Small and medium span bridge deflection prediction system and method based on signal decomposition and two-stage LSTM

Abstract

This invention provides a deflection prediction system and method for small-to-medium span bridges based on signal decomposition and dual-stage LSTM, belonging to the field of bridge health monitoring technology. The system includes: S1, data acquisition and standardization; S2, Gaussian filtering decomposition of the deflection signal; S3, enhancement of physical features; S4, construction of a dual LSTM model for prediction; and S5, superposition of high- and low-frequency prediction values ​​to arrive at the final deflection. This invention employs the aforementioned deflection prediction system and method for small-to-medium span bridges based on signal decomposition and dual-stage LSTM, solving the problem that existing bridge health monitoring technologies struggle to fully exploit the nonlinear correlations of high-dimensional time-series data when processing complex deflection signals involving environmental and traffic coupling effects. While traditional signal decoupling methods can capture dynamic features, deep learning models suffer from high computational costs due to excessive network complexity, failing to balance prediction accuracy and real-time performance requirements.

Description

Technical Field

[0001] This invention relates to the field of bridge health monitoring technology, and in particular to a deflection prediction system and method for small and medium-span bridges based on signal decomposition and two-stage LSTM. Background Technology

[0002] In modern transportation infrastructure networks, bridges serve as critical nodes, and their safe operation directly impacts the smooth flow of traffic and the stable operation of social production activities. In recent years, highway traffic volume has experienced explosive growth, posing unprecedented challenges to the load-bearing capacity and durability of existing bridge structures. Against this backdrop, how to accurately and in real-time monitor the service status of bridges and promptly identify potential safety hazards has become a critical issue urgently needing resolution in the field of bridge engineering. Bridge deflection, as an important parameter for assessing the overall stiffness and load-bearing capacity of a bridge structure, directly reflects the vertical stiffness characteristics of the bridge in terms of its magnitude and shape. Abnormal deflection data often foreshadows problems such as structural stiffness degradation, material fatigue, or bearing damage. Therefore, continuous monitoring of bridge deflection has become one of the core tasks of structural health monitoring (SHM) systems. However, bridge deflection signals are a comprehensive feedback from the combined effects of environmental and traffic loads, exhibiting significant complexity and multi-scale characteristics, which presents numerous difficulties for traditional monitoring and analysis methods.

[0003] For a long time, bridge condition assessment has mainly relied on regular manual inspections and visual checks. However, this method has significant limitations: on the one hand, visual inspections are highly dependent on the subjective experience of the inspectors, making them inefficient and difficult to standardize and quantify; on the other hand, they can usually only detect visible macroscopic damage such as concrete spalling and cracks, and often cannot detect hidden defects such as internal structural stiffness degradation or abnormal dynamic response in a timely manner, resulting in a time lag in detection and diagnosis. To overcome the bottlenecks of traditional monitoring methods, structural health monitoring systems have emerged, which integrate sensing technology and data transmission networks to achieve continuous perception of bridge structural behavior.

[0004] Scholars both domestically and internationally have conducted extensive research in this field, developing various real-time monitoring technologies, such as compact vision systems, non-contact deflection measurement methods involving multiple UAVs, and wireless SmartVision systems. These technologies have effectively solved the spatiotemporal alignment problems in real-time, high-precision measurement of displacement in long-span bridges and multi-point monitoring. However, while generating massive amounts of monitoring data, these technologies also place higher demands on data processing and analysis capabilities.

[0005] The complexity of bridge deflection data lies in its dual influence from low-frequency environmental trends and high-frequency traffic dynamics. The response characteristics of these two factors overlap, and directly relying on the raw data for structural performance assessment is prone to misjudgment due to the failure to distinguish between interfering factors. To address this, researchers have proposed various signal decoupling methods, such as the EEMD-GSA-LSSVM hybrid algorithm and block recursive sliding variational mode decomposition (RSVMD), to separate environmental effects from traffic load effects. While these methods have made some progress, they still struggle to fully extract complex nonlinear temporal correlations when processing massive, high-dimensional data, and their processing efficiency and adaptability need improvement. Against this backdrop, deep learning technology, with its powerful feature extraction capabilities, has shown great potential in bridge health monitoring. In particular, Long Short-Term Memory (LSTM) networks and their variants, with their unique gating mechanism, effectively overcome the gradient vanishing problem of traditional recurrent neural networks when processing long sequence data, becoming an important tool for predicting bridge dynamic response. However, existing algorithms still tend to improve performance by increasing network complexity in handling complex signal problems, resulting in high computational costs and failing to meet the needs of real-time on-site monitoring. Summary of the Invention

[0006] The purpose of this invention is to provide a deflection prediction system and method for small and medium-span bridges based on signal decomposition and two-stage LSTM. This invention solves the problem that when dealing with complex deflection signals that include environmental and traffic coupling effects, existing bridge health monitoring technologies cannot fully exploit the nonlinear correlation of high-dimensional time-series data using traditional signal decoupling methods. While deep learning models can capture dynamic features, their high network complexity leads to high computational costs, making it impossible to balance prediction accuracy and real-time requirements.

[0007] To achieve the above objectives, this invention provides a method for predicting the deflection of small-to-medium span bridges based on signal decomposition and two-stage LSTM, comprising the following steps: S1. Collect the original deflection monitoring signals, environmental temperature and humidity monitoring data, and traffic load WIM monitoring data of small and medium span bridges, and perform Z-Score standardization preprocessing on the original monitoring data. S2. The preprocessed original deflection monitoring signal is decomposed using a Gaussian low-pass filter to obtain the low-frequency trend component dominated by environmental effects and the high-frequency detail component dominated by traffic load transient impact. The optimal filtering step size of the Gaussian low-pass filter is determined based on the best balance between the fitting residual and the trend smoothness. S3. Physical feature enhancement processing is performed on the low-frequency trend component and the high-frequency detail component respectively to obtain effective temperature features and dynamic load flow features. S4. Construct a two-stage parallel LSTM prediction model. The two-stage parallel LSTM prediction model includes a parameter-independent trend sub-model LSTM-Trend and a detail sub-model LSTM-Detail. Input the effective temperature characteristics and historical data of the low-frequency trend components into LSTM-Trend to obtain the low-frequency deflection prediction value, and input the dynamic load flow characteristics and historical data of the high-frequency detail components into LSTM-Detail to obtain the high-frequency deflection prediction value. S5. Linearly superimpose the predicted low-frequency deflection value with the predicted high-frequency deflection value to obtain the final predicted deflection value of the bridge.

[0008] Preferably, the process of enhancing the physical features of the low-frequency trend component to obtain the effective temperature feature includes: Based on Newton's law of cooling, a first-order linear ordinary differential equation for the effective temperature of the structure is constructed, expressed as: ; in, for The measured ambient temperature at any given time; Thermal conductivity is related to the specific heat capacity and thermal conductivity of a material. for Effective temperature of the structure at any given time; The first-order linear ordinary differential equation is approximated using the Euler method, with the time step set to... A recursive physical model in the form of an exponentially weighted moving average is derived: ; in, The thermal decay coefficient; Establish thermal attenuation coefficient With physical lag time Mapping function: ; in, To accommodate time scale factors with minute-level sampling frequencies; Global grid optimization is performed within the preset physical search interval τ∈[τmin,τmax] with a step size of 0.05h, and the optimal lag time is determined by a dual-index collaborative objective function. : ; in, For low-frequency deflection trend components, For Pearson correlation operators, is the weighting factor, N is the sample size, and a and b are both linear regression coefficients; Based on the optimal lag time The reconstructed effective temperature characteristics are precisely phase-aligned with the low-frequency deflection trend components. .

[0009] Preferably, the process of obtaining dynamic load flow characteristics by physical feature enhancement of high-frequency detail components includes: Based on the kinematic equations, the real-time trajectory of the vehicle on the bridge is deduced. For the j-th vehicle, its instantaneous longitudinal coordinate expression at time t is: ; in, Let be the speed of the j-th vehicle. Let j be the time when the j-th vehicle arrives at the bridgehead; Define the set of valid vehicles within the calculated span L of the bridge at time t, expressed as: = ; Based on the triangular distribution characteristics of the influence line of mid-span deflection in a simply supported beam, a normalized influence operator is defined. : ; Where x is the longitudinal distance between the vehicle and the support; Based on the principle of linear superposition of elastic systems, the total effect of dynamic effective load on the bridge at time t is calculated: ; in, Let be the measured mass of the j-th vehicle.

[0010] Preferably, the LSTM neural units of both the trend sub-model LSTM-Trend and the detail sub-model LSTM-Detail include a forget gate, an input gate, an output gate, and a cell state, and the input gates have different frequency domain sensitivity. The input gate of the trend sub-model LSTM-Trend is designed for long-cycle thermal accumulation effects and maintains high sensitivity to smooth gradients of environmental temperature changes. The input gate of the detail sub-model LSTM-Detail is designed for transient traffic load impacts and is used to instantaneously capture the pulse characteristics of high-frequency vehicle data. The forget gate has an adaptive denoising function, which attenuates random environmental noise that is independent of the bridge structural state by dynamically adjusting the information retention rate.

[0011] Preferably, the computation process of an LSTM neural unit is as follows: Activation function via Sigmoid Calculate the forget gate at time t Input gate With output gate Activation status: ; in, The input feature vector at time t, The hidden state at time t-1 , , These are the weight matrices for the forget gate, input gate, and output gate, respectively. , , These are the bias vectors for the forget gate, input gate, and output gate, respectively. Candidate memories at time t are generated using the Tanh function. : ; in, The weight matrix for candidate memories. The bias vector for candidate memories; Update the cell state at time t using the Hadamard product. With hidden layer output : ; ; in, The cell state at time t-1.

[0012] Preferably, when constructing the two-stage parallel LSTM prediction model, a control model for comparative verification is also constructed, including the purely data-driven naive model LSTM-Naive and the physical feature-enhanced integrated model LSTM-Integrated, and the total number of parameters of the two-stage parallel LSTM prediction model, the naive model LSTM-Naive, and the integrated model LSTM-Integrated are kept consistent.

[0013] Preferably, the input vector for the naive LSTM-Naive model is: ; in, Historical deflection data, Real-time temperature without considering thermal hysteresis The original traffic flow statistics lack spatial weights; The input vector for the overall LSTM-Integrated model is: ; in, For effective temperature characteristics, This represents the characteristics of dynamic load flow.

[0014] Preferably, the method further includes a performance evaluation step for the bridge deflection prediction results, using root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) as evaluation indicators, calculated using the following formulas: ; ; ; Where N is the total number of samples in the test set. This represents the actual measured value of deflection. These are the values ​​predicted by the deflection model. This represents the average value of the actual monitored deflection values.

[0015] A deflection prediction system for medium- and small-span bridges based on signal decomposition and two-stage LSTM includes: The data acquisition module is used to collect the original deflection monitoring signals, environmental temperature and humidity monitoring data, and traffic load WIM monitoring data of small and medium span bridges. The data preprocessing module is used to perform Z-Score normalization preprocessing on the raw monitoring data collected by the data acquisition module. At the same time, a Gaussian low-pass filter is used to decompose the preprocessed raw deflection monitoring signal to obtain low-frequency trend components and high-frequency detail components. The physical feature enhancement module is connected to the data preprocessing module and the data acquisition module respectively. It is used to reconstruct the effective temperature features of the low-frequency trend components and construct the dynamic load flow features of the high-frequency detail components. The two-stage LSTM prediction module, connected to the physical feature enhancement module, includes a trend sub-model LSTM-Trend and a detail sub-model LSTM-Detail that run in parallel with independent parameters, to output low-frequency deflection prediction values ​​and high-frequency deflection prediction values ​​respectively. The result fusion module, connected to the two-stage LSTM prediction module, is used to linearly superimpose the low-frequency deflection prediction value with the high-frequency deflection prediction value to obtain the final deflection prediction value of the bridge. The performance evaluation module, connected to the result fusion module and the data acquisition module respectively, is used to evaluate the accuracy and stability of the final deflection prediction value of the bridge.

[0016] Preferably, the physical feature enhancement module includes a temperature feature reconstruction unit and a load flow feature construction unit; The temperature feature reconstruction unit optimizes the objective function based on Newton's law of cooling and a dual-index collaborative objective function to reconstruct the effective temperature features. The load flow characteristic construction unit is based on kinematic equations, normalized influence operators and the principle of linear superposition of elastic systems to realize the construction of dynamic load flow characteristics; The two-stage LSTM prediction module's trend sub-model LSTM-Trend and detail sub-model LSTM-Detail support parallel computation, improving computational efficiency without changing the total amount of computation.

[0017] Therefore, the present invention employs the above-mentioned deflection prediction system and method for small-to-medium span bridges based on signal decomposition and dual-stage LSTM, and the technical effects are as follows: 1. Improve the accuracy of bridge deflection prediction and accurately capture multi-scale coupled response features: Decompose the original deflection signal into low-frequency trend components dominated by the environment and high-frequency detail components dominated by traffic. Combined with physical feature enhancement strategies, reconstruct the effective temperature considering thermal hysteresis and the dynamic load flow features based on influence line weights respectively. Correct the phase hysteresis of temperature-deflection from a physical perspective and make up for the lack of spatiotemporal mapping of traffic loads. Solve the prediction bias problem caused by coupling signal interference and insufficient feature representation in traditional models.

[0018] 2. Enhance model prediction stability and improve generalization ability under complex conditions: The two-stage LSTM sub-model has made frequency domain sensitivity differentiation design for the physical characteristics of low frequency and high frequency components. The trend sub-model focuses on long-cycle thermal accumulation effect, the detail sub-model focuses on transient traffic load impact, and the forget gate has an adaptive denoising function, which can effectively attenuate random environmental noise that is unrelated to the structural state and reduce the interference of outliers on the prediction results.

[0019] 3. Achieve doubled computational efficiency and meet the timeliness requirements of real-time bridge deflection monitoring: The dual-stage LSTM model adopts a parameter-independent parallel architecture. The trend sub-model and the detail sub-model are mathematically independent and uncoupled, supporting independent parallel computation. It does not require stacking deep networks and increasing model complexity to improve accuracy. By decoupling signals, the learning difficulty of the model is reduced, achieving a lightweight design. It can also run efficiently on edge computing devices with limited computing power and can be directly adapted to the engineering requirements of real-time bridge monitoring. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the overall process framework of the deflection prediction system for small-span bridges in this invention. Figure 2 This is a schematic diagram of the internal workings of the LSTM system for predicting the deflection of small-span bridges in this invention. Figure 3 This is a schematic diagram of the bridge measuring points and sensor layout in the small-span bridge deflection prediction system of this invention; Figure 4 This is a traffic flow heatmap of the deflection prediction system for small-span bridges in this invention. Figure 5 This is an environmental temperature and humidity diagram for the deflection prediction system for small-span bridges in this invention. Figure 6This is a schematic diagram of the dynamic load flow model of the deflection prediction system for small-span bridges in this invention; Figure 7 This is a detailed diagram of the Naive model prediction in an embodiment of the present invention; Figure 8 This is a detailed diagram of the Baseline model prediction in an embodiment of the present invention; Figure 9 This is a detailed prediction diagram of the LSTM-TD model in an embodiment of the present invention; Figure 10 This is a statistical comparison chart of model predictions in an embodiment of the present invention; Figure 11 This is a scatter regression analysis plot of the predicted values ​​and the true values ​​of the Naive model in an embodiment of the present invention. Figure 12 This is a scatter regression analysis plot of the predicted values ​​and the true values ​​of the Baseline model in an embodiment of the present invention. Figure 13 This is a scatter regression analysis plot of the predicted values ​​and the true values ​​of the LSTM-TD model in an embodiment of the present invention. Figure 14 This is a schematic diagram of the probability density function of the prediction error in an embodiment of the present invention; Figure 15 This is a schematic diagram of the cumulative distribution function of the prediction error in an embodiment of the present invention; Figure 16 This is a schematic diagram comparing the computation time of the model in an embodiment of the present invention. Detailed Implementation

[0021] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0022] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0023] Example 1 like Figure 1 As shown, this invention provides a deflection prediction system and method for small-to-medium span bridges based on signal decomposition and a two-stage LSTM. It employs a Gaussian low-pass filter to decompose the original deflection signal into low-frequency and high-frequency components, and performs feature enhancement on each component. Then, by constructing two parallel Long Short-Term Memory (LSTM) networks, the final prediction result is synthesized by superimposing the outputs of the two sub-models. The method includes the following steps: S1. Collect the original deflection monitoring signals, environmental temperature and humidity monitoring data, and traffic load WIM monitoring data of small and medium span bridges, and perform Z-Score standardization preprocessing on the original monitoring data. S2. The preprocessed original deflection monitoring signal is decomposed using a Gaussian low-pass filter to obtain the low-frequency trend component dominated by environmental effects and the high-frequency detail component dominated by traffic load transient impact. The optimal filtering step size of the Gaussian low-pass filter is determined based on the best balance between the fitting residual and the trend smoothness. S3. Physical feature enhancement processing is performed on the low-frequency trend component and the high-frequency detail component respectively to obtain effective temperature features and dynamic load flow features. S4. Construct a two-stage parallel LSTM prediction model. The two-stage parallel LSTM prediction model includes a parameter-independent trend sub-model LSTM-Trend and a detail sub-model LSTM-Detail. Input the effective temperature characteristics and historical data of the low-frequency trend components into LSTM-Trend to obtain the low-frequency deflection prediction value, and input the dynamic load flow characteristics and historical data of the high-frequency detail components into LSTM-Detail to obtain the high-frequency deflection prediction value. S5. Linearly superimpose the predicted low-frequency deflection value with the predicted high-frequency deflection value to obtain the final predicted deflection value of the bridge.

[0024] Through such Figure 3 The sensors deployed as shown synchronously collect three types of data: original deflection monitoring signals at the bridge mid-span, real-time environmental temperature and humidity data, and traffic load WIM data (vehicle arrival time, speed, measured mass, and traffic flow). The thermal characteristics of the traffic flow are as follows: Figure 4 As shown, it exhibits a significant diurnal periodicity, with dense traffic during the day and sparse traffic at night; the environmental temperature and humidity change patterns are as follows: Figure 5 As shown, temperature fluctuates between day and night, and humidity is negatively correlated with temperature, which are typical characteristics of natural environmental changes. Z-score standardization was performed on all raw monitoring data to eliminate interference from sensor noise and dimensional differences.

[0025] The normalized original deflection signal is decomposed using a Gaussian low-pass filter. The core is to decouple the coupled signal into low-frequency trend components and high-frequency detail components with clear physical meaning. The filter step size is determined by the optimal balance between the fitting residual and the trend smoothness to avoid empirical errors.

[0026] For the two decomposed components, physical characteristics are enhanced by combining heat transfer mechanism, structural mechanics principle, and kinematic principle to reconstruct effective temperature characteristics (for low-frequency components) and dynamic load flow characteristics (for high-frequency components), thus making up for the lack of physical information in the original data.

[0027] The process of obtaining effective temperature features by physical feature enhancement of low-frequency trend components includes: Assuming the bridge structure is a uniformly heated body, and the rate of heat exchange within it is proportional to the ambient temperature difference, a first-order linear ordinary differential equation for the effective temperature of the structure is constructed based on Newton's law of cooling. The expression is as follows: ; in, for The measured ambient temperature at any given time; Thermal conductivity is related to the specific heat capacity and thermal conductivity of a material. for Effective temperature of the structure at any given time; The first-order linear ordinary differential equation is approximated using the Euler method, with the time step set to... A recursive physical model in the form of an exponentially weighted moving average is derived: ; in, The thermal decay coefficient, Physically, it represents the structure's ability to "memorize" the temperature state at a previous moment. The larger the value, the stronger the thermal inertia of the structure and the longer the hysteresis time.

[0028] To overcome the reliance on experience in selecting attenuation coefficients To address the subjectivity of the problem, a dual-driven parameter identification strategy based on both physics and data is proposed. This involves establishing the thermal attenuation coefficient. With physical lag time Mapping function: ; in, To accommodate time scale factors with minute-level sampling frequencies; Global grid optimization is performed within the preset physical search interval τ∈[τmin,τmax] with a step size of 0.05h, and the optimal lag time is determined by a dual-index collaborative objective function. : ; in, For low-frequency deflection trend components, For Pearson correlation operators, is the weighting factor, N is the sample size, and a and b are both linear regression coefficients; Based on the optimal lag time The reconstructed effective temperature characteristics are precisely phase-aligned with the low-frequency deflection trend components. This ensures that the reconstructed effective temperature remains highly synchronized with the deflection trend in phase. Maximize), while eliminating the hysteresis loop characteristic in the temperature-deflection relationship ( Minimize, thereby achieving precise physical alignment between environmental effects and structural responses.

[0029] To address the issues of discreteness and lack of spatial weighting in raw traffic data, dynamic load flow characteristics are constructed by combining the influence lines of simply supported beams and the superposition principle of elastic systems. The process of obtaining dynamic load flow characteristics by physically enhancing high-frequency detail components includes: Traffic load increases significantly during the day with increasing traffic volume, and then falls back to a baseline level at night, exhibiting a significant diurnal periodicity. Based on this physical law, this study logically optimizes the traffic input characteristics and constructs a dynamic load flow model based on influence line weights.

[0030] To transform discrete traffic WIM data into physical characteristics that can map continuous structural responses, a dynamic load-flow model based on spatiotemporal kinematics principles was constructed. For example... Figure 6 As shown, the model first derives the real-time trajectory of vehicles on the bridge using kinematic equations. Assuming the bridge is a one-dimensional linear space with the traffic flow direction as the positive direction, the real-time trajectory of vehicles on the bridge is derived based on the kinematic equations. For the j-th vehicle, its instantaneous longitudinal coordinate expression at time t is: ; in, Let be the speed of the j-th vehicle. Let j be the time when the j-th vehicle arrives at the bridgehead; Define the set of valid vehicles within the calculated span L of the bridge at time t, expressed as: = ; Furthermore, considering that the mid-span deflection response of a simply supported hollow slab bridge is highly sensitive to the load location, this study introduces a normalized influence coefficient function. This is used to quantify the contribution weights of loads at different locations. Based on structural mechanics principles, the influence line of mid-span deflection approximately exhibits a triangular distribution; therefore, a normalized influence operator is defined. : ; Where x is the longitudinal distance between the vehicle and the support, quantifying the contribution weight of the vehicle's position to the mid-span deflection; this physical model clarifies the boundary conditions: when the vehicle is located at the support ( or It does not contribute to the mid-span deflection when the vehicle is in the mid-span, but when the vehicle travels to the mid-span ( The contribution weight reaches its peak at this time.

[0031] Based on the principle of linear superposition of elastic systems, the total effect of dynamic effective load on the bridge at time t is calculated: ; in, To determine the measured mass of the j-th vehicle, the discrete WIM data is transformed into a continuous load intensity time series synchronized with the deflection sampling frequency, thus giving the traffic data a clear structural mechanical meaning.

[0032] like Figure 2 As shown, a parameter-independent two-stage parallel LSTM model (LSTM-TD) is constructed, including a trend sub-model (LSTM-Trend) and a detail sub-model (LSTM-Detail). The internal structure of the LSTM neuron is as follows. Figure 2 As shown, the two sub-models are designed with frequency domain sensitivity differentiation for different components of physical features, supporting independent parallel training and prediction.

[0033] Both the trend sub-model LSTM-Trend and the detail sub-model LSTM-Detail have LSTM neural units that include a forget gate, an input gate, an output gate, and a cell state, with the input gates exhibiting differences in frequency domain sensitivity. The input gate of the trend sub-model LSTM-Trend is designed for long-cycle thermal accumulation effects and maintains high sensitivity to smooth gradients in environmental temperature changes. The input gate of the detail sub-model LSTM-Detail is designed for transient traffic load impacts and is used to instantaneously capture the pulse characteristics of high-frequency vehicle data. The forget gate has an adaptive denoising function, which attenuates random environmental noise independent of the bridge structural state by dynamically adjusting the information retention rate.

[0034] The LSTM-Trend input consists of effective temperature features and historical data of low-frequency trend components, and outputs predicted low-frequency deflection values; the LSTM-Detail input consists of dynamic load flow features and historical data of high-frequency detail components, and outputs predicted high-frequency deflection values; the LSTM-Naive input consists of raw temperature and humidity data and raw traffic flow data; and the LSTM-Integrated input consists of enhanced physical features, using a single LSTM network architecture.

[0035] The input vector for the naive LSTM-Naive model is: ; in, Historical deflection data, Real-time temperature without considering thermal hysteresis The original traffic flow statistics lack spatial weights; The input vector for the overall LSTM-Integrated model is: ; in, For effective temperature characteristics, This represents the characteristics of dynamic load flow.

[0036] The computation process of an LSTM neural unit is as follows: Activation function via Sigmoid Calculate the forget gate at time t Input gate With output gate Activation status: ; in, The input feature vector at time t, The hidden state at time t-1 , , These are the weight matrices for the forget gate, input gate, and output gate, respectively. , , These are the bias vectors for the forget gate, input gate, and output gate, respectively. In the trend sub-model (LSTM-Trend), the input gate is guided to capture long-period heat accumulation effects, maintaining high sensitivity to smooth gradients of environmental temperature changes. In the detail sub-model (LSTM-Detail), this gating mechanism focuses on identifying transient... Meanwhile, the Gate of Oblivion It is equipped with adaptive noise reduction function, which effectively attenuates random environmental noise that is unrelated to the state of the structure itself by dynamically adjusting the information retention rate.

[0037] The system simulates the impact of traffic loads to ensure that the pulse characteristics of high-frequency vehicle data are captured instantaneously.

[0038] Candidate memories at time t are generated using the Tanh function. : ; in, The weight matrix for candidate memories. The bias vector for candidate memories; Update the cell state at time t using the Hadamard product. With hidden layer output : ; ; in, The cell state at time t-1.

[0039] Through this mechanism, cell state It serves as a long-term carrier of physical information, effectively suppressing noise interference while accurately maintaining the nonlinear evolution trend of bridge deflection, thereby ensuring the numerical stability and physical consistency of the model in long-sequence prediction tasks.

[0040] To quantitatively evaluate the model's prediction accuracy for vehicle-induced deflection, this paper selects the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (CDO). This is used as the core evaluation indicator. Specifically: In bridge health monitoring, RMSE directly reflects the numerical deviation between predicted and actual deflection. Because it squares the error, it is highly sensitive to outliers and extreme biases in the data. Its calculation formula is as follows: ; MAE represents the average absolute error between predicted and actual values. Compared to RMSE, MAE more robustly reflects the average error level of predicted values ​​and is less susceptible to excessive interference from extreme outliers. Its calculation formula is as follows: ; Coefficient of determination ( This metric measures the proportion of the variance in the actual data explained by the model's predictions, reflecting the goodness of fit between the predicted and actual curves. Its calculation formula is as follows: ; Where N is the total number of samples in the test set. This represents the actual measured value of deflection. These are the values ​​predicted by the deflection model. This represents the average value of the actual monitored deflection values. When... The closer the value is to 1, the more effectively the model can capture the trend changes caused by environmental effects and the high-frequency deflection fluctuation characteristics caused by traffic load.

[0041] A deflection prediction system for medium- and small-span bridges based on signal decomposition and two-stage LSTM includes: The data acquisition module is used to collect the original deflection monitoring signals, environmental temperature and humidity monitoring data, and traffic load WIM monitoring data of small and medium span bridges. The data preprocessing module is used to perform Z-Score normalization preprocessing on the raw monitoring data collected by the data acquisition module. At the same time, a Gaussian low-pass filter is used to decompose the preprocessed raw deflection monitoring signal to obtain low-frequency trend components and high-frequency detail components. The physical feature enhancement module is connected to the data preprocessing module and the data acquisition module respectively. It is used to reconstruct the effective temperature features of the low-frequency trend components and construct the dynamic load flow features of the high-frequency detail components. The two-stage LSTM prediction module, connected to the physical feature enhancement module, includes a trend sub-model LSTM-Trend and a detail sub-model LSTM-Detail that run in parallel with independent parameters, to output low-frequency deflection prediction values ​​and high-frequency deflection prediction values ​​respectively. The result fusion module, connected to the two-stage LSTM prediction module, is used to linearly superimpose the low-frequency deflection prediction value with the high-frequency deflection prediction value to obtain the final deflection prediction value of the bridge. The performance evaluation module, connected to the result fusion module and the data acquisition module respectively, is used to evaluate the accuracy and stability of the final deflection prediction value of the bridge.

[0042] The physical feature enhancement module includes a temperature feature reconstruction unit and a load flow feature construction unit; The temperature feature reconstruction unit optimizes the objective function based on Newton's law of cooling and a dual-index collaborative objective function to reconstruct the effective temperature features. The load flow characteristic construction unit is based on kinematic equations, normalized influence operators and the principle of linear superposition of elastic systems to realize the construction of dynamic load flow characteristics; The two-stage LSTM prediction module's trend sub-model LSTM-Trend and detail sub-model LSTM-Detail support parallel computation, improving computational efficiency without changing the total amount of computation.

[0043] An experimental dataset was constructed based on long-term monitoring data from a 30m prestressed concrete hollow slab bridge in service. Data was collected at a frequency of 1Hz, covering a continuous monitoring period of one month, totaling 2,677,794 sampling points. This massive dataset comprehensively records the macroscopic trend drift caused by diurnal temperature variations and the transient impacts caused by random traffic flow. To eliminate sensor noise interference and standardize the units of measurement, all input data underwent Z-score normalization.

[0044] like Figures 7-9 As shown, all three models generally capture the global trend of the deflection time series. However, the Naive and Baseline models fail to accurately track fluctuations and peak amplitudes caused by temperature changes, exhibiting significant deviations from the true values. In contrast, the two-stage model's predicted trajectory closely matches the true values ​​throughout the entire period. Figure 10 Statistical comparisons further confirm this superiority. The LSTM-TD model will use R... 2 The efficiency was improved to over 0.98, and the RMSE was reduced by 49.4% and MAE by 55.6% compared to the baseline. Therefore, these results confirm that the proposed strategy is an effective solution for accurate structural health monitoring of small and medium-span bridges.

[0045] Figures 11-15The probability density function (PDF) and cumulative distribution function (CDF) of the prediction error are presented. The Trend-Detail model exhibits a significant, sharp, and narrow peak centered at zero in the PDF plot, indicating a significant reduction in error dispersion compared to the Naive and Baseline models. Furthermore, the CDF curve shows that the proposed model achieves a 95% confidence level at a lower error threshold, validating its superior stability and accuracy in structural response reconstruction.

[0046] Figure 16 The computation time of each model was compared. Data shows that since the total computational load is roughly the same when processing data of the same scale, the time consumption in serial mode is basically consistent. However, unlike other models, the two sub-models of the trend-detail model do not interfere with each other and support independent operation. When a parallel computing strategy is adopted, the model's running efficiency is improved by 1.91 times. This characteristic is crucial for bridge monitoring systems with high real-time requirements, and better meets the timeliness needs of engineering early warning.

[0047] Experimental results show that the LSTM model can effectively fit the nonlinear relationship between environmental loads and structural response. Even the naive model with a simple structure has a high coefficient of determination. The efficiency score also reached 0.95. This indicates that the data-driven approach is effective in handling such long sequence dependency problems, providing a reliable foundation for further model optimization.

[0048] The coefficient of determination of the proposed method ( The mean square error (RMSE) was improved to 0.98, and the root mean square error (RMSE) was reduced to 0.80 mm, a decrease of approximately 49.4% compared to the baseline model. The predicted residuals of this model exhibit a more concentrated zero-mean normal distribution, with a significant reduction in outliers, indicating that it has good stability under different traffic flow and environmental conditions.

[0049] Because the two sub-models of the two-stage model are mathematically independent, the framework supports parallel computing. With a roughly consistent total computational load, the two-stage model achieves a 1.9x speedup in parallel processing. This makes the algorithm easier to run on edge computing devices with limited computing power, meeting the real-time engineering requirements of bridge structural health monitoring.

[0050] Therefore, this invention adopts the above-mentioned deflection prediction system and method for small and medium-span bridges based on signal decomposition and dual-stage LSTM. It enhances physical features (reconstructs effective temperature and dynamic load flow characteristics) through heat transfer mechanism and structural mechanics principles. It achieves targeted learning of multi-scale features through the frequency domain sensitivity differentiation design of dual-stage parallel LSTM sub-model. Finally, through the superposition of component prediction results and parallel computation, it achieves a significant improvement in the accuracy and stability of deflection prediction for small and medium-span bridges and an optimization of computational efficiency by 1.91 times. It successfully balances real-time performance and engineering adaptability, and solves the pain points of high computational cost and insufficient physical consistency of traditional models.

[0051] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting the deflection of small-to-medium span bridges based on signal decomposition and two-stage LSTM, characterized in that, Includes the following steps: S1. Collect the original deflection monitoring signals, environmental temperature and humidity monitoring data, and traffic load WIM monitoring data of small and medium span bridges, and perform Z-Score standardization preprocessing on the original monitoring data. S2. The preprocessed original deflection monitoring signal is decomposed using a Gaussian low-pass filter to obtain the low-frequency trend component dominated by environmental effects and the high-frequency detail component dominated by traffic load transient impact. The optimal filtering step size of the Gaussian low-pass filter is determined based on the best balance between the fitting residual and the trend smoothness. S3. Physical feature enhancement processing is performed on the low-frequency trend component and the high-frequency detail component respectively to obtain effective temperature features and dynamic load flow features. S4. Construct a two-stage parallel LSTM prediction model. The two-stage parallel LSTM prediction model includes a parameter-independent trend sub-model LSTM-Trend and a detail sub-model LSTM-Detail. Input the effective temperature characteristics and historical data of the low-frequency trend components into LSTM-Trend to obtain the low-frequency deflection prediction value, and input the dynamic load flow characteristics and historical data of the high-frequency detail components into LSTM-Detail to obtain the high-frequency deflection prediction value. S5. Linearly superimpose the predicted low-frequency deflection value with the predicted high-frequency deflection value to obtain the final predicted deflection value of the bridge.

2. The method for predicting the deflection of small-to-medium span bridges based on signal decomposition and two-stage LSTM according to claim 1, characterized in that, The process of obtaining effective temperature features by physical feature enhancement of low-frequency trend components includes: Based on Newton's law of cooling, a first-order linear ordinary differential equation for the effective temperature of the structure is constructed, expressed as: ； in, for The measured ambient temperature at any given time; Thermal conductivity is related to the specific heat capacity and thermal conductivity of a material. for Effective temperature of the structure at any given time; The first-order linear ordinary differential equation is approximated using the Euler method, with the time step set to... A recursive physical model in the form of an exponentially weighted moving average is derived: ； in, The thermal decay coefficient; Establish thermal attenuation coefficient With physical lag time Mapping function: ； in, To accommodate time scale factors with minute-level sampling frequencies; Global grid optimization is performed within the preset physical search interval τ∈[τmin,τmax] with a step size of 0.05h, and the optimal lag time is determined by a dual-index collaborative objective function. : ； in, For low-frequency deflection trend components, For Pearson correlation operators, is the weighting factor, N is the sample size, and a and b are both linear regression coefficients; Based on the optimal lag time The reconstructed effective temperature characteristics are precisely phase-aligned with the low-frequency deflection trend components. .

3. The method for predicting the deflection of small-to-medium span bridges based on signal decomposition and two-stage LSTM according to claim 1, characterized in that, The process of obtaining dynamic load flow characteristics by physical feature enhancement of high-frequency detail components includes: Based on the kinematic equations, the real-time trajectory of the vehicle on the bridge is deduced. For the j-th vehicle, its instantaneous longitudinal coordinate expression at time t is: ； in, Let be the speed of the j-th vehicle. Let j be the time when the j-th vehicle arrives at the bridgehead; Define the set of valid vehicles within the calculated span L of the bridge at time t, expressed as: = ； Based on the triangular distribution characteristics of the influence line of mid-span deflection in a simply supported beam, a normalized influence operator is defined. : ； Where x is the longitudinal distance between the vehicle and the support; Based on the principle of linear superposition of elastic systems, the total effect of dynamic effective load on the bridge at time t is calculated: ； in, Let be the measured mass of the j-th vehicle.

4. The method for predicting the deflection of small-to-medium span bridges based on signal decomposition and two-stage LSTM according to claim 1, characterized in that, Both the trend sub-model LSTM-Trend and the detail sub-model LSTM-Detail have LSTM neural units that include a forget gate, an input gate, an output gate, and a cell state, with the input gates exhibiting differences in frequency domain sensitivity. The input gate of the trend sub-model LSTM-Trend is designed for long-cycle thermal accumulation effects and maintains high sensitivity to smooth gradients in environmental temperature changes. The input gate of the detail sub-model LSTM-Detail is designed for transient traffic load impacts and is used to instantaneously capture the pulse characteristics of high-frequency vehicle data. The forget gate has an adaptive denoising function, which attenuates random environmental noise independent of the bridge structural state by dynamically adjusting the information retention rate.

5. The method for predicting the deflection of small-to-medium span bridges based on signal decomposition and two-stage LSTM according to claim 4, characterized in that, The computation process of an LSTM neural unit is as follows: Activation function via Sigmoid Calculate the forget gate at time t Input gate With output gate Activation status: ； in, The input feature vector at time t, The hidden state at time t-1 , , These are the weight matrices for the forget gate, input gate, and output gate, respectively. , , These are the bias vectors for the forget gate, input gate, and output gate, respectively. Candidate memories at time t are generated using the Tanh function. : ； in, The weight matrix for candidate memories. The bias vector for candidate memories; Update the cell state at time t using the Hadamard product. With hidden layer output : ； ； in, The cell state at time t-1.

6. The method for predicting the deflection of small-to-medium span bridges based on signal decomposition and two-stage LSTM according to claim 1, characterized in that, When constructing the two-stage parallel LSTM prediction model, a control model for comparison and verification was also constructed, including the purely data-driven naive model LSTM-Naive and the physical feature-enhanced integrated model LSTM-Integrated, and the total number of parameters of the two-stage parallel LSTM prediction model, the naive model LSTM-Naive, and the integrated model LSTM-Integrated were kept consistent.

7. The method for predicting the deflection of small-to-medium span bridges based on signal decomposition and two-stage LSTM according to claim 6, characterized in that, The input vector for the naive LSTM-Naive model is: ； in, Historical deflection data, Real-time temperature without considering thermal hysteresis The original traffic flow statistics lack spatial weights; The input vector for the overall LSTM-Integrated model is: ； in, For effective temperature characteristics, This represents the characteristics of dynamic load flow.

8. The method for predicting the deflection of small-to-medium span bridges based on signal decomposition and two-stage LSTM according to claim 1, characterized in that, The method also includes a performance evaluation step for the bridge deflection prediction results, using root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) as evaluation indicators. The calculation formulas are as follows: ； ； ； Where N is the total number of samples in the test set. This represents the actual measured value of deflection. These are the values ​​predicted by the deflection model. This represents the average value of the actual monitored deflection values.

9. A deflection prediction system for small-to-medium span bridges based on signal decomposition and two-stage LSTM, used to implement any one of the deflection prediction methods for small-to-medium span bridges based on signal decomposition and two-stage LSTM as described in claims 1-8, characterized in that, include: The data acquisition module is used to collect the original deflection monitoring signals, environmental temperature and humidity monitoring data, and traffic load WIM monitoring data of small and medium span bridges. The data preprocessing module is used to perform Z-Score normalization preprocessing on the raw monitoring data collected by the data acquisition module. At the same time, a Gaussian low-pass filter is used to decompose the preprocessed raw deflection monitoring signal to obtain low-frequency trend components and high-frequency detail components. The physical feature enhancement module is connected to the data preprocessing module and the data acquisition module respectively. It is used to reconstruct the effective temperature features of the low-frequency trend components and construct the dynamic load flow features of the high-frequency detail components. The two-stage LSTM prediction module, connected to the physical feature enhancement module, includes a trend sub-model LSTM-Trend and a detail sub-model LSTM-Detail that run in parallel with independent parameters, to output low-frequency deflection prediction values ​​and high-frequency deflection prediction values ​​respectively. The result fusion module, connected to the two-stage LSTM prediction module, is used to linearly superimpose the low-frequency deflection prediction value with the high-frequency deflection prediction value to obtain the final deflection prediction value of the bridge. The performance evaluation module, connected to the result fusion module and the data acquisition module respectively, is used to evaluate the accuracy and stability of the final deflection prediction value of the bridge.

10. The deflection prediction system for small-to-medium span bridges based on signal decomposition and two-stage LSTM according to claim 9, characterized in that, The physical feature enhancement module includes a temperature feature reconstruction unit and a load flow feature construction unit; The temperature feature reconstruction unit optimizes the objective function based on Newton's law of cooling and a dual-index collaborative objective function to reconstruct the effective temperature features. The load flow characteristic construction unit is based on kinematic equations, normalized influence operators and the principle of linear superposition of elastic systems to realize the construction of dynamic load flow characteristics; The two-stage LSTM prediction module's trend sub-model LSTM-Trend and detail sub-model LSTM-Detail support parallel computation, improving computational efficiency without changing the total amount of computation.

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