A prediction method for the stress and strain of reinforced soil based on time series and modal decomposition

Abstract

The present invention relates to a method for predicting the stress and strain of reinforced soil based on time series and modal decomposition, which is characterized by including: obtaining the stress and strain data to be predicted, and constructing a combined learning model, where the combined learning model includes: a long short-term memory network model and an XGBoost integrated model; among them, the combined learning model is obtained by training with a training set; using the training set to train the combined learning model includes: performing sequence decomposition on the training set to obtain a number of intrinsic mode functions, replacing the deviator stress data in the training set with the ordinate values of the time series in a number of intrinsic mode functions, so as to merge the multi-sample data in the training set into a number of one-dimensional time series, performing time series reconstruction on the number of one-dimensional time series respectively, and training the combined learning model; inputting the stress and strain data to be predicted into the combined learning model to obtain the stress and strain prediction results of the reinforced soil.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering construction, and particularly to a method for predicting the stress and strain of reinforced soil based on time series and modal decomposition. Background Art

[0002] In recent years, with the continuous, healthy and rapid development of the national economy, the construction of infrastructure such as highways, railways, and airports has been developing at an unprecedented high speed. Reinforced slopes, reinforced soil retaining walls, and reinforced foundations have been widely used in civil engineering construction due to their unique advantages of simple construction, low cost, and landscape beautification. A geocell is a three-dimensional reticular geosynthetic material formed by ultrasonic welding, riveting, or plugging of wide strips of high molecular polymers (such as high-density polyethylene, polypropylene, or polyester). Geocells are convenient for transportation. When in use, they are opened and filled with earth and stone materials or concrete materials to build structures such as reinforced foundations, reinforced slopes, and reinforced retaining walls, and are widely used in various fields of civil engineering. Due to its special three-dimensional shape, compared with two-dimensional planar reinforcement materials such as geogrids, geotextiles, and geomembranes that only rely on their own tensile strength and the friction and interlocking with soil to exert the reinforcement effect, a geocell not only has tensile strength itself, but also has mutual friction between the cell sheets and the soil, and can also provide strong lateral restraint to the filler. Therefore, the cohesive strength of the reinforced soil increases greatly, and the reinforcement effect is better than that of two-dimensional geosynthetics. Due to its excellent reinforcement effect, geocells have been widely used in the construction of reinforced foundations, reinforced slopes, and reinforced retaining walls. However, there is still no mature design method and design specification for geocell-reinforced soil structures. In particular, there is still no theoretical determination method for the important design parameters of the equivalent strength and equivalent stiffness of geocell-reinforced soil as a composite material. The theoretical research lags behind the engineering practice, which restricts the design calculation of new geocell-reinforced soil structures and their application in engineering practice. Summary of the Invention

[0003] The object of the present invention is to propose a method for predicting the stress and strain of reinforced soil based on time series and modal decomposition to solve the problems existing in the above-mentioned prior art. Relying on the in-depth analysis of extensive test data and the systematic summary of historical experience, the development of the constitutive model is promoted, aiming to obtain a prediction model for the stress and strain of soil with unknown combinations of basic properties.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] A method for predicting the stress and strain of reinforced soil based on time series and modal decomposition, comprising:

[0006] Obtain the stress-strain data to be predicted, and construct an integrated prediction model. The integrated prediction model includes a number of combined learning models, and the combined learning model includes: a long short-term memory network model and an XGBoost integrated model; wherein, the integrated prediction model is trained using a training set.

[0007] Training the integrated prediction model using the training set includes: performing sequence decomposition on the training set to obtain a number of intrinsic mode functions, replacing the deviator stress data in the training set with the ordinate values of the time series in a number of intrinsic mode functions, so as to merge the multi-sample data in the training set into a number of one-dimensional time series, performing temporal reconstruction on the number of one-dimensional time series respectively, and training the integrated prediction model.

[0008] Input the stress-strain data to be predicted into the integrated prediction model to obtain the stress-strain prediction result of the reinforced soil.

[0009] Optionally, before training the combined learning model using the training set, it includes:

[0010] Performing data cleaning on the original data set, performing one-hot encoding on the cell material features in the original data set after data cleaning, performing correlation analysis on the one-hot encoded original data set to obtain a number of highly correlated features, further constructing a data set, and dividing the data set into a training set, a test set, and a validation set.

[0011] Optionally, obtaining the number of intrinsic mode functions includes:

[0012] S1.1. Obtain a random number consistent with the number of training set samples, that is, Gaussian white noise, and select the Gaussian white noise as the initial intrinsic mode function.

[0013] S1.2. Perform Hilbert transform on the initial intrinsic mode function to obtain the envelope function of the initial intrinsic mode function.

[0014] S1.3. Separate the frequency information and smooth components of the initial intrinsic mode function according to the envelope function to obtain a rough intrinsic mode function.

[0015] S1.4. Deduct the rough intrinsic mode function from the training set to generate a residual signal.

[0016] S1.5. Use the residual signal as a new initial intrinsic mode function, and repeat S1-S4 until the envelope function of the initial intrinsic mode function meets the preset convergence or accuracy requirements.

[0017] S1.6. Sort all the initial intrinsic mode functions in ascending order of scale to form the number of intrinsic mode functions.

[0018] Optionally, training the integrated prediction model includes:

[0019] S2.1. Set the hyperparameter space, select a set of hyperparameters, and use the sliding window mechanism to input a certain row sequence in the several one-dimensional time series into the several combined learning models for training respectively;

[0020] S2.2. After the training in step S2.1 is completed, fuse the current row sequence and all sequences in the previous row of the current row sequence with the next row sequence as the fused sequence and input it into the several combined learning models for training;

[0021] S2.3. Repeat step S2.2 until all row sequences and hyperparameters are input into the several combined learning models for training, obtain several hyperparameter optimization results, obtain several optimal combined learning models according to the several hyperparameter optimization results, and obtain the integrated prediction model based on the several optimal combined learning models.

[0022] Optionally, obtaining several hyperparameter optimization results includes:

[0023] Use the validation set to test the combined learning models containing each set of hyperparameters during the training process, record the error of the validation set, and select the optimal error of the validation set as the hyperparameter optimization result.

[0024] Optionally, obtaining the integrated prediction model includes:

[0025] Obtain the best validation set error of the long short-term memory network model and the best validation set error of the XGBoost integrated model in the combined learning models containing the optimal hyperparameter optimization results;

[0026] Set an error threshold, calculate the best validation set error of the long short-term memory network model and the best validation set error of the XGBoost integrated model, compare the calculation result with the error threshold. If the error threshold is greater than the calculation result, then weight and add the long short-term memory network model and the XGBoost integrated model to form the optimal combined learning model. If the error threshold is less than the calculation result, then judge the best validation set error of the long short-term memory network model and the best validation set error of the XGBoost integrated model, and use the model with the minimum best validation set error as the optimal combined learning model, and further obtain several optimal combined learning models

[0027] Perform weighted combination on the several optimal combined learning models to obtain the integrated prediction model.

[0028] Optionally, the method for obtaining the stress-strain prediction result of a single optimal combined learning model is:

[0029]

[0030] Among them, y test is the stress-strain prediction result of reinforced soil, and W LSTM is the best validation set error of the long short-term memory network model, is the optimal long short-term memory network model, and W XGB is the best validation set error of the XGBoost ensemble model, is the optimal XGBoost ensemble model.

[0031] The beneficial effects of the present invention are as follows:

[0032] By introducing the time series processing idea and the LSTM model of deep learning, the new technology can deeply mine the historical data of the soil body, significantly improve the model's understanding and prediction ability of data timeliness, and effectively solve the problem that the original model ignores timeliness.

[0033] Using one-hot encoding technology to process categorical features enhances the model's expression and understanding ability of categorical features, avoids the loss of key information caused by simple numerical assignment, and thus optimizes the model's learning and prediction of categorical features.

[0034] Applying the Z-score method and VMD sequence decomposition technology for data cleaning and waveform decomposition effectively processes rare samples and complex stress-strain sequences, significantly improves the generalization ability and performance of the model, and solves the problem that the model's inductive and generalization abilities are limited when dealing with special data.

[0035] Overall, the integration of these advanced technologies not only significantly improves the prediction accuracy, but also significantly enhances the model's analysis and prediction ability of complex soil body behaviors, making the model more applicable and effective in practical applications, and providing more reliable and efficient technical support for the prediction and analysis of soil engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0037] Figure 1 is a schematic diagram of the application of the sequence decomposition algorithm in the embodiment of the present invention;

[0038] Figure 2 is a schematic diagram of the one-hot encoding process in the embodiment of the present invention;

[0039] Figure 3 Temporal reconstruction of the dataset in the embodiment of the present invention;

[0040] Figure 4 Principle process of the integrated algorithm model in the embodiment of the present invention;

[0041] Figure 5 Detection results of the z - quantile method for each feature in the embodiment of the present invention;

[0042] Figure 6 Discrimination results of the Pearson correlation coefficient in the embodiment of the present invention;

[0043] Figure 7 Discrimination results of the Pearson correlation coefficient after descending order in the embodiment of the present invention;

[0044] Figure 8 Decomposition results of the VMD algorithm sequence in the embodiment of the present invention;

[0045] Figure 9 Detailed decomposition diagrams of each sequence in the embodiment of the present invention;

[0046] Figure 10 Decomposition results of the EEMD technology sequence in the embodiment of the present invention;

[0047] Figure 11 Detailed decomposition diagrams of each sequence in the embodiment of the present invention;

[0048] Figure 12 Performance comparison of the final prediction results in the embodiment of the present invention; where (a) are the prediction performance indicators of the test set, and (b) are the prediction performance indicators of the training set;

[0049] Figure 13 Comparison of the prediction results of the test sets of each group of experiments in the embodiment of the present invention;

[0050] Figure 14 Comparison of the prediction results of the model training sets of Experiment 1 and Experiment 2 in the embodiment of the present invention. Specific embodiments

[0051] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0052] To make the above - mentioned objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0053] Variational Mode Decomposition (VMD) is a technique applied in signal processing to decompose a signal into multiple Intrinsic Mode Functions (IMFs) in order to reveal various vibration modes within the signal. By solving a variational problem, VMD can identify independent frequency components within the signal, where each IMF represents a characteristic vibration frequency of the signal. This method is widely used in multiple fields such as engineering, economy, and medicine for tasks such as signal analysis, feature extraction, and data preprocessing, and is particularly suitable for processing complex non-linear and non-stationary signals.

[0054] The decomposition process of VMD is based on the variational principle and is carried out as follows: Initialization: Select Gaussian white noise as the starting point for the initial Intrinsic Mode Function (IMF). Hilbert transform: Perform the Hilbert transform on the current IMF to calculate its envelope function, which is achieved by adjusting the Fast Fourier Transform (FFT) spectrum of the signal. Frequency extraction: Apply a regularization technique to the envelope function to separate the frequency information of the current IMF from the smooth component, thereby obtaining a rougher IMF. Residual calculation: Subtract the current IMF from the original signal to generate a residual signal, which will be used as the input for the next iteration loop. Iterative loop: Repeat steps 2 to 4 until a predetermined stopping condition is reached, usually when the convergence or accuracy of the current IMF meets the requirements. Signal reconstruction: Sort all IMFs in ascending order of scale to form the final signal decomposition result. By iteratively extracting the local frequency information in the signal, VMD effectively decomposes the signal into several IMFs, where each IMF reveals a specific vibration mode in the signal, demonstrating excellent adaptive capabilities in non-linear and non-stationary signal processing.

[0055] Whether to adopt the sequence decomposition algorithm has nothing to do with the machine learning model used in the prediction process. The only difference is that after decomposing the original sequence data using the sequence decomposition algorithm, it is respectively substituted into the machine learning model for separate training. Finally, the results are added together. The principle process is as Figure 1 shown.

[0056] One-Hot Encoding is a technique commonly used to process categorical data, especially suitable for situations where there is no clear ordering between categories. This encoding method can convert categorical data into a numerical format that can be effectively processed by machine learning models, enabling this data to be used in further data analysis and model training processes. Specifically, One-Hot Encoding maps each category to a unique binary vector, effectively avoiding the possibility that the model misinterprets these categories as having some ordered relationship, which is of great significance for processing data with no natural ordering relationship between categories.

[0057] The Z - quantile detection method is a statistical technique used to identify outliers or anomalies in a dataset. This method is based on the concept of standard scores, which compares each data point with the mean of the dataset and takes into account the standard deviation of the data. The Z - score method is widely applied in various fields, especially in data cleaning, anomaly detection, and quality control. The following is the calculation process of the Z - quantile:

[0058] Calculate the mean according to Equation (3.1):

[0059] where: x i is the value of each data point, and n is the total number of data points.

[0060] Calculate the standard deviation according to Equation (3.2):

[0061] Calculate the quantile of this data point according to Equation (3.3):

[0062] To ensure the quality of the dataset, the present invention uses the Z - quantile detection method to detect outliers in the dataset. In this method, the threshold of the Z - value is set to 3 to identify and process potential abnormal data points. For missing values in the dataset, they are first assigned zero values and then removed from the dataset.

[0063] In addition, with the excellent performance of machine - learning models demonstrated in other fields, for the same purpose, a large number of studies on the stress - strain response of soil using machine learning are emerging. However, when dealing with the problem of soil stress - strain prediction, many traditional machine - learning models often regard data as a series of isolated sample points, ignoring their changes in the time series, especially not considering the stress path of the soil. Such an approach ignores a key fact: the shear strength of the soil not only depends on its current stress state but is also closely related to the process by which it reaches the current state. Therefore, for machine - learning models, how to effectively integrate the stress - path information of the soil has become a key challenge in improving prediction accuracy.

[0064] The time series model is a type of statistical model that is specifically used to analyze and predict data sequences arranged in chronological order. The model can help understand past behavior and predict future trends by observing the evolution of data in the time dimension. It can be seen that the introduction of the time series model, compared with traditional machine learning technology, realizes the effective use of historical data changes for prediction results. This method effectively considers the historical stress path of the soil before reaching the current stress-strain state by tracking and analyzing the changes in data at various time points in the past, which is closely related to the needs of soil stress-strain prediction in geotechnical engineering. It can integrate the influence of historical data to provide accurate predictions for predicting soil behavior, especially when considering stress paths, which is significantly better than traditional models, providing a more reasonable and efficient method for the construction of geotechnical engineering prediction models.

[0065] Dataset preprocessing:

[0066] In order to further explore the effects of different basic geotechnical parameters and geocell specifications on the stress-strain response of reinforced sand, extensive data on the properties of sand and geocells were collected. Based on this strategy, the effectiveness of geocells in soil fill reinforcement was analyzed in depth.

[0067] In order to maintain data quality and ensure the accuracy of analysis results, the Z quantile method was selected as the main technical means of data cleaning. This method effectively identifies and processes outliers, provides high-quality data for subsequent analysis, and ensures the accuracy and credibility of research results. The threshold of the Z quantile method is set to 3. It is worth noting that the cell material and the height-to-diameter ratio of the sample have a small number of values ​​that fall within the range of data cleaning.

[0068] Given that geocells made of different materials have inconsistent reinforcement properties for internal fill, it is necessary to distinguish between geocell reinforced soil triaxial tests and sand soil triaxial tests using different materials. However, the traditional method of using different numerical values ​​for the same feature such as 0, 1, and 2 may give the machine learning model an incorrect indication, that is, it may mislead the machine learning model into thinking that these codes reflect the inherent order between certain material properties, which is not true. Therefore, using unique hot encoding to process cell material features can effectively avoid this potential misunderstanding. By converting categorical features into a series of binary variables, it ensures that each material is treated equally and independently, which is crucial to improving the accuracy of data processing and the reliability of model predictions. Specific practices such as Figure 2 shown.

[0069] Correlation analysis: Before substituting the data into the integrated learning model, to ensure the prediction performance of this machine learning model, it is necessary to optimize the number of variables. By using the Pearson correlation coefficient matrix analysis, based on the correlation between each feature and the deviator stress, 8 features with high correlation with the prediction target are selected. The purpose of this variable optimization process is to improve the prediction accuracy and efficiency of the model. By reducing the interference of irrelevant variables, it ensures that the model can focus more on the key factors that have a significant impact on the prediction performance.

[0070] Window partitioning and construction of feature vectors: The multivariate time series prediction model uses features in multiple dimensions to predict the values of one or more target features at future time steps. Different from univariate time series prediction, this method not only relies on the historical data of the target variable, but also comprehensively considers the history of other relevant features and their potential impact on the future values of the target variable.

[0071] For the multivariate time series prediction model, the model is divided into two categories according to the knowability of future features: prediction of knowable future features and prediction of unknowable future features. Based on the known situation of the basic geotechnical parameters of sandy soil, the geocell material and its shape specifications at the target location, the present invention aims to predict the stress-strain curve of geocell-reinforced soil. Therefore, this research belongs to the category of prediction of knowable future features, that is, the model construction is based on the known state of the input features, which is used as the basis for predicting the future stress-strain response.

[0072] When constructing a multivariate time series prediction model for knowable future features, the key lies in incorporating historical stress information and historical input features into the existing data set as supplementary features for in-depth learning. This process is implemented through a sliding window mechanism, which allows the model to move forward step by step on the data set and continuously predict future values. This method not only enhances the utilization efficiency of the model for historical data, but also effectively improves the prediction accuracy and reliability by finely adjusting the window movement strategy. The specific processing logic of the data set is as Figure 3 shown.

[0073] Figure 3 The input data of the machine learning model in the figure is composed of two sets of historical input features, 4 sets of historical prediction sequence points and the known prediction data features at the current time step. Specifically, the dimension of the input feature vector is 2n + 4×1 + n = 3n + 4, where n represents the dimension of the original known data features. By shifting the data window down one position after each prediction, the model continuously performs subsequent prediction tasks. Compared with the traditional model that only predicts based on n-dimensional known data features, the present invention substantially increases the information volume of 2n + 4 by expanding to a 3n + 4-dimensional input feature vector. This improvement significantly enhances the prediction performance of the machine learning model for data sets such as the stress-strain response of the soil loading process with a fixed time series, providing a more abundant information basis.

[0074] Sequence decomposition: The stress-strain data of the soil body is decomposed using the VMD sequence decomposition technique.

[0075] Framework ensemble learning model: To enhance the prediction ability of the machine learning model, the present invention adopts the form of ensemble learning. Ensemble learning is a method of constructing a strong learner by integrating multiple weak learners, aiming to achieve superior generalization performance that is difficult to reach by a single model. This method is based on two core principles: the accuracy and diversity of individual learners. By adopting different sample sampling or data preprocessing techniques, differential base learners are constructed, and these base learners are appropriately weighted and combined to form an integrated model with stronger comprehensive performance. The ensemble learning method improves the accuracy and robustness of the prediction model on unknown data and is an effective way to enhance the generalization ability of the machine learning model.

[0076] In the ensemble learning strategy, the model combination aims to optimize and integrate the advantages of each model. However, simply combining two models often results in the performance of the integrated model being only between the original models. This indicates that the quality of the ensemble effect not only depends on the performance of individual models, but more importantly, on the difference and complementarity between models. Therefore, an effective combination should pursue the diversity between models and their complementary roles in specific tasks, so as to improve the overall prediction performance through a carefully designed combination strategy.

[0077] After a detailed comparison of the model performance, the present invention determines to adopt the combination of the long short-term memory network (LSTM) and the XGBoost integrated model as the learning model. This combined model makes full use of the ability of LSTM to capture long-term dependence relationships in processing time series data and the superiority of XGBoost in feature selection and classification performance. This kind of model combination aims to deeply explore the time dynamic characteristics of the data through the LSTM model and use the powerful learning ability of XGBoost to perform effective regression prediction on these characteristics, in order to achieve the optimal performance in specific prediction tasks. Figure 4 This is the principle process of the ensemble algorithm model adopted by the present invention.

[0078] The specific process is as follows: Determination of the hyperparameter space: First, define a hyperparameter space to facilitate parameter selection during model training. Model training and validation: After selecting a set of hyperparameters, use the training set to train the model and test it on the validation set, and record the error of the validation set. Optimization iteration: Repeat the above process until the optimal model parameters that produce the best validation set error are identified. Model selection and combination: Compare the best errors of the two models on the validation set; if the error gap is significant, select the model with the smaller error as the final model. If the errors of the two models are less than the preset threshold, adopt the method of weighted summation of the prediction results of the two models to form the final integrated prediction model. Among them, the error E LSTM , E XGB is represented by the mean absolute error MAE.

[0079] The configuration of the main model this time is shown in Table 1-5 below:

[0080] Table 1 LSTM model configuration

[0081]

[0082] Table 2 Bayesian algorithm configuration of the LSTM model

[0083]

[0084] Table 3 Improved grey wolf optimization algorithm configuration of the LSTM model

[0085]

[0086] Table 4 XGBoost model configuration

[0087]

[0088] Table 5 Improved grey wolf optimization algorithm configuration of the XGBoost model

[0089]

[0090] Data collection and experimental scheme design:

[0091] This invention relies on a series of large-scale triaxial tests on reinforced soil, combines the test results of reinforced sand, and uses the triaxial test of sand as a supplement. The total dataset includes 133 groups of test samples, among which the number of triaxial test samples of geocell-reinforced soil is 81 groups, accounting for 60% of the total number of samples. The remaining 52 groups of samples are triaxial tests of sand, accounting for 40% of the total number of samples.

[0092] The dataset contains 16 features, namely the coefficient of uniformity C u , the coefficient of curvature C c , the specific gravity G s , d60 (mm), d 50 (mm), d 10 (mm), γ dmax (kN / m3), γ dmin (kN / m3), relative density D r (%), cellular material (without cellular, HDPE, PP), specimen height-diameter ratio (2 and 2.45), cellular height H (mm), cellular stiffness M t (kN / m), confining pressure σ 3 (kPa), vertical strain ε (%), and deviator stress Δσ 1 (kPa). Among them, the deviator stress is used as the prediction feature and the rest are used as input features.

[0093] In view of the limitations of the existing prediction models, the present invention introduces the time-series feature reconstruction, the sequence decomposition algorithm, and the ensemble learning technology, aiming to improve the prediction performance of the machine learning model for the stress-strain response of geocell-reinforced soil. Through the comprehensive application of these three technologies, the research will deeply evaluate their individual and combined effects on the prediction accuracy. For this purpose, the present invention constructs multiple models based on the orthogonal experimental design to systematically explore the specific contributions of each technology in optimizing the prediction model, so as to achieve the goal of improving the overall prediction ability of the model.

[0094] In the design of the present model test, considering that the test involves three factors and each factor is set at two levels, therefore, the L 4 (2 3 ) orthogonal array is used for the test layout. This orthogonal array allows for a comprehensive and efficient exploration of all factors and their two-level combinations to ensure the comprehensiveness and accuracy of the test results. The configurations of each model test are shown in Table 6.

[0095] Table 6 Model Test Scheme

[0096]

[0097] It should be noted that for the tests involving sequence decomposition, the VMD and EEMD technologies will be implemented separately in the research. The purpose is to select the best-performing technology for subsequent analysis by comparing and analyzing their performance in specific applications. This strategy ensures the optimization of the sequence decomposition process, aiming to improve the model prediction performance while enhancing the model's adaptability to complex signal processing. In addition, the Bayes and I-GWO optimization algorithms are defaultly used in the test to search the hyperparameter space, and the optimal result is selected for the later performance comparison.

[0098] Dataset preprocessing: The dataset used in this study contains 3,465 data points. To maintain data quality and ensure the accuracy of the analysis results, the Z-score method was selected as the main technical means for data cleaning. This method effectively identifies and processes outliers, providing high-quality data for subsequent analysis and ensuring the accuracy and reliability of the research results. The threshold of the Z-score method was set to 3. It should be noted that only three types of cellular materials and two types of specimen height-diameter ratios are not within the scope of data cleaning.

[0099] Since there are significant differences in the dimensions and numerical ranges of the various features involved, the method of setting the ordinate of the scatter plot to the quantile values of each data point was adopted to achieve effective comparison between different data. When the quantile of a data point is less than -3 or greater than 3, these points will be marked in red and identified as outliers. From the analysis results, it can be seen that there are relatively few outliers detected in the minimum dry density γ dmin and the confining pressure σ 3 These outliers are usually caused by specific rare soil samples or high confining pressure test conditions. It should be noted that in the deviator stress parameters, a large number of data points exceeding the conventional quantile range were introduced by the high-strength geocell-reinforced soil triaxial tests using a high confining pressure of 800 kPa. To optimize the performance of the dataset, the data points containing these outliers were selected for deletion.

[0100] Correlation analysis: To ensure the prediction performance of the machine learning model in this study, it is necessary to optimize the number of variables. By using the Pearson correlation coefficient matrix analysis, starting from the initial 17 sample features (including 3 features obtained through one-hot encoding), 8 features with high correlation with the prediction target were selected based on the correlation between each feature and the deviator stress. The purpose of this variable optimization process is to improve the prediction accuracy and efficiency of the model. By reducing the interference of irrelevant variables, it ensures that the model can focus more on the key factors that have a significant impact on the prediction performance. As Figure 6 shown.

[0101] To deeply analyze the correlation strength between different feature vectors and the vertical strain of soil samples, the data was sorted in descending order according to the absolute value of the correlation between the feature vector and the vertical stress. The correlations of the features after rearrangement are as Figure 7 shown.

[0102] The vertical strain and the cell stiffness show the strongest positive correlation with the vertical deviator stress of the soil sample. It should be noted that since most of the experimental data in this study are based on sand samples reinforced with HDPE materials and the corresponding characteristics are uniquely coded with a value of 1, the numerator of the fraction approaches zero. Therefore, a weak correlation is shown in the matrix. In addition, it can be found that there is an obvious negative correlation between the unreinforced soil and the vertical strain, indicating that the characteristics of the unreinforced soil have an obvious negative effect on the vertical deviator stress. On the contrary, the PP material has a greater positive correlation and can significantly increase the vertical deviator stress of the cell.

[0103] It can be seen that the vertical strain and the cell stiffness show a significant positive correlation with the vertical deviator stress of the soil sample in the analysis. However, it should be particularly noted that a large amount of experimental data comes from sand samples reinforced with high-density polyethylene (HDPE) materials. The unique coding method of its related characteristics leads to ∑x approaching n and ∑xy approaching ∑y in the Pearson correlation coefficient formula (Equation 4.1), resulting in the numerator tending to zero and thus showing a weak correlation in the correlation matrix. In addition, the analysis results also show that there is a significant negative correlation between the unreinforced soil and the vertical strain, indicating that the characteristics of the unreinforced soil may play a negative role in the prediction of the vertical deviator stress. In contrast, the soil samples reinforced with polypropylene (PP) materials show a strong positive correlation, meaning that the reinforcement effect of the PP material is more significant in enhancing the vertical deviator stress of the soil sample.

[0104]

[0105] According to Figure 7 the sorting results in, the top 8 features with higher correlations are selected as the input data set (within the purple box). It should be particularly noted that most of the samples in the data set come from sand samples reinforced with high-density polyethylene (HDPE) materials. During the data coding process, when the characteristics of the unreinforced soil and the polypropylene (PP) material are both coded as 0, the sample corresponding to this coding scheme is the soil sample reinforced with the HDPE material.

[0106] Data set division: After selecting the top 8 features with higher correlations as the input data set, the data set needs to be divided according to the following requirements. The data set consists of two types of data: geocell-reinforced sand and unreinforced sand. The introduction of the latter is to expand the scope of the data set and enhance the diversity of the training set. Based on this, the data set division strategy is as follows: Randomly select 10% of the samples from the geocell-reinforced sand data set as the validation set, and another 10% of the samples as the test set. The remaining reinforced sand data and all the unreinforced sand data together form the training set. It should be noted that only the training set and the validation set are involved in the model training. The test set is used to accurately evaluate the model performance, and there is no intersection between its internal data and the training set and the validation set.

[0107] Sequence decomposition: To ensure that the ensemble learning model can fully learn the complex stress-strain relationship of geocell-reinforced soil, the present invention refers to the methods in the field of signal processing. First, we regard the stress and strain change curves of the reinforced soil as complex signals. Subsequently, using the variational mode decomposition (VMD) technique, we decompose these data into three more easily describable intrinsic mode functions (IMFs), and each IMF can capture specific frequency components in the data.

[0108] The stress and strain change curves of the reinforced soil are the feature 8 (strain) and the predicted feature (stress) of the training set. Copy the stress-strain data from the test set, and then replace the strain data with 1 - n (n is the total number of samples in the test set). After the above operations, a curve is obtained, and this curve is the complex signal.

[0109] It should be noted that the sequence decomposition technique decomposes the data on the y-axis (stress). After decomposition, three groups of curves will be obtained. Therefore, after constructing the input data set, the present invention copies the stress and strain (Δσ, ε) data of the reinforced soil in the input data set, and replaces the strain value ε (x-axis) with the sample index having the same sequence characteristics, so as to merge multiple sample data into a complete one-dimensional time series. Figure 8 In the figure, waveform 1 is the original waveform of the vertical deviator stress. Waveform indices 2 - 4 (IMF1 - 3) correspond to the high frequency to low frequency of the decomposed sequence respectively, and waveform index 5 is the residual sequence. The detailed decomposition diagrams of each sequence are as Figure 9 shown.

[0110] After processing the deviator stress data through the variational mode decomposition (VMD), the analysis results reveal the different characteristics of the intrinsic mode functions (IMFs). Specifically, IMF1 exhibits high-frequency fluctuations with a small amplitude, indicating that there are certain noise components in the original deviator stress sequence. Relatively speaking, IMF2 shows obvious periodic fluctuations and a large amplitude, reflecting the main oscillation mode in the sequence. While IMF3 shows relatively slow fluctuations with a large amplitude, meaning that there are low-frequency trend components in the original sequence.

[0111] In addition, the results of decomposing the deviator stress sequence using the EEMD technique are as Figure 10 shown.

[0112] As Figure 11As shown, the VMD technique is clearer than EEMD in the expression of modal fluctuations and periodicity. EEMD alleviates modal aliasing in EMD by adding white noise, but it results in high-frequency noise, especially in the waveforms of IMF1 and IMF2, affecting effective waveform separation. It can be seen that although the introduction of this random noise in EEMD effectively reduces modal aliasing, it also brings differences in results, thus affecting the robustness of the results to a certain extent.

[0113] In summary, variational mode decomposition (VMD) is more suitable than ensemble empirical mode decomposition (EEMD) for the scenario of clearly separating and identifying the main components in the soil stress-strain fluctuation sequence.

[0114] Overall architecture of the machine learning model: It should be added that the modal decomposition technique can not only decompose complex waveforms into intrinsic mode functions, but also ensure that the decomposed waveforms are superimposed to completely restore the original complex waveform. Based on this key feature, the following overall architecture of the machine learning model will be designed.

[0115] Fuse the data processed by the VMD technique into the input dataset. The operation steps are as follows: First, copy the input dataset (including feature data) into three copies. Subsequently, replace the deviator stress data in each of these three datasets with the ordinate values of the three time series obtained by VMD decomposition. Finally, obtain the final prediction result by superimposing the prediction results of the three machine learning models.

[0116] Construction of the ensemble learning model in a single training process: In this example, a combination of a long short-term memory network (LSTM) and an XGBoost ensemble model is used as the learning model. This combined model makes full use of the ability of LSTM to capture long-term dependencies in processing time series data and the superiority of XGBoost in feature selection and classification performance. The following processes are carried out in accordance with the following procedures for all three training processes:

[0117] Determination of the hyperparameter space: First, define a hyperparameter space to facilitate parameter selection during model training.

[0118] The defined hyperparameter space includes the basic configuration parameters of the LSTM and XGBoost models, as well as the search ranges of the corresponding hyperparameters of the optimization algorithms selected for each model. The specific details are shown in Table 7-11 below

[0119] Table 7 LSTM model configuration

[0120]

[0121]

[0122] Table 8 Bayesian algorithm configuration of the LSTM model

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[0124] Table 9 Improved Grey Wolf Optimization Algorithm Configuration for LSTM Model

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[0126] Table 10 Bayesian Algorithm Configuration for XGBoost Model

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[0128] Table 11 Improved Grey Wolf Optimization Algorithm Configuration for XGBoost Model

[0129]

[0130]

[0131] Model Training and Validation: After selecting the above hyperparameters, the model is trained using the training set and tested on the validation set, and the error of the validation set is recorded.

[0132] It should be added that before passing the data of the data set (training set, validation set, and test set) into the model, it is necessary to use the window partitioning technique to reconstruct the input feature vectors.

[0133] In addition, the error E LSTM , E XGB is represented by the mean absolute error MAE, and the calculation method is In the formula, is the predicted value, is the actual value, and n is the number of observation points.

[0134] Optimization Iteration: Repeat the above process until the optimal model parameters that produce the best validation set error are identified.

[0135] Model Selection and Combination: Compare the best errors of the two models on the validation set; if the error gap is significant, select the model with the smaller error as the final model. If the errors of the two models are less than the preset threshold, the prediction results of the two models are weighted and added to form the final integrated prediction model.

[0136] After obtaining the final prediction model, the test set data is used to reconstruct the feature vectors. Subsequently, the feature vectors are substituted into the model to obtain the final prediction results, as shown in Figure 12 (a)-(b).

[0137] The final achieved effect of the invention:

[0138] It can be seen that the models used in Test 1 and Test 2 effectively reconstruct the input feature information after integrating the soil stress path information into the feature vectors, thus significantly improving the prediction accuracy of the models. When comparing this method with the models without feature reconstruction, it shows excellent performance in key prediction performance indicators such as RMSE, MAE, and R 2 etc. However, for Test 2, its MaxError index is similar to that of Test 3 using the same single model (i.e., SVM), indicating that although introducing the soil stress path information can improve the error distribution of the model in most cases, the improvement in the prediction effect of extreme values is relatively limited. By comparing Test 1 and Test 4, it can be found that using the VMD sequence decomposition technology only has a limited improvement in the final prediction performance of the model. Finally, the performance of the LSTM-XGBoost integrated learning model independently used in Test 4 in terms of the MaxError index is significantly better than that of Test 3 using only the single SVM model, which shows the significant advantage of the integrated learning model in dealing with extreme value prediction.

[0139] Through the comparison using the above indicators, although the prediction performance of each model can be evaluated from a macroscopic perspective, it should be noted that relying solely on the analysis of performance indicators has certain limitations, and these indicators cannot fully reflect the prediction ability of the model. Therefore, the comparative analysis between the specific predicted values and the actual values is not only necessary but also can identify the performance differences of the model under specific conditions, thus providing strong theoretical support for the further optimization and application of the model.

[0140] It should be noted that the test set in this study uses the triaxial test data of reinforced sand. To more accurately compare the prediction performance of different models, the present invention adopts an innovative data processing method. Specifically, we improve the traditional single-sample stress-strain analysis method by replacing the strain value (x-axis) with the sample index having the same sequence characteristics, so as to show the stress-strain responses of multiple samples in one picture. The comparison results are shown by Figure 13 as follows.

[0141] Through the comparative analysis of the measured values and model predicted values of the soil stress-strain behavior in each test, it can be found that whether it is Test 2 using a single model or Test 1 using an integrated model, the stress-strain trajectory of the geocell-reinforced soil can be accurately predicted by incorporating the geocell soil stress path information. Especially in Test 2 where the input features are reconstructed, compared with Test 3 using the same model framework, it shows a significant improvement in predicting the behavior of geocell soil under low strain conditions. In addition, by comparing Test 1 and Test 4, it can be found that the LSTM-XGBoost integrated learning model has a certain ability to capture the stress-strain response of geocell soil; however, there are still errors in the prediction of the vertical deviator stress of the model under high strain conditions. It is worth noting that introducing the soil stress path information into the feature vector effectively compensates for the deficiency of the LSTM-XGBoost integrated learning model in this regard.

[0142] Through the above comparative analysis, it can be found that both the Test 1 model and the Test 2 model exhibit relatively excellent performance. This finding preliminarily indicates that the Test 1 and Test 2 models have a certain generalization ability. However, this result alone is not sufficient to fully prove that these two models have the same level of inductive ability when dealing with the training set or known data. The generalization ability refers to the ability of the model to process unseen data, while the inductive ability focuses on how the model learns from the known dataset and forms general conclusions. Although the two are closely related, their focuses are different. Therefore, to prevent the model from misinducing past experiences, it is necessary to compare the prediction effects of the model training sets, which is crucial for comprehensively evaluating the performance of the model. The comparison between the predicted values and the true values of the Test 1 and Test 2 model training sets is as Figure 14 shown.

[0143] As Figure 14 shown, Test 1 can relatively accurately predict the stress-strain response of the geocell, reflecting the efficient induction and integration ability of the model for historical data. In contrast, Test 2 has a relatively accurate prediction ability for the vertical deviator stress of the geocell-reinforced specimen under high strain conditions; however, the negative prediction in the low strain state and the overestimation of the vertical stress when the vertical strain is zero reveal that it induces an incorrect model during the learning process of the training set, thus being unable to reasonably predict the stress-strain response of the geocell-reinforced soil sample in practical applications in reality.

[0144] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A reinforced soil stress-strain prediction method based on temporal sequence and modal decomposition, characterized in that: include: Obtain the stress and strain data to be predicted, and construct an integrated prediction model, wherein the integrated prediction model includes several combined learning models, and the combined learning model includes: a long short-term memory network model and an XGBoost integrated model; wherein the integrated prediction model is obtained by training with a training set; the stress and strain data to be predicted include: non-uniformity coefficient, curvature coefficient, specific gravity, relative density, cell material, specimen height-to-diameter ratio, cell height, cell stiffness, confining pressure, and vertical strain; Using the training set to train the integrated prediction model includes: performing sequence decomposition on the stress-strain data in the training set to obtain a number of intrinsic mode functions, replacing the deviatoric stress data in the training set with the ordinate values ​​of the time series in the several intrinsic mode functions, thereby merging the multiple sample data in the training set into a number of one-dimensional time series, performing temporal reconstruction on the several one-dimensional time series respectively, and training the integrated prediction model; The stress-strain data to be predicted are input into the integrated prediction model to obtain the stress-strain prediction result of the reinforced soil.

2. The reinforced soil stress-strain prediction method based on temporal sequence and modal decomposition according to claim 1 is characterized in that: Before using the training set to train the combined learning model, the method includes: The original data set is cleaned, the cell material features in the original data set after data cleaning are one-hot encoded, the original data set after one-hot encoding is subjected to correlation analysis to obtain several highly correlated features, and the data set is further constructed and divided into a training set, a test set and a validation set.

3. The reinforced soil stress-strain prediction method based on temporal sequence and modal decomposition according to claim 1 is characterized in that: Acquiring the plurality of intrinsic mode functions comprises: S1.

1. Obtain a random number that is consistent with the number of samples in the training set, that is, Gaussian white noise, and select the Gaussian white noise as the initial intrinsic mode function; S1.2, performing Hilbert transform on the initial intrinsic mode function to obtain an envelope function of the initial intrinsic mode function; S1.3, separating the frequency information and smoothing component of the initial intrinsic mode function according to the envelope function to obtain a rough intrinsic mode function; S1.4, deducting the rough intrinsic mode function from the training set to generate a residual signal; S1.5, taking the residual signal as a new initial intrinsic mode function, repeating S1-S4 until the envelope function of the initial intrinsic mode function meets the preset convergence or accuracy requirements; S1.

6. Sort all the initial intrinsic mode functions from low to high according to the scale to form the plurality of intrinsic mode functions.

4. The reinforced soil stress-strain prediction method based on temporal sequence and modal decomposition according to claim 1 is characterized in that: Training the integrated prediction model includes: S2.

1. Set a hyperparameter space, select a set of hyperparameters, and use a sliding window mechanism to input a row sequence of the plurality of one-dimensional time series into the plurality of combined learning models for training; S2.2, after the training of step S2.1 is completed, the current row sequence and all the sequences in the previous row of the current row sequence are fused with the next row sequence as a fused sequence and input into the plurality of combined learning models for training; S2.

3. Repeat step S2.2 until all row sequences and hyperparameters are input into the several combined learning models for training, and several hyperparameter optimization results are obtained. According to the several hyperparameter optimization results, several optimal combined learning models are obtained. Based on the several optimal combined learning models, the integrated prediction model is obtained.

5. The reinforced soil stress-strain prediction method based on time series and modal decomposition according to claim 4 is characterized in that: Obtaining several hyperparameter optimization results includes: The combined learning model containing each set of hyperparameters in the training process is tested using the validation set, the error of the validation set is recorded, and the error of the optimal validation set is selected as the hyperparameter optimization result.

6. The reinforced soil stress-strain prediction method based on time series and modal decomposition according to claim 4 is characterized in that: Acquiring the integrated prediction model includes: Obtain the best validation set error of the long short-term memory network model and the best validation set error of the XGBoost ensemble model in the combined learning model with the best hyperparameter optimization results; An error threshold is set, the best validation set error of the long short-term memory network model and the best validation set error of the XGBoost integrated model are calculated, and the calculation result is compared with the error threshold. If the error threshold is greater than the calculation result, the long short-term memory network model and the XGBoost integrated model are weighted added to form the optimal combined learning model. If the error threshold is less than the calculation result, the best validation set error of the long short-term memory network model and the best validation set error of the XGBoost integrated model are judged, and the model with the minimum best validation set error is used as the optimal combined learning model, and several optimal combined learning models are further obtained. The plurality of optimal combination learning models are weightedly combined to obtain the integrated prediction model.

7. The reinforced soil stress-strain prediction method based on temporal sequence and modal decomposition according to claim 4 is characterized in that: The method for obtaining the stress-strain prediction results of reinforced soil of the optimal combination learning model is: Among them, y test is the stress-strain prediction result of reinforced soil, W LSTM is the best validation set error of the long short-term memory network model, is the optimal long short-term memory network model, W XGB is the best validation set error of the XGBoost ensemble model, It is the optimal XGBoost ensemble model.

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