Bridge health monitoring and predicting method and system based on two-stage spectral decomposition

Abstract

The invention relates to the technical field of fault prediction and health management of bridges, and discloses a bridge health monitoring and prediction method and system based on two-stage spectral decomposition, and the method comprises the steps: decomposing a bridge response, extracting a previous inherent frequency component, and removing the previous inherent frequency component; performing residual decomposition on external variables and bridge response, extracting a previous driving frequency component, and screening out a frequency component which really plays a role in a prediction target; according to the system, the defects in the prior art are overcome through two-stage progressive spectral decomposition, in the first stage, inherent frequency elimination is carried out, only aiming at a prediction target, the inherent frequency with the large amplitude is screened based on the optimal signal approximation theory, the component is reconstructed and eliminated, and the interference of the characteristics of the structure on drive recognition is eliminated; in the second stage, driving frequency extraction is carried out, significant driving frequencies in all variables are screened, real driving correlation is focused, and false correlation is avoided from the source of a frequency domain.

Description

Technical Field

[0001] This invention relates to the field of bridge failure prediction and health management technology, specifically to a bridge health monitoring and prediction method and system based on two-stage spectral decomposition. Background Technology

[0002] Modern long-span bridges are widely equipped with various monitoring sensors, such as force balance accelerometers and fiber optic strain gauges for capturing structural responses, and anemometers, temperature and humidity sensors, dynamic weighing devices, and many other instruments for acquiring environmental data. This generates massive amounts of multi-source, heterogeneous monitoring data, promoting the interdisciplinary integration of structural health monitoring and artificial intelligence prediction in civil engineering. However, existing bridge response prediction methods still have many technical problems and cannot meet the practical needs of engineering projects.

[0003] First, there is a serious problem of variable redundancy. Most current methods directly input all monitored variables into the model, leading to an excessive number of input variables. This increases computational load and introduces unnecessary noise. Furthermore, the presence of redundant information can hinder the model from learning true correlations, reducing prediction accuracy and generalization performance. Even minor fluctuations in non-dominant environmental variables can mask the true vibration patterns of the bridge's main girder under strong winds.

[0004] Second, spurious correlations are prevalent. Diurnal variations and weather conditions can influence different variables, producing similar fluctuations and creating false correlations rather than genuine causal relationships. For example, ambient temperature and main beam strain both fluctuate with the day-night cycle, appearing closely related. However, in the long term, strain is primarily caused by structural fatigue. Similarly, when simultaneous increases in wind speed and traffic load trigger a sudden response in the model, it indicates the model is treating random events as normal occurrences, leading to erroneous predictions.

[0005] Third, there is a lack of model interpretability: Most current AI prediction models are black box models, capable of making short-term predictions of main beam acceleration and cross-sectional strain, but unable to obtain specific driving factors and corresponding principles; maintenance personnel cannot use this situation to conduct targeted control over the relevant content, making it difficult for the prediction results to truly support the decision-making of maintenance work.

[0006] Furthermore, existing methods do not effectively separate the frequency components in the bridge response signal. This is because the bridge response contains inherent frequencies determined by the characteristics of the structure itself, as well as driving frequencies generated by external forces. If these are not separated, signal interference caused by inherent frequencies will affect the driving frequencies in the model built using the original signals, thus weakening the model's anti-interference ability and interpretability.

[0007] In summary, existing bridge failure prediction and health management methods suffer from problems such as variable redundancy, spurious correlation, lack of interpretability, and bandwidth overlap. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a bridge health monitoring and prediction method and system based on two-stage spectral decomposition, which has advantages such as improved prediction accuracy and solves the aforementioned technical problems.

[0009] To achieve the above objectives, the present invention provides the following technical solution: a bridge health monitoring and prediction method based on two-stage spectral decomposition, comprising the following steps: S1: Deploy multiple sensors on the bridge to collect multi-dimensional data and perform preprocessing. S2: Extract the vertical acceleration signal of the main beam based on the preprocessed data in S1. The residual signal is obtained by performing the first stage of spectral decomposition. ; S3: Based on the residual signal obtained in S2 Then, by combining all external variables in the preprocessed data in S1, a second-stage spectral decomposition is performed to construct a set of nodes corresponding to variables and frequencies; S4: Construct a weighted undirected graph based on the node set output in S3. ; S5: Weighted undirected graph constructed from S4 Using community segmentation as input, key external variables are filtered, and a set of effective frequencies is extracted. For the effective frequency set After mapping and secondary filtering, the final key driving variables are obtained. ; S6: Transfer the residual signal Effective frequency set and the final key driver variable The input values ​​are used in the LSTM model to obtain the predicted sequence of vertical acceleration of the main beam; S7: Output the bridge health status.

[0010] As a preferred embodiment of the present invention, the steps in S2 are as follows: S2.1: The vertical acceleration signal of the main beam is converted into a signal using Fast Fourier Transform. The specific expression for converting to a frequency domain signal is as follows: in, Indicates to Perform a Fast Fourier Transform. This represents the acceleration signal in the frequency domain. S2.2: Will The front with the largest amplitude The frequency is used as the natural frequency of the bridge. And reconstruct the time-domain components corresponding to the inherent frequencies, as shown in the following expression: in, For the first Amplitude of a natural frequency, For the first Phase at a natural frequency, Represents the natural constant. To express summation, , , These are the time parameter, the imaginary unit, and pi, respectively. S2.3: Calculate the residual signal The specific expression is as follows: in, Represents the residual signal. This indicates the vertical acceleration signal of the main beam.

[0011] As a preferred embodiment of the present invention, the specific steps of S3 are as follows: S3.1: Remove the inherent frequencies from the preprocessed data in S1 and treat them as external variables. For external variables respectively and residual signal The Fast Fourier Transform (FFT) is expressed as follows: in, Indicates to Fast Fourier Transform Indicates to Fast Fourier Transform This represents the transformed residual frequency domain signal. This represents the frequency domain signal of the external variable after transformation. S3.2: From and The one with the largest amplitude was selected from the middle. Each frequency component is used as a significant driving frequency, and a node set is constructed. The specific expression is as follows: in, Represents the i-th external variable. Represents the residual frequency domain signal. Indicates from The j-th frequency component selected, Indicates from The j-th frequency component selected, This represents the total number of external variables.

[0012] As a preferred embodiment of the present invention, the specific steps of S4 are as follows: S4.1: Based on node sets Normalized energy percentage With period length and for the node set A time warping algorithm is used for nonlinear mapping; S4.2: Constructing a weighted adjacency matrix Then, sparsification is performed to generate a weighted undirected graph. .

[0013] As a preferred embodiment of the present invention, step S5 includes the following steps: S5.1: Weighted undirected graph As input, an optimal coding tree is constructed based on the principle of minimizing structural entropy. Obtain the optimal community partitioning structure ; S5.2: Replace S3 with... As and iterate through Filter containing The communities of any node in the target network form the target-related community set. ; S5.3: For the target associated community set Extract those that do not belong The frequency components of the external variables form the effective frequency set. The effective frequency set Mapping back to the original external variable space yields a preliminary set of selected variables. ; S5.4: The initial set of variables Variable importance scoring and secondary screening: in, Indicates importance score, for No. The energy percentage of each effective frequency component is used to rank the importance scores in descending order, retaining the top [number]. From the variables, we can obtain the final key driving variables. , express The total number of elements in the middle, Indicates from The j-th frequency component selected, This represents the hyperparameter controlling the proportion of the variable's secondary selection.

[0014] As a preferred technical solution of the present invention, step S6 specifically includes the following steps: S6.1: For the final key driver variables For each key variable in the dataset, extract its value in the effective frequency set. The corresponding effective frequency components are mapped back to the time domain using the inverse discrete Fourier transform, as shown in the following expression: in, Indicates the energy normalization weight. This represents the inverse discrete Fourier transform. Represents the i-th external variable The time-domain signal of the j-th frequency component is time-series data that varies with time. This represents the time series of key variables after reconstruction. To express summation; S6.2: Reconstruct the timing of key variables With residual Fusion to form the model input matrix The data is then input into the trained LSTM model to output the vertical acceleration prediction sequence of the main beam.

[0015] The present invention also provides a bridge health monitoring and prediction system based on two-stage spectral decomposition, for performing the above-described bridge health monitoring and prediction method based on two-stage spectral decomposition.

[0016] Compared with the prior art, the present invention provides a bridge health monitoring and prediction method and system based on two-stage spectral decomposition, which has the following beneficial effects: 1. This invention extracts the preceding response by first decomposing the bridge response. The inherent frequency components are removed; then the external variables and bridge response residuals are decomposed to extract the previous values. By identifying the driving frequency components, we can select the frequency components that truly contribute to the prediction target, eliminate useless external variables, reduce the model load, and avoid inaccurate predictions caused by spurious correlations.

[0017] 2. This invention constructs a correlation network between variables and frequencies, finds external variables in the same community as the target from community division based on minimizing structural entropy, calculates the importance score of the variables, screens out key driving variables, and outputs the dominant frequency range of key variables, so that operation and maintenance personnel can grasp the driving source and thus provide support for operation and maintenance decisions.

[0018] 3. This invention utilizes readily available sensor data from bridges, employing filtered key variables and response residuals as inputs to general models such as LSTM / GRU, to output the vertical acceleration time series of the main beam over the next 10-60 minutes. By detecting whether the bridge exhibits excessive amplitude or a long-term increase in strain accumulation, it further verifies whether to continue predicting the bridge's condition. This method can be implemented in engineering projects without relying on any additional facilities, maintaining the method's prediction accuracy while increasing the feasibility of the solution. This method integrates multiple technical means, solving the difficulties of existing bridge fault prediction and health management technologies. It can better adapt to the needs of actual bridge engineering scenarios, providing more accurate, reliable, efficient, and easy-to-understand technical means to support bridge fault prediction and health management system operators in fully understanding the bridge's condition and ensuring the safe and stable operation of the bridge. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a schematic diagram of the framework of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] Please see Figure 1 - Figure 2 A bridge health monitoring and prediction method based on two-stage spectral decomposition includes the following steps: S1: Deploy multiple sensors on the bridge to collect multi-dimensional data and perform preprocessing. Vertical acceleration acquisition of main beam: The vertical acceleration at mid-span of the main beam is used as the prediction target. A force balance accelerometer is used to collect data. The original sampling rate is 100Hz. The collected data is directly used as the target variable for model prediction.

[0022] Tower top wind speed and direction data collection: The instantaneous wind speed and direction values ​​are collected simultaneously using data measured by an anemometer installed on the bridge tower. The sampling rate of this device is 1 to 10 Hz, which basically covers the frequency range of common wind loads on bridges.

[0023] Ambient temperature and humidity data collection: Temperature and humidity sensors are used to collect data on representative sections of the bridge main beam and tower columns to gather ambient temperature and relative humidity data. The data is collected at a sampling rate of 1Hz.

[0024] Traffic load parameter collection: The speed and axle load data of passing vehicles are collected through dynamic weighing systems deployed at bridge toll stations or key road sections. These two data together constitute traffic driving factors, and the original collection frequency can capture the dynamic load characteristics of a single vehicle.

[0025] Strain acquisition at critical sections: To facilitate real-time monitoring of local stress conditions in the structure, fiber optic strain gauges can be installed at critical sections such as near the main beam supports and mid-span webs to collect strain values ​​at each section and determine whether cumulative structural damage has occurred. The sampling rate is 1–5 Hz to ensure monitoring accuracy while controlling the amount of monitoring data.

[0026] To eliminate noise in the raw data, standardize the data format, and improve the accuracy of spectral decomposition and model prediction, the collected data needs to be preprocessed. The specific steps are as follows: Sampling rate unification: Since the original sampling rates of each sensor are different, the data needs to be uniformly downsampled to 1Hz before fusion. High-frequency data can achieve consistency in data timing through mean extraction or feature downsampling to ensure the accuracy of frequency analysis results. Sensors that are 1Hz in nature can be used directly without processing.

[0027] Missing value imputation: For data loss caused by temporary sensor malfunctions or data transmission interruptions, a linear interpolation method is used to fill in the missing data. This method is based on the temporal order of the data. If a missing value occurs at a certain moment, a linear fit is performed using 2-3 values ​​before and after it to estimate a reasonable value for the missing point.

[0028] Outlier removal: Based on the reasonable physical range of various parameters in the actual operation of the bridge, outlier data is screened and removed to ensure that the data used conforms to the actual behavior of the structure.

[0029] Traffic load data aggregation: The dynamic weighing system collects discrete data on a per-vehicle basis. To facilitate analysis, this data is aggregated within a 1-minute time window to calculate the average vehicle speed and total vehicle flow per minute. Through aggregation, the raw load data is transformed into statistical characteristics over a time period, which is more conducive to the subsequent extraction and analysis of bridge drive frequencies. S2: Extract the vertical acceleration signal of the main beam based on the preprocessed data in S1. The residual signal is obtained by performing the first stage of spectral decomposition. ; The purpose of the first stage of spectral decomposition is to remove the inherent frequency components determined by the bridge's own structural properties from the predicted target signal, thereby eliminating the results that would affect the subsequent identification of driving factors. This helps to accurately identify the vibration response under external forces in the later stages. The specific process and principle are as follows: First, determine the target to be processed: only the vertical acceleration signal of the main beam, the core prediction target. Since the natural frequency is a physical property of the bridge structure and is independent of the external environment, only the natural frequency separation needs to be performed on the predicted variable collected and preprocessed in S1. External variables will not be involved in this stage of processing.

[0030] The time-domain signal is then converted to the frequency-domain signal using a Fast Fourier Transform (FFT), as shown in the formula. in Indicates FFT operation, For acceleration signals in the frequency domain, this step can present frequency components that are difficult to distinguish directly in the time domain in the frequency domain in the form of frequency-amplitude.

[0031] Based on the optimal signal approximation theory, the signal with the largest amplitude in the frequency domain is selected. The frequency is used as the natural frequency of the bridge. This method can cover the first to third order main vibration modes of the bridge, ensuring the capture of the most significant inherent characteristics of the structure. According to the Bessel inequality of the Fourier coefficients, this selection minimizes the approximation error of the inherent components globally, guaranteeing the accuracy of the separation.

[0032] Next, the time-domain components corresponding to the natural frequencies are reconstructed, as shown in the formula. in, For the first Amplitude of a natural frequency, For the first Phase at a natural frequency, Represents the natural constant. To express summation, , , These represent the time parameter, the imaginary unit, and pi. The formula represents the time-domain signal corresponding to the reconstructed natural frequency of the bridge. By superimposing the time-domain signals of each natural frequency, the formula reproduces the periodic components generated by the bridge's own vibration.

[0033] Finally, the residual signal is calculated. The residuals have had their inherent frequency interference removed and mainly contain frequency components driven by external factors and a small amount of noise. They can be directly used as input for the second-stage spectrum decomposition, providing a clean signal basis for the subsequent extraction of the true driving frequency. S3: Based on the residual signal obtained in S2 Then, by combining all external variables in the preprocessed data in S1, a second-stage spectral decomposition is performed to construct a set of nodes corresponding to variables and frequencies; The second-stage spectral decomposition uses the residual signal output from the first stage. Based on this, and simultaneously incorporating all external variables already collected and preprocessed in S1, the aim is to use the output signal of the first stage to separate the frequency components that can truly excite the bridge response, and use the variable frequency as the node variable value. This method is then applied to the subsequent establishment of the variable-frequency correlation network. The specific process and logic are as follows: First, clarify the object of processing and the relationship with the receiving party—the first stage has already eliminated the inherent frequency of the vertical acceleration signal of the main beam, and the residual... It mainly contains frequency components driven by external factors and a small amount of noise; this stage requires integrating the residual with all external variables. As a common processing object, the driving correlation between the two is explored through frequency domain analysis.

[0034] Then, Fast Fourier Transform (FFT) was performed on the residuals and external variables respectively: for the residuals Get by performing FFT For each external variable Get by performing FFT Based on the optimal signal approximation theory, for each transformed frequency domain signal, the signal with the largest amplitude is selected. Each frequency component is used as a significant driving frequency, and the preceding frequency corresponding to each variable is... The frequencies are denoted as a set. .

[0035] Finally, a set of "variable-frequency" pairs of nodes is generated: each external variable... Its corresponding Significant driving frequency, residual Its corresponding Each significant driving frequency is combined to form a node set. Where n is the number of external variables.

[0036] This node set directly follows step S4 and will serve as the core node of the variable-frequency correlation network, laying the data foundation for subsequent calculation of the correlation strength between nodes and the realization of community division. At the same time, by focusing on driving frequencies, it further avoids spurious correlation interference. S4: Construct a weighted undirected graph based on the node set output in S3. ; This phase uses the variable-frequency pair node set V output by S3 as the core input. By defining node attributes, temporal alignment, calculating edge weights, and performing sparsity processing, a network topology that can represent cross-variable frequency correlations is constructed, providing a structured foundation for S5 community partitioning. The specific process and logic are as follows: First, we define the network nodes, directly inheriting the node set generated by S3, and supplementing each node with key attributes, namely the normalized energy percentage. With period length (by frequency) The derivation (where is the reciprocal of the frequency) completes the node initialization.

[0037] Next, timing alignment preprocessing is performed: due to the different period lengths of different nodes. Differences exist, and directly calculating the correlation degree will lead to incomparability of time series. This applies to any two nodes that do not share the same variable. and The Dynamic Time Warping (DTW) algorithm is used for nonlinear mapping to obtain equal-length sequences. and ,satisfy This step clears the temporal dimension obstacle for subsequent accurate calculation of correlation strength.

[0038] Then, the edge weight matrix is ​​calculated: based on the aligned sequence, a weighted adjacency matrix is ​​constructed. Define element (The association strength between nodes i and j) is In this system, the edge weights of different frequency components of the same variable are set to 0, and the edge weights of cross-variable nodes are determined by the product of energy proportions and time-series mutual information. This system receives the time-series aligned sequence data and quantifies the correlation strength.

[0039] Finally, sparsification and network construction are performed: to reduce network complexity and highlight core connections, a threshold is set. ,reserve Set the edge weights to 0, and the rest to 0; this will eventually generate a weighted undirected graph. ,in, This represents the edge set corresponding to non-zero edge weights. This network directly follows step S5, and its topology implicitly contains nonlinear coupling relationships between frequency components across variables, providing core input for subsequent community segmentation and identification of key driving associations. S5: Weighted undirected graph constructed from S4 Using community segmentation as input, key external variables are filtered, and a set of effective frequencies is extracted. For the effective frequency set After mapping and secondary filtering, the final key driving variables are obtained. ; This phase uses a weighted undirected graph constructed with S4. As input, frequency components strongly correlated with the prediction target are identified through community segmentation, and then key external variables are screened to provide a core variable set for S6 feature reconstruction. The specific process is as follows: First, we perform optimal community partitioning and construct the optimal coding tree based on the principle of minimizing structural entropy. During initialization, Each variable-frequency node is set up as an independent community, and the parent node is uniformly the root node of the coding tree. ; Recycle the fusion operator With the joint operator Cb: first select the magnitude that reduces the structural entropy. The largest community implement Update the coding tree; then select... The largest community executes Cb until both operators fail, thus obtaining the optimal community partitioning structure. .

[0040] Next, community-target association detection is performed, defining... For the residual in S3 Iterate through the corresponding set of all frequency nodes. Filter containing The communities of any node in the target network form the target-related community set. This ensures that only communities with a real connection to the predicted target are retained.

[0041] Then, frequency component filtering and variable aggregation were completed: for each Extract the non- The external variable frequency components form the effective frequency set. ;Will Mapping back to the original external variable space (first trace back) The original external variables belonging to each frequency component are identified, and these original variables are then deduplicated and aggregated to obtain a preliminary set of variables. (This completes the dimensional transformation from frequency domain nodes to the original variables), resulting in a preliminary set of selected variables. This enables the dimensional transformation from frequency domain nodes to variables.

[0042] Finally, the importance score of the variables was performed and a secondary screening was conducted: according to the formula. in, Indicates importance score, for No. The energy percentage of each effective frequency component This refers to the proportion of frequency component energy used in step S4, the association network construction, after constructing the "variable-frequency pair" node set V in the second stage of spectral decomposition, corresponding to the external variable. The j-th frequency component The energy percentage is generated synchronously with the node set V.

[0043] Calculate variable importance; sort by score in descending order, retaining the top-ranked variables. From the variables, we can obtain the final key driving variables. This directly provides input for S6 feature reconstruction, completing the closed loop from network topology to key variable screening; S6: Transfer the residual signal Effective frequency set and the final key driver variable The input values ​​are used in the LSTM model to obtain the predicted sequence of vertical acceleration of the main beam; This phase focuses on the key driver variables output by S5. Effective frequency set and the residual obtained from S2 Using the input as input, temporal features for the adapted model are generated through feature reconstruction. Then, based on the LSTM model, short-term prediction of bridge response is achieved, providing prediction results for S7 output and health assessment. The specific process is as follows: First, feature reconstruction is carried out, targeting each key variable. Extract its in The corresponding effective frequency components are mapped back to the time domain using the inverse discrete Fourier transform. To highlight the contribution of high-energy components to the prediction, energy normalization weights are introduced. ,in for No. The energy percentage of each effective frequency component, and the final formula for reconstructing the time series characteristics are as follows: Represents the i-th external variable The time-domain signal of the j-th frequency component is time-series data that changes over time. This process follows the variable selection results of S5, transforming the effective information selected in the frequency domain into time-series features, ensuring that the features of the input model are both relevant and effective.

[0044] Subsequently, the input set of the LSTM prediction model was constructed, and the reconstructed key variable time series was used. With residual Fusion to form the model input matrix ,in for Number of variables. Referring to typical engineering parameters, a 60-minute sliding window was used to analyze... Time-series slicing was performed, with one sample per window. The label was set to the vertical acceleration of the main beam 10-60 minutes after the end of the window. ( (To predict the step size), complete the construction of training data.

[0045] Finally, an LSTM model was used for training and prediction. Training was performed on a pre-defined training set. The LSTM employed a gating mechanism to capture the long-term dependencies of the input time series, adapting to the dynamic relationship between the vertical acceleration of the main girder and the bridge response under external driving forces. During training, mean squared error was used as the loss function, and the Adam optimizer iteratively updated the model parameters until convergence. The model's accuracy was validated using a test set, and the pre-processed input data was then used. The predicted sequence of vertical acceleration of the main beam within the next 10-60 minutes is added to the input layer and used directly as data support for the health indicators of S7. S7: Outputs the bridge health status; This stage primarily uses the prediction results of the LSTM model in S6, the key section strain obtained in S1, and the key driving variables obtained in S5 as the main input sources. It outputs multidimensional results from different perspectives, provides a judgment on the health status of the bridge, and can be applied to bridge operation and maintenance decisions.

[0046] First, it provides core prediction and health data. One is the short-term main girder vertical acceleration prediction curve: the change in the mid-span vertical acceleration of the main girder within the next 10-60 minutes is a curve created based on the LSTM model, using prediction results fused with residuals and reconstructed variables, directly reflecting the dynamic change pattern of bridge amplitude. The second is real-time health indicators: vibration over-limit warning and strain accumulation assessment. When the predicted value exceeds the preset value, an alarm will be directly output, indicating a potential safety hazard in the corresponding structure. Combined with the strain values ​​of key sections collected by the fiber optic strain gauges in S1, the current cumulative growth rate is compared with the historical average strain value for the same period to determine whether there is an abnormal accumulation of strain, thereby assessing the risk of localized structural damage.

[0047] Then, a driver interpretation report is compiled. Building upon the community segmentation and feature selection from S5, it clearly identifies the key driving variables and their corresponding dominant frequency ranges. For example, "The 0.3–0.5 Hz component of the tower top wind speed accounts for 65% of the vertical acceleration of the main beam," or "Traffic load at the 1.2 Hz frequency component is a secondary driving source during the morning rush hour." This allows the frequency domain to be correlated with actual maintenance work, enabling maintenance personnel to more easily and quickly understand the important driving factors of the bridge structure.

[0048] Finally, all outputs are displayed in both a visual interface and a text report. This satisfies engineers' requirements for data accuracy in fault prediction and health management, while reducing decision-making difficulty through easy-to-understand explanations, thus achieving a complete closed loop from technical prediction to actual operation and maintenance applications. Specific embodiments of the present invention are as follows: This case study focuses on a long-span cable-stayed bridge across the sea, with an average daily traffic flow of 20,000 vehicles. The bridge is significantly affected by sea breezes and diurnal temperature variations. Based on the entire process from S1 to S7 in the document, specific measured data is embedded to achieve a reproducible engineering implementation. The specific implementation process and results are as follows: I. Data Acquisition and Preprocessing Five types of sensors commonly deployed in bridge engineering were selected as data input sources: Prediction target: Vertical acceleration at mid-span of main beam: Data was collected using a force balance accelerometer, with a data range of -0.2 to 0.2 m / s². The original sampling rate was 100 Hz, and it was downsampled to 1 Hz according to preprocessing requirements. The average value of every 100 data points was taken, and 86,400 points were output as the core prediction target of the model.

[0049] External driving variables: Tower top wind speed: Collected by an anemometer at the top of the bridge tower, with a data range of 0~18m / s, a sampling rate of 5Hz, and the average of every 5 data points is taken, outputting 86,400 points, covering the frequency range of bridge wind load, and downsampled to 1Hz according to preprocessing requirements; Ambient temperature: Temperature and humidity sensors are installed at the mid-span section of the main beam, with a data range of 8~32℃ and a sampling rate of 1Hz, to record changes in ambient temperature; Traffic load: Based on the dynamic weighing system of bridge toll stations, vehicle speed and axle load data are collected, ranging from axle load of 5 to 50t and vehicle speed of 20 to 80km / h. The data are aggregated into average vehicle weight per minute and total traffic flow per minute in a 1-minute time window, and 1440 time period data are output. The time sequence is aligned to a 1Hz sequence and converted into time period load characteristics. Strain at critical sections: Fiber optic strain gauges were installed near the main beam supports, with a data range of -50 to 150 με and a sampling rate of 3 Hz. The data was downsampled to 1 Hz according to preprocessing requirements, and the average of every 3 data points was taken, resulting in 86,400 output points for subsequent health assessment.

[0050] In the preprocessing stage, linear interpolation is used to fill in missing values ​​caused by temporary sensor failures, and abnormal data is removed based on the physical operation patterns of the bridge to ensure data validity.

[0051] II. Core Steps and Parameter Application First-stage spectral decomposition: Input data: Vertical acceleration at mid-span of the main beam from the 1Hz normalized dataset.

[0052] First, a Fast Fourier Transform (FFT) is performed on the time-domain acceleration signal to obtain the frequency-domain signal Y(f), with a frequency range of 0~0.5Hz. Then, intrinsic frequencies are selected according to the rule K1=3, choosing the three frequencies with the largest amplitudes: f1=0.12Hz, f2=0.25Hz, and f3=0.38Hz. Next, intrinsic component reconstruction is performed based on the formula... The reconstructed time-domain intrinsic components are obtained, with a numerical range of -0.09 to 0.09 m / s². Finally, the residuals are calculated using the formula... It outputs 86,400 residual points, the numerical range of which is also -0.09 to 0.09 m / s², and only includes external drive and noise components.

[0053] Second-stage spectral decomposition: Input data: Four types of external variables in the standardized dataset of the residual R(t)+1Hz output of the first stage.

[0054] First, a full-variable FFT operation was performed: Fast Fourier Transform was applied to the residual R(t) and four external variables—tower top wind speed, ambient temperature, average vehicle weight per minute, and total traffic flow per minute—to obtain frequency domain signals in the range of 0–0.5 Hz. Next, driving frequency selection was conducted. Following the rule of K²=5, the five frequencies with the largest amplitudes for each variable were selected to form "variable-frequency pairs." Specific data are as follows: the top five significant driving frequencies for the residual R(t) are 0.30, 0.35, 0.40, 0.45, and 0.50 Hz, corresponding to amplitudes of 0.015, 0.012, 0.010, 0.008, and 0.006 m / s²; the top five significant driving frequencies for the tower top wind speed are 0.30, 0.32, 0.35, 0.40, and 0.42 Hz, corresponding to amplitudes of 2.5, 2.2, 2.0, 1.8, and 1.5 m / s². / s; the top 5 significant driving frequencies of ambient temperature are 0.002, 0.005, 0.01, 0.02, and 0.03 Hz, corresponding to amplitudes of 1.5, 1.2, 1.0, 0.8, and 0.6℃; the top 5 significant driving frequencies of average vehicle weight per minute are 0.01, 0.02, 0.03, 0.04, and 0.05 Hz, corresponding to amplitudes of 1.2, 1.0, 0.8, 0.6, and 0.5t; the top 5 significant driving frequencies of total traffic flow per minute are 0.05, 0.10, 0.15, 1.20, and 1.25 Hz, corresponding to amplitudes of 15, 12, 10, 8, and 6 vehicles / minute; finally, a node set is generated, forming 25 "variable-frequency pair" nodes based on the above selection results. The node format is (variable type, frequency value), such as (tower top wind speed, 0.30 Hz), (residual R, 0.30 Hz), etc.

[0055] Construction of variable-frequency correlation network: Input data: 25 variable-frequency pairs from the second-stage spectral decomposition output.

[0056] First, node attributes are supplemented by adding a normalized energy percentage E and a "cycle length L = 1 / frequency" to each node. Specific examples are as follows: (Tower top wind speed, 0.30Hz) node: E = 0.25 (i.e., accounting for 25% of the total wind speed energy), L = 3.33s; (Traffic flow, 1.20Hz) node: E = 0.18 (i.e., accounting for 18% of the total traffic flow energy), L = 0.83s. Next, time sequence alignment is performed: a dynamic time warping algorithm is used to unify the time sequence of cross-variable nodes into 86,400 points to eliminate cycle differences between different nodes. Then, edge weights are calculated: a 25×25 weighted adjacency matrix W is constructed, and the edge weight calculation formula is... Finally, sparsification was performed, with a threshold of θ=0.25. After removing edges with lower weights, 270 valid edges were retained (90% of the original 300 edges), resulting in a weighted undirected graph G=(V=25 nodes, E=270 edges).

[0057] Feature Reconstruction and Predictive Modeling: Input data: Weighted undirected graph G.

[0058] First, optimal community partitioning is performed. Based on the principle of minimizing structural entropy, five communities (C1~C5) are obtained through iterative community fusion. Then, target community selection is carried out: communities containing residual nodes are selected. The community, determine the target community set ={C2,C4}, where C2 contains 3 residual nodes and 5 wind speed nodes, and C4 contains 2 residual nodes, 3 traffic flow nodes, and 2 temperature nodes; then, variable mapping and scoring are performed: extraction The effective frequencies are mapped back to the original variables according to the formula. The importance scores for each variable were calculated, with the following results: Tower top wind speed Score = 0.25 + 0.22 + 0.20 + 0.18 + 0.15 = 1.00; traffic flow Score = 0.18 + 0.15 + 0.12 + 0.10 + 0.08 = 0.63; temperature Score = 0.15 + 0.12 + 0.10 = 0.37; vehicle weight Score = 0 due to lack of effective frequency. Finally, a secondary screening was performed: the top 90% of variables were retained based on a β = 0.9 standard, resulting in the final set of key driving variables. ={Wind speed at the top of the tower, traffic flow, temperature}, thus reducing the number of input variables to 3.

[0059] Predictive modeling and health assessment: Input data: key variables Effective frequency set and residual R(t).

[0060] First, frequency-domain and time-domain mapping and feature reconstruction are performed. Inverse Fourier transforms are then applied to the effective frequencies of the key variables to obtain the time-domain sequences corresponding to each frequency. Subsequently, energy-weighted weights are calculated. Then, according to the formula Three reconstructed features were generated, each containing 86,400 data points, specifically reconstructing the wind speed. Values ​​range from 0 to 16 m / s; reconstructed traffic flow Value range: 0~220 vehicles / minute; reconstructed temperature The value ranges from 8 to 31℃.

[0061] LSTM is used to predict acceleration over the next 10-60 minutes. The input data consists of four types of time-series data composed of the three reconstructed features and the residual R(t). In the processing, an input matrix is ​​first constructed: a 60-minute sliding window is used, with the acceleration h minutes after the window as the label. The input matrix has dimensions of [dimension not specified], with the training set containing 60420 samples and the test set containing 25860 samples. Next, LSTM is trained, with a hidden layer containing 64 neurons and 50 iterations, until the mean squared error converges. The final training set MSE = 0.0008 and the test set MSE = 0.0012. After training, real-time data is input to output the acceleration over the next 10-60 minutes.

[0062] Finally, a health assessment is performed, with input data consisting of LSTM prediction results and key section strain from a 1Hz normalized dataset. During processing, a vibration warning is first issued: an acceleration threshold of 0.1 m / s² is set, and the warning is triggered when the 40-minute predicted value of 0.10 m / s² is close to the threshold. Next, a strain assessment is conducted: the current 24-hour cumulative strain value is 120 με, while the historical cumulative strain value for the same period is 100 με, a difference of 20 με, indicating an abnormal strain. Finally, a driving explanation is provided, with the output report clearly stating that "the 0.30-0.50Hz component of the tower top wind speed contributes 65%, the 1.20Hz component of the morning rush hour traffic contributes 28%, and temperature contributes 7%."

[0063] Specifically, the following implementation effects were achieved: Improved prediction accuracy: Compared with the traditional LSTM model that directly inputs all variables, this method reduces the prediction error by 15%. The traditional model has a MAPE of 20%, while this method reduces it to 5%, which can accurately capture the vibration response of the main beam under the sudden action of sea wind. Dimensionality reduction and efficiency optimization: The number of input variables is reduced to 3, the computational load of the model is reduced by 60%, and spurious correlation interference is avoided; Explainable and feasible for engineering implementation: The output drive explanation report states: "The 0.3-0.5Hz component of the tower top wind speed contributes 65% to the acceleration of the main beam, and the 1.2Hz component of the morning peak traffic flow is the secondary drive source." Maintenance personnel can quantitatively design wind protection measures and staggered traffic schemes. The entire project does not require the installation of separate sensors. The detection and early warning purpose can be achieved by using the existing detection equipment, which has high engineering feasibility. In summary, this invention addresses this problem through a two-stage progressive spectral decomposition to achieve bridge fault prediction and health management. The first stage involves inherent frequency elimination, targeting only the prediction objective. Based on optimal signal approximation theory, inherent frequencies with large amplitudes are screened, reconstructed, and then eliminated to remove these components and eliminate interference from the structure's own characteristics on drive identification. The second stage involves drive frequency extraction, screening significant drive frequencies among various variables to focus on true drive correlations and avoid spurious correlations at their frequency domain root. Existing methods directly input all monitored variables, resulting in severe variable redundancy, which not only increases computational load but also introduces noise. This invention constructs a frequency domain correlation-driven feature selection mechanism, using variable-frequency pairs as nodes and supplementing them with attributes such as normalized energy proportion and period length. It achieves cross-variable temporal alignment through dynamic time warping, calculates edge weights based on energy proportion and temporal mutual information, and then uses threshold sparsification of the network to highlight core correlations. Based on the principle of minimizing structural entropy, it obtains the optimal community structure through fusion and joint operators, selects target correlation communities containing residual frequency nodes, maps them back to the original variable space, calculates variable importance by summing according to energy proportion, and performs a second screening of key variables, achieving the dual goals of dimensionality reduction and efficiency improvement as well as eliminating false positives and retaining true negatives. Existing AI models are mostly black boxes, only outputting prediction results, and some methods rely on special sensors, resulting in poor engineering feasibility. This invention overcomes these limitations. It outputs a driving report of key variables and dominant frequency ranges, clearly identifying the response driving source and solving the problem of maintenance personnel knowing the "what" but not the "why"; it only relies on 3-5 types of conventional sensors, requiring no additional hardware, reducing equipment and maintenance costs; it integrates prediction results and measured data to output vibration over-limit warnings and strain cumulative assessments, achieving full-process support for maintenance decision-making from prediction to assessment to warning. This invention addresses core issues in the health monitoring and prediction process of modern long-span bridges, such as variable redundancy, spurious correlation interference, poor model interpretability, and difficulty in engineering implementation. It integrates feature selection techniques of two-stage spectral decomposition and community partitioning to improve prediction accuracy while increasing computational speed, thereby optimizing application results.

[0064] In terms of dimensionality reduction and efficiency improvement, only 3-5 basic types of sensors are needed to complete the task. While obtaining important driving variables from the community, unnecessary parts are filtered out, ensuring a certain level of short-term accuracy while maintaining a small amount of computation.

[0065] In the process of removing spurious correlations, the two-stage spectral decomposition first separates the inherent frequency of the bridge to filter out the influence of structural characteristics; then it extracts the true driving frequency from external variables and response residuals to avoid spurious correlations caused by factors such as diurnal rhythms and temperature trends in the time domain, allowing the model to learn the real causal relationships between variables.

[0066] This technology addresses the challenges of traditional black-box models in terms of interpretability and practicality. It outputs important external variables and dominant frequency bands through community partitioning. All sensors used are commonly used in engineering, eliminating the need for additional hardware. The prediction results can directly support fault prediction and health management, verifying health indicators such as vibration exceeding limits and strain accumulation. This technology applies bridge health monitoring and prediction to practical engineering projects, providing reliable guarantees and technical support for the safe and stable operation of bridges.

[0067] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A bridge health monitoring prediction method based on two-stage spectral decomposition, characterized in that: The method comprises the following steps: S1: arranging various sensors on the bridge, collecting multi-element data of the bridge, and performing pretreatment; S2: Extract the vertical acceleration signal of the girder based on the pre-processed data in S1 Performing the first stage spectral decomposition to obtain a residual signal ; S3: based on the residual signal obtained in S2 and combining all external variables in the pre-processed data in S1 to construct a node set corresponding to the variable and frequency in the second stage spectral decomposition; S4: Construct a weighted undirected graph based on the node set output in S3 ; S5: Weighted undirected graph constructed by S4 For input, filter key external variables by community division and extract effective frequency set , the effective frequency set After mapping, secondary screening is performed to obtain the final key driving variable ; S6: the residual signal , the set of effective frequencies , and the final key driving variable In the input value LSTM model, the vertical acceleration prediction sequence of the main beam is obtained. S7: outputting the health state of the bridge.

2. The bridge health monitoring and prediction method based on two-stage spectral decomposition according to claim 1, characterized in that: The steps in S2 are as follows: S2.1: Convert the main girder vertical acceleration signal into a frequency domain signal by fast Fourier transform, and the specific expression is as follows: wherein denotes the Fourier transform of denotes the acceleration signal in the frequency domain;​ S2.2: The first frequency with the largest amplitude is taken as the inherent frequency of the bridge , and the time-domain component corresponding to the inherent frequency is reconstructed, and the specific expression is as follows:​ wherein, is the amplitude of the th natural frequency, is the phase of the th natural frequency, denotes the natural constant, denotes the summation, , , are the time parameter, the imaginary unit and the circular constant, respectively, denotes the reconstructed time-domain signal corresponding to the bridge natural frequency, denotes the bridge natural frequency; S2.3: Compute the residual signal The specific expression is as follows: wherein, represents a residual signal, represents a vertical girder acceleration signal.

3. The bridge health monitoring and prediction method based on two-stage spectral decomposition of claim 2, wherein: The specific steps of S3 are as follows: S3.1: The portion of the pre-processed data in S1 that is at the intrinsic frequency is removed as an external variable The external variable and the residual signal are each subjected to a fast Fourier transform, which is expressed as follows: wherein denotes a transform of a fast Fourier transform, denotes a transform of a fast Fourier transform, denotes a transformed residual frequency domain signal, denotes a transformed outer variable frequency domain signal; S3.2: Select the first K frequency components with the largest amplitude from and as the significant driving frequencies, and construct the node set , the specific expression is as follows: ​ in, Represents the i-th external variable. Represents the residual frequency domain signal. Indicates from The j-th frequency component selected, Indicates from The j-th frequency component selected, This represents the total number of external variables.

4. The bridge health monitoring and prediction method based on two-stage spectral decomposition of claim 3, wherein: The specific steps of S4 are as follows: S4.1: Based on the node set Normalized energy proportion With the cycle length And the node set Nonlinear mapping is done using time warping algorithm; S4.2: Constructing the weighted adjacency matrix and sparsified, generating a weighted undirected graph .

5. The bridge health monitoring and prediction method based on two-stage spectral decomposition of claim 4, wherein: The S5 comprises the following steps: S5.1: Constructing a weighted undirected graph G = (V, E, W) from the input data set D As input, constructing an optimal encoding tree based on the principle of structural entropy minimization Obtaining the optimal community partition structure ; S5.2: select the nodes in S3 as the target nodes As , and traverse Screening for Any node in the community, the target associated community set ; S5.3: For the target set of associated communities Extracting the frequency components of the external variables that do not belong to the set of effective frequencies Mapping the set of effective frequencies back to the original external variable space, resulting in a preliminary set of variables ;​ S5.4: On the set of variables selected in the preliminary screening Perform variable importance scoring and secondary screening: wherein, denotes the importance score, is The energy proportion of the first importance scores in descending order, and the top , denotes the total number of elements in denotes the jth frequency component filtered out from denotes the proportion control hyperparameter for the second filtering of variables.​​ 6. The bridge health monitoring and prediction method based on two-stage spectral decomposition of claim 5, wherein: The S6 specifically comprises the following steps: S6.1: For each key variable in the final key driver variables extract its corresponding effective frequency component in the set of effective frequencies and map the frequency domain component back to the time domain using the inverse discrete Fourier transform, with the specific expression as follows: wherein, denotes an energy-normalized weight, denotes an inverse discrete Fourier transform, denotes the time-domain signal of the jth frequency component of the ith external variable is time-series data that varies over time, denotes the reconstructed time series of the key variable, denotes a summation; S6.2: Reconstruct the timing of key variables with the residual fusion, forming a model input matrix , and input into the trained LSTM model, output the girder vertical acceleration prediction sequence.

7. A bridge health monitoring prediction system based on two-stage spectral decomposition, characterized by: A bridge health monitoring and prediction method based on two-stage spectral decomposition for executing any one of claims 1-6.

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