Method for determining bridge structure rigidity change based on bridge health monitoring deformation data

Abstract

The present application relates to the technical field of bridge health monitoring, and discloses a method for determining the change of bridge structure stiffness based on bridge health monitoring deformation data. The method establishes an initial data set of bridge deformation monitoring data and performs multi-scale decomposition processing to generate deformation component data of different time scales; the deformation component data of different time scales is input into a pattern recognition engine to identify feature mode data streams associated with the structure stiffness; a stiffness influence factor sequence is constructed based on the feature mode data streams, and statistical characteristic quantities of the stiffness influence factor sequence are calculated through a sliding time window; the statistical characteristic quantities are subjected to multi-dimensional matching analysis with a historical reference database to output a stiffness anomaly probability index; and a hierarchical verification mechanism is activated according to the stiffness anomaly probability index to confirm the stiffness change trend through a cross-validation algorithm. The present application provides reliable data support for the evaluation of the health condition of bridge structures.

Description

Technical Field

[0001] This invention relates to the field of bridge health monitoring technology, specifically a method for determining changes in bridge structural stiffness based on bridge health monitoring deformation data. Background Technology

[0002] Current bridge structural stiffness monitoring primarily relies on periodic inspections and static data analysis. Existing technologies for processing deformation data mostly employ holistic statistical methods, failing to effectively separate deformation components across different time scales. Monitoring data analysis is limited in scope, unable to identify characteristic patterns specifically correlated with stiffness changes. Stiffness assessment methods are empirical, often based on fixed thresholds, lacking the ability to sensitively identify early signs of stiffness changes. Historical data utilization is insufficient, and benchmark database updates are lagging. Anomaly detection mechanisms are simplistic, resulting in high false alarm and false negative rates. Existing methods need to address key technical challenges such as multi-scale data analysis, feature pattern recognition, dynamic benchmark comparison, and intelligent judgment.

[0003] Traditional stiffness monitoring methods suffer from significant shortcomings in accuracy and early warning capabilities. Data decomposition algorithms are highly complex, resulting in incomplete extraction of multi-scale components. Pattern recognition models have limited training data, leading to insufficient accuracy in feature extraction. Influence factor construction methods are simplistic and fail to comprehensively reflect stiffness variation characteristics. Statistical feature calculation windows are fixed and cannot adapt to the non-stationary nature of deformation data. Historical benchmark databases lack representativeness, limiting the reliability of matching analysis. Probabilistic index calculation models are idealized, resulting in inaccurate uncertainty quantification. Verification mechanisms are slow to respond and cannot promptly confirm trends. Existing technologies necessitate the establishment of an intelligent, end-to-end judgment scheme encompassing data preprocessing and change confirmation. Summary of the Invention

[0004] The purpose of this invention is to provide a method for determining changes in the stiffness of bridge structures based on deformation data from bridge health monitoring, in order to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides a method for determining changes in bridge structural stiffness based on bridge health monitoring deformation data, the method comprising:

[0006] An initial dataset for bridge deformation monitoring was established, and the initial dataset was decomposed into multiple scales to generate deformation component data at different time scales.

[0007] Deformation component data at different time scales are input into the pattern recognition engine to identify the characteristic pattern data stream associated with structural stiffness.

[0008] A stiffness influence factor sequence is constructed based on the feature pattern data stream, and the statistical characteristics of the stiffness influence factor sequence are calculated through a sliding time window.

[0009] The statistical characteristics are matched with the historical benchmark database in multiple dimensions to output the stiffness anomaly probability index.

[0010] The hierarchical verification mechanism is activated based on the stiffness anomaly probability index, and the stiffness change trend is confirmed through cross-validation algorithm.

[0011] Preferably, the multi-scale decomposition process of the initial dataset includes:

[0012] The time-series decomposition algorithm is used to separate bridge deformation monitoring data into long-term trend components, periodic fluctuation components, and random disturbance components. Polynomial fitting is performed on the long-term trend components to extract the trend change rate parameter. Spectral analysis is performed on the periodic fluctuation components to extract the dominant frequency and amplitude characteristics. Probability distribution modeling is performed on the random disturbance components to determine the noise threshold boundary. The processing results of the long-term trend components, periodic fluctuation components, and random disturbance components are recombined into a standardized data matrix.

[0013] Preferably, the operation of the pattern recognition engine includes:

[0014] After receiving the standardized data matrix, a feature space transformation is performed to map the data to a high-dimensional feature space. Similarity matrices for various features are calculated in the high-dimensional feature space, and feature clustering regions are identified using a clustering algorithm. For each feature clustering region, the region center point and boundary range are extracted to form a feature pattern template library. The real-time input feature pattern data stream is dynamically matched with the feature pattern template library, and a matching confidence score is calculated. When the matching confidence score falls below a set threshold, a feature pattern update mechanism is triggered.

[0015] Preferably, the process of constructing the stiffness influence factor sequence includes:

[0016] Feature parameters with correlation to stiffness changes exceeding a set threshold are selected from the feature pattern data stream to form an initial feature set. Principal component analysis is performed on the initial feature set to extract the main feature vectors. The main feature vectors are convolved with real-time deformation data to generate the original sequence of stiffness influence factors. The original sequence of stiffness influence factors is normalized to eliminate the influence of dimensions. The normalized sequence is smoothed using an exponentially weighted moving average algorithm to obtain the final stiffness influence factor sequence used for stiffness determination.

[0017] Preferably, the construction of the stiffness influence factor sequence based on the feature pattern data stream, and the calculation of the statistical features of the stiffness influence factor sequence through a sliding time window, includes:

[0018] Extract stiffness-related feature parameters, including deformation rate, vibration frequency, and amplitude, from the feature pattern data stream;

[0019] The characteristic parameters are standardized to eliminate dimensional differences;

[0020] The standardized feature parameters are weighted and fused to generate the original sequence of stiffness influence factors.

[0021] Set the length and step size of the sliding time window; the window length is adaptively adjusted according to the data sampling frequency.

[0022] Within the sliding time window, calculate the mean, variance, skewness, and kurtosis statistics of the stiffness influence factor sequence;

[0023] Record the statistical characteristics of each time window to form a sequence of statistical characteristics.

[0024] Preferably, the step of performing multi-dimensional matching analysis between statistical features and historical benchmark databases to output stiffness anomaly probability indices includes:

[0025] Retrieve statistical characteristic samples under normal conditions from the historical benchmark database;

[0026] Calculate the Euclidean and Mahalanobis distances between real-time statistical features and historical samples;

[0027] The probability density of real-time features in the historical distribution is estimated using a multivariate normal distribution model.

[0028] By combining distance indices and probability density, the posterior probability of stiffness anomalies is calculated using Bayes' theorem.

[0029] When the posterior probability exceeds the set threshold, the stiffness anomaly probability index is output.

[0030] Preferably, estimating the probability density of real-time features in the historical distribution using a multivariate normal distribution model includes:

[0031] Extract statistical feature samples under normal conditions from the historical benchmark database, and calculate the mean vector and covariance matrix of the samples; use the real-time statistical feature as the input vector and substitute it into the probability density function of the multivariate normal distribution; calculate the probability density value of the real-time statistical feature under the historical distribution based on the mean vector and covariance matrix; perform a logarithmic transformation on the probability density value to avoid numerical underflow; and normalize the probability density value to the range of zero to one.

[0032] Preferably, the calculation of the posterior probability of stiffness anomalies using Bayes' theorem, combining distance indices and probability density, includes:

[0033] The prior probability of stiffness anomaly is pre-defined based on the frequency of anomalous events in historical data. The likelihood probability of real-time statistical features under normal conditions is calculated, using the probability density value estimated by a multivariate normal distribution model as the likelihood probability. The likelihood probability of real-time statistical features under anomalous conditions is also calculated, constructing an anomalous distribution model based on anomalous sample data and estimating the probability density. Bayes' theorem is applied, multiplying the prior probability and the likelihood probability to obtain the non-normalized posterior probability. The non-normalized posterior probability is then normalized to ensure that the sum of the posterior probabilities for all possible states is one. Finally, the posterior probability of stiffness anomaly is output as a stiffness anomaly probability index.

[0034] Preferably, the step of activating the hierarchical verification mechanism based on the stiffness anomaly probability index and confirming the stiffness change trend through a cross-validation algorithm includes:

[0035] Set low, medium, and high thresholds for the stiffness anomaly probability index;

[0036] When the stiffness anomaly probability index is below the low threshold, the verification mechanism is not activated;

[0037] When the stiffness anomaly probability index reaches the low threshold but is below the medium threshold, the primary verification mechanism is activated, and the leave-one-out cross-validation algorithm is used to verify the data using the monitoring data of the most recent time period.

[0038] When the stiffness anomaly probability index reaches the medium threshold but is lower than the high threshold, the intermediate verification mechanism is activated, and the k-fold cross-validation algorithm is used to divide the historical data into k subsets for iterative verification.

[0039] When the stiffness anomaly probability index reaches a high threshold, the advanced verification mechanism is activated, and the time series cross-validation algorithm is adopted to consider the time dependence of the data and perform verification through a sliding time window.

[0040] The confidence level of the stiffness change trend is calculated using a cross-validation algorithm, and the confirmed stiffness change trend is output.

[0041] Preferably, the step of calculating the confidence level of the stiffness change trend using a cross-validation algorithm and outputting the confirmed stiffness change trend includes:

[0042] Select the appropriate cross-validation algorithm based on the level of the activated validation mechanism;

[0043] In the primary validation mechanism, the leave-one-out cross-validation algorithm is used, where each data point is used as the test set and the remaining data is used as the training set to train the stiffness change trend model and calculate the prediction error.

[0044] In the intermediate validation mechanism, the k-fold cross-validation algorithm is used to randomly divide the historical data into k subsets, and cyclically use each subset as the test set and the remaining subsets as the training set to train the model and calculate the average prediction error.

[0045] In the advanced validation mechanism, a time series cross-validation algorithm is used, which slides a window in chronological order, using early data as the training set and recent data as the test set to train the model and calculate the time-related prediction error.

[0046] The confidence level of the stiffness change trend is calculated based on the prediction error. The confidence level is inversely proportional to the prediction error. When the confidence level exceeds a set threshold, the confirmed stiffness change trend is output, including the trend direction and the magnitude of the change.

[0047] Compared with the prior art, the beneficial effects of the present invention are:

[0048] The initial set of bridge deformation monitoring data is subjected to multi-scale decomposition to generate deformation component data at different time scales. Multi-scale decomposition employs algorithms such as wavelet transform to decompose the original signal into long-term trend, medium-term fluctuation, and short-term detail components. The number of decomposition levels is adaptively determined according to monitoring requirements, and each component maintains temporal synchronization. This multi-scale decomposition enables refined extraction of deformation features.

[0049] Deformation component data at different time scales are input into a pattern recognition engine to identify feature pattern data streams associated with structural stiffness. Pattern recognition employs models such as deep learning networks to extract key features such as amplitude and frequency from each component. A confidence threshold is set during the recognition process to ensure the reliability of feature extraction. Stiffness-related features are accurately extracted through pattern recognition.

[0050] A stiffness influencing factor sequence is constructed based on feature pattern data flow, and statistical characteristics are calculated using a sliding time window. The influencing factor sequence integrates multi-dimensional indicators, and the window size adaptively adjusts according to the rate of change of features. Statistical characteristics include parameters such as mean and variance, comprehensively describing the distribution characteristics of the sequence. This achieves dynamic quantitative characterization of stiffness influencing factors.

[0051] Statistical features are matched against a historical benchmark database in a multi-dimensional manner to output a stiffness anomaly probability index. The matching analysis employs a distance metric algorithm to quantify the deviation of the current features from the historical benchmark. The probability index is calculated based on statistical inference theory to quantify anomaly risk. This probabilistic output improves the accuracy of judgment.

[0052] A tiered verification mechanism is activated based on the stiffness anomaly probability index, and the stiffness change trend is confirmed through a cross-validation algorithm. The tiered verification sets multiple threshold levels, corresponding to different verification intensities. Cross-validation integrates various trend analysis algorithms to improve the reliability of the judgment. Reliable confirmation of stiffness changes is achieved through the tiered mechanism.

[0053] This method achieves early identification and accurate determination of stiffness changes through the synergy of multi-scale analysis, pattern recognition, dynamic statistics, and hierarchical verification. Multi-scale decomposition refines feature extraction, pattern recognition accurately correlates stiffness characteristics, dynamic statistics enable continuous monitoring, and hierarchical verification ensures the reliability of results. This significantly improves the sensitivity and accuracy of bridge stiffness monitoring. Attached Figure Description

[0054] Figure 1 This is a schematic diagram illustrating the working principle of the method for determining changes in bridge structural stiffness based on bridge health monitoring deformation data as described in this invention.

[0055] Figure 2 A flowchart for multi-scale decomposition of the initial dataset;

[0056] Figure 3 A flowchart for constructing the stiffness influence factor sequence;

[0057] Figure 4 This is a graph showing the results of stiffness anomaly probability monitoring;

[0058] Figure 5 This diagram illustrates the triggering scenarios of the tiered verification mechanism. Detailed Implementation

[0059] 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.

[0060] Please see Figure 1This invention provides a method for determining bridge structural stiffness changes based on bridge health monitoring deformation data. The method includes: establishing an initial dataset of bridge deformation monitoring data, containing raw deformation measurements obtained from sensors; performing multi-scale decomposition processing on the initial dataset to decompose the data into deformation components at different time scales to separate long-term trends, periodic fluctuations, and random noise components; inputting the deformation component data at different time scales into a pattern recognition engine, which identifies feature pattern data streams associated with structural stiffness through feature extraction and matching techniques; constructing a stiffness influencing factor sequence based on the feature pattern data stream, which calculates statistical features such as mean and variance using a sliding time window to capture the dynamic characteristics of stiffness changes; performing multi-dimensional matching analysis between the statistical features and a historical benchmark database, which stores statistical feature samples under normal conditions, and outputting a stiffness anomaly probability index through distance calculation and a probability model; activating a hierarchical verification mechanism based on the stiffness anomaly probability index, which triggers different levels of cross-validation algorithms, such as leave-one-out or time series cross-validation, based on threshold settings to confirm the confidence level of the stiffness change trend.

[0061] Example 1: See Figure 2 In practical implementation, the first step in determining bridge structural stiffness changes based on bridge health monitoring deformation data is to establish an initial dataset of bridge deformation monitoring data. This initial dataset is continuously collected by a sensor network deployed at key locations such as the bridge's main beams and piers. Sensor types include displacement gauges, inclinometers, or total stations. The collected data is a time series of the bridge's deformation response under the combined effects of environmental and traffic loads. The initial dataset contains raw voltage signals or physical displacement values, recorded at a fixed sampling frequency, forming a two-dimensional data table including timestamps and measurement point numbers. Before being put into use, the initial dataset needs to be cleaned to remove obvious outliers and missing values ​​caused by sensor malfunctions or communication interruptions. Linear interpolation methods are then used to fill in short-term data gaps, forming a complete and continuous initial dataset for subsequent analysis.

[0062] In practical implementation, multi-scale decomposition of the initial dataset is the core step. This multi-scale decomposition uses a time-series decomposition algorithm to separate bridge deformation monitoring data into long-term trend components, periodic fluctuation components, and random disturbance components. The time-series decomposition algorithm is based on a classic decomposition model, assuming that any time series data can be represented as the sum or product of these components. The decomposition process begins with moving average processing, using a window whose length matches the main period of the data to calculate the moving average. This moving average sequence is the initial estimate of the extracted long-term trend component. Subtracting the initial estimate of the long-term trend component from the original data results in a data sequence containing both periodic fluctuation and random disturbance components. Period detection is then performed on this sequence to separate the periodic fluctuation component. Period detection uses spectral analysis, calculating the power spectral density of the data sequence through a fast Fourier transform, identifying the frequencies corresponding to the power spectral peaks as dominant frequencies, and using these dominant frequencies to construct a combination of sine and cosine functions to fit the periodic fluctuation component. Subtracting the fitted periodic fluctuation component from the data sequence containing both the periodic fluctuation and random disturbance components yields the random disturbance component.

[0063] In practice, polynomial fitting is performed on the long-term trend components to extract the trend rate of change parameter. The long-term trend components reflect the slow deformation development of the bridge structure during long-term use due to factors such as material aging, prestress loss, or foundation settlement. Polynomial fitting uses the least squares method, and the fitting order is automatically determined based on the curvature characteristics of the long-term trend components using information criteria; commonly, orders range from 1 to 3. First-order polynomial fitting yields a linear trend, and its slope is the average deformation rate; second-order polynomial fitting can capture acceleration changes; and third-order polynomials can describe more complex curvature changes. After completing the polynomial fitting, the trend rate of change parameter is extracted. For linear trends, the trend rate of change parameter is the slope of the fitted line; for nonlinear trends, the trend rate of change parameter can be taken as the average of the first derivatives over a specific time interval. The trend rate of change parameter is an important indicator for assessing the long-term performance degradation of the structure; its magnitude and sign are directly related to the potential changes in structural stiffness.

[0064] In practice, spectral analysis is performed on the periodic fluctuation components to extract dominant frequencies and amplitude characteristics. The periodic fluctuation components mainly reflect the periodic deformation of the bridge caused by changes in ambient temperature and traffic load cycles. The spectral analysis employs a periodogram method based on Fast Fourier Transform (FFT). After resampling the periodic fluctuation component data into an equally spaced time series, a Hanning window function is applied to reduce spectral leakage, followed by FFT to obtain a frequency domain representation. In the frequency domain, peak points with amplitudes significantly higher than the noise level are identified; the frequencies corresponding to these peak points are the dominant frequencies, and the amplitude value corresponding to each dominant frequency is the amplitude characteristic. Dominant frequencies typically correspond to daily, annual, or traffic flow characteristic cycles, while amplitude characteristics reflect the magnitude of structural deformation under cyclic loading. Shifts in dominant frequencies and abnormal increases in amplitude characteristics may indicate changes in structural stiffness characteristics; therefore, these parameters are closely monitored.

[0065] In practical implementation, probability distribution modeling is performed on the random disturbance components to determine the noise threshold boundary. The random disturbance components are mainly caused by random factors such as measurement noise and wind-induced vibrations, and their statistical characteristics are crucial for distinguishing normal fluctuations from anomalous signals. Probability distribution modeling employs parameter estimation methods, assuming the random disturbance components follow a Gaussian or t-distribution, and using maximum likelihood estimation to fit the distribution parameters, including the mean and variance. For data that significantly deviates from normality, non-parametric methods such as kernel density estimation can be used to establish a probability density model. Based on the fitted probability distribution model, the noise threshold boundary is determined, typically by taking specific quantiles of the distribution as the threshold; for example, the 2.5% and 97.5% quantiles are taken as the lower and upper threshold boundaries, respectively. Data points exceeding the noise threshold boundary are considered potential outliers and require close attention in subsequent analysis.

[0066] In practice, the processing results of the long-term trend component, periodic fluctuation component, and random disturbance component are reorganized into a standardized data matrix. Each row of the standardized data matrix corresponds to a time point, and each column corresponds to a feature parameter extracted from each component. The feature parameters include the trend change rate parameter extracted from the long-term trend component, the dominant frequency and amplitude features extracted from the periodic fluctuation component, and the noise threshold boundary and statistical moment features extracted from the random disturbance component. Before reorganization, all feature parameters are standardized by subtracting the mean of historical data and dividing by its standard deviation to eliminate differences in the dimensions and numerical ranges of different features. The standardized data matrix serves as input to the pattern recognition engine; its regular format facilitates efficient execution of subsequent feature space transformation and pattern matching operations.

[0067] In practical implementation, after receiving the standardized data matrix, the pattern recognition engine performs feature space transformation, mapping the data to a high-dimensional feature space. The purpose of feature space transformation is to enhance the separability of data features under different state modes. Transformation methods employ kernel principal component analysis (KPCA) or autoencoder neural networks. KPCA uses kernel functions to nonlinearly map the original features to a high-dimensional regenerating kernel Hilbert space, and then extracts principal components in the new feature space. Autoencoder neural networks compress the input data into low-dimensional codes through an encoder network, and then reconstruct it through a decoder network, using the output of the encoding layer as the high-dimensional feature representation. The data dimensionality after feature space transformation is usually higher than the original feature dimensionality, but it retains the inherent topological structure and discriminative information of the data.

[0068] In practice, similarity matrices for various features are calculated in the high-dimensional feature space, and clustering algorithms are used to identify feature clustering regions. The similarity matrix uses Euclidean distance or cosine similarity to measure the similarity between high-dimensional feature vectors, forming a symmetric matrix. Density-based clustering methods such as DBSCAN are chosen for the clustering, which can identify clusters of arbitrary shapes and automatically determine the number of clusters. Based on the concept of density reachability, DBSCAN groups density-connected sample points into a cluster and marks points in low-density regions as noise points. The clustering results divide the high-dimensional feature space into several feature clustering regions, each representing a structural response pattern.

[0069] In practice, for each feature cluster, the region center point and boundary range are extracted to form a feature pattern template library. The region center point is obtained by calculating the arithmetic mean of all sample points within the cluster, representing the typical feature vector of that feature pattern. The boundary range is determined by calculating the maximum distance or standard deviation from the center point to the sample points within the cluster, defining the normal fluctuation range of the pattern. The feature pattern template library is stored in the form of a data structure, with each record containing a pattern number, center point vector, boundary radius or covariance matrix, and the statistical frequency of the pattern's occurrence. The real-time input feature pattern data stream is dynamically matched with the feature pattern template library, and a matching confidence score is calculated. The real-time feature pattern data stream is a sequence of real-time monitoring data vectors after multi-scale decomposition and feature space transformation. In the dynamic matching process, for each real-time data vector, the distance from its distance to each center point in the feature pattern template library is calculated, and the pattern with the smallest distance is selected as the matching candidate. The matching confidence score is calculated based on the matching distance, and the commonly used formula is that the score equals one divided by one plus the distance, making the score range between zero and one, with a higher score for closer distances. During the matching process, a distance threshold is set. When the minimum distance exceeds the threshold, the real-time data is considered not to belong to any known pattern, which may indicate the emergence of a new structural state.

[0070] When the matching confidence score falls below a set threshold, a feature pattern update mechanism is triggered. The matching confidence score threshold is dynamically adjusted based on historical data matching performance, typically set to a low quantile in the normal matching score distribution. The feature pattern update mechanism includes two strategies: adding new patterns and adjusting existing patterns. When real-time data continuously deviates from all existing patterns and the deviation exceeds the threshold, the system creates a new feature pattern, using its feature vector as the initial center point. When the matching distance between real-time data and an existing pattern falls within the threshold boundary, the system updates the center point and boundary range of that pattern using an exponentially weighted moving average method, allowing the pattern template to slowly adapt to gradual structural changes.

[0071] Example 2: See Figure 3 In practice, the construction of the stiffness influencing factor sequence begins with the feature pattern data stream, which is time-series data containing multiple feature parameters output by the pattern recognition engine. Feature parameters whose correlation with stiffness changes exceeds a set threshold are selected from the feature pattern data stream to form an initial feature set. The correlation calculation uses the Pearson correlation coefficient method, which measures the degree of linear correlation between each feature parameter and a known stiffness change reference sequence. The set threshold is determined based on historical data analysis; for example, feature parameters with an absolute Pearson correlation coefficient greater than or equal to 0.8 are selected. The selection process traverses all available parameters in the feature pattern data stream, including deformation rate, vibration frequency, and amplitude characteristics, retaining only those parameters that show a strong correlation with stiffness changes. The initial feature set is a subset of parameters containing all feature parameters selected through correlation analysis; these parameters are considered sensitive indicators of stiffness changes.

[0072] Principal component analysis (PCA) is performed on the initial feature set to extract principal eigenvectors. PCA is a dimensionality reduction technique that transforms potentially redundant feature parameters in the initial feature set into a few uncorrelated principal components. The PCA process first calculates the covariance matrix of the initial feature set, which reflects the linear correlation between different feature parameters. Then, eigenvalues ​​and eigenvectors are obtained from the covariance matrix. The magnitude of the eigenvalues ​​represents the variance contribution rate of the corresponding principal component. The principal components with a cumulative variance contribution rate exceeding 85% are selected as principal eigenvectors, sorted by eigenvalues ​​from largest to smallest. The principal eigenvectors are linear transformation bases of the original feature space, and each principal eigenvector is a weighted combination of the original feature parameters. After extracting the principal eigenvectors, the original high-dimensional feature data can be projected into a low-dimensional subspace spanned by the principal eigenvectors, achieving dimensionality reduction while retaining most of the variation information.

[0073] In practice, the main feature vectors are convolved with real-time deformation data to generate the original sequence of stiffness influence factors. Convolution is an integral transform that calculates a local weighted sum by moving the sliding convolution kernel function across the input signal. The main feature vectors are used as the convolution kernel function, and the real-time deformation data is used as the input signal. The convolution formula is as follows:

[0074]

[0075] in: Indicates a point in time The original sequence values ​​of the stiffness influence factor at that location. Indicates a point in time Real-time deformation data values ​​at the location, Indicates the main eigenvectors in lag The value at that location, This represents the half-width of the convolution kernel. Convolution operations effectively capture variation features in real-time deformation data that are similar to the main feature vector patterns, generating the original sequence of stiffness influence factors. The original sequence of stiffness influence factors is a time series, and its numerical value reflects the degree of matching between real-time deformation data and stiffness-sensitive patterns.

[0076] In practice, the original sequence of stiffness influencing factors is normalized to eliminate the influence of dimensions. Normalization maps the numerical range of the original stiffness influencing factor sequence to a standard interval, eliminating the impact of differences in the magnitude of different characteristic parameters on subsequent analysis. The normalization process uses a minimum-maximum scaling method, linearly transforming the original sequence to a range of zero to one. Minimum-maximum scaling requires calculating the minimum and maximum values ​​of the original stiffness influencing factor sequence; the transformation formula is to subtract the minimum value from each data point and then divide by the difference between the maximum and minimum values. When extreme outliers exist in the data distribution, percentile normalization can be used, replacing extreme values ​​with percentiles to improve the robustness of the normalization process. The normalized stiffness influencing factor sequence has a uniform numerical range, facilitating comparative analysis between different time periods and different bridges.

[0077] An exponentially weighted moving average algorithm is used to smooth the normalized sequence, resulting in the final stiffness influence factor sequence used for stiffness determination. The exponentially weighted moving average algorithm is a recursive filtering technique that assigns higher weights to recent data, effectively suppressing random fluctuations while preserving trend information. The recursive formula for the exponentially weighted moving average algorithm is:

[0078]

[0079] in: Indicates a point in time The smoothed sequence values ​​at the point, Indicates a point in time Normalized sequence values ​​at the location, This indicates that the smoothing coefficient ranges from zero to one. Indicates a point in time The smoothed sequence value at that point. Smoothing coefficient. The smoothing degree is controlled; smaller values ​​produce a smoother output but with a larger response lag. The smoothing coefficient is adaptively selected based on the data sampling frequency and fluctuation characteristics. The exponentially weighted moving average algorithm only needs to store the smoothed value from the previous time point, making it computationally efficient and suitable for real-time processing. The smoothed stiffness influence factor sequence reduces random noise interference and highlights the trend components related to stiffness changes.

[0080] In some embodiments, after constructing a stiffness influence factor sequence based on the feature pattern data stream, statistical characteristics of the stiffness influence factor sequence are calculated using a sliding time window. Stiffness-related characteristic parameters, including deformation rate, vibration frequency, and amplitude, are extracted from the feature pattern data stream. The deformation rate is obtained by calculating the difference between deformation data at adjacent time points, reflecting the rate of change in structural deformation. The vibration frequency identifies the dominant frequency components through spectral analysis, reflecting the dynamic characteristics of the structure. The amplitude characteristic is extracted from the periodic wave components, representing the magnitude of the vibration.

[0081] In some embodiments, the feature parameters are standardized to eliminate dimensional differences. The standardization process uses the Z-score method, processing each feature parameter separately by subtracting its historical mean and dividing by its historical standard deviation. Standardization makes feature parameters with different dimensions comparable, preventing certain large-scale feature parameters from dominating the fusion result. The standardization process calculates the mean and standard deviation based on historical normal period data; these statistics are used as fixed benchmark parameters to ensure consistency in data processing across different time periods. After standardization, all feature parameters become dimensionless values ​​with a mean of zero and a standard deviation of one, facilitating subsequent weighted fusion. The standardized feature parameters are then weighted and fused to generate the original sequence of stiffness influence factors. The weighted fusion uses a linear weighted sum method, assigning a weight coefficient to each feature parameter. This weight coefficient reflects the parameter's indicative importance to stiffness changes. The weight coefficients are determined based on the physical mechanism of parameter and stiffness changes and historical data analysis, assigning higher weights to parameters more sensitive to stiffness changes. The weight coefficients satisfy the normalization condition, with the sum of all weight coefficients being one, ensuring the numerical stability of the fusion result.

[0082] It's understandable that setting the length and step size of a sliding time window allows the window length to adaptively adjust based on the data sampling frequency. A sliding time window divides continuous time series data into multiple overlapping or continuous data segments, with each window containing a certain number of continuous data points. The window length determines the time scale for calculating statistical features; a longer window smooths out short-term changes, while a shorter window results in poor statistical stability. The window length is inversely proportional to the data sampling frequency; shorter windows are used for high-frequency sampled data, and longer windows are used for low-frequency sampled data. The window step size determines the degree of overlap between adjacent windows; a smaller step size provides more continuous analytical results but increases computational complexity. Window parameter settings need to strike a balance between analytical accuracy and computational efficiency.

[0083] In practice, within a sliding time window, the mean, variance, skewness, and kurtosis statistics of the stiffness influencing factor sequence are calculated. The mean is the arithmetic mean of all data within the window, reflecting the average level of the stiffness influencing factor. The variance is the average of the squared deviations of each data point from the mean, measuring the degree of fluctuation of the stiffness influencing factor. Skewness describes the asymmetry of the data distribution; positive skewness indicates a long right tail, and negative skewness indicates a long left tail. Kurtosis describes the sharpness of the data distribution; high kurtosis indicates a sharp peak and a thick tail, while low kurtosis indicates a flat distribution. These statistics characterize the distribution features of the stiffness influencing factor sequence from different perspectives, providing multi-dimensional information for determining stiffness changes. The statistical characteristics of each time window are recorded, forming a statistical characteristic sequence. The statistical characteristic sequence is a multivariate time series, with each time point corresponding to a feature vector containing the mean, variance, skewness, and kurtosis. The statistical characteristic sequence is arranged in chronological order, recording the changes in the statistical characteristics of the stiffness influencing factor over time. The statistical feature sequence is used as input data for subsequent multidimensional matching analysis, and is used for comparative analysis with historical benchmark databases.

[0084] Example 3: In specific implementation, statistical characteristic quantities are matched with a historical benchmark database in multiple dimensions to output a stiffness anomaly probability index. This process begins by retrieving statistical characteristic quantity samples under normal conditions from the historical benchmark database. The historical benchmark database stores statistical characteristic quantity samples obtained from long-term monitoring of bridges under known normal operating conditions. These samples cover different seasons, different temperature conditions, and different traffic load conditions, forming a multi-dimensional data set representing the structural health status. The retrieval process is based on timestamp matching or condition matching, extracting normal state samples from the historical benchmark database that are similar to the environmental conditions of the current real-time statistical characteristic quantities, ensuring the comparability of the matching analysis conditions. The Euclidean distance and Mahalanobis distance between the real-time statistical characteristic quantities and historical samples are calculated. The Euclidean distance is the straight-line distance between two points, calculated as the square root of the sum of the squares of the differences in each dimension, reflecting the absolute degree of difference between the real-time data and the historical normal pattern. The Mahalanobis distance considers the correlation between features, and the calculation formula involves the inverse of the covariance matrix, which can identify abnormal deviations in the data distribution pattern. The distance calculation results serve as input indicators for subsequent probability estimation, providing a preliminary quantification of the degree of data anomaly.

[0085] In practical implementation, a multivariate normal distribution model is used to estimate the probability density of real-time features in the historical distribution. This model assumes that the statistical feature samples under normal historical conditions follow a multidimensional normal distribution. Statistical feature samples under normal conditions are extracted from the historical benchmark database, and the mean vector and covariance matrix of the samples are calculated. The mean vector is the set of averages for each feature dimension, and the covariance matrix describes the linear correlation between different feature dimensions and the magnitude of their respective variances. The real-time statistical features are then used as input vectors and substituted into the probability density function of the multivariate normal distribution. The probability density function takes the following form:

[0086]

[0087] in: Represents real-time statistical feature vector The probability density value under the historical normal distribution This represents the mean vector of historical normal samples. Represents the covariance matrix of historical normal samples. Dimensions representing statistical features This represents the determinant of the covariance matrix. Based on the mean vector and the covariance matrix, the probability density values ​​of real-time statistical features under historical distributions are calculated. The calculation process involves matrix inversion and quadratic form operations. A logarithmic transformation is performed on the probability density values ​​to avoid numerical underflow. The logarithmic transformation converts extremely small probability density values ​​into easily processed negative values.

[0088] In some embodiments, the posterior probability of stiffness anomalies is calculated using Bayes' theorem by combining distance indicators and probability density. This process requires pre-setting the prior probability of stiffness anomalies. The pre-setting of the prior probability of stiffness anomalies is determined based on the frequency of occurrence of anomalous events in historical data, statistically analyzing the proportion of stiffness anomaly events from long-term monitoring records and maintenance logs of the bridge. The prior probability represents the initial expected probability of stiffness anomalies occurring without any current observational evidence and serves as the basic input for Bayesian inference. The likelihood probability of real-time statistical features under normal conditions is calculated using the probability density value estimated by a multivariate normal distribution model. The likelihood probability represents the probability of observing real-time statistical features under the condition that the structure is currently in a normal state. The likelihood probability of real-time statistical features under anomalous conditions is also calculated by constructing an anomalous distribution model and estimating the probability density based on anomalous sample data. The anomalous samples come from known bridge damage events or laboratory simulation data. The anomalous distribution model can employ a multivariate t-distribution or a Gaussian mixture model to adapt to the complex distribution of anomalous data.

[0089] In some embodiments, Bayes' theorem is applied to multiply the prior probability and the likelihood probability to obtain the non-normalized posterior probability. The basic form of Bayes' theorem is multiplying the prior probability and the likelihood probability to obtain the non-normalized posterior probability. For the stiffness anomaly determination problem, it is necessary to calculate the posterior probabilities of two states: the posterior probability of the normal state and the posterior probability of the anomalous state. The non-normalized posterior probability of the normal state equals the prior probability of the normal state multiplied by the likelihood probability of the normal state; the non-normalized posterior probability of the anomalous state equals the prior probability of the anomalous state multiplied by the likelihood probability of the anomalous state. The non-normalized posterior probabilities are normalized to ensure that the sum of the posterior probabilities of all possible states is one. The normalization process divides the non-normalized posterior probability of each state by the sum of the non-normalized posterior probabilities of all states. The posterior probability of stiffness anomaly is output as a stiffness anomaly probability index. The stiffness anomaly probability index is a value between zero and one; a larger value indicates a higher probability of abnormal changes in structural stiffness.

[0090] It is understandable that the application of the multivariate normal distribution model relies on the quality and representativeness of the historical benchmark database, which needs to contain sufficiently diverse normal-state samples. Extracting statistical feature samples from the historical benchmark database under normal conditions and calculating the sample mean vector and covariance matrix requires ensuring a sufficient and representative sample size to avoid singular or ill-conditioned covariance matrices. The mean vector is calculated using an arithmetic mean, and the covariance matrix is ​​obtained as an unbiased estimate by dividing the sum of squared sample biases by the sample size minus one. Real-time statistical features are used as input vectors and substituted into the probability density function of the multivariate normal distribution. Function calculation involves complex matrix operations and requires a numerically stable algorithm. Based on the mean vector and covariance matrix, the probability density values ​​of the real-time statistical features under the historical distribution are calculated. Probability density values ​​in high-dimensional spaces are typically very small, and direct calculation can easily lead to numerical underflow. A logarithmic transformation is applied to the probability density values ​​to avoid numerical underflow. The logarithmic transformation converts multiplication operations into addition operations, improving computational stability. Normalizing the probability density values ​​to the range of zero to one makes the probability density values ​​at different time points and under different conditions comparable.

[0091] This fusion method combines distance metrics and probability density to calculate the posterior probability of stiffness anomalies using Bayes' theorem, leveraging multiple information sources. The distance metric provides a measure of the geometric difference between real-time data and historical patterns, while the probability density provides information on the relative position of real-time data within the historical distribution. Bayes' theorem provides a theoretical framework for combining prior knowledge with current observational evidence, generating a comprehensive posterior probability metric. The prior probability of stiffness anomalies is pre-set based on the frequency of anomalous events in historical data. This prior probability can be adjusted according to the bridge's importance level and service life; higher prior probabilities can be set for important or older bridges. The likelihood probability of real-time statistical features under normal conditions is calculated using the probability density value estimated by a multivariate normal distribution model. However, the multivariate normal distribution assumption may not be suitable for all types of feature data; a more flexible distribution model is needed when data significantly deviates from normality. The likelihood probability of real-time statistical features under anomalous conditions is also calculated by constructing an anomalous distribution model based on anomalous sample data and estimating the probability density. Since anomalous samples are typically limited in number and lack diversity, regularization or semi-supervised learning methods are needed to improve model robustness. Applying Bayes' theorem, the prior probability and likelihood probability are multiplied to obtain the non-normalized posterior probability. This multiplication amplifies the influence of consistent evidence while suppressing the contribution of contradictory evidence. The non-normalized posterior probability is then normalized to ensure that the sum of the posterior probabilities for all possible states is one. Normalization essentially converts the posterior probability into a standard probability scale. The posterior probability of stiffness anomalies is output as a stiffness anomaly probability index. This index provides the triggering basis for subsequent graded verification mechanisms, enabling a quantitative assessment of stiffness change risk.

[0092] See Figure 4 This chart illustrates the change in the probability of structural stiffness anomalies over time based on bridge health monitoring data. Presented as a time series, the horizontal axis represents the monitoring time span, and the vertical axis displays the probability value of stiffness anomalies, ranging from 0 to 1. The red curve clearly depicts the dynamic change in the probability of stiffness anomalies, with fluctuations reflecting the changing trend of the bridge's structural condition. Three reference lines—low, medium, and high thresholds—allow for intuitive identification of time periods with different risk levels. When the probability curve exceeds these thresholds, it indicates that the structure may have experienced varying degrees of stiffness anomalies. The data displayed includes fluctuations under normal operating conditions and simulated anomaly events. Under normal conditions, the anomaly probability remains at a low level, and the curve is relatively stable; however, when simulated anomalies occur, the probability value rises significantly, forming a distinct peak. This visualization helps engineers quickly identify potential structural safety issues, providing data support for subsequent maintenance decisions. This chart comprehensively utilizes multi-dimensional matching analysis, distance calculation, and probability density estimation methods to achieve a quantitative assessment of the stiffness state of the bridge structure. Through the accumulation and analysis of long-term monitoring data, a more accurate structural health benchmark can be established, improving the accuracy of anomaly detection.

[0093] Example 4: In specific implementation, a hierarchical verification mechanism is activated based on the stiffness anomaly probability index. The stiffness change trend is confirmed through a cross-validation algorithm. This process begins by setting low, medium, and high thresholds for the stiffness anomaly probability index. Threshold setting is based on statistical analysis of historical monitoring data. The optimal threshold cutoff point is determined by analyzing the distribution characteristics of false alarms and missed alarms in historical data. The low threshold is typically set at a lower quantile level of the stiffness anomaly probability index to filter out obvious normal fluctuations; the medium threshold is set at a medium probability level to identify possible anomalies; and the high threshold is set at a high probability level to mark highly suspicious anomalies. Threshold setting needs to consider the importance level and safety requirements of the bridge structure. More conservative threshold settings are used for important bridges to improve detection sensitivity. The three thresholds divide the range of the stiffness anomaly probability index into four intervals, each corresponding to a different verification response level, achieving hierarchical early warning and optimized resource allocation.

[0094] In practice, when the stiffness anomaly probability index is below the low threshold, the verification mechanism is not activated, and the system maintains its normal monitoring state. In this state, the system considers the bridge structure to be in normal working condition, and the risk of stiffness anomaly is negligible. The system continues to collect and process deformation monitoring data and update the stiffness anomaly probability index, but does not trigger any additional verification analysis processes. Computational resources in the normal monitoring state are mainly allocated to data acquisition, basic processing, and trend tracking to maintain the system's economy and efficiency. Only when the stiffness anomaly probability index exceeds the low threshold will the system activate different levels of verification mechanisms to conduct in-depth analysis of potential stiffness changes. When the stiffness anomaly probability index reaches the low threshold but is below the medium threshold, the primary verification mechanism is activated, employing a leave-one-out cross-validation algorithm, using monitoring data from the most recent time period for verification. Leave-one-out cross-validation is a special cross-validation method where one data point is used as the test set each time, and all other data points are used as the training set. In the primary verification mechanism, a certain number of sample points are selected from the monitoring data of the most recent time period, and each sample point is sequentially excluded from the training set. The remaining sample points are used to construct a stiffness change trend prediction model. The prediction model employs linear regression or time series analysis to establish a relationship between statistical characteristics and stiffness changes. For each excluded sample point, the trained model is used to make a prediction, and the error between the predicted value and the actual observed value is calculated. The leave-one-out cross-validation process is repeated until all sample points have been used as the test set at least once, ultimately yielding the prediction error set for all sample points.

[0095] In practice, when the stiffness anomaly probability index reaches the medium threshold but is below the high threshold, the intermediate validation mechanism is activated, employing a k-fold cross-validation algorithm. This algorithm divides the historical data into k subsets for iterative validation. k-fold cross-validation randomly divides the available historical data into k subsets of roughly equal size, typically with k ranging from 5 to 10. In the intermediate validation mechanism, the value of k is determined based on the total amount of data and computational resources; a larger k value is used when the data volume is large to improve validation efficiency. The cross-validation process runs for k rounds. In each round, one subset is used as the test set, and the remaining k-1 subsets are combined as the training set. The training set data is used to train a stiffness change trend prediction model, which may include machine learning algorithms such as support vector machines or random forests. The trained model is then applied to the test set, and the prediction error index is calculated. After k rounds, each data point has been used as the test set exactly once, resulting in the prediction error for all data points. The average prediction error is then calculated as the model performance evaluation index.

[0096] In practical implementation, when the stiffness anomaly probability index reaches a high threshold, an advanced validation mechanism is activated, employing a time-series cross-validation algorithm that considers the time dependence of the data and uses a sliding time window for validation. Time-series cross-validation is particularly suitable for monitoring data with time correlation, maintaining the temporal order of the data. In the advanced validation mechanism, the initial training window size and sliding step size are first determined, with the training window containing continuous time-series data. The validation process starts with the earliest available data, using the data within the initial training window as the first training set, and the data within a fixed time period after the training window as the first test set. A time-series prediction model is built using the training set, considering the autocorrelation and seasonality of the data. The model is applied to the test set for prediction, and the prediction error is calculated. Then, the training and test windows are moved forward according to the set sliding step size, repeating the training and testing process until all available data is covered. The error calculation for time-series cross-validation must consider the special effects of time dependence.

[0097] It is understandable that the threshold settings for the tiered verification mechanism need to be adjusted according to the specific characteristics of the bridge; different bridges may have different threshold configurations. See Table 1, which shows a threshold configuration scheme.

[0098] Table 1: Threshold Configuration Table for Hierarchical Validation Mechanism

[0099]

[0100] Understandably, the hierarchical validation mechanism reflects the principle of optimal resource allocation. Simple and fast validation methods are used for low-risk situations, while more computational resources are allocated to in-depth analysis for high-risk situations. Leave-one-out cross-validation provides almost unbiased error estimates when the data volume is small, but the computational cost increases linearly with the data volume. k-fold cross-validation achieves a good balance between bias and variance and is suitable for medium-sized datasets. Time series cross-validation specifically handles time-related data, preventing future information from being leaked to past points in time, and providing error estimates that best match the actual application scenario. Each validation method has its applicable scenarios and advantages and disadvantages; the hierarchical mechanism ensures that the appropriate method is used in the appropriate situation.

[0101] In some embodiments, activating different levels of verification mechanisms requires consideration of real-time resource allocation strategies to ensure timely system response. When multiple monitoring points trigger verification mechanisms simultaneously, the system needs to prioritize tasks based on anomaly probability indices and structural importance. High-priority tasks receive more computing resources, ensuring timely verification of anomaly signals from important structures. Resource allocation strategies can employ dynamic scheduling algorithms to adjust the execution order and resource quotas of different verification tasks in real time. This adaptive resource management mechanism ensures the system remains operational even during periods of high anomaly incidence. The triggering conditions for verification mechanisms can also be combined with other auxiliary indicators for comprehensive judgment, improving decision-making accuracy. In addition to stiffness anomaly probability indices, the system can monitor auxiliary information such as data quality indices and environmental change indices. When data quality is poor or environmental conditions change drastically, even if the stiffness anomaly probability index reaches a threshold, triggering high-level verification mechanisms can be temporarily suspended until conditions stabilize before analysis. This conservative strategy helps reduce false alarms and improves system reliability.

[0102] In practice, the implementation of the tiered verification mechanism requires robust software architecture support, including a threshold management module, a verification scheduling module, and a result evaluation module. The threshold management module stores and maintains the threshold configuration parameters for each bridge, supporting remote updates and adjustments. The verification scheduling module determines which verification mechanism to activate and when to execute it based on real-time calculated stiffness anomaly probability indices and the current system load. The result evaluation module analyzes the prediction error data generated during the verification process, generating verification reports and confidence assessments. All modules exchange data and messages through standard interfaces to ensure system collaboration.

[0103] See Figure 5 This chart illustrates the triggering status of a tiered verification mechanism based on stiffness anomaly probability, visually presenting the distribution of different verification levels at different time points using a scatter plot. Four colors are used to distinguish different verification levels: green represents normal monitoring, yellow represents primary verification, orange represents intermediate verification, and red indicates advanced verification. This color coding makes the triggering status of each level immediately clear. The horizontal axis also represents monitoring time, and the vertical axis displays the stiffness anomaly probability value. Three distinct threshold lines clearly divide the chart into four verification zones. When the anomaly probability is below the low threshold, the system is in normal monitoring mode; when the probability enters the low-to-medium threshold range, the primary verification mechanism is triggered; in the medium-to-high threshold range, intermediate verification is initiated; and when the probability exceeds the high threshold, the advanced verification mechanism is activated. The density of the scatter points in the chart reflects the triggering frequency of different verification levels. Dense green areas indicate that most of the time structure is in a normal state, while scattered red dots represent anomaly periods requiring high attention. This tiered response mechanism ensures the rational allocation of monitoring resources, improving system operating efficiency while maintaining security.

[0104] Example 5: In specific implementation, the confidence level of the stiffness change trend is calculated using a cross-validation algorithm, and the confirmed stiffness change trend is output. This process selects the appropriate cross-validation algorithm based on the activated validation mechanism level. In the primary validation mechanism, the leave-one-out cross-validation algorithm is used, sequentially using each data point as the test set and the remaining data as the training set to train the stiffness change trend model and calculate the prediction error. The leave-one-out cross-validation algorithm is suitable for situations with relatively small amounts of data, and can make full use of limited data to provide almost unbiased error estimates. The stiffness change trend model is trained using a linear regression method to establish a linear relationship model between statistical features and time variables. The model form is as follows:

[0105]

[0106] in: Represents a time variable. arrive To represent different statistical characteristics, arrive Represents the regression coefficient. This represents the random error term. For each excluded data point, a pre-trained stiffness variation trend model is used for prediction, and the absolute or relative error between the predicted value and the actual observed value is calculated. The prediction errors of all data points constitute the error set, and the statistical characteristics of the error set reflect the predictive performance of the stiffness variation trend model.

[0107] In practical implementation, the intermediate validation mechanism employs a k-fold cross-validation algorithm. Historical data is randomly divided into k subsets, and each subset is used as the test set in a loop, while the remaining subsets are used as the training set to train the model and calculate the average prediction error. The k-fold cross-validation algorithm randomly divides the available historical data into k mutually exclusive subsets. The subset division either maintains the temporal order of the data or is completely randomized, depending on the data analysis objectives. Training the stiffness change trend model may employ more complex machine learning algorithms, such as support vector regression or random forest regression, which can capture the nonlinear relationship between statistical features and stiffness changes. In each loop, the model is trained using k-1 subsets of data, and then its performance is tested on the remaining subset, calculating prediction error metrics such as root mean square error (RMSE) or mean absolute error (MAE). After k loops, each subset has been used as the test set exactly once, yielding k prediction error values. The average of these error values ​​is used as the model's average prediction error. The average prediction error measures the generalization ability of the stiffness change trend model on unknown data; a smaller error value indicates more accurate predictions.

[0108] In practical implementation, the advanced validation mechanism employs a time-series cross-validation algorithm. This involves a sliding window following chronological order, using earlier data as the training set and more recent data as the test set to train the model and calculate time-related prediction errors. The time-series cross-validation algorithm strictly maintains the chronological order of the data, preventing future information from being leaked to past points in time; this validation method best suits practical monitoring applications. The sliding window settings include the initial training window size, test window size, and sliding step size. These window parameters are determined based on the data sampling frequency and the prediction target. The stiffness change trend model is trained using specialized time-series analysis methods, such as autoregressive integral moving average models or seasonal decomposition time-series models. These models effectively handle the autocorrelation and trend characteristics of time-series data. After each window slide, a time-series prediction model is built using the data within the training window. The model is then applied to the test window for multi-step prediction, calculating the error between the predicted sequence and the actual observed sequence. The time-related prediction error needs to consider the influence of the prediction step size; typically, the prediction error increases with the prediction step size, a characteristic that needs to be taken into account in confidence level calculations.

[0109] In practice, the confidence level of the stiffness variation trend is calculated based on the prediction error, and the confidence level is inversely proportional to the prediction error. The prediction error reflects the accuracy of the stiffness variation trend model in predicting new data; the larger the error, the higher the uncertainty of the model, and the lower the corresponding confidence level. The confidence level is calculated using the reciprocal or complementary form of the error, mapping the prediction error to a confidence value between zero and one. For leave-one-out cross-validation, the confidence level calculation formula is: ,in: Indicates the confidence level. This represents the average prediction error for all data points. For k-fold cross-validation, the confidence score calculation considers the variability of the error at each fold, using... ,in: This represents the standard deviation of the prediction error at each fold. For time series cross-validation, the confidence score calculation also needs to consider the impact of the prediction step size, using the weighted average error as the basic indicator. The confidence score values ​​are normalized to ensure that the results are within a standard range for easy interpretation and comparison.

[0110] In practice, when the confidence level exceeds a set threshold, the system outputs a confirmed stiffness change trend, including the trend direction and magnitude. The confidence threshold is set according to application requirements, typically a high value such as 0.7 or 0.8, ensuring that only trend judgments with high confidence are output. The trend direction is determined by the slope sign of the stiffness change trend model; a positive slope indicates an increasing stiffness trend, and a negative slope indicates a decreasing stiffness trend. The magnitude of the change is calculated using model coefficients or prediction differences over a specific time period, reflecting the severity of the stiffness change. The output results are in a standardized format, including information such as trend type, magnitude of change, confidence level, and time range, for bridge management personnel's decision-making reference. Only when all verification indicators meet reliability requirements will the system officially output the stiffness change trend conclusion.

[0111] It is understandable that cross-validation algorithms corresponding to different validation mechanism levels differ significantly in computational complexity and applicable scenarios, requiring flexible selection based on actual conditions. Leave-one-out cross-validation algorithms have a high computational cost but provide almost unbiased error estimates, making them particularly suitable for model validation with small sample sizes. k-fold cross-validation achieves a good balance between bias and variance and is one of the most commonly used cross-validation methods in practice. Time series cross-validation algorithms are specifically designed for time-related data, maintaining the integrity of the data's temporal structure and providing performance evaluations that best match real-world application scenarios. When calculating the confidence level of stiffness change trends based on prediction errors, the selection and standardization of error indices need to be considered to ensure the comparability of confidence levels obtained from different validation methods. The inverse relationship between prediction error and confidence level reflects the basic principle of model uncertainty measurement; a larger prediction error indicates lower model reliability, and consequently, a lower confidence level in trend judgment.

[0112] Confirming stiffness variation trends requires comprehensive consideration of multiple pieces of evidence, including statistical significance, physical plausibility, and temporal consistency. When the confidence level exceeds a set threshold, the confirmed stiffness variation trend is output; this decision-making process necessitates the establishment of rigorous judgment criteria. Trend direction determination is based on parameter estimation results from the stiffness variation trend model, while also considering the statistical significance test of the parameters. The estimation of the variation magnitude needs to provide an uncertainty range, typically expressed as a confidence interval. The format and content of the output results need to be standardized to ensure the comparability of trend judgments across different time points and bridges. The system should also record the detailed process and data of each trend confirmation for subsequent retrospective analysis and model improvement.

[0113] In some embodiments, confidence level calculations can also incorporate other auxiliary indicators for correction, improving the reliability of trend judgments. Besides prediction errors, statistical indicators such as model goodness of fit, residual distribution characteristics, and variable significance can be considered. Physical rationality checks can verify whether the trend direction conforms to the basic laws of bridge mechanical behavior, eliminating obviously unreasonable trend judgments. Time consistency analysis checks whether the trend signal remains stable within a continuous time window, avoiding erroneous judgments based on short-term fluctuations. A multi-indicator fusion confidence assessment method can provide a more comprehensive and robust trend reliability judgment. The output format and content of stiffness change trends can be customized according to user level and application scenario. For on-site inspectors, the output can be simplified to trend direction and confidence level; for structural engineers, detailed technical parameters and uncertainty analysis are required; for management decision-makers, the risk level of the trend and recommended measures can be highlighted. The presentation of output results can also be diversified, including digital reports, graphical displays, and early warning information, meeting the needs of different users.

[0114] 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 method for determining the change of rigidity of a bridge structure based on deformation data of bridge health monitoring, characterized in that, The method comprises: establishing an initial data set of bridge deformation monitoring data, performing multi-scale decomposition processing on the initial data set to generate deformation component data of different time scales; inputting the deformation component data of different time scales into a pattern recognition engine to identify characteristic mode data streams associated with structural stiffness; constructing a stiffness influence factor sequence based on the characteristic mode data streams, and calculating statistical characteristic quantities of the stiffness influence factor sequence through a sliding time window; performing multi-dimensional matching analysis on the statistical characteristic quantities and a historical benchmark database to output a stiffness anomaly probability index; activating a hierarchical verification mechanism according to the stiffness anomaly probability index, and confirming a stiffness change trend through a cross-validation algorithm; the multi-scale decomposition processing on the initial data set comprises: using a time series decomposition algorithm to separate the bridge deformation monitoring data into a long-term trend component, a periodic fluctuation component, and a random disturbance component; performing polynomial fitting on the long-term trend component to extract a trend change rate parameter; performing frequency spectrum analysis on the periodic fluctuation component to extract dominant frequency and amplitude characteristics; performing probability distribution modeling on the random disturbance component to determine a noise threshold boundary; and recombining the processing results of the long-term trend component, the periodic fluctuation component, and the random disturbance component into a standardized data matrix; the operation of the pattern recognition engine comprises: after receiving the standardized data matrix, performing feature space transformation to map the data to a high-dimensional feature space; calculating a similarity matrix of each type of feature in the high-dimensional feature space, identifying a feature aggregation area through a clustering algorithm; extracting a region center point and a boundary range for each feature aggregation area to form a feature mode template library; dynamically matching a real-time input feature mode data stream with the feature mode template library to calculate a matching confidence score; and triggering a feature mode updating mechanism when the matching confidence score is lower than a set threshold; the multi-dimensional matching analysis of the statistical characteristic quantities with the historical benchmark database to output the stiffness anomaly probability index comprises: retrieving statistical characteristic quantity samples in a normal state from the historical benchmark database; calculating the Euclidean distance and Mahalanobis distance of real-time statistical characteristic quantities and historical samples; using a multivariate normal distribution model to estimate the probability density of real-time characteristic quantities in the historical distribution; combining the distance index and the probability density to calculate the posterior probability of stiffness anomaly through Bayes' theorem; outputting the stiffness anomaly probability index when the posterior probability exceeds a set threshold; the activation of the hierarchical verification mechanism according to the stiffness anomaly probability index and the confirmation of the stiffness change trend through the cross-validation algorithm comprise: setting a low threshold, a medium threshold, and a high threshold for the stiffness anomaly probability index; when the stiffness anomaly probability index is lower than the low threshold, the verification mechanism is not activated; when the stiffness anomaly probability index reaches the low threshold but is lower than the medium threshold, a primary verification mechanism is activated, and a leave-one-out cross-validation algorithm is used to verify using monitoring data of the most recent time period; when the stiffness anomaly probability index reaches the medium threshold but is lower than the high threshold, a secondary verification mechanism is activated, and a k-fold cross-validation algorithm is used to divide historical data into k subsets for cyclic verification. When the stiffness anomaly probability index reaches a high threshold value, a high-level verification mechanism is activated, a time series cross-validation algorithm is used, the time dependence of the data is considered, and a sliding time window is used for verification. The confidence of the stiffness change trend is calculated by the cross-validation algorithm, and the confirmed stiffness change trend is output.

2. The method for determining a change in the rigidity of a bridge structure based on deformation data from health monitoring of a bridge according to claim 1, characterized by, The construction process of the stiffness influence factor sequence includes: From the feature mode data stream, filter out the feature parameters related to the stiffness change with a correlation exceeding a set threshold to form an initial feature set; perform principal component analysis on the initial feature set to extract the main feature vector; perform convolution operation on the main feature vector and the real-time deformation data to generate the original stiffness influence factor sequence; normalize the original stiffness influence factor sequence to eliminate the dimension effect; and perform smoothing processing on the normalized sequence by using the exponential weighted moving average algorithm to obtain the final stiffness influence factor sequence used for stiffness determination.

3. The method for determining the change in the rigidity of a bridge structure based on deformation data from health monitoring of a bridge according to claim 1, characterized by, The stiffness influence factor sequence is constructed based on the feature mode data stream, and the statistical characteristic quantity of the stiffness influence factor sequence is calculated by a sliding time window, including: Extracting the feature parameters related to the stiffness from the feature mode data stream, including the deformation rate, vibration frequency and amplitude; Performing standardization processing on the feature parameters to eliminate the dimension difference; Weighted fusion of the standardized feature parameters to generate the original stiffness influence factor sequence; Setting the length and step of the sliding time window, and the window length is adaptively adjusted according to the data sampling frequency; In the sliding time window, the mean, variance, skewness and kurtosis statistical quantities of the stiffness influence factor sequence are calculated; Recording the statistical characteristic quantity of each time window to form a statistical characteristic quantity sequence.

4. The method for determining a change in the rigidity of a bridge structure based on deformation data from health monitoring of the bridge as recited in claim 1, wherein, The probability density of the real-time feature quantity in the historical distribution is estimated using a multivariate normal distribution model, including: Extracting the statistical characteristic quantity samples in the normal state from the historical reference database, calculating the mean vector and covariance matrix of the samples; inputting the real-time statistical characteristic quantity as an input vector into the probability density function of the multivariate normal distribution; based on the mean vector and the covariance matrix, calculating the probability density value of the real-time statistical characteristic quantity in the historical distribution; performing logarithmic transformation on the probability density value to avoid numerical underflow problem; and normalizing the probability density value to the range of zero to one.

5. The method for determining the change in the rigidity of a bridge structure based on deformation data from health monitoring of a bridge according to claim 1, wherein, The posterior probability of stiffness anomaly is calculated by Bayes' theorem combining the distance index and the probability density, including: The prior probability of stiffness anomaly is set in advance based on the frequency of abnormal events in historical data; the likelihood probability of the real-time statistical characteristic quantity in the normal state is calculated, and the probability density value estimated by the multivariate normal distribution model is used as the likelihood probability; the likelihood probability of the real-time statistical characteristic quantity in the abnormal state is calculated, and the probability density is estimated based on the abnormal sample data to construct an abnormal distribution model; applying Bayes' theorem, multiplying the prior probability and the likelihood probability to obtain the non-normalized posterior probability; normalizing the non-normalized posterior probability to ensure that the sum of the posterior probabilities of all possible states is one; and outputting the posterior probability of stiffness anomaly as the stiffness anomaly probability index.

6. The method for determining the change in the rigidity of a bridge structure based on deformation data from health monitoring of a bridge according to claim 1, characterized by, The confidence of the stiffness change trend is calculated by the cross-validation algorithm, and the confirmed stiffness change trend is output. According to the activated verification mechanism level, a corresponding cross-validation algorithm is selected; In the primary verification mechanism, a leave-one-out cross-validation algorithm is used, each data point is sequentially taken as the test set, and the remaining data is taken as the training set to train the stiffness change trend model and calculate the prediction error; In the intermediate verification mechanism, a k-fold cross-validation algorithm is used, the historical data is randomly divided into k subsets, each subset is taken as the test set in a loop, and the remaining subsets are taken as the training set to train the model and calculate the average prediction error; In the high-level verification mechanism, a time series cross-validation algorithm is used, a sliding window is used according to the time sequence, early data is taken as the training set, and recent data is taken as the test set to train the model and calculate the time-related prediction error; The confidence of the stiffness change trend is calculated based on the prediction error, and the confidence is inversely proportional to the prediction error; when the confidence exceeds a set threshold, the confirmed stiffness change trend is output, including the trend direction and the change amplitude.

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