Dam deformation behavior analysis method and system

Abstract

The invention provides a dam deformation behavior analysis method and system, and belongs to the field of dam safety monitoring, and the method comprises the steps: obtaining InSAR data and Beidou monitoring data covering a target dam region, and carrying out the preprocessing; physical factors influencing dam deformation are analyzed, modeling of a deformation model is carried out, and a modeling rule is used for guiding training and prediction of a physical constraint deep learning model; constructing a physical constraint deep learning model; training and optimizing a physical constraint deep learning model by using the preprocessed InSAR data and Beidou monitoring data; and inputting to-be-analyzed dam InSAR data and Beidou monitoring data into the optimized physical constraint deep learning model to obtain a deformation analysis result of the dam. According to the invention, the problem that the existing dam deformation monitoring technology is insufficient in consideration of space coverage, monitoring precision, automation degree and physical factors is overcome.

Description

Technical Field

[0001] The present invention belongs to the field of dam safety monitoring, and in particular relates to a dam deformation behavior analysis method and system. Background Art

[0002] As crucial water conservancy infrastructure, dams play an irreplaceable role in flood control, power generation, irrigation, and water supply. Their safe operation is directly linked to the safety of life and property in downstream areas, as well as the stable socioeconomic development. Therefore, real-time monitoring and precise analysis of dam deformation behavior have long been a research priority in the engineering field. Traditional dam deformation monitoring methods primarily include leveling, total station measurements, and Global Navigation Satellite System (GNSS) measurements. These methods provide highly accurate point-to-point deformation information and are widely used for dam safety monitoring. However, limited by the density of monitoring equipment and observation frequency, these traditional methods lack significant spatial coverage, automation, and cost-effectiveness, making them inadequate for comprehensive dam deformation monitoring in large-scale, complex environments.

[0003] In recent years, with the advancement of remote sensing technology, interferometric synthetic aperture radar (InSAR) has emerged as an emerging method for dam deformation monitoring. InSAR utilizes radar wave phase difference information to acquire surface deformation data over large areas with centimeter- or even millimeter-level accuracy. This technology offers the advantages of wide coverage and non-contact measurement. However, in practical applications, this technology is susceptible to interference from factors such as atmospheric delay, temporal decoherence, and difficulties in phase unwrapping, which can affect the reliability and stability of deformation monitoring results. Furthermore, the complex processing of InSAR data requires high computing resources and specialized technical expertise, limiting its widespread application in real-time dam monitoring. Meanwhile, the Beidou satellite navigation system, an independently developed global satellite navigation system, has demonstrated significant potential in high-precision positioning. Using real-time kinematic (RTK) or precise point positioning (PPP), the Beidou system can achieve sub-centimeter-level positioning accuracy, which has been verified in multiple dam deformation monitoring cases. Compared to traditional GNSS, the Beidou system offers unique advantages in signal coverage, anti-interference capabilities, and autonomous controllability. Combining InSAR technology with BeiDou system data can achieve complementary advantages: InSAR provides a wide range of surface deformation information, while BeiDou data provides high-precision, high-frequency deformation monitoring results for key points, thus forming a more comprehensive and reliable basis for dam deformation property analysis.

[0004] In recent years, deep learning technology has demonstrated powerful data processing and analysis capabilities in the fields of Earth observation and engineering monitoring. By constructing neural network models, deep learning can mine complex nonlinear relationships from massive amounts of monitoring data, improving the accuracy of deformation prediction. However, deep learning methods that rely solely on data often lack the constraints of physical laws, resulting in insufficient generalization. When faced with unseen data or extreme working conditions, predictions can deviate from physical reality, making them difficult to interpret from an engineering perspective. To address this issue, physics-informed machine learning (Physics-Informed Machine Learning) has emerged. By incorporating physical constraints (such as mechanical equations and boundary conditions) into the deep learning framework, this approach not only improves the model's prediction accuracy and physical plausibility, but also enhances the interpretability of the results, making them more applicable to engineering practice. Although existing methods exist for dam deformation monitoring using InSAR or BeiDou satellites alone, as well as research on applying deep learning to remote sensing data analysis, these approaches are mostly developed independently and fail to fully exploit the synergistic potential of multi-source data. In particular, research on effectively fusing InSAR and Beidou data, combined with physical constraints and deep learning techniques, to construct comprehensive methods for intelligent diagnosis of dam deformation behavior remains relatively scarce. Existing deformation monitoring technologies often exhibit problems such as insufficient adaptability, poor synergy between data and mechanisms, and poor real-time performance when faced with complex environments (such as extreme weather and geological changes). Furthermore, while traditional numerical simulation methods can analyze dam behavior by integrating physical mechanisms, they place extremely high demands on data quality and boundary conditions, and the computational process is time-consuming, making them unable to meet the urgent needs of real-time monitoring and early warning. Traditional dam deformation monitoring methods, such as manual measurement (total stations or levels), global navigation satellite systems (GNSS), and optical total stations, have significant limitations in practical applications. Manual measurement is time-consuming and labor-intensive, providing only discrete point data and making it difficult to achieve continuous, wide-area monitoring of the dam and surrounding areas. While GNSS offers automation capabilities, its accuracy is susceptible to interference from satellite visibility and multipath effects. Optical total stations are subject to line-of-sight obstructions and environmental factors in complex terrain or inclement weather, resulting in insufficient temporal and spatial resolution for comprehensive, real-time assessments of dam safety. While synthetic aperture radar interferometry (InSAR) technology enables high-precision monitoring over large areas, it is limited by atmospheric delay, temporal and geometric incoherence, difficulties in phase unwrapping, and low sensitivity to deformation in specific directions. Furthermore, the resolution of free data is limited, reducing reliability in areas with dense vegetation or smooth surfaces. Errors are easily introduced when decomposing line-of-sight deformation into three-dimensional components, making it difficult to provide consistently accurate deformation information in isolation. The Beidou satellite navigation system performs excellently in positioning accuracy and signal coverage, but high-precision equipment can only obtain single-point results and needs to be combined with other technologies to improve performance.Furthermore, existing InSAR and BeiDou data fusion methods lack the technology to effectively integrate spatial and time series information. Simple overlays fail to fully leverage their complementary advantages and cannot achieve the monitoring goals of high precision, high spatiotemporal resolution, and wide coverage. Existing deep learning models often lack constraints on the physical properties of dams in deformation analysis. Purely data-driven predictions struggle to ensure physical rationality, and generalization capabilities are limited when training data is insufficient. This results in insufficient reliability and engineering applicability of analysis results under complex working conditions. In summary, existing technologies are deficient in spatiotemporal coverage, monitoring accuracy, automation, and physical rationality, necessitating an urgent need for a comprehensive solution.

[0005] In summary, there is an urgent need to develop an intelligent diagnosis method for dam safety status that integrates multi-source data fusion, physical constraints and deep learning technology to overcome the limitations of existing technologies, improve the accuracy, reliability and real-time performance of dam deformation monitoring, and provide more scientific and efficient technical support for ensuring the safe operation of dams. Summary of the Invention

[0006] In response to the above-mentioned deficiencies in the prior art, the present invention provides a dam deformation behavior analysis method and system. The purpose of the present invention is to overcome the problems of the existing dam deformation monitoring technology in terms of insufficient spatial coverage, monitoring accuracy, degree of automation and consideration of physical factors.

[0007] In order to achieve the above objectives, the present invention adopts a technical solution: a dam deformation state analysis method, comprising the following steps: S1. Obtain InSAR data and BeiDou monitoring data covering the target dam area and perform preprocessing; S2. Analyze the physical factors that affect dam deformation and model them. The modeling rules are used to guide the training and prediction of the physical constraint deep learning model. S3. Build a physical constraint deep learning model; S4. Use the pre-processed InSAR data and BeiDou monitoring data to train and optimize the physical constraint deep learning model; S5. Input the InSAR data and Beidou monitoring data of the dam to be analyzed into the optimized physical constraint deep learning model to obtain the deformation analysis results of the dam and complete the analysis of the deformation properties of the dam.

[0008] Furthermore, the S1 is specifically: Acquire InSAR data covering the target dam area and preprocess the InSAR data, where the InSAR data is vertical deformation value; Acquire Beidou monitoring data and preprocess it to obtain the three-dimensional displacement time series (X, Y, Z) of the monitoring points, where the deformation in the X and Y directions serves as a supplement to the overall deformation of the dam; The preprocessed InSAR data are aligned with the three-dimensional displacement time series in time and space to fuse the InSAR data and Beidou monitoring data to complete the preprocessing process.

[0009] Furthermore, the physical factors include the water level of the reservoir and ambient temperature changes , the dam deformation caused by the reservoir water level H(t) is driven by hydrostatic pressure; the ambient temperature changes The deformation of the dam is affected by the thermal expansion effect.

[0010] Furthermore, the modeling of the physical factors includes: The dam deformation caused by the reservoir water level H(t) is:

[0011]

[0012] in, represents the dam deformation caused by the reservoir water level H(t), represents the pressure deformation coefficient, represents the hydrostatic pressure, represents the water density, represents the acceleration due to gravity; Dam deformation caused by thermal expansion effect , which is:

[0013] in, represents the thermal expansion coefficient of the material, Represents the local characteristic length of the dam body. Furthermore, the loss function of the physical constraint deep learning model is expressed as follows:

[0014]

[0015]

[0016]

[0017]

[0018] in, represents the loss function of the physical constraint deep learning model, represents the deformation data loss function, and Both represent weighting coefficients, used to balance the importance of loss, represents the deformation caused by the hydrostatic pressure of the water level, represents the temperature loss function, represents the local characteristic length of the dam body, represents the regularization coefficient, represents the number of observation points, i represents an observation point, represents the solution predicted by the neural network, The true value of the deformation, represents the hydrostatic strain-deformation conversion coefficient, represents the theoretical strain calculated by the hydrostatic pressure formula, represents the spatial and temporal coordinates of the data points, represents the hydrostatic pressure, represents the thermal expansion coefficient of the material, represents the theoretical strain due to temperature, Indicates additional constraints based on the difference between predicted and physical values, Indicates systematic error.

[0019] Furthermore, the physical constraint deep learning model includes: The input layer is used to receive multiple data sources and perform normalization on them; the data sources include InSAR deformation data , Beidou displacement time series And auxiliary information; auxiliary information is reservoir water level and temperature changes ; The spatial feature extraction branch is used to extract the normalized InSAR deformation data. , using convolutional neural networks to extract the spatial distribution characteristics of the dam surface deformation and output spatial feature tensors ; The time feature extraction branch is used to extract the normalized Beidou displacement time series. Extract features with auxiliary information and output temporal feature tensor ; Physical branch layer, used to transform the temporal feature tensor Spatial feature tensor Perform splicing. Based on the splicing results, use the convolution layer to extract physical features, and use the maximum pooling layer to compress the data size. The output layer is used to obtain the deformation analysis results of the dam based on the compressed physical characteristics.

[0020] The present invention also provides a dam deformation state analysis system, comprising: The first processing module is used to obtain InSAR data and BeiDou monitoring data covering the target dam area and perform preprocessing; The second processing module is used to analyze the physical factors that affect dam deformation and model the physical factors. The modeling rules are used to guide the training and prediction of the physical constraint deep learning model; The third processing module is used to build a physical constraint deep learning model; The fourth processing module is used to train and optimize the physical constraint deep learning model using pre-processed InSAR data and BeiDou monitoring data; The fifth processing module is used to input the InSAR data of the dam to be analyzed and the Beidou monitoring data into the optimized physical constraint deep learning model to obtain the deformation analysis results of the dam and complete the analysis of the deformation properties of the dam.

[0021] Beneficial effects of the present invention: (1) The present invention provides a method for analyzing the deformation behavior of dams by using interferometric synthetic aperture radar (InSAR) and BeiDou satellite navigation system data, combined with physical mechanism constraints and deep learning technology. This method aims to fully utilize the advantages of InSAR technology in spatial continuity and the capability of BeiDou system in high-precision point monitoring. By efficiently integrating multi-source data and combining the physical characteristics of the dam (such as material properties, structural characteristics, water pressure, etc.), a physical constraint deep learning model is constructed to achieve accurate, reliable and intelligent analysis of the deformation behavior of the dam. By introducing the physical information neural network (PINN) framework, the present invention ensures that the prediction results conform to the laws of mechanics and engineering practice, improves the generalization ability and interpretability of the model, and solves the problems of limited spatiotemporal resolution of traditional methods, environmental interference of InSAR data quality, insufficient BeiDou coverage and lack of physical constraints in existing deep learning. Ultimately, the present invention aims to provide a high-precision, high-efficiency and wide-coverage automated technical means for dam safety monitoring, provide a scientific basis for real-time evaluation of dam operation status, abnormal deformation detection and future trend prediction, and ensure the safe operation of the dam and the safety of life and property of people in downstream areas.

[0022] (2) By fusing InSAR spatial information with BeiDou's high-precision point information and incorporating physical constraints, this method can more accurately reflect the true deformation state of the dam. The introduction of physical constraints improves the physical rationality of the prediction results, reduces noise interference, and achieves higher accuracy and reliability.

[0023] (3) The present invention uses InSAR to provide the overall deformation field of the dam and its surrounding areas, and Beidou provides three-dimensional displacement information of key points. Combining the two can obtain more comprehensive dam deformation information.

[0024] (4) The deep learning-based model of the present invention can automatically extract deformation features, realize intelligent analysis and prediction of dam deformation properties, reduce manual intervention, improve efficiency, and has automation and intelligence.

[0025] (5) Potential predictive ability: By learning from historical data, the model can predict the deformation trend of the dam in the future, providing a scientific basis for dam safety management and risk prevention.

[0026] (6) This invention deeply integrates InSAR and BeiDou data and innovatively incorporates physical constraints into the deep learning model, overcoming the limitations of a single data source, improving the accuracy and reliability of deformation analysis, and providing a more advanced technical means for dam safety monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Flow chart of the method of the present invention.

[0028] Figure 2 Schematic diagram of the physical constraint deep learning model PINN.

[0029] Figure 3 Schematic diagram of another physical constraint deep learning model PINN.

[0030] Figure 4 Schematic diagram of InSAR dam monitoring results.

[0031] Figure 5 Schematic diagram of another InSAR dam monitoring result.

[0032] Figure 6 Schematic diagram of the system structure of the present invention. DETAILED DESCRIPTION

[0033] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0034] Example 1 like Figure 1 As shown, the present invention provides a method for analyzing dam deformation behavior, and its implementation method is as follows: S1. Obtain InSAR data and BeiDou monitoring data covering the target dam area and perform preprocessing, specifically: Acquire InSAR data covering the target dam area and preprocess the InSAR data, where the InSAR data is vertical deformation value; Obtain Beidou monitoring data and preprocess it to obtain the three-dimensional displacement time series of the monitoring points , where the deformations in the X and Y directions serve as supplements to the overall deformation of the dam; The preprocessed InSAR data are aligned with the three-dimensional displacement time series in time and space to fuse the InSAR data and Beidou monitoring data to complete the preprocessing process.

[0035] In this example, InSAR data and BeiDou monitoring data covering the target dam area are acquired. The InSAR data undergoes preprocessing, including registration, differential interferometry, phase unwrapping, atmospheric correction, and geocoding. The BeiDou monitoring data undergoes preprocessing, including quality inspection, cycle slip correction, and precise point positioning or baseline calculation, to obtain a 3D displacement time series of the monitoring points. The InSAR deformation information and the BeiDou displacement time series are then aligned in time and space.

[0036] S2. Analyze the physical factors that affect dam deformation and model them. The modeling rules are used to guide the training and prediction of the physical constraint deep learning model. In this embodiment, the physical factors that affect dam deformation are analyzed, including but not limited to the dam reservoir water level, temperature changes, and geological conditions. Mathematical models or rules related to these physical factors are established to guide the training and prediction of the deep learning model.

[0037] Physical elements mainly include reservoir water level and temperature changes The dam deformation caused by the reservoir water level H(t) (unit: m) is mainly driven by hydrostatic pressure; the ambient temperature changes (Unit: °C) Affects dam deformation through thermal expansion effect.

[0038] Mathematical modeling: (1) Water pressure effect: hydrostatic pressure ,in, represents water density, g represents acceleration due to gravity, represents the pressure deformation coefficient. Therefore, the deformation response is: ; (2) Temperature effect: thermal expansion deformation , where α represents the thermal expansion coefficient of the material, It represents the local characteristic length of the dam body (unit: m, which can be determined according to the geometric structure of the dam body). ΔT(t) is obtained in real time through a weather station or sensor.

[0039] Therefore, the output of the physical model includes: reservoir water level deformation and temperature deformation , which will serve as a physical constraint reference for the deep learning model.

[0040] S3. Build a physical constraint deep learning model, where the physical constraint deep learning model includes: The input layer is used to receive multiple data sources and perform normalization on them; the data sources include InSAR deformation data , Beidou displacement time series And auxiliary information; auxiliary information is reservoir water level and temperature changes Since InSAR deformation data is the average deformation value over a certain period of time (such as one year), while BeiDou data is the three-dimensional deformation data of a series of points, it is necessary to normalize the two types of deformation data; The spatial feature extraction branch is used to extract the normalized InSAR deformation data. , using convolutional neural networks to extract the spatial distribution characteristics of the dam surface deformation and output spatial feature tensors ; The time feature extraction branch is used to extract the normalized Beidou displacement time series. Extract features with auxiliary information and output temporal feature tensor ; Physical branch layer, used to transform the temporal feature tensor Spatial feature tensor Perform splicing. Based on the splicing results, use the convolution layer to extract physical features, and use the maximum pooling layer to compress the data size. The output layer is used to obtain the deformation analysis results of the dam based on the compressed physical characteristics.

[0041] In this embodiment, the physical constraint deep learning model can receive the fused InSAR and BeiDou data and related auxiliary information (such as reservoir water level, temperature, etc.) as input. and temperature deformation , output high-precision dam deformation field , meeting the requirements of high precision, physical rationality and generalization ability for dam deformation monitoring.

[0042] The physical constraint deep learning model PINN adopts a multi-input, multi-branch deep learning framework with the following structure: Input layer: InSAR deformation data , a two-dimensional tensor with dimensions H×W×TH (e.g. 256×256×T), representing the change of the spatial deformation field over time. BeiDou displacement time series , a one-dimensional tensor of size N × T. Auxiliary Information: Reservoir water level and temperature changes , a one-dimensional time series with a size of 1×𝑇. Input preprocessing, normalize all input data to the [0,1] interval.

[0043] Spatial feature extraction branch: processing The spatial pattern of the convolutional network is composed of: Convolutional layer 1: 32 3×3 convolution kernels, stride 1, activation function ReLU, output 256×256×32; Pooling layer 1: 2×2 max pooling, output 128×128×32; Convolutional layer 2: 64 3×3 convolution kernels, stride 1, activation function ReLU, output 128×128×64; Pooling layer 2: 2×2 maximum pooling, output 64×64×64; Output: spatial feature tensor , with dimensions of 64×64×64:

[0044] in, , Both represent the convolution kernel weights, , Both indicate bias.

[0045] Temporal feature extraction branch (LSTM): processing The time dependence of , T is time, the network composition is: LSTM layer 1: 64 hidden units, output ; LSTM layer 2: 32 hidden units, output ; Assumptions: The current hidden state, the final time feature is , the calculation formula is: , )

[0046] The loss function of the physical constraint deep learning model is constructed as follows: The loss function for integrating physical constraints is:

[0047]

[0048]

[0049]

[0050]

[0051] in, represents the loss function of the physical constraint deep learning model, represents the deformation data loss function, and Both represent weighting coefficients, used to balance the importance of loss, represents the deformation caused by the hydrostatic pressure of the water level, represents the temperature loss function, represents the local characteristic length of the dam body, represents the regularization coefficient, represents the number of observation points, i represents an observation point, represents the solution predicted by the neural network, The true value of the deformation, represents the hydrostatic strain-deformation conversion coefficient, represents the theoretical strain calculated by the hydrostatic pressure formula, represents the spatial and temporal coordinates of the data points, represents the hydrostatic pressure, represents the thermal expansion coefficient of the material, represents the theoretical strain due to temperature, Indicates additional constraints based on the difference between predicted and physical values, represents the systematic error, and Initially set to 0.1 and dynamically adjusted. S4. Use the pre-processed InSAR data and BeiDou monitoring data to train and optimize the physical constraint deep learning model; In this example, a deep learning model is trained using historical InSAR and BeiDou data and corresponding physical constraints. A suitable optimization algorithm (such as Adam or SGD) is used to minimize a loss function that includes both a data-driven loss term and a loss term related to the physical constraints. Model hyperparameters are adjusted using a validation set to prevent overfitting and improve model generalization.

[0052] The dataset is divided into 70% training, 15% validation, and 15% testing. The Adam optimizer is used with a learning rate of 0.001 and a batch size of 32.

[0053] The accuracy evaluation uses RMSE:

[0054] Where N represents the number of observation points, represents the solution predicted by the neural network, Represents the ground truth deformation value.

[0055] S5. Input the InSAR data and Beidou monitoring data of the dam to be analyzed into the optimized physical constraint deep learning model to obtain the deformation analysis results of the dam and complete the analysis of the deformation properties of the dam.

[0056] In this embodiment, deformation behavior analysis and prediction involves inputting InSAR and Beidou data of the dam to be analyzed into a trained physical-constrained deep learning model to obtain deformation analysis results for the dam, including but not limited to high-resolution deformation maps, displacement time series of key monitoring points, and overall deformation trends and status assessments. Furthermore, the physical-constrained deep learning model can also be used to predict the deformation trend of the dam over a period of time.

[0057] The present invention will be further described below.

[0058] This invention provides a dam deformation analysis method based on a physical information neural network (PINN) collaboratively driven by InSAR and Beidou data. This method is implemented using a reservoir dam in southern China as an example. The dam is located in a certain river basin and is a clay slope rockfill dam with a maximum height of 81.3 meters, a crest length of 215 meters, and a crest elevation of 225.2 meters. The dam foundation is made of sandstone. Its primary functions include flood control, power generation, and water supply. The following details the implementation steps of the invention: Step 1: Data acquisition and preprocessing The data collected includes the following: InSAR data: C-band SAR images covering the Nanshui Reservoir Dam were acquired using the Sentinel-1 satellite. The wavelength is λ = 5.6 cm and the time span is from January 2023 to December 2024. An image is acquired every 12 days with a resolution of 5 m × 20 m.

[0059] BeiDou data: 10 BeiDou high-precision receivers were installed at key locations of the dam (such as the crest, abutment, and foundation) with a sampling frequency of 1 Hz to obtain three-dimensional displacement time series. .

[0060] Auxiliary data: The reservoir water level H(t) (unit: m) and ambient temperature ΔT(t) (unit: °C) are recorded in real time through the water level sensor and weather station.

[0061] Step 2: Data Preprocessing (1) InSAR processing: Image registration: Geometric correction is performed using precise orbit data and SRTM 30m DEM, and the pixel alignment error is controlled within 1 / 8 pixel.

[0062] Differential interferometry: Using the small baseline set algorithm, the time baseline of 40d and the spatial baseline of 300m were selected as thresholds to generate the interferometric phase map.

[0063] Phase unwrapping: The SNAPHU algorithm is used to unwrap the phase, and the number of iterations is set to 100 to restore the continuous deformation field.

[0064] Atmospheric correction: The atmospheric delay is estimated using the GACOS model (based on ECMWF meteorological data).

[0065] Geocoding: Projected to WGS84 coordinate system.

[0066] (2) Beidou data processing: Quality check: Observations with a signal-to-noise ratio below 30 dB were eliminated, and multipath effects were detected (error threshold 5 mm).

[0067] Cycle slip repair: The third-order difference method is used to detect cycle slips, and the carrier phase observation value is calculated after repair.

[0068] High-precision positioning: Use PPP technology, input IGS precise ephemeris and clock error files, and solve three-dimensional coordinates.

[0069] (3) Data fusion Time alignment: Based on the InSAR data timestamp (12-day interval), linear interpolation is performed on the BeiDou data and auxiliary data to ensure time synchronization.

[0070] Step 3: Physical Constraint Deep Learning Model Construction (1) Reservoir water level deformation model Calculate the water pressure according to the formula: ; .in, =2.5×10 −9 m / Pa (fitted by historical deformation data of Nanshui Dam), , assuming that the deformation is linearly distributed, the deformation at the dam bottom is small and the deformation at the dam top is large.

[0071] (2) Temperature deformation model Thermal expansion deformation:

[0072] α=1×10−5 °C -1 . is 215m, for example, when ΔT(t)=20°, =0.043m.

[0073] (3) Boundary constraint extraction Boundary constraint: dam bottom deformation D(x,y base ,t)=0.

[0074] (4) Construction of physical information neural network PINN The physical information neural network PINN adopts a multi-input, multi-branch deep learning framework, such as Figures 2 to 3 As shown, it can simultaneously process InSAR spatial deformation data, BeiDou time series data, and constraint data generated by physical models, among which, Figure 2 Where M and N represent the number of rows and columns of the input observation matrix, ReLU represents the activation function, b1 and b2 both represent the offset matrix, Figure 3 In the neural network Represents the jth neuron in the i-th layer. The network architecture is divided into the following key parts: The input layer receives a variety of data sources, including InSAR deformation maps, displacement time series of BeiDou monitoring points, and auxiliary information (such as reservoir water level and temperature). Specifically, InSAR data is input as a two-dimensional grid covering a 256×256 grid area of ​​the Nanshui Reservoir Dam; BeiDou data is collected from 10 monitoring points and contains the three-dimensional displacement of each point over time; and auxiliary data is input as a time series, recording the hourly changes in water level and temperature. In addition, reservoir water level and temperature deformation data generated by the physical model are also included in the input layer as part of the physical constraints. All input data is normalized before entering the network to ensure a consistent numerical range and improve training stability.

[0075] The spatial branch uses a convolutional neural network (CNN) to process InSAR deformation maps, aiming to extract the spatial distribution of dam surface deformation. This branch consists of two convolutional layers and two pooling layers. The first convolutional layer uses 32 3×3 convolution kernels to scan the InSAR data and capture local deformation patterns. A 2×2 max pooling layer then reduces the size of the feature map. The second convolutional layer uses 64 3×3 convolution kernels to further extract deeper spatial features, followed by another pooling layer for data compression. Reluctant Unit (ReLU) activation functions are used after each convolutional layer to enhance nonlinear representation, ultimately outputting a spatial feature tensor for subsequent fusion.

[0076] The temporal branch uses a long short-term memory (LSTM) network to process the time series of Beidou displacement data and auxiliary information, aiming to capture the temporal evolution of deformation. This branch first concatenates the Beidou displacement data (from 10 monitoring points) and auxiliary data (water level, temperature) into a unified input sequence, which is then processed through a two-layer LSTM network. The first LSTM layer contains 64 hidden units, learning short-term dependencies in the time series; the second LSTM layer has 32 hidden units, extracting more abstract temporal features. The LSTM network memorizes long-term trends and filters noise, ultimately outputting a temporal feature tensor. To match the spatial branch, the temporal features are expanded to the appropriate dimension using a fully connected layer.

[0077] The physics branch specifically processes the reservoir water level and temperature deformation data generated by the physical model, enhancing the model's ability to perceive physical laws. This branch concatenates the two types of deformation data and feeds them into a single convolutional layer, extracting physical features using 16 3×3 convolution kernels. This layer then compresses the data using a 2×2 max pooling layer. The goal of the physics branch is to preserve the spatial characteristics of the water level and temperature effects, ensuring consistency with the InSAR and BeiDou data during fusion.

[0078] The loss function consists of a data-driven component and a physical constraint component. The data-driven component measures the difference between the predicted deformation and the actual observed data (InSAR and BeiDou fusion data). The physical constraint component includes three items: a constraint based on reservoir water level deformation to ensure that the predicted deformation is consistent with the water pressure effect; a constraint based on temperature deformation to reflect the influence of thermal expansion; and a constraint based on mechanical equilibrium to ensure the physical rationality of the deformation field. Each constraint is weighted to adjust its importance. The initial weight is set based on experience and dynamically optimized during training.

[0079] Step 4: Model training process The training process aims to optimize the PINN network parameters to achieve high accuracy and physical consistency in the deformation prediction of the Nanshui Reservoir Dam: (1) Hardware environment Training was conducted on high-performance computing equipment, using an NVIDIA A40 GPU (48GB of video memory) and an Intel i9-12900K CPU, which supports large-scale matrix operations and parallel computing within deep learning frameworks. The dataset covers dam monitoring data from January 2023 to December 2024, including InSAR deformation maps, Beidou displacement series, and reservoir water level and temperature records. The dataset was partitioned into 70% training, 15% validation, and 15% test sets. The training set was used for parameter learning, the validation set for hyperparameter tuning, and the test set for final performance evaluation.

[0080] (2) Optimization strategy The Adam optimizer was used for network training, with an initial learning rate of 0.001. This learning rate was decayed by 0.5 every 20 training epochs to avoid rapid convergence or falling into local optima. The batch size was set to 32 to ensure a balance between GPU memory utilization and computational efficiency. Training lasted for a total of 150 epochs to fully optimize the network weights.

[0081] (3) Hyperparameter adjustment and verification During training, model performance is monitored using a validation set. Key evaluation metrics include the average error between the predicted deformation and the observed data and the degree of physical constraint satisfaction. If physical constraints perform poorly (e.g., excessive mechanical equilibrium residuals), the weight of the corresponding constraint is appropriately increased. If the training set error decreases while the validation set error increases, training is stopped early to prevent overfitting. The model version that performs best on the validation set is ultimately selected for subsequent predictions.

[0082] (4) Implementation effect After training, the PINN network was able to effectively process deformation data from the Nanshui Reservoir Dam. During the testing phase (January to March 2025), the model maintained its prediction accuracy under varying water levels and temperatures. The training process was stable, and after convergence, the model not only fitted the observed data but also satisfied the physical laws of water pressure and temperature, providing a reliable foundation for subsequent deformation behavior analysis, such as Figure 4 and Figure 5 shown.

[0083] Example 2 like Figure 6 As shown, the present invention provides a dam deformation state analysis system, comprising: The first processing module is used to obtain InSAR data and BeiDou monitoring data covering the target dam area and perform preprocessing; The second processing module is used to analyze the physical factors that affect dam deformation and model the physical factors. The modeling rules are used to guide the training and prediction of the physical constraint deep learning model; The third processing module is used to build a physical constraint deep learning model; The fourth processing module is used to train and optimize the physical constraint deep learning model using pre-processed InSAR data and BeiDou monitoring data; The fifth processing module is used to input the InSAR data of the dam to be analyzed and the Beidou monitoring data into the optimized physical constraint deep learning model to obtain the deformation analysis results of the dam and complete the analysis of the deformation properties of the dam.

[0084] Figure 6 The dam deformation behavior analysis system provided in the illustrated embodiment can implement the technical solution shown in the dam deformation behavior analysis method in the above method embodiment. Its implementation principle and beneficial effects are similar and will not be repeated here.

[0085] In this embodiment, the present application can divide functional units according to the dam deformation state analysis method. For example, each function can be divided into functional units, or two or more functions can be integrated into a single processing unit. The above-mentioned integrated unit can be implemented in the form of hardware or software functional units. It should be noted that the division of units in the present invention is schematic and is only a logical division. In actual implementation, other division methods may be used.

[0086] In this embodiment, the dam deformation behavior analysis system includes hardware structures and / or software modules that perform corresponding functions in order to realize the principles and beneficial effects of the dam deformation behavior analysis method. It should be readily appreciated by those skilled in the art that, in combination with the various schematic units and algorithm steps described in the embodiments disclosed herein, the present invention can be implemented in the form of hardware and / or a combination of hardware and computer software. Whether a function is executed in a hardware- or computer software-driven manner depends on the specific application and design constraints of the technical solution. Different methods can be used for each specific application to implement the described function, but such implementation should not be considered to be beyond the scope of this application.

Claims

1. A method for analyzing dam deformation behavior, characterized in that: The following steps are involved: S1. Obtain InSAR data and BeiDou monitoring data covering the target dam area and perform preprocessing; S2. Analyze the physical factors that affect dam deformation and model them. The modeling rules are used to guide the training and prediction of the physical constraint deep learning model. S3. Build a physical constraint deep learning model; S4. Use the pre-processed InSAR data and BeiDou monitoring data to train and optimize the physical constraint deep learning model; S5. Input the InSAR data and Beidou monitoring data of the dam to be analyzed into the optimized physical constraint deep learning model to obtain the deformation analysis results of the dam and complete the analysis of the deformation properties of the dam.

2. The dam deformation state analysis method according to claim 1, characterized in that: The S1 is specifically: Acquire InSAR data covering the target dam area and preprocess the InSAR data, where the InSAR data is vertical deformation value; Obtain Beidou monitoring data and preprocess it to obtain the three-dimensional displacement time series of the monitoring points , where the deformations in the X and Y directions serve as supplements to the overall deformation of the dam; The preprocessed InSAR data are aligned with the three-dimensional displacement time series in time and space to fuse the InSAR data and Beidou monitoring data to complete the preprocessing process.

3. The dam deformation state analysis method according to claim 1, characterized in that: The physical factors include reservoir water level and ambient temperature changes , the dam deformation caused by the reservoir water level H(t) is driven by hydrostatic pressure; the ambient temperature changes The deformation of the dam is affected by the thermal expansion effect.

4. The dam deformation state analysis method according to claim 3, characterized in that: The modeling of physical factors includes: The dam deformation caused by the reservoir water level H(t) is: in, represents the dam deformation caused by the reservoir water level H(t), represents the pressure deformation coefficient, represents the hydrostatic pressure, represents the water density, represents the acceleration due to gravity; Dam deformation caused by thermal expansion effect , which is: in, represents the thermal expansion coefficient of the material, Represents the local characteristic length of the dam body.

5. The dam deformation state analysis method according to claim 1, characterized in that: The loss function of the physical constraint deep learning model is expressed as follows: in, represents the loss function of the physical constraint deep learning model, represents the deformation data loss function, and Both represent weighting coefficients, used to balance the importance of loss, represents the deformation caused by the hydrostatic pressure of the water level, represents the temperature loss function, represents the local characteristic length of the dam body, represents the regularization coefficient, represents the number of observation points, i represents an observation point, represents the solution predicted by the neural network, The true value of the deformation, represents the hydrostatic strain-deformation conversion coefficient, represents the theoretical strain calculated by the hydrostatic pressure formula, represents the spatial and temporal coordinates of the data points, represents the hydrostatic pressure, represents the thermal expansion coefficient of the material, represents the theoretical strain due to temperature, Indicates additional constraints based on the difference between predicted and physical values, Indicates systematic error.

6. The dam deformation state analysis method according to claim 1, characterized in that: The physical constraint deep learning model includes: The input layer is used to receive multiple data sources and perform normalization on them; the data sources include InSAR deformation data , Beidou displacement time series And auxiliary information; auxiliary information is reservoir water level and temperature changes ; The spatial feature extraction branch is used to extract the normalized InSAR deformation data. , using convolutional neural networks to extract the spatial distribution characteristics of the dam surface deformation and output spatial feature tensors ; The time feature extraction branch is used to extract the normalized Beidou displacement time series. Extract features with auxiliary information and output temporal feature tensor ; Physical branch layer, used to transform the temporal feature tensor Spatial feature tensor Perform splicing. Based on the splicing results, use the convolution layer to extract physical features, and use the maximum pooling layer to compress the data size. The output layer is used to obtain the deformation analysis results of the dam based on the compressed physical characteristics.

7. A dam deformation behavior analysis system, which is used to execute the dam deformation behavior analysis method according to any one of claims 1 to 6, characterized in that: include: The first processing module is used to obtain InSAR data and BeiDou monitoring data covering the target dam area and perform preprocessing; The second processing module is used to analyze the physical factors that affect dam deformation and model the physical factors. The modeling rules are used to guide the training and prediction of the physical constraint deep learning model; The third processing module is used to build a physical constraint deep learning model; The fourth processing module is used to train and optimize the physical constraint deep learning model using pre-processed InSAR data and BeiDou monitoring data; The fifth processing module is used to input the InSAR data of the dam to be analyzed and the Beidou monitoring data into the optimized physical constraint deep learning model to obtain the deformation analysis results of the dam and complete the analysis of the deformation properties of the dam.

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