases and generate a standardized training dataset; wherein, the site parameters include soil layer parameters and seismic motion parameters. The deep model initialization module is used to construct a deep neural network prediction model based on the feature dimensions in the training dataset, taking the samples of the training dataset as input and the predicted pore water pressure ratio as output; and to input the samples of the training dataset into the deep neural network prediction model for forward propagation to generate an initial predicted pore water pressure ratio value. The physical constraint loss calculation module is used to calculate the physical constraint loss value based on the initial predicted pore water pressure ratio and the corresponding initial effective stress value in the training dataset. The monotonicity constraint loss calculation module is used to calculate the monotonicity constraint loss value based on the changing trends of key sample features in the training dataset and the corresponding changing trends of the initial predicted pore water pressure ratio. The data fitting loss calculation module is used to calculate the data fitting loss value based on the initial predicted pore water pressure ratio and the actual pore water pressure ratio in the training dataset. The loss function aggregation module is used to perform a weighted summation of the data fitting loss value, the physical constraint loss value, and the monotonic constraint loss value to generate a total loss function value. The model training iteration module is used to update the parameters of the deep neural network prediction model based on the total loss function value through the backpropagation algorithm, and to iteratively train the deep neural network prediction model to obtain a pre-trained pore water pressure ratio prediction model. The liquefaction prediction output module is used to input standardized site parameters of the site to be predicted into the pore water pressure ratio prediction model and output the predicted pore water pressure ratio; based on the predicted pore water pressure ratio, sand liquefaction is determined to obtain the earthquake sand liquefaction prediction result.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 5.

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