Data-physical hybrid driven advanced safety early warning method and equipment for tunnel construction

Abstract

The invention belongs to the field of tunnel construction, and discloses a data-physical hybrid-driven tunnel construction advanced safety early warning method and equipment, and the method comprises the steps: deducing a physical rule for calculating the ultimate bearing capacity of a tunneling working face from the working mechanism of an EPB tunnel boring machine; integrating the physical law into the loss function, and establishing a physical information deep neural network (PDNN) based on the physical law; the model performance is evaluated by predicting accuracy indicators, and the model is interpreted to check whether it is well constrained by physical laws. According to the method, by embedding physical-based constraints, the reasonability of the hidden variable relationship is ensured, and the reliability and the interpretability are improved. The method represents an important step of applying the PIML to tunnel construction, and the gap between a data driving method and domain knowledge is filled up.

Description

Technical Field

[0001] The present invention belongs to, but is not limited to, the technical field of tunnel construction, and in particular relates to a data-physics hybrid driven advanced safety warning method and device for tunnel construction. Background Art

[0002] With the acceleration of urbanization and continued population growth, the demand for the development and utilization of underground space has increased significantly, particularly in the field of tunnel construction. For example, as of 2019, Beijing had a permanent population of nearly 21 million and a total area of 16,410 square kilometers. It has built one of the world's largest subway systems, with 22 lines, 391 stations, and a total operating mileage of 637 kilometers. At the same time, with the widespread application of digital technologies and big data in engineering practice, the tunnel construction industry is undergoing a profound transformation. For example, modern tunnel boring machines (TBMs) can collect large amounts of data in real time during construction, providing important support for the application of machine learning (ML) in tunnel design and construction, particularly in providing information feedback and supporting decision-making. Although machine learning technology has been widely applied in tunnel engineering, relying on massive amounts of data obtained from geological surveys and equipment monitoring, existing methods still have room for improvement in terms of reliability and engineering interpretability. On the one hand, multi-step time series forecasting often suffers from the problem of precision degradation when the sample size is limited. On the other hand, traditional "black box" machine learning models lack engineering interpretability and physical consistency of their prediction results, making them difficult to meet the requirements of high-reliability engineering decision-making. To this end, researchers proposed and introduced the physical information machine learning (PIML) framework to integrate domain knowledge and data-driven methods to improve the generalization ability and physical consistency of the model, and further expanded the application of this method to tunnel engineering scenarios to meet the modeling and prediction challenges under complex construction conditions.

[0003] In recent years, earth pressure balance shield machines (EPB TBMs) have been widely used in urban tunnel excavation projects due to their efficient construction capabilities and minimal impact on the surrounding environment. The operating principle of EPB TBMs relies on the pressure balance between the underground soil and the earth ballast chamber. Therefore, earth ballast chamber pressure (SCP) has become one of the most critical operating parameters during tunneling. Typically, operators control SCP based on pre-excavation geological assessments and design parameters. However, due to the limitations of sensors in TBM equipment, current monitoring systems can only provide real-time information on soil pressure. If anomalies occur during construction, timely adjustments are often difficult, potentially adversely affecting construction safety and efficiency. Therefore, predicting SCP in advance is crucial for risk control and process optimization in tunnel construction. With the recent development of deep learning methods, time-series-based TBM parameter prediction has become a research hotspot. Among these, the gated recurrent unit (GRU) and long short-term memory (LSTM) network are two of the most widely used neural network architectures. However, these methods suffer from significant performance bottlenecks when processing datasets with small sample sizes and short time durations. Furthermore, when forecasting multi-step time series, model accuracy often decreases as the step size increases. This is because such models rely entirely on data patterns for training, making it difficult to break through the performance ceiling set by the data itself. In other words, traditional data-driven methods lack the physical constraints needed to accurately model the inherent relationships between variables, resulting in insufficient generalization and reliability in complex engineering applications.

[0004] On the other hand, traditional machine learning technology is often criticized as a "black box" model, that is, the model can receive input and output results, but it cannot provide users with a physically explainable reasoning process. When tunnel engineering problems rely entirely on data-driven machine learning models, engineers often find it difficult to understand the mechanism of action of variables within the model, and it is also difficult to trace how the input affects the output. In extreme cases, the model's prediction results may even violate known physical laws, which is unacceptable in engineering applications. For example, if the model performs well on certain data, but its prediction logic is inconsistent with the basic theory, its reliability on new samples will be greatly reduced. More seriously, the traditional unsupervised "black box" model lacks effective control over the model's behavior during training, resulting in the following key problems: (1) strong dependence on high-quality data and high data acquisition costs; (2) the model is difficult to reflect physical laws or engineering knowledge and lacks physical consistency; (3) when faced with new working conditions or unseen samples, the model's generalization ability is insufficient and the prediction performance is greatly reduced. PIML embeds physical laws, boundary conditions, or engineering prior knowledge into machine learning algorithms, effectively constraining the model's learning process. This allows it to maintain data-driven capabilities while also adhering to physical laws, thereby improving the model's interpretability, reliability, and generalization capabilities. This is precisely why PIML has shown broad application prospects in complex physical environments such as tunnel engineering.

[0005] PIML combines physics-based methods (such as physical laws and numerical simulation) with modern artificial intelligence (AI) technology. Its core advantages lie in: the former ensures the rationality and physical consistency of model predictions, while the latter significantly improves modeling efficiency and accuracy. However, due to the high complexity of real-world environments, accurate modeling based solely on physical laws is often difficult to achieve. Although decades of development in numerical simulation technology have enabled engineers and scientists to construct complex models with millions of degrees of freedom to approximate real-world conditions, such high-fidelity models often require enormous computing resources and struggle to meet the timeliness requirements of engineering practice. While simplified models offer higher computational efficiency, the idealized assumptions and simplifications they require can lead to significant prediction errors. In practical engineering applications, engineers often face a trade-off between accuracy and efficiency. While physics-based methods have strong theoretical support, they struggle to fully capture the complexity of real-world conditions. Data-driven machine learning methods, while offering powerful fitting capabilities, lack an understanding of the underlying physics. Therefore, relying solely on either approach is insufficient to effectively address complex tunnel engineering problems. Combining physical knowledge with data-driven methods not only helps improve the generalization and reliability of models but also provides a new technical path for intelligent tunnel engineering. However, to our knowledge, no research has successfully applied the PIML model, embedded with physical constraints, to the predictive analysis of actual TBM monitoring data in the context of real tunnel construction. The limited research currently available is mostly based on idealized conditions, validated with numerical simulations or experimental data, and lacks in-depth integration with measured engineering data. Therefore, successfully constructing and validating the PIML model based on measured TBM data under real-world conditions would bring significant theoretical and practical breakthroughs to this field and promote the development of intelligent tunnel construction technology.

[0006] In view of the above analysis, the technical problems that need to be urgently solved in the existing technology are: (1) excessive reliance on data-driven models, lack of physical interpretability, and data quality and quantity limitations significantly affect prediction performance; (2) lack of constraints on physical laws, and the prediction results may violate engineering reality; (3) the model has poor generalization ability to new working conditions or emergencies. Therefore, it is urgent to develop PIML methods that integrate physical knowledge and data learning to improve the reliability, real-time performance and interpretability of the model and promote the establishment of TBM intelligent risk identification and early warning systems. However, although PIML has shown its high reliability and interpretability in engineering problems, its application in tunnel construction, especially in real-world data, remains largely unexplored. Summary of the Invention

[0007] In response to the problems existing in the prior art, the present invention provides a data-physics hybrid driven advanced safety warning method for tunnel construction.

[0008] The present invention is achieved by providing a data-physical hybrid-driven tunnel construction advance safety warning method, characterized in that the data-physical hybrid-driven tunnel construction advance safety warning method specifically includes:

[0009] S1: Based on the working mechanism of EPBTBM, the physical laws for calculating the ultimate bearing capacity of the tunneling working face are derived;

[0010] S2: Incorporate physical laws into the loss function and establish a physical information deep neural network (PDNN) based on physical laws;

[0011] S3: Evaluate model performance through prediction accuracy metrics and interpret the model to check whether it is well-constrained by the laws of physics.

[0012] Furthermore, the working mechanism of the S1,EPBTBM can be expressed as follows:

[0013] σ TBM =σ' γ +σ w +σ s (1)

[0014] Among them, σ TBM represents the soil pressure inside the room σ' γ ,σ w , and σ s They represent the effective earth pressure, pore water pressure, and additional load on the ground, respectively. First, determining the lateral pressure of the soil and the pile load depends on the state of the TBM machine. Depending on the magnitude of the thrust, the equation for calculating SCP can be expanded to three different conditions. The SCP under different conditions can be calculated using the following formula:

[0015]

[0016] where γ' is the unit weight of the soil, which can be taken as the average value of all soil layers; γ w is the unit weight of water; h is the depth of the TBM; h w is the depth of the groundwater level; q is the additional load on the ground; K0, K a and K p are the lateral earth pressure coefficients under static, active and passive conditions, K0, K a and K p It can be estimated as:

[0017]

[0018] where φ is the friction angle of the soil.

[0019] Furthermore, the S2, according to σ TBMThe derivative of the tunnel depth can be derived as the ordinary differential equation (ODE):

[0020]

[0021] During TBM excavation, there are 6 sensors in the soil chamber to measure the soil pressure. Based on the measurement results of the 6 sensors, the change of SCP with depth can be calculated. The change should be equal to

[0022]

[0023] Among them, P bottom and P top represent the average SCP from the bottom and top sensors, respectively. bottom And P top It can be calculated as:

[0024]

[0025] Among them, P bottom,L and P top,L represent the bottom and top SCP measured by the left sensor, P bottom,R and P top,R Denote the top and bottom SCPs measured by the right sensor, respectively. By taking the measured middle SCP as output data, the loss function can be defined by adding the physical target to the general squared error function. The final loss function will consist of two parts, including the observation loss of the measurement error prediction and observation, and the physical loss of measuring the difference between the ideal and real physical mechanisms:

[0026]

[0027] Where λ is the weight of physical loss, is the SCP predicted by the DNN model.

[0028] Furthermore, the root mean square error (RMSE), mean absolute error (MAE), variance fraction (VAF), a20_index and R 2 Four performance indicators are used to comprehensively evaluate the model performance; the SHAP method is used to explain the relationship between the input and output parameters of the model. Its basic logic is to simplify the complex model into a linear form using the additive feature attribution method shown below:

[0029]

[0030] Where K measures the dimension of the input features, x' i represents the simplified i-th feature, φ iEnumerates the Shapley value of the target feature, which is a key coefficient of the technique that describes the importance of features. The Shapley base value is φ0, which is calculated as the average of the model output values.

[0031] The present invention also provides a data-physical hybrid driven advanced safety warning device for tunnel construction, comprising:

[0032] Multi-array earth pressure sensor module, data acquisition unit, edge computing module, deep neural network inference unit, physical supervision and control module and alarm output unit;

[0033] in,

[0034] The multi-array earth pressure sensor module is installed near the working face of the shield machine and is used to collect top and bottom earth pressure data in real time;

[0035] The data acquisition unit is connected to the sensor module and is used for data synchronization, calibration and preprocessing;

[0036] The edge computing module has a built-in ultimate bearing capacity model and a lateral earth pressure model to perform physical derivation and discrete gradient calculation;

[0037] The deep neural network inference unit uses the collected data and physically derived quantities as input to predict the soil pressure in the central area and perform continuous stiffness estimation;

[0038] The physical supervisory control module performs error correction on the neural network output according to the physical model constraints;

[0039] The alarm output unit outputs a warning signal based on a comparison result between the predicted earth pressure and a set safety threshold.

[0040] Furthermore, the edge computing module further includes:

[0041] a physical calculation unit configured to dynamically update parameters of an earth pressure model according to a tunneling depth, including soil unit weight, pore water pressure, lateral pressure coefficient, and additional load;

[0042] A gradient estimation unit is configured to calculate discrete gradients using bottom and top soil pressure sensor data, and compare the calculated gradients with derivative results of the ultimate bearing capacity model to form a physical error index for use in deep neural network training.

[0043] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0044] This invention significantly improves prediction accuracy with relatively small amounts of training data. The loss of precision in multi-step time series predictions is significantly reduced. This invention successfully controls deep learning models to adhere to fundamental mechanisms, making the models more reliable and easier to generalize. Even if other types of algorithms can still produce acceptable accuracy, the internal relationships between variables may still be illogical. With the stable support of physical laws, black-box models can follow engineering mechanisms through an unsupervised learning process. This successful experiment will significantly improve the reliability of deep learning technology and promote its application in tunnel construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is a flow chart of a data-physics hybrid driven tunnel construction advance safety warning method provided by an embodiment of the present invention;

[0046] Figure 2 This is the working mechanism of the EPB TBM provided by the embodiment of the present invention;

[0047] Figure 3 This is the general physical structure of the DNN network provided by the embodiment of the present invention;

[0048] Figure 4 The embodiment of the present invention provides a time series PDNN that embeds physical laws in the loss function;

[0049] Figure 5 The sensor installation in the EPB TBM provided by the embodiment of the present invention is as follows: (a) the EPB TBM chamber with the cutterhead removed, and (b) the layout and location of the SCP sensors;

[0050] Figure 6 The route planning and geological conditions of the Singapore C885 project provided by the embodiment of the present invention are as follows: (a) route planning; (b) geological conditions of IB; (c) geological conditions of OB;

[0051] Figure 7 is the distribution of SCPs provided by the embodiment of the present invention in the entire data set;

[0052] Figure 8 The training performance of the PDNN model provided by the embodiment of the present invention at different learning rates;

[0053] Figure 9 The training performance of the PDNN model provided by the embodiment of the present invention at different learning rates;

[0054] Figure 10 is the performance of the PDNN model with different weights λ of the physical law on (a) training data and (b) test data provided by an embodiment of the present invention;

[0055] Figure 11The performance of the model was evaluated by linear regression using (a) DNN, (b) GRU, (c) LSTM, (d) PDNN, and (e) physical law (best fit) according to an embodiment of the present invention, showing the sample density described from red (sparse) to blue (dense);

[0056] Figure 12 is the performance of the model provided by the embodiment of the present invention on (a) training data and (b) test data using different DNN algorithms and different sample numbers;

[0057] Figure 13 The present invention provides an embodiment of the present invention using (a) DNN and (b) PDNN to draw a Bland-Altman plot with a 99% confidence interval;

[0058] Figure 14 1 is a summary diagram of SHAP analysis of (a) PDNN and (b) DNN trained models provided by an embodiment of the present invention;

[0059] Figure 15 SHAP analysis results of tunnel depth in the models trained by (a) PDNN and (b) DNN provided in embodiments of the present invention;

[0060] Figure 16 The performance of the model using DNN, GRU, LSTM and PDNN to predict different time steps is provided in the embodiment of the present invention, and is evaluated by (a) RMSE, (b) MAE, (c) VAF, (d) a20_index and (e) R 2 ;

[0061] Figure 17 is the performance of the model provided by the embodiment of the present invention on (a) training data and (b) test data using different DNN algorithms with different numbers of samples to predict time step t+2;

[0062] Figure 18 is the performance of the model provided by the embodiment of the present invention on (a) training data and (b) test data, using different DNN algorithms and different numbers of samples for the prediction time step t+3. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0064] like Figure 1 As shown, an embodiment of the present invention provides a data-physical hybrid driven advanced safety warning method for tunnel construction, which specifically includes:

[0065] S1: Based on the working mechanism of EPBTBM, the physical laws for calculating the ultimate bearing capacity of the tunneling working face are derived;

[0066] S2: Incorporate physical laws into the loss function and establish a physical information deep neural network (PDNN) based on physical laws;

[0067] S3: Evaluate model performance through prediction accuracy metrics and interpret the model to check whether it is well-constrained by the laws of physics.

[0068] The outstanding feature of the S1 Earth Pressure Balance TBM is that it uses the excavated soil as a support medium. During excavation, the cutterhead excavates the soil and pushes it through the opening into the excavation chamber. The stability of the excavation face and the ground surface is controlled by monitoring and adjusting the earth pressure within the chamber to maintain a balance with the earth pressure in front of the cutterhead. Figure 2 As shown, the working mechanism of EPBTBM can be expressed as follows:

[0069] σ TBM =σ' γ +σ w +σ s (1)

[0070] Among them, σ TBM represents the soil pressure inside the room σ' γ ,σ w , and σ s They represent the effective earth pressure, pore water pressure and additional load on the ground respectively.

[0071] Theoretically, the calculation of SCP is not complicated, but directly using this equation to predict SCP faces many difficulties in practical applications. First, determining the lateral pressure of the soil and the pile load depends on the state of the TBM machine. Depending on the magnitude of the thrust, the equation for calculating SCP can be expanded to three different conditions. If the thrust is relatively small, the TBM working face will be subject to active lateral earth pressure, which is the lower limit of SCP during construction. According to the contract, if the thrust is relatively large, the TBM working face will be subject to passive lateral earth pressure, which is the upper limit. When the soil is not disturbed by TBM excavation, the TBM working face will be subject to static lateral earth pressure. SCP under different conditions can be calculated by the following formula:

[0072]

[0073] where γ' is the unit weight of the soil, which can be taken as the average value of all soil layers; γ w is the unit weight of water; h is the depth of the TBM; h w is the depth of the groundwater level; q is the additional load on the ground; K0, K aand K p are the lateral earth pressure coefficients under static, active and passive conditions, K0, K a and K p It can be estimated as:

[0074]

[0075] where φ is the friction angle of the soil.

[0076] During excavation, the SCP should be a value between the active and passive lateral earth pressures, depending on the TBM's operation, making it difficult to accurately estimate the SCP. Furthermore, there are other unknown or inaccurate parameters. For example, most of the additional load comes from the active load of the vehicle, which can only be accounted for by making conservative assumptions. As for the pressures from the soil and water, the information obtained from the borehole is always too discrete to provide a precise description. Therefore, the present invention develops a time series DNN model to overcome these shortcomings.

[0077] DNNs, developed from artificial neural networks (ANNs), consist of multiple hidden layers and are used to describe complex relationships and achieve better performance. Thanks to their complex structure, DNNs have a strong ability to map robust nonlinear relationships, which has been proven to be an effective method for predicting geological problems.

[0078] In S2, since the present invention aims to simulate the earth pressure during TBM excavation, DNN is selected as the basis for developing the PDNN algorithm to fully utilize its advantages in simulating complex geological relationships, especially to maintain the nonlinearity of the model. The physical laws in PDNN are integrated into the loss function. The general form of the physical constraint DNN is as follows: Figure 3 shown.

[0079] like Figure 3 As shown in Figure 1, the basic DNN structure is a multi-layer feedforward neural network. This structure consists of three main components: an input layer, a hidden layer, and an output layer, where the number of hidden layers is typically greater than two. Each layer consists of a varying number of neurons that transform information within the network. The value of each neuron is determined by transforming the weighted sum of the neurons in the previous layer using an active function:

[0080]

[0081] in represents the jth neuron in the i-th layer, is the weight of the corresponding neuron, b i is the additional bias in the i-th layer, and f(x) is the activation function to introduce nonlinearity into the DNN to control the convergence during training. In this study, the Tanh function is selected to activate neurons:

[0082]

[0083] The final output after multiple layers of activation will be a function of the input, weights, and biases.

[0084] In order to embed the physical laws into the loss function, various types of equations should be used depending on the simulation problem. In this paper, the physical laws proposed in equation (2) are incorporated into the loss function to control the training process, so that the trained model will follow the physical properties, the details of which are as follows Figure 4 As mentioned above, the SCP during excavation depends largely on the state of the thrust, and there will be three different situations. Therefore, it is important to simplify the problem by finding the general characteristics in the equation. According to σ TBM The derivative of the tunnel depth can be derived into an ODE:

[0085]

[0086] It can be clearly seen that Its derivative is always a constant under all conditions. In this case, the uncertainty of groundwater level and surcharge is also eliminated.

[0087] As the equations are simplified to a general physical law, a new objective can now be added to the loss function to evaluate the adaptability of the trained model to the physical rules. During the TBM excavation process, there are 6 sensors in the soil chamber to measure the soil pressure, such as Figure 5 According to the measurement results of the six sensors, the change of SCP with depth can be calculated, which should be equal to

[0088]

[0089] Among them, P bottom and P top represent the average SCP from the bottom and top sensors, respectively. bottom And P top It can be calculated as:

[0090]

[0091] Among them, P bottom,L and P top,L represent the bottom and top SCP measured by the left sensor, P bottom,R and P top,R Represent the top and bottom SCP measured by the right sensor, respectively.

[0092] By taking the measured intermediate SCP as output data, the loss function can be defined by adding the physical objective to the general squared error function. Therefore, the final loss function will consist of two parts, the observation loss for the measurement error prediction and observation, and the physical loss for measuring the difference between the ideal and real physical mechanisms:

[0093]

[0094] Where λ is the weight of the physical loss is the SCP predicted by the DNN model. In addition to accuracy, the new loss function further considers the physical logic in the model. Therefore, it is expected that models trained using the PDNN algorithm will be more accurate, less overfitted, and better reflect the engineering mechanism.

[0095] Algorithm 1 illustrates the proposed DNN algorithm using physical laws.

[0096]

[0097]

[0098] In particular, the present invention considers time series prediction, which uses data from historical time steps to predict future time steps. In this study, each ring was considered as a time step to track the excavation process. Therefore, the operator will notice possible anomalies when excavating the next few rings. Since the tunnel depth of the latest step is closest to the actual depth of the next ring, the change in tunnel depth over time is not considered. In tunnel construction, other traditional time series prediction methods only learn from historical data and lack the reliability of controlling physical laws that cannot be considered in normal deep learning models. Alternatively, PDNN learns from historical data and controlling physical laws simultaneously, so the trained model can be well constrained and responds well to the working mechanism of the EPB TBM.

[0099] In S3, the model is evaluated and interpreted using root mean square error (RMSE), mean absolute error (MAE), variance fraction (VAF), a20_index, and R 2 The four performance indicators are used to comprehensively evaluate the model performance. Their efficiency in evaluating prediction accuracy has been proven by many studies. The calculation is as follows:

[0100]

[0101]

[0102] Where n is the measurement sample size, and y describe the predicted and observed values, Calculated based on the average value of all samples, m 20 Describes the sample size with an error of no more than ±20% of the observations. For an ideal model, RMSE and MAE are expected to be equal to 0, VAF, a20_index, R 2 are all equal to 1. In engineering problems, it is of special significance to use a20_index to measure the reliability of a model with a 20% tolerance.

[0103] In addition to improving prediction accuracy by using PIML, the model will also be constrained to follow the laws of physics. The PIML model naturally brings interpretability, but its effectiveness still needs to be tested. This is an important part of testing the superiority of the PDNN method by revealing the hidden relationship between the input and output variables. If the model produces some unreasonable relationships, it cannot be regarded as reliable even if it has acceptable accuracy, especially in the engineering field. In addition, those variables that are excluded from the laws of physics still lack interpretability. Therefore, it is necessary to adopt explainable artificial intelligence (XAI) technology to reveal the hidden relationship between input and output. Since the SHAP method can explain the black box model, the present invention adopts the SHAP method. Its basic logic is to simplify the complex model into a linear form using the additive feature attribution method as shown below:

[0104]

[0105] Where K measures the dimension of the input features, x' i represents the simplified i-th feature, φ i Enumerate the Shapley value of the target feature, which is a key coefficient of the technology that describes the importance of the feature. The Shapley base value is φ0, which is calculated as the average of the model output values. Simplified process x'∈{0,1} K Each feature in the sample is mapped to a value through the transformation function. If x' i = 0, this feature has no effect on the output, indicating that the Shapley value is 0. If x' i =1, the Shapley value will be determined directly from the observed value. Specifically, the Shapley value can be calculated as follows:

[0106]

[0107] where S collects all non-zero entries, N contains all features, and f x (S) is derived from the output of the original model, f x (S) = E[f(x)|x S ].

[0108] The specific application fields or related products of the present invention.

[0109] (1) Case Background

[0110] This paper takes Singapore C885 project tunnel as a case study. This paper uses the data measured by EPBTBM. Figure 6 As shown, this construction project, located in the heart of Singapore's Central Business District, consists of two tunnels under the Singapore Circle Line, connecting Cantonment Station and Prince Edward Road Station. The tunnels are 1.003 kilometers long and range in depth from 10 to 20 meters. The permanent tunnel lining consists of 718 tunnel rings, each composed of seven precast segments. Tunneling was carried out using an EPB TBM with an outer diameter of 6.68 meters and a total length of 9.81 meters. The outer boundary (OB) tunnel was constructed first, followed by the inner boundary (IB) tunnel. TBM data recorded from the IB construction was used to train the model.

[0111] The entire dataset contains hundreds of active and passive parameters that indicate the TBM's state. However, many parameters are highly correlated, and some contain a large amount of missing data. Therefore, to avoid redundancy and improve computational efficiency, only four basic TBM active parameters were considered to predict SCP, including total thrust (TF), penetration rate (PR), cutterhead torque (CT), and screw conveyor torque (SCT). Among these parameters, TF, PR, and CT primarily control the TBM machine's propulsion, while SCT and SCP are directly related to the chamber pressure. In addition to these TBM parameters, tunnel depth is the most important feature as it governs the physical laws in the method.

[0112] The geological conditions encountered in the project were categorized into three types: marine clay, Jurong Formation Types III-IV, and Jurong Formation Types V-VI. However, the geological data measured during the field survey was too coarse to accurately reflect the soil characteristics surrounding each tunnel ring. As explained in the methodology, the estimated geological parameters were always too inaccurate to be used for model training. As many researchers have pointed out, TBM parameters can be used to reflect geological conditions through machine learning methods. Therefore, the present invention does not select additional geological parameters as input features, thus avoiding the unreliability of geological parameters.

[0113] All TBM features except tunnel depth consider three historical steps (t, t-1, t-2) to predict SCP. No more historical steps are considered to ensure that soil conditions do not change significantly. For tunnel depth, only the latest time step is calculated for derivative calculation. In addition, the depth of the most recently constructed ring is closer to the depth of the future step, which is more reliable for prediction and reflects the laws of physics. The details of the input features are shown in Table 1. Since the input features include time series data, the input parameters at time step t are statistically analyzed and plotted in Figure 7 middle.

[0114] Table 1 Features considered in DNN model training

[0115]

[0116] *Based on data at time step t.

[0117] (2) Model development

[0118] After filtering out some unavailable data measured in 718 rings, 660 samples were used to train the PDNN model. The distribution of SCP values in these samples is shown in Figure 2. Figure 8 As shown, the majority of samples are concentrated in the range of 180 kPa to 220 kPa. Another local peak frequency occurs between 260 kPa and 280 kPa. 75% of these samples were randomly selected as the training dataset, and the remainder as the test dataset. Input features were processed using the min-max normalization method according to the following equation. The spacing between the top and bottom SCP sensors is approximately 4.29 meters.

[0119] To test the superiority of using physical laws in the loss function, hyperparameters were adjusted based on a standard DNN model. Considering the small size and simple structure of the dataset, the hyperparameters were determined by trial and error for ease of implementation and computational efficiency. Table 2 summarizes the details of the test candidates and optimized values. Figure 9 It can be seen that when the learning rate is 0.01, the training process converges faster and does not converge to the local optimum. When the learning rate is too small (0.001), the algorithm is difficult to converge. When the learning rate is too large (0.05), the algorithm may converge to the local optimal solution, which will affect the accuracy of the model. After the DNN model is properly trained, the weight of the physical loss is determined to train the PDNN model. Figure 10 As shown, the model performance λ was tested in the range of 0 to 1, and it was found that the best performing model was trained with λ = 0.5, which represents the equal importance of observation and physical losses. In addition, it can be said that when training a model using real-world measurement data, the laws of physics can only be used as constraints to limit the training process.

[0120] Table 2 Hyperparameters used in PDNN model training

[0121]

[0122] *After obtaining the best DNN model, determine the weight of the physical loss.

[0123] To demonstrate the superiority of the PDNN approach, additional models were trained using the DNN, GRU, and LSTM approaches with the same training (and testing) datasets and network architectures for comparison. As mentioned above, the baseline DNN model consists of three layers with 10 neurons in each layer. The training of the LSTM and GRU models follows the same settings as the baseline model, except that the hidden layers are replaced by LSTM and GRU layers, respectively. Considering that PDNN, LSTM, and GRU are all advanced DNNs, keeping the same hyperparameter settings as the baseline DNN model ensures a fair comparison as much as possible. Any advantages of these advanced models should benefit from their network architectures, providing clear evidence for the analysis of the results. In addition, the results predicted by various DNN networks were compared with the results simulated using the physical laws in Equation (2). Since the TBM state is inconsistent with the recorded data, a set of best results that conform to the physical laws was obtained by searching for the most accurate estimates using static, active, and passive equations. The geological parameters were collected from the site investigation report. According to the design report of Singapore Contract 855, the pile load was assumed to be 20 kPa and the groundwater level was at the surface. The detailed results and corresponding analysis are discussed in the next section.

[0124] (3) Results analysis

[0125] Model performance is measured by RMSE, VAF, a20_index, and R 2 The measurements were performed using DNN, GRU, and LSTM. The PDNN and physical laws are reported in Table 3, and the linear regression of the predicted results is plotted in Figure 11 Since no model training is required, all samples are used as the test dataset when using physical laws. In addition to physical laws, all four deep learning network models were further examined using different dataset sizes, ranging from 20%, 40%, 60%, and 80% of the original dataset. Figure 12 Summarizes the performance. Figure 13 In particular, the significance of the prediction errors using DNN and PDNN at 99% confidence intervals was examined. Finally, the impact of using physical laws in the algorithm was studied using SHAP, focusing on models trained using DNN and PDNN. The SHAP analysis results are shown in Figure 2. Figure 14 and Figure 15 The research results are summarized as follows:

[0126] (1) Using only physical laws cannot accurately estimate SCP. According to Table 2, the performance of using equations for prediction under static, active, and passive conditions is always poor, where the best result using the active equation can only reach R 2-4.30. After manually selecting the best fitting equation for estimation, a20_index reached 0.99, which has a relatively high reliability in the engineering sense. However, the overall accuracy is still low, R 2 -0.18. As emphasized in previous sections, such a large error primarily stems from inaccuracies in soil parameters and assumptions about unknown information. Unlike other safety-related design criteria, the SCP is an operational parameter whose prediction should be as accurate as possible. Therefore, the use of artificial intelligence techniques to achieve more reliable results is crucial.

[0127] (2) Compared with traditional deep learning techniques, PDNN can perform self-verification without setting any verification dataset, effectively preventing overfitting while maintaining high prediction accuracy. As shown in Table 2, R 2 The scores of DNN, GRU, LSTM and PDNN on the training data are 0.9, 0.98, 0.98 and 0.97 respectively, among which PDNN has no obvious advantage. However, compared with other algorithms, PDNN performs best on the test data, with aR 2 is 0.96 and RMSE is 7.09 kPa, which is the least overfitting. If the physical law is not adopted, the RMSER of DNN 2 and RMSE are only 0.92 and 9.46 kPa respectively. GRU improves these two standards to 0.94 and 8.47 kPa. LSTM has similar performance to PDNN, aR 2 is 0.95, and the RMSE is 7.47 kPa, but the model is overfitted. In addition, it can be seen that according to Figure 13 , all residuals using the PDNN method are within or very close to the 99% confidence interval. However, two obvious outliers are observed using the DNN method. Based on this result, it can be seen that the PDNN method produces more stable prediction results by eliminating significant outliers and is more reliable in practical applications.

[0128] (3) PDNN significantly outperforms other methods when processing small-scale datasets. Compared with DNN and PDNN, GRU and LSTM are more sensitive to data volume, and their accuracy drops rapidly when 20% or more samples are discarded. This finding is supported by a study conducted by Yan et al. in 2019, which showed that LSTM is not suitable for analyzing short, small-scale time series data. In contrast, simple deep learning (used for DNN and PDNN) structures have been shown to have lower sample size requirements. Figure 12 As can be seen, with the use of DNN and PDNNR 2 As the dataset size grows, the value of the training data gradually decreases, while the value of the test data increases, which indicates that the model is more likely to overfit with less data. In addition, R2 Even with 20% of the data, the PDNN model is still able to achieve 0.84, which is an excellent performance compared to other algorithms. Therefore, it is reasonable to conclude that the adoption of physical laws in deep learning algorithms significantly improves the model's ability to handle small sample sizes, which has made great progress in the application of deep learning to tunnel problems.

[0129] (4) After adopting the physical laws, the PDNN model shows higher rationality and reliability by accurately describing the relationship between SCP and tunnel depth. Referring to equation (2), the soil pressure is affected by the unit weight and depth of the tunnel. Figure 14 and Figure 15 It can be seen that the SHAP value is always positive as the tunnel depth (x1) increases, and negative otherwise. Figure 14 In the figure, it can be seen that after incorporating physical laws into the algorithm, the SHAP values for tunnel depth become more concentrated. This makes sense because the samples were obtained from the same track. For adjacent tunnel rings with similar depth and soil conditions, the effect of tunnel depth on SCP will naturally be similar. Furthermore, the PDNN model reflects a perfect positive correlation between tunnel depth and its SHAP value, while the model trained without physical laws exhibits unreasonable fluctuations in this relationship. Since soil generally becomes denser (increases unit weight) in deeper soil layers, the influence of depth also increases as tunnels are built deeper. Therefore, if the model is well constrained by physical laws, the significance of depth should also follow this trend. The results show that the PDNN model significantly improves the reliability, rationality, and interpretability of the engineering mechanism.

[0130] Table 3 Model performance using physical laws and different DNN algorithms to predict time t+1

[0131]

[0132]

[0133] A model with three-step output is trained using DNN, GRU, LSTM, and PDNN. The algorithm settings are the same as in the case study. Model performance measured by RMSE, VAF, a20_index R 2 Summarized in Table 4 and plotted in Figure 16 The models for predicting time t+2 and t+3 were also tested using 20%, 40%, 60% and 80% of the data set, and the results are as follows: Figure 17 and Figure 18 The results of this analysis can be summarized as follows:

[0134] (1) All algorithms perform worse in predicting the future, but the model trained with PDNN is the least affected. The degradation of accuracy in multi-step time series forecasting has been a major problem in the field. Since the laws of physics are not employed (DNN, GRU, and LSTM), the model tends to overfit more and more when predicting further time steps. 2 When using DNN, the performance of the test data dropped from 0.92 to 0.89, when using GRU, it dropped from 0.94 to 0.89%, and when using LSTM, it dropped from 0.95 to 0.90. In contrast, except for the DNN model whose performance on the training data remained fairly stable, the RMSE of the training data decreased from 4.92 kPa to 1.77 kPa and from 4.61 kPa to 1.88 kPa when using GRU and LSTM, respectively. However, in the case of PDNN, the performance of the model on both training and test data dropped, with R 2 On the training data, the accuracy gradually decreased from 0.97 to 0.96, then to 0.95, and on the test data, it gradually decreased from 0.96 to 0.94, and then to 0.93. This further proves that using physical laws in deep learning can effectively prevent model overfitting and maintain high accuracy. This makes PDNN very effective in multi-step time series forecasting problems.

[0135] (2) The advantage of PDNN in processing small datasets is maintained while predicting multiple time steps. Similar to the prediction time t+1, when predicting time t+2 and t+3, the models trained with GRU and LSTM are very sensitive to the dataset size. When the data is less than 80%, the model performance drops rapidly. For DNN and PDNN, the two algorithms are still less affected by the data size, among which the model trained by PDNN outperforms the other algorithms. In addition, it can be found that the trend of accuracy decay occurs regardless of the size of the dataset. For example, when only 20% of the data is used, R 2 The ratio of the test data decreases from 0.84 to 0.83 and then to 0.81. Therefore, the stability and reliability of PDNN in multi-step time series forecasting are further demonstrated.

[0136] Table 4. Model performance for prediction time steps t+1 to t+3 using different DNN algorithms.

[0137]

[0138] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware portion can be implemented using dedicated logic; the software portion can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. Those skilled in the art will appreciate that the above-mentioned devices and methods can be implemented using computer-executable instructions and / or contained in processor control code, for example, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, or can be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0139] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A data-physics hybrid driven tunnel construction advanced safety warning method, characterized by: The following steps are involved: (1) Based on the structure and stress mechanism of the earth pressure balance shield tunneling machine, a model of the ultimate bearing capacity of the tunneling working face is constructed. The bearing capacity is composed of effective earth pressure, pore water pressure and additional load pressure; (2) Establish lateral earth pressure models under three working conditions, corresponding to the static state, active failure state, and passive failure state, respectively, and introduce soil unit weight, water unit weight, excavation depth, groundwater level depth, additional load, soil friction angle, cohesion, and lateral pressure coefficient parameters; (3) Based on the excavation depth, the first-order derivative of the ultimate bearing capacity model is calculated to derive the constant corresponding relationship between the depth change and the bearing capacity change. The constant depends on the lateral pressure coefficient and unit weight under different working conditions; (4) Using the top and bottom soil pressure data obtained by multiple sets of upper and lower sensor arrays, a discrete expression of the depth-direction soil pressure difference is constructed; (5) Construct a weighted loss function that includes measurement error terms and physical error terms, and introduce the error between the discrete gradient calculated based on sensor measurement data and the model predicted gradient as a physical supervision term into the neural network training process; (6) Establishing and training a deep neural network structure, the soil pressure measured by the central sensor is used as the model prediction target output, and the model parameter update is guided by the weighted loss function; (7) The performance of the neural network is evaluated by using root mean square error, mean absolute error, variance explanation rate, determination coefficient and custom threshold indicators, and the feature attribution method based on Shapley value is used to explain the importance of input variables.

2. The method according to claim 1, wherein The ultimate bearing capacity model of the excavation working face is: the algebraic sum of the effective earth pressure, the pore water pressure and the additional load pressure.

3. The method according to claim 1, wherein The lateral pressure coefficient is "1 minus the sine of the soil friction angle" in the static state, "tangent function 45 degrees minus half the square of the soil friction angle" in the active state, and "tangent function 45 degrees plus half the square of the soil friction angle" in the passive state.

4. The method according to claim 1, wherein The theoretical derivative of the depth gradient is a constant under the three working conditions, and is respectively formed by multiplying the lateral pressure coefficient by the sum of the soil unit weight and the water unit weight.

5. The method according to claim 1, wherein The bottom and top soil pressures are respectively the average values of the values measured by the left and right bottom sensors and the average value of the value measured by the top sensor, and the difference between them is divided by the distance between the upper and lower sensors as the discrete gradient approximation.

6. The method according to claim 1, wherein The loss function is a weighted sum of a prediction error term and a physical error term, where the physical error term is defined as the squared difference between the model prediction gradient and the measured gradient, and the prediction error term is the squared difference between the measured value and the model output value.

7. The method according to claim 1, wherein The feature attribution method expresses the model as a linear combination of the benchmark output and the Shapley values corresponding to several features, where each Shapley value corresponds to the marginal contribution of an input variable to the model prediction.

8. A data-physical hybrid driven tunnel construction advanced safety warning device, characterized by: include: Multi-array earth pressure sensor module, data acquisition unit, edge computing module, deep neural network inference unit, physical supervision and control module and alarm output unit; in, The multi-array earth pressure sensor module is installed near the working face of the shield machine and is used to collect top and bottom earth pressure data in real time; The data acquisition unit is connected to the sensor module and is used for data synchronization, calibration and preprocessing; The edge computing module has a built-in ultimate bearing capacity model and a lateral earth pressure model to perform physical derivation and discrete gradient calculation; The deep neural network inference unit uses the collected data and physically derived quantities as input to predict the soil pressure in the central area and perform continuous stiffness estimation; The physical supervisory control module performs error correction on the neural network output according to the physical model constraints; The alarm output unit outputs a warning signal based on a comparison result between the predicted earth pressure and a set safety threshold.

9. The device according to claim 8, characterized in that The edge computing module further includes: a physical calculation unit configured to dynamically update parameters of an earth pressure model according to a tunneling depth, including soil unit weight, pore water pressure, lateral pressure coefficient, and additional load; A gradient estimation unit is configured to calculate discrete gradients using bottom and top soil pressure sensor data, and compare the calculated gradients with derivative results of the ultimate bearing capacity model to form a physical error index for use in deep neural network training.

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