Large-span bridge vibration response prediction method based on data driving

Abstract

The invention discloses a large-span bridge vibration response prediction method based on data driving, and relates to the technical field of bridge vibration response prediction, and the method comprises the following steps: arranging a plurality of sensors at a plurality of key structure parts of a bridge, collecting vibration response data of the bridge during operation in real time based on an initial sampling frequency set based on the inherent frequency of the bridge structure; performing frequency domain analysis on the collected vibration response data, extracting a main excitation frequency component under the current working condition, and constructing a current excitation frequency spectrum; the method comprises the following steps: calling structural modal parameters obtained in a design stage, a static load test or a modal test of a bridge, extracting the natural vibration frequency of each order of structure, and constructing a bridge inherent frequency feature library; according to the method, the resonance state is dynamically identified through frequency domain analysis and the fuzzy risk index, the sampling frequency is intelligently adjusted, high-frequency response accurate capture and resource efficiency optimization are realized, and the sensitivity, the real-time performance and the safety of a bridge health monitoring system are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge vibration response prediction, and in particular to a data-driven method for predicting the vibration response of a long-span bridge. Background Art

[0002] Data-driven prediction of the vibration response of long-span bridges refers to the process of collecting vibration monitoring data (such as acceleration, displacement, strain, etc.) of the bridge under different operating conditions (such as vehicle loads, wind loads, earthquakes, etc.) to construct a relationship model between the bridge structure and external excitations, thereby predicting future vibration responses. This method does not rely on traditional finite element models or structural analytical formulas. Instead, it uses data-driven algorithms such as machine learning and deep learning to automatically extract features and patterns from large amounts of historical monitoring data to capture the dynamic response characteristics of the bridge structure under actual operating conditions. Its core advantage lies in its ability to better adapt to factors that are difficult to accurately model, such as structural nonlinearity, material aging, and complex operating conditions, thereby improving the accuracy and timeliness of vibration predictions. It is widely used in bridge health monitoring, early warning assessment, and maintenance decision support.

[0003] The existing technology has the following deficiencies:

[0004] Existing technologies typically use fixed sampling strategies based on the structure's natural frequency to monitor the vibration response of bridges under different operating conditions. This makes it difficult to dynamically adjust sampling accuracy for complex operating conditions with rapidly changing excitation frequencies during actual operation. This is especially true when two or more high-speed trains pass through different spans of a bridge simultaneously. This can easily trigger lateral or vertical coupled resonance effects, causing the bridge's excitation frequency to approach the structure's natural frequency, leading to unsteady-state vibrations with a rapidly amplified response amplitude within a short period of time. Because the high-frequency dynamic response induced by coupled resonance is characterized by short duration and extremely high local amplitudes, if the vibration data acquisition frequency fails to meet the analytical requirements for high-frequency responses, critical bridge components (such as hangers, cables, and connection nodes) will be subjected to repeated impact loads without effective monitoring. This can accelerate fatigue damage accumulation and induce latent failure behaviors such as local yielding, structural fracture, or loose fasteners. This can ultimately lead to cascading structural failures or even total collapse, seriously threatening bridge operation safety and the reliability of public transportation systems.

[0005] The following is a detailed explanation of the "fixed sampling strategy based on the structural natural frequency setting":

[0006] A fixed sampling strategy based on the structural natural frequency setting refers to a bridge vibration monitoring system that presets a fixed sampling frequency based on the structural natural frequency (i.e., the natural frequency of the bridge when it vibrates freely without external excitation) identified during the bridge design phase or initial testing. This is used to collect and analyze vibration signals during subsequent operation. This strategy assumes that the structural response frequency will not deviate significantly from its natural frequency under actual operating conditions. Therefore, the sampling frequency is typically set according to the Nyquist sampling theorem (e.g., 2 to 5 times the natural frequency) to capture the dominant vibration mode.

[0007] The above information disclosed in this Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not form the prior art that is already known to a person of ordinary skill in the art. Summary of the Invention

[0008] The purpose of the present invention is to provide a data-driven method for predicting the vibration response of large-span bridges. The main excitation frequency is extracted through real-time frequency domain analysis, and the proximity relationship between the excitation and the structure is quantified by combining the structural natural frequency feature library and the frequency proximity algorithm. The frequency proximity trend change rate is further introduced to construct a fuzzy risk index, and whether the bridge is in a resonance-sensitive state is intelligently judged. The sampling frequency is dynamically adjusted accordingly, and finally the coordinated optimization between monitoring accuracy and system efficiency is achieved. It not only improves the ability to capture instantaneous high-frequency resonance responses, but also avoids resource redundancy and monitoring blind spots, significantly enhancing the sensitivity, real-time performance and safety assurance capabilities of the bridge structure health monitoring system, so as to solve the problems in the above-mentioned background technology.

[0009] To achieve the above object, the present invention provides the following technical solution: a data-driven method for predicting the vibration response of a long-span bridge, comprising the following steps:

[0010] Multiple sensors are deployed at multiple key structural locations of the bridge, including but not limited to the bridge deck, main beams, and supports. Based on a starting sampling frequency set based on the natural frequency of the bridge structure, real-time vibration response data generated by the bridge during operation under vehicle loads, wind loads, or other external excitations is collected.

[0011] Perform frequency domain analysis on the collected vibration response data, extract the main excitation frequency components under the current working conditions, and construct the current excitation spectrum;

[0012] Call the structural modal parameters obtained during the bridge design phase, static load test or modal test, extract the natural frequencies of each order of the structure, and build a bridge natural frequency feature library;

[0013] A frequency proximity algorithm, including the normalized frequency difference calculation method or the Gaussian kernel similarity function, is used to analyze the proximity between the current excitation frequency and the natural frequencies of each order of the bridge structure. The excitation-structure frequency proximity index is calculated based on the weighted average of the proximity of each order of frequency.

[0014] The current excitation-structure frequency approach index and its historical change rate are combined to characterize the structural frequency response to dynamically identify whether the bridge structure is in a resonance-sensitive state. If so, the sampling frequency of the vibration response data is dynamically increased to meet the monitoring needs of high-frequency non-steady-state responses; if not, the regular sampling frequency is maintained to optimize data processing efficiency.

[0015] Preferably, the setting of the initial sampling frequency includes the following technical measures:

[0016] First, based on the modal analysis results obtained during the bridge design phase, the first several natural frequencies of the bridge structure are extracted, preferably the first five. Second, according to the requirements of the Shannon sampling theorem, the starting sampling frequency of the sensor is set based on 2 to 4 times the lowest natural frequency of the bridge structure to ensure that the frequency response characteristics of the bridge under typical excitation can be fully captured. Finally, the starting sampling frequency serves as the initial reference value for the subsequent dynamic adjustment of the sampling frequency, which is used to adapt to the adaptive adjustment of vibration characteristics under different working conditions.

[0017] Preferably, the collected vibration response data is subjected to frequency domain analysis to extract the main excitation frequency components under the current working condition, and the steps of constructing the current excitation spectrum include the following: using spectrum analysis methods such as fast Fourier transform (FFT) or short-time Fourier transform (STFT) to perform time-frequency transformation on the original vibration response signal collected by the sensor to generate a vibration spectrum diagram under the current working condition; in the spectrum diagram, a spectrum peak recognition algorithm, such as peak detection, energy threshold filtering or improved envelope analysis, is further used to automatically extract one or more dominant frequency components with the largest energy proportion in the spectrum as the main excitation frequency characterizing the current excitation characteristics; finally, the extracted main excitation frequency components are organized in the order of monitoring time to form a continuous and updateable current working condition excitation spectrum sequence, which serves as the basic data for subsequent comparison and analysis with the natural frequency of the bridge structure, and is used to determine whether the bridge is in a potential resonance sensitive state and to drive dynamic adjustment of the sampling frequency.

[0018] Preferably, the steps of calling the structural modal parameters obtained during the design phase, static load test or modal test of the bridge, extracting the natural frequencies of each order of the structure, and constructing the natural frequency characteristic library of the bridge include the following: obtaining the theoretical modal parameters of the bridge structure, including basic characteristics such as modal order, natural frequency, vibration mode and damping ratio, through finite element modeling and modal analysis performed during the bridge design phase; comparing and calibrating the design parameters with the static load test data after the completion of the bridge and the modal test results of the actual bridge, preferably using frequency response function (FRF) fitting analysis, modal parameter inversion technology or experimental-theoretical modal coupling identification method to realize the correction and error control of the theoretical modal results, thereby improving The reliability and adaptability of modal parameters under actual operating conditions; extract the stable natural frequency parameters of each order of the structure from the above-mentioned processed modal data, preferably the first 10 orders, and number and group them according to the modal order, while recording the energy concentration, vibration mode directionality and local distribution characteristics corresponding to the order frequency; all extracted structural natural frequencies and their associated parameters are uniformly incorporated into the bridge natural frequency feature library. The feature library is constructed using a scalable standard data structure to support subsequent comparison, dynamic update and adaptive discrimination operations of the real-time excitation spectrum, thereby enhancing the system's data support capabilities and response accuracy in the frequency approach analysis and resonance risk identification process.

[0019] Preferably, the process of analyzing the proximity between the current excitation frequency and the natural frequencies of each order of the bridge structure is as follows:

[0020] For the main excitation frequency extracted under the current working condition, the Gaussian kernel similarity function is used to calculate the proximity weight with the natural frequency in the bridge natural frequency feature library. The proximity weight is determined by the following formula:

[0021]

[0022] Where: f exc is the current main excitation frequency, indicating the dominant frequency component of the current external excitation; f i is the i-th order natural frequency of the bridge structure, which comes from the frequency feature library; σ is the frequency sensitivity coefficient, which determines the analytical resolution of the frequency proximity, and is preferably set to 20% to 50% of the average spacing of the natural frequencies; ρ i Indicates the similarity weight between the current excitation frequency and the i-th order modal frequency. The closer the value is to 1, the closer it is. ρ i ∈(0,1].

[0023] Preferably, the step of calculating the excitation-structure frequency approach index according to the weighted average of the proximity of each order frequency includes the following:

[0024] When obtaining the proximity weights ρ of all orders iFinally, the contribution factors of each modal order are introduced to calculate the excitation-structure frequency approach index. The calculation formula is as follows:

[0025]

[0026] Where: γ i is the contribution factor of the i-th order mode (reflecting the energy proportion of the i-th order mode in the vibration response); N represents the total number of modal orders included in the calculation, preferably the first 10 orders; η is the excitation-structure frequency approach index, reflecting the overall closeness between the current excitation frequency and the natural frequencies of each order of the bridge structure.

[0027] Preferably, the fuzzy risk index is calculated by combining the current excitation-structure frequency approach index and its historical change rate to characterize the dynamic risk trend of the structural frequency response. Based on the fuzzy risk index, it is dynamically identified whether the bridge structure is in a resonance-sensitive state. The calculation formula of the fuzzy risk index is:

[0028]

[0029] Where: η is the excitation-structure frequency approach index calculated at the current moment, reflecting the overall closeness between the current excitation frequency and the natural frequencies of each order bridge structure; represents the rate of change of the excitation-structure frequency approach index per unit time, which is used to describe the rising speed of the bridge structure resonance risk; μ is the trend enhancement factor, which is used to adjust the sensitivity of risk changes to system response, with an optimal value of 0.5 to 2; R f It is the fuzzy risk index calculated at the current moment, reflecting the closeness between the excitation frequency and the natural frequency of the structure and its changing trend.

[0030] Preferably, if the vibration response data is in a resonance sensitive state, the sampling frequency of the vibration response data is dynamically increased. The specific steps are as follows:

[0031] When the fuzzy risk index is greater than the fuzzy risk threshold, the bridge is determined to be in a potential resonance-sensitive state. The vibration response data sampling frequency control mechanism is activated. Based on the degree to which the fuzzy risk index exceeds the threshold, the sampling frequency is adjusted to a level that is suitable for high-risk states, thereby improving the monitoring capability of sudden resonance responses. The sampling frequency is determined by the following formula:

[0032]

[0033] Where: f sample is the adjusted sampling frequency, that is, the data acquisition rate currently applied to the sensor; f base is the basic sampling frequency, which indicates the sampling rate of the system default configuration under normal operation; θ is the frequency adjustment gain coefficient, which is used to control the amplitude of the sampling frequency increase caused by the increase in fuzzy risk, and is preferably set to 0.5 to 1.5; Rth is the fuzzy risk threshold, which is used to define the judgment boundary of the resonance sensitive state; k is the nonlinear enhancement index, which determines the sensitivity of the sampling frequency to the fuzzy risk index exceeding the fuzzy risk threshold, and is preferably 2.

[0034] In the above technical solution, the technical effects and advantages provided by the present invention are:

[0035] The present invention extracts the main excitation frequency through real-time frequency domain analysis, and combines the structural natural frequency feature library with the frequency proximity algorithm to quantify the proximity relationship between the excitation and the structure; further introduces the frequency proximity trend change rate, constructs a fuzzy risk index, intelligently judges whether the bridge is in a resonance-sensitive state, and dynamically adjusts the sampling frequency accordingly, ultimately achieving coordinated optimization between monitoring accuracy and system efficiency. It not only improves the ability to capture instantaneous high-frequency resonance responses, but also avoids resource redundancy and monitoring blind spots, significantly enhancing the sensitivity, real-time performance and safety assurance capabilities of the bridge structure health monitoring system. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, a brief introduction to the drawings required for use in the embodiments will be given below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0037] Figure 1 This is a flow chart of a method for predicting vibration response of a large-span bridge based on data-driven method according to the present invention. DETAILED DESCRIPTION

[0038] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these example embodiments are provided so that the description of this disclosure will be thorough and complete and will fully convey the concepts of the example embodiments to those skilled in the art.

[0039] The present invention provides Figure 1 A data-driven long-span bridge vibration response prediction method is shown, comprising the following steps:

[0040] Multiple sensors are deployed at multiple key structural locations of the bridge, including but not limited to the bridge deck, main beams, and supports. Based on a starting sampling frequency set based on the natural frequency of the bridge structure, real-time vibration response data generated by the bridge during operation under vehicle loads, wind loads, or other external excitations is collected.

[0041] The key structural parts of a bridge refer to the parts that are representative and important in terms of structural stress, vibration propagation or fatigue damage sensitivity, mainly including the following aspects:

[0042] It includes bridge deck (used to sense local vibrations directly under the action of vehicle movement), main beams (such as box beams or truss beams, which are the main load-bearing components of the bridge and reflect the vertical and torsional responses of the overall structure), bridge towers or piers (sensitive to vertical, lateral and wind-induced vibration responses, especially critical in cable-stayed bridges or suspension bridges), hangers or cables (flexible connection components, easily affected by high-frequency dynamic loads, and are key areas for fatigue monitoring), bridge connection nodes (key positions connecting various components, and weak points for stress concentration and damage accumulation), supports (bearing the rotational force and deformation between the bridge and the pier, and easily affected by nonlinear deformation) and expansion joint areas (typical locations for sudden structural response changes and impact load transmission).

[0043] Deploying various types of sensors such as accelerometers, displacement meters, and strain gauges at these locations can more comprehensively and accurately collect the vibration response characteristics of the bridge under different working conditions, providing a high-quality data basis for subsequent dynamic response prediction and resonance risk assessment.

[0044] The setting of the initial sampling frequency includes the following technical measures:

[0045] First, based on the modal analysis results obtained during the bridge design phase, the first several natural frequencies of the bridge structure are extracted, preferably the first five. Second, according to the requirements of the Shannon sampling theorem, the starting sampling frequency of the sensor is set based on 2 to 4 times the lowest natural frequency of the bridge structure to ensure that the frequency response characteristics of the bridge under typical excitation can be fully captured. Finally, the starting sampling frequency serves as the initial reference value for the subsequent dynamic adjustment of the sampling frequency, which is used to adapt to the adaptive adjustment of vibration characteristics under different working conditions.

[0046] The purpose of this step is to provide high-quality, continuous raw monitoring data for the bridge vibration response prediction system, thereby laying a data foundation for subsequent frequency analysis, structural state identification, and prediction model construction. As a civil structure significantly affected by dynamic loads, bridges are subject to a complex and diverse range of excitations during operation, including periodic pulses from vehicle loads, quasi-static and dynamic disturbances caused by wind loads, and sudden strong vibrations caused by earthquakes. These external excitations will induce vibration responses in the bridge structure with varying amplitudes, frequencies, and propagation paths. Because these response characteristics are time-varying, nonlinear, and multi-scale, sensors must be deployed at multiple key locations on the structure to achieve comprehensive perception.

[0047] Key structural components, such as the bridge deck, main beam, and supports, each bear different functions and forces: the deck is the load input location, the main beam is the primary load-bearing member, and the supports are responsible for force transmission and vibration isolation. Any anomaly in any of these locations could reflect changes in the overall state of the structure. By deploying various types of sensors (such as accelerometers, strain gauges, and displacement gauges) in these locations and appropriately setting the initial sampling frequency based on the structure's natural frequency, we can ensure that the collected data has sufficient time-frequency resolution, avoiding distortion of high-frequency responses while reducing data redundancy and processing burden. This step, especially when the structure is near resonance or subjected to short-term strong excitation (such as the passage of multiple high-speed trains), enables accurate capture of unsteady-state responses, greatly improving the system's ability to identify risk states and the accuracy of response predictions. It is the foundation and prerequisite for the entire data-driven prediction process.

[0048] Perform frequency domain analysis on the collected vibration response data, extract the main excitation frequency components under the current working conditions, and construct the current excitation spectrum;

[0049] The collected vibration response data is subjected to frequency domain analysis to extract the main excitation frequency components under the current operating condition. The steps for constructing the current excitation spectrum include the following: using spectrum analysis methods such as fast Fourier transform (FFT) or short-time Fourier transform (STFT) to perform time-frequency transformation on the original vibration response signal collected by the sensor to generate a vibration spectrum diagram under the current operating condition; in the spectrum diagram, a peak recognition algorithm such as peak detection, energy threshold filtering, or improved envelope analysis is further used to automatically extract one or more dominant frequency components with the largest energy proportion in the spectrum as the main excitation frequency representing the current excitation characteristics; finally, the extracted main excitation frequency components are organized according to the monitoring time sequence to form a continuous and updateable current operating condition excitation spectrum sequence, which serves as the basic data for subsequent comparison and analysis with the natural frequency of the bridge structure, and is used to determine whether the bridge is in a potential resonance-sensitive state and to drive dynamic adjustment of the sampling frequency.

[0050] The main function of this step is to convert the time-domain vibration response signal into frequency-domain information, thereby revealing the frequency distribution characteristics of the external excitation on the bridge structure under the current operating conditions, extracting the dominant excitation frequency components, and constructing a complete excitation spectrum, providing a key basis for subsequent resonance risk assessment and dynamic sampling control. In actual operation, bridges are subject to a variety of complex excitations, including vehicle loads, wind loads, seismic waves, or temperature gradients. These excitations often have distinct frequency characteristics, and the structural responses induced by different excitation types and intensities are also different. It is difficult to accurately identify these frequency characteristics through time-domain signals alone, so frequency-domain analysis must be used to decompose and quantify the frequency components of the vibration signal.

[0051] By performing time-frequency analysis on the vibration response data collected by the sensor using methods such as fast Fourier transform (FFT) or short-time Fourier transform (STFT), the frequency region with the most concentrated energy in the signal at the current moment can be identified, namely the main excitation frequency. This main excitation frequency reflects the frequency component that has the most significant impact on the structure under the current external working conditions, and is of great significance for determining whether there is a potential resonance risk close to the natural frequency of the structure. Furthermore, the main excitation frequencies identified in each time period are organized into a continuous excitation spectrum sequence in chronological order. This can not only monitor the frequency change trend in real time, but also be used for comparative analysis with the natural frequency of the bridge structure, thereby identifying whether it has entered the frequency approaching zone, driving the data sampling rate to adaptively adjust, and enhancing the sensitivity and response capability of the entire system to high-risk working conditions such as non-steady-state vibration and coupled resonance.

[0052] Call the structural modal parameters obtained during the bridge design phase, static load test or modal test, extract the natural frequencies of each order of the structure, and build a bridge natural frequency feature library;

[0053] The steps of calling the structural modal parameters obtained during the design phase, static load test or modal test of the bridge, extracting the natural frequencies of each order of the structure, and constructing the natural frequency feature library of the bridge include the following: obtaining the theoretical modal parameters of the bridge structure through finite element modeling and modal analysis performed during the bridge design phase, including basic characteristics such as modal order, natural frequency, vibration mode and damping ratio; comparing and calibrating the design parameters with the static load test data after the completion of the bridge and the modal test results of the actual bridge, preferably using frequency response function (FRF) fitting analysis, modal parameter inversion technology or experimental-theoretical modal coupling identification method to realize the correction and error control of the theoretical modal results, thereby improving the modal The reliability and adaptability of the parameters under actual operating conditions; extract the stable natural frequency parameters of each order of the structure from the above-mentioned processed modal data, preferably the first 10 orders, and number and group them according to the modal order, and record the energy concentration, vibration mode directionality and local distribution characteristics of the frequency order; all extracted structural natural frequencies and their associated parameters are uniformly included in the bridge natural frequency feature library. The feature library is constructed with an extensible standard data structure to support subsequent comparison, dynamic update and adaptive discrimination operations of the real-time excitation spectrum, thereby enhancing the system's data support capabilities and response accuracy in the frequency approach analysis and resonance risk identification process.

[0054] The core purpose of this step is to provide an accurate, comprehensive, and engineering-adaptable bridge natural frequency benchmark system for subsequent excitation-structure frequency comparison analysis and resonance sensitivity identification. During actual operation, the dynamic response of a bridge structure is primarily determined by the relationship between the external excitation frequency and the structure's natural frequency. In particular, when the excitation frequency approaches a certain order of the structure's natural frequency, resonance is highly likely to occur, leading to local response amplification, component fatigue accumulation, and even structural failure. Therefore, constructing a comprehensive and accurate library of structural natural frequency characteristics is a prerequisite for resonance risk assessment. First, through finite element modeling and modal analysis during the design phase, theoretical modal characteristics of the bridge under ideal boundary and structural parameters are obtained, including modal order, natural frequency, mode shape, and damping ratio. These theoretical results provide a fundamental description of the structure's dynamic behavior. Second, combined with static load test and actual bridge modal test results, the theoretical data is calibrated through methods such as modal parameter inversion and frequency response function fitting. This eliminates deviations caused by construction errors, material heterogeneity, or simplified boundary conditions, ensuring that the natural frequencies more closely reflect actual operating conditions. Subsequently, the stable natural frequencies of each order, especially the first 10 frequencies, are extracted from the corrected modal parameters. These frequencies usually cover the main frequency domain where the structure may respond under operating conditions. While extracting the frequencies, it is also necessary to record the auxiliary characteristic information, such as modal energy concentration and vibration mode directionality, to support subsequent multi-dimensional comparative analysis and risk weight judgment. Ultimately, these frequencies and their related attributes are uniformly organized and constructed into a bridge natural frequency feature library, which is organized in a standardized and scalable data structure. This not only facilitates dynamic updates of new data, but also supports online frequency matching and adaptive adjustment of sampling strategies.

[0055] In summary, this step is the basic supporting link for realizing the data-driven vibration response prediction system architecture identification and risk analysis capabilities, and is of decisive significance for improving the intelligence, autonomy and prediction accuracy of the entire system.

[0056] A frequency proximity algorithm, including the normalized frequency difference calculation method or the Gaussian kernel similarity function, is used to analyze the proximity between the current excitation frequency and the natural frequencies of each order of the bridge structure. The excitation-structure frequency proximity index is calculated based on the weighted average of the proximity of each order of frequency.

[0057] The process of analyzing the proximity between the current excitation frequency and the natural frequencies of the bridge structure is as follows:

[0058] For the main excitation frequency extracted under the current working condition, the Gaussian kernel similarity function is used to calculate the proximity weight with the natural frequency in the bridge natural frequency feature library. The proximity weight is determined by the following formula:

[0059]

[0060] Where: f exc is the current main excitation frequency, indicating the dominant frequency component of the current external excitation; f i is the i-th order natural frequency of the bridge structure, which comes from the frequency feature library; σ is the frequency sensitivity coefficient, which determines the analytical resolution of the frequency proximity, and is preferably set to 20% to 50% of the average spacing of the natural frequencies; ρ i Indicates the similarity weight between the current excitation frequency and the i-th order modal frequency. The closer the value is to 1, the closer it is. ρ i ∈(0,1];

[0061] The purpose of this step is to overcome the problem that the traditional frequency difference absolute value algorithm cannot distinguish the potential resonance risk in the "close but not equal" situation through the fuzzy weight mechanism, and realize the accurate modeling and quantitative representation of the nonlinear proximity between the excitation frequency and each modal frequency, providing high-resolution frequency domain weight information for the subsequent construction of the excitation-structure frequency approach index.

[0062] The steps for calculating the excitation-structure frequency proximity index based on the weighted average of the proximity of each order frequency include the following:

[0063] When obtaining the proximity weights ρ of all orders i Finally, the contribution factors of each modal order are introduced to calculate the excitation-structure frequency approach index. The calculation formula is as follows:

[0064]

[0065] Where: γ i is the contribution factor of the i-th order mode (reflecting the energy proportion of the i-th order mode in the vibration response); N represents the total number of modal orders included in the calculation, preferably the first 10 orders; η is the excitation-structure frequency approach index, reflecting the overall closeness between the current excitation frequency and the natural frequencies of each order of the bridge structure;

[0066] This step introduces a modal importance weighting mechanism, ensuring that the excitation-structure frequency approximation index not only reflects the degree of matching between the excitation and structural frequencies but also fully accounts for the uneven contributions of different modes to the structural response. The resulting excitation-structure frequency approximation index can be used as a quantitative indicator of potential resonance risk under the current operating conditions of the bridge structure.

[0067] The core function of this step is to establish a quantitative indicator to determine whether the excitation frequency under the current working condition of the bridge is close to its natural frequency, thereby evaluating whether the bridge has potential resonance risks and providing a decision-making basis for the dynamic adjustment of the subsequent sampling frequency. In bridge structural dynamics, resonance is one of the most destructive risks. It usually occurs when the external excitation frequency (such as the periodic excitation induced by train loads) is very close to a certain order of natural frequency of the structure. Even a short-term proximity may cause a sharp amplification of the local response, resulting in rapid accumulation of fatigue damage and even structural instability. Therefore, it is not enough to simply judge the numerical difference between the excitation frequency and the natural frequency. A more robust and analytical frequency proximity measurement method is needed.

[0068] To this end, this step introduces a frequency proximity algorithm and uses a Gaussian kernel similarity function as a core metric. This function quantifies the proximity between the excitation frequency and each order of the bridge structure's natural frequency as a continuous similarity weight. The advantage of this function lies in its adjustable parameters (such as the standard deviation), which allows for flexible adjustment of judgment accuracy based on frequency density. Its smoothness and sensitivity to small variations make it suitable for handling the uncertainty introduced by frequency fluctuations in real-world bridge monitoring data.

[0069] After calculating the proximity between each frequency order, modal weights or energy contribution factors are introduced for weighted averaging, ultimately yielding a unified excitation-structure frequency proximity index. This excitation-structure frequency proximity index comprehensively reflects the proximity of the current excitation frequency to multiple modes of the structure in the spectrum, and is a dimensionality reduction and fusion expression of high-dimensional frequency proximity information. The higher its value, the more significant the trend of multiple modal frequencies approaching the excitation frequency, and the stronger the resonant sensitivity of the structure; conversely, it indicates that the structure is in a frequency safety range. Through the real-time calculation and tracking of this excitation-structure frequency proximity index, not only can potential risk conditions be dynamically identified, but the increase in data acquisition frequency can also be accurately triggered, thereby ensuring that high-frequency dynamic responses are fully captured and improving the safety and intelligence of the bridge vibration prediction system. Therefore, this step is the key logical center for realizing the linkage between frequency sensitivity identification, adaptive control, and risk warning in the entire prediction method.

[0070] The current excitation-structure frequency approach index and its historical change rate are combined to characterize the structural frequency response to dynamically identify whether the bridge structure is in a resonance-sensitive state. If so, the sampling frequency of the vibration response data is dynamically increased to meet the monitoring needs of high-frequency non-steady-state responses. If not, the regular sampling frequency is maintained to optimize data processing efficiency.

[0071] The fuzzy risk index is calculated by combining the current excitation-structure frequency approach index and its historical change rate to characterize the dynamic risk trend of the structural frequency response. Based on the fuzzy risk index, it is dynamically identified whether the bridge structure is in a resonance-sensitive state. The calculation formula of the fuzzy risk index is:

[0072]

[0073] Where: η is the excitation-structure frequency approach index calculated at the current moment, reflecting the overall closeness between the current excitation frequency and the natural frequencies of each order bridge structure; represents the rate of change of the excitation-structure frequency approach index per unit time, which is used to describe the rising speed of the bridge structure resonance risk; μ is the trend enhancement factor, which is used to adjust the sensitivity of risk changes to system response, with an optimal value of 0.5 to 2; R f The fuzzy risk index calculated at the current moment reflects the closeness between the excitation frequency and the natural frequency of the structure and its changing trend;

[0074] The purpose of this step is to construct a fuzzy risk index, which can be used to dynamically determine whether the bridge is in a potential resonance-sensitive state. This fuzzy risk index not only considers the proximity between the current excitation frequency and the natural frequency of the bridge structure (i.e., the excitation-structure frequency approach index), but also introduces its rate of change to reflect the trend of increasing risk. Compared with the traditional method that relies solely on static frequency difference judgment, this method can identify the critical state where the frequency is rapidly approaching the natural frequency in real time, perceive the resonance risk in advance, and enhance the system's response to sudden and non-steady-state vibrations. It is the key foundation for realizing intelligent control of sampling frequency and bridge vibration early warning.

[0075] If it is in a resonance-sensitive state, the sampling frequency of the vibration response data is dynamically increased. The specific steps are as follows:

[0076] When the fuzzy risk index is greater than the fuzzy risk threshold, the bridge is determined to be in a potential resonance-sensitive state. The vibration response data sampling frequency control mechanism is activated. Based on the degree to which the fuzzy risk index exceeds the threshold, the sampling frequency is adjusted to a level that is suitable for high-risk states, thereby improving the monitoring capability of sudden resonance responses. The sampling frequency is determined by the following formula:

[0077]

[0078] Where: f sample is the adjusted sampling frequency, that is, the data acquisition rate currently applied to the sensor; f base is the basic sampling frequency, which indicates the sampling rate of the system default configuration under normal operation; θ is the frequency adjustment gain coefficient, which is used to control the amplitude of the sampling frequency increase caused by the increase in fuzzy risk, and is preferably set to 0.5 to 1.5; R this the fuzzy risk threshold, which is used to define the judgment boundary of the resonance sensitive state; k is the nonlinear enhancement index, which determines the sensitivity of the sampling frequency to the fuzzy risk index exceeding the fuzzy risk threshold, and is preferably 2;

[0079] The design of this mechanism fully considers the dual factors of frequency proximity and trend change, and forms dynamic judgment through fuzzy risk index, which has stronger adaptability and robustness. When the risk gradually increases or changes suddenly in a short time, the system can immediately and smoothly increase the sampling frequency to prevent high-frequency non-steady-state responses from being missed; when the risk does not increase significantly, the sampling frequency is maintained at a conventional level with low energy consumption and high efficiency to avoid resource waste; in addition, the nonlinear frequency enhancement model (R f -R th ) k Compared with the linear gain strategy, it can achieve a stronger risk response amplification effect, ensuring sufficient early warning of potentially destructive dynamic events. It is suitable for application in engineering scenarios such as high-speed railway bridges and large-span continuous beam bridges that require extremely high accuracy in vibration response monitoring.

[0080] In bridge health monitoring systems, different types of vibration response data (such as acceleration, displacement, strain, and velocity) have distinct physical response characteristics and application scenarios. Therefore, differentiated sampling frequency strategies should be adopted to better match the actual monitoring objectives and structural response characteristics. Acceleration signals are primarily used to capture high-frequency dynamic responses and short-duration impact events, typically reflecting changes in the overall structural stiffness or localized impact disturbances. Their signal bandwidth is relatively wide, requiring a higher sampling frequency (e.g., 200 Hz or even higher). Strain signals, on the other hand, are more suitable for reflecting the deformation evolution and fatigue accumulation of component materials. Their response frequency is relatively low, and a sampling frequency of 10 to 50 Hz is generally sufficient for analysis. Displacement or velocity signals are often used in scenarios such as long-term structural displacement trends, wind-induced vibration, and low-frequency response. Sampling strategies must balance time span and accuracy. Furthermore, for complex operating condition identification tasks such as modal identification, damage identification, or resonance warning, the system may need to incorporate segmented sampling or multi-channel adaptive sampling mechanisms to simultaneously address the analysis requirements for both high- and low-frequency responses. Therefore, dynamic sampling frequency control cannot rely on a fixed, uniform standard. Instead, adaptive sampling rules with categorical attributes should be developed based on the three-dimensional coupling relationship of "response type, monitoring target, and operating condition risk." The final sampling frequency should be intelligently adjusted based on the system's currently identified excitation-structure frequency approximation indicator, the fuzzy risk level, and the corresponding response type requirements. This ensures that critical response information is not lost, while achieving optimal allocation of data storage and processing resources, comprehensively improving the system's real-time performance and efficiency in multi-source vibration information perception and risk warning.

[0081] The purpose of this step is to establish an intelligent judgment and dynamic response mechanism based on the excitation-structure frequency relationship to identify in real time whether the bridge structure is in a potential resonance-sensitive state and adaptively adjust the sampling frequency of the vibration response data accordingly. In actual operation, bridge structures are subject to a variety of complex external excitations (such as high-speed trains, wind loads, earthquakes, etc.), which may cause the excitation frequency to temporarily or continuously approach a certain order of natural frequency of the bridge structure, thereby triggering resonance or even coupled resonance, which in turn leads to high-frequency, short-term, non-steady-state violent vibration response. If this response is not effectively sampled or recorded, it is very likely to cause fatigue acceleration, local yielding, or even hidden failure of key components, ultimately affecting structural safety.

[0082] This step introduces an excitation-structure frequency approach index to quantify the proximity between the current excitation frequency and each order of the structure's natural frequencies. Combined with its changing trend, it determines whether there is a risk of frequency resonance. When the excitation-structure frequency approach index is large or shows a rapid upward trend, it indicates that the structure is entering or about to enter a resonance-sensitive zone. The system automatically increases the sampling frequency from the normal level to a higher level to capture key information from the unsteady high-frequency response. Conversely, when there is no significant risk, the sampling frequency is maintained at a low level to conserve data storage, computing, and energy resources.

[0083] The above method can realize the dynamic identification and response control of the potential resonance risk of the bridge under actual complex operating conditions, thereby effectively solving the technical problem that the traditional fixed sampling strategy cannot adapt to the rapid changes of the excitation frequency and has difficulty in capturing high-frequency non-steady-state responses. This method extracts the main excitation frequency through real-time frequency domain analysis, and combines the structural natural frequency feature library with the frequency proximity algorithm to quantify the proximity relationship between the excitation and the structure; it further introduces the frequency proximity trend change rate to construct a fuzzy risk index, intelligently judges whether the bridge is in a resonance-sensitive state, and dynamically adjusts the sampling frequency accordingly. Ultimately, this method achieves the coordinated optimization between monitoring accuracy and system efficiency, not only improving the ability to capture instantaneous high-frequency resonance responses, but also avoiding resource redundancy and monitoring blind spots, significantly enhancing the sensitivity, real-time performance and safety assurance capabilities of the bridge structure health monitoring system.

[0084] The above formulas are all dimensionless and numerical calculations. The formulas are obtained by collecting a large amount of data and performing software simulation to obtain the most recent real situation. The preset parameters in the formulas are set by technicians in this field according to actual conditions.

[0085] The above description is merely illustrative of certain exemplary embodiments of the present invention. It goes without saying that those skilled in the art will be able to modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the above drawings and description are illustrative in nature and should not be construed as limiting the scope of protection of the claims.

[0086] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0087] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0088] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0089] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0090] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection of the claims.

Claims

1. A data-driven long-span bridge vibration response prediction method, characterized in that: The steps include: Multiple sensors are deployed at multiple key structural locations on the bridge to collect real-time vibration response data of the bridge during operation based on a starting sampling frequency set based on the natural frequency of the bridge structure. Perform frequency domain analysis on the collected vibration response data, extract the main excitation frequency components under the current working conditions, and construct the current excitation spectrum; Call the structural modal parameters obtained during the bridge design phase, static load test or modal test, extract the natural frequencies of each order of the structure, and build a bridge natural frequency feature library; The frequency proximity algorithm is used to analyze the proximity between the current excitation frequency and the natural frequencies of each order of the bridge structure. The excitation-structure frequency proximity index is calculated based on the weighted average of the proximity of each order of frequency. The frequency proximity algorithm is a Gaussian kernel similarity function. The current excitation-structure frequency approach index and its historical change rate are combined to characterize the structural frequency response to dynamically identify whether the bridge structure is in a resonance-sensitive state. If so, the sampling frequency of the vibration response data is dynamically increased to meet the monitoring needs of high-frequency non-steady-state responses. If it is not in a resonance-sensitive state, the normal sampling frequency is maintained to optimize data processing efficiency.

2. The data-driven long-span bridge vibration response prediction method according to claim 1 is characterized in that: The setting of the initial sampling frequency includes the following technical measures: Based on the modal analysis results obtained during the bridge design phase, the first several natural frequencies of the bridge structure are extracted; According to the requirements of Shannon sampling theorem, the starting sampling frequency of the sensor is set based on 2 to 4 times the lowest order natural frequency of the bridge structure.

3. The data-driven long-span bridge vibration response prediction method according to claim 1 is characterized in that: Perform frequency domain analysis on the collected vibration response data, extract the main excitation frequency components under the current working conditions, and construct the current excitation spectrum as follows: The spectrum analysis method is used to perform time-frequency transformation on the original vibration response signal collected by the sensor to generate a vibration spectrum diagram under the current working condition; In the spectrum diagram, a spectrum peak recognition algorithm is used to automatically extract one or more dominant frequency components with the largest energy proportion in the spectrum as the main excitation frequency to characterize the current excitation characteristics; The extracted main excitation frequency components are organized according to the monitoring time sequence to form a continuous and updateable current working condition excitation spectrum sequence, which serves as the basic data for subsequent comparison and analysis with the natural frequency of the bridge structure.

4. The data-driven long-span bridge vibration response prediction method according to claim 1 is characterized in that: The steps for calling the structural modal parameters obtained during the bridge design phase, static load test, or modal test, extracting the natural frequencies of each order of the structure, and building a bridge natural frequency feature library include the following: Obtain theoretical modal parameters of the bridge structure through finite element modeling and modal analysis during the bridge design phase; Compare and calibrate the design parameters with the static load test data after the completion of the bridge and the modal test results of the actual bridge to correct and control the errors of the theoretical modal results; Extract the stable natural frequency parameters of each order of the structure from the processed modal data, number and group them according to the modal order, and record the energy concentration, mode directionality and local distribution characteristics of the frequency order. All extracted structural natural frequencies and their associated parameters are uniformly incorporated into a bridge natural frequency feature library. The feature library is constructed using a scalable standard data structure to support subsequent comparison, dynamic updating, and adaptive discrimination of real-time excitation spectra.

5. The data-driven long-span bridge vibration response prediction method according to claim 1, characterized in that: The process of analyzing the proximity between the current excitation frequency and the natural frequencies of the bridge structure is as follows: For the main excitation frequency extracted under the current working condition, the Gaussian kernel similarity function is used to calculate the proximity weight with the natural frequency in the bridge natural frequency feature library. The proximity weight is determined by the following formula: Where: f exc is the current main excitation frequency, indicating the dominant frequency component of the current external excitation; f i is the i-th order natural frequency of the bridge structure, which comes from the frequency feature library; σ is the frequency sensitivity coefficient, which determines the analytical resolution of the frequency proximity; ρ i Represents the similarity weight between the current excitation frequency and the i-th order modal frequency, ρ i ∈(0,1].

6. The data-driven long-span bridge vibration response prediction method according to claim 5 is characterized in that: The steps for calculating the excitation-structure frequency proximity index based on the weighted average of the proximity of each order frequency include the following: When obtaining the proximity weights ρ of all orders i Finally, the contribution factors of each modal order are introduced to calculate the excitation-structure frequency approach index. The calculation formula is as follows: Where: γ i is the contribution factor of the i-th mode; N represents the total number of modes included in the calculation; η is the excitation-structure frequency approach index, which reflects the overall closeness between the current excitation frequency and the natural frequencies of each order bridge structure.

7. The data-driven long-span bridge vibration response prediction method according to claim 6 is characterized in that: The fuzzy risk index is calculated by combining the current excitation-structure frequency approach index and its historical change rate to characterize the dynamic risk trend of the structural frequency response. Based on the fuzzy risk index, it is dynamically identified whether the bridge structure is in a resonance-sensitive state. The calculation formula of the fuzzy risk index is: Where: η is the excitation-structure frequency approach index calculated at the current moment, reflecting the overall closeness between the current excitation frequency and the natural frequencies of each order bridge structure; represents the rate of change of the excitation-structure frequency approach index per unit time, which is used to describe the rising speed of the bridge structure resonance risk; μ is the trend enhancement factor, which is used to adjust the sensitivity of risk changes to system response; R f It is the fuzzy risk index calculated at the current moment, reflecting the closeness between the excitation frequency and the natural frequency of the structure and its changing trend.

8. The data-driven long-span bridge vibration response prediction method according to claim 7 is characterized in that: If it is in a resonance-sensitive state, the sampling frequency of the vibration response data is dynamically increased. The specific steps are as follows: When the fuzzy risk index is greater than the fuzzy risk threshold, the bridge is determined to be in a potential resonance-sensitive state. The vibration response data sampling frequency control mechanism is activated. Based on the degree to which the fuzzy risk index exceeds the threshold, the sampling frequency is adjusted to a level that is suitable for high-risk states, thereby improving the monitoring capability of sudden resonance responses. The sampling frequency is determined by the following formula: Where: f sample is the adjusted sampling frequency, that is, the data acquisition rate currently applied to the sensor; f base is the basic sampling frequency, which indicates the sampling rate of the system default configuration under normal operation; θ is the frequency adjustment gain coefficient, which is used to control the amplitude of the sampling frequency increase caused by the increase in fuzzy risk; R th is the fuzzy risk threshold; k is the nonlinear enhancement index, which determines the sensitivity of the sampling frequency to the fuzzy risk index exceeding the fuzzy risk threshold.

Images