A highway bridge strong dynamic environment structure inclination angle signal processing method and system

Abstract

The application relates to the technical field of structural health monitoring, intelligent signal processing and structural dynamics, and discloses a highway bridge strong dynamic environment structure inclination signal processing method and system, which comprises the following steps: calculating instantaneous vibration inertia according to a three-axis acceleration signal; constructing a multi-order memory kernel function; normalizing a forward memory potential to a preset interval to obtain a normalized forward memory potential; constructing a state vector containing a quasi-static inclination component and a vibration coupling component; weighting and recursively updating the state vector by using power-law weight coefficients of each order; obtaining a current output inclination signal; updating the multi-order memory kernel function by using a gradient descent method according to a prediction error; and outputting, storing or sending the inclination signal of a current sampling point. The application can accurately depict the memory strength difference in different time scales in a real highway bridge structure.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of structural health monitoring, intelligent signal processing, and structural dynamics. Specifically, it relates to a method and system for processing the tilt angle signal of a highway bridge in a strong dynamic environment. Background Technology

[0002] Bridge structures are subjected to the continuous coupled effects of multiple dynamic sources, including traffic loads, temperature effects, and wind-induced vibrations, throughout their service life. The tilt angle signal, as a core indicator reflecting the structural spatial attitude, directly impacts the reliability of structural safety assessments due to its measurement accuracy and stability. However, in actual monitoring, tilt angle sensors are often deployed in environments with strong vibrations and shocks. The actual structural attitude changes in the measured tilt angle signal are highly coupled with the vibration disturbance components, causing serious interference to subsequent analysis.

[0003] Kalman filtering, currently the most widely used state estimation method for bridge structure tilt and vibration signal processing, is based on the assumption that the system model is precisely known and that both process noise and observation noise are Gaussian white noise. However, this theoretical framework has fundamental limitations when facing the highly dynamic environment of highway bridges. First, Kalman filtering requires the accurate pre-setting of the initial state matrix and the measurement noise covariance matrix. However, under highly dynamic conditions such as heavy vehicle traffic, strong winds, and earthquakes, the noise statistical characteristics exhibit significant non-stationarity and non-Gaussian features. The pre-set covariance parameters cannot match the time-varying characteristics of the actual noise, leading to a severe decrease in filtering accuracy or even divergence. Second, Kalman filtering is essentially a first-order Markov model, recursively updating the state only using the current observation values, and cannot effectively utilize the long-range historical information of the vibration response. Studies have shown that when a bridge structure tilts, a tilt angle of 0.1° can cause an acceleration measurement deviation of more than 10 mm / s², and this deviation is difficult to effectively compensate for under the conventional Kalman filtering framework. Third, existing methods such as extended Kalman filtering cannot effectively track real-time changes in structural parameters when dealing with time-varying systems, and lack adaptive tracking capabilities for long-term evolution processes such as bridge stiffness degradation. Fourth, Kalman filtering in multi-sensor fusion scenarios highly relies on the assumption that external excitations are known or observable, while external excitations in the highly dynamic environment of bridges are often unknown and cannot be directly measured.

[0004] Besides the fundamental theoretical limitations mentioned above, conventional Kalman filtering also faces inherent measurement time delay problems in real-time online processing. When there is a time delay in sensor measurements, the current information corresponds to the past state of the system rather than the current state, causing the estimation error to accumulate continuously with the delay time. Even if the filter has converged to a steady state, its low-pass filtering characteristics will still produce a non-negligible phase lag in dynamic scenarios. More complexly, the delay values ​​in engineering practice are usually unknown and time-varying, and cannot be compensated for by simple time shifting. At the same time, for the non-Gaussian, non-stationary vibration noise commonly present in the strong dynamic environment of bridges, Kalman filtering only uses its first and second-order statistics for estimation, and the lack of higher-order statistical information further exacerbates the systematic bias in state estimation.

[0005] Besides Kalman filtering, existing tilt angle processing methods generally suffer from the following technical shortcomings: they all assume that the vibration response of the structure is an instantaneous and independent Markov process, neglecting the long-tailed energy dissipation characteristic commonly found in civil engineering structures. In actual bridges, the vibration energy decays slowly in a power-law manner after impact, but existing methods completely fail to utilize this. When dealing with the memory effect, a single exponential decay weight or a single power-law decay weight is typically used, which cannot describe the physical phenomenon of "different memory intensities at different time scales" in real structures. In actual bridge vibrations, the decay patterns of recent memory and long-term memory often differ, which existing techniques fail to characterize.

[0006] There are currently no effective solutions to the problems in the relevant technologies. Summary of the Invention

[0007] To address the problems in related technologies, this invention proposes a method and system for processing the tilt angle signal of a highway bridge in a strong dynamic environment, in order to overcome the aforementioned technical problems existing in the existing related technologies.

[0008] Therefore, the specific technical solution adopted by the present invention is as follows: According to one aspect of the present invention, a method for processing the tilt angle signal of a highway bridge in a strong dynamic environment is provided, comprising: S1. Collect the original tilt angle signal and triaxial acceleration signal of the highway bridge structure; S2. Calculate the instantaneous vibration inertia based on the triaxial acceleration signal; construct a multi-order memory kernel function; wherein, the multi-order memory kernel function includes the exponential decay rate, the order of each power-law term, and the amplitude coefficient; S3. Using the multi-order memory kernel function at the current moment, predict the influence intensity of several future sampling points on the current instantaneous vibration inertia and accumulate them to obtain the forward memory potential. Then, normalize the forward memory potential to a preset interval to obtain the normalized forward memory potential. S4. Construct a state vector containing quasi-static tilt angle components and vibration coupling components; dynamically adjust the order of each power law term according to the forward memory potential, and use the power law weight coefficient of each order to perform weighted recursion on the historical state vector to update the state vector; add the error between the original tilt angle signal and the current reconstructed tilt angle to the quasi-static tilt angle component for correction, and obtain the current output tilt angle signal. S5. Use the multi-order memory kernel function at the current moment to weight the historical instantaneous vibration inertia to predict the current instantaneous vibration inertia, and use the gradient descent method to update the multi-order memory kernel function according to the prediction error. S6. Output the tilt angle signal of the current sampling point and store or send it.

[0009] Furthermore, S2 includes: S21. Obtain the sensitivity coefficient of the offline calibration; calculate the square of the acceleration vector magnitude based on the triaxial acceleration signal of the current sampling point; calculate the magnitude of the jerk term based on the acceleration vector of the current sampling point and the previous sampling point; multiply the square of the acceleration vector magnitude and the magnitude of the jerk term by the sensitivity coefficient and add them together to obtain the instantaneous vibration inertia of the current sampling point. S22. Obtain the inherent value of the exponential decay rate, the inherent order and inherent amplitude coefficient of each power law term, and construct a multi-order memory kernel function for each historical moment within a preset range, which is a weighted superposition of the exponential decay term and multiple power law decay terms of different orders. S23. Calculate the magnitude of the difference between the acceleration vector of the current sampling point and the previous sampling point as the acceleration change; if the change is greater than the preset threshold, increase the exponential decay rate, decrease the order of each power-law term, and redistribute the amplitude coefficient to enhance the weight of the lower-order terms; otherwise, restore to the inherent value of the offline calibration.

[0010] Furthermore, the formula for obtaining the instantaneous vibration inertia at the current sampling point is: ; In the formula, Indicates the first Instantaneous vibration inertia at each sampling point; Indicates the first The magnitude of the triaxial acceleration vector at each sampling point; Indicates the sensitivity coefficient; This represents the magnitude of the difference in acceleration vectors between adjacent sampling points; Indicates the sampling interval.

[0011] Furthermore, the formula for constructing a multi-order memory kernel function, which is a weighted superposition of an exponentially decaying term and multiple power-law decaying terms of different orders, is as follows: ; In the formula, Indicates the first Multi-order memory kernel function under each sampling point; Indicates a time delay; Indicates the number of power-law terms; Indicates the first Time-varying exponential decay rate at each sampling point; Indicates the first The amplitude coefficient of each power-law term; Indicates the first The sampling point at the th sampling point The order of each power-law term.

[0012] Furthermore, S3 includes: S31. Obtain the preview window length for offline calibration. The preview window length is used to limit the number of sampling points for forward prediction. S32. At the current sampling point, obtain the multi-order memory kernel function and instantaneous vibration inertia at the current moment; for each future sampling point within the preset range, use the parameters of the multi-order memory kernel function at the current moment to calculate the influence intensity of the current instantaneous vibration inertia on each future sampling point; sum up all the predicted influence intensities to obtain the forward memory potential of the current sampling point. S33. Obtain the reference value of the forward memory potential calibrated offline, divide the forward memory potential by the reference value, if the obtained value is greater than one, take one, and normalize the forward memory potential to a preset range of zero to one to obtain the normalized forward memory potential.

[0013] Furthermore, S4 includes: S41. Initialize the state vector, set the initial vibration coupling component to zero, and assign the quasi-static tilt component to the acquired original tilt signal. S42. Calculate the weighted average of the normalized forward memory potential and the trend of memory potential change, and adaptively update the order of each power-law term based on the weighted average and the trend of change. S43. Calculate the power-law weight coefficients corresponding to each order, perform weighted processing on the historical state vector, solve for the state increment and update the state vector. S44. Calculate the error between the original tilt angle signal and the current reconstructed tilt angle. Multiply the error by the learning rate and correct only the static tilt angle component, while keeping the vibration coupling component unchanged. S45. Add the corrected quasi-static tilt component to the vibration coupling component to obtain the current output tilt signal.

[0014] Furthermore, S42 includes: S421. Using weights isomorphic to the multi-order memory kernel function, perform weighted operations on the historical normalized forward memory potential to obtain the weighted average value of the normalized forward memory potential. S422. Take the difference between the current weighted average and the weighted average at the previous moment to obtain the trend of the memory potential. S423. Based on the inherent order of each power-law term, and combining the exponential compression relationship determined by the weighted average and the trend modulation relationship determined by the trend of change, the updated order of each power-law term is calculated. S424. Verify the value range of each power-law term after the update, and sort each power-law term in ascending order.

[0015] Furthermore, S43 includes: S431. Read the order and sampling interval of each power-law term; S432. According to the preset definition of fractional calculus, solve the power law weight coefficients corresponding to each order in turn according to each historical delay time. S433. Call the preset driving function, and combine the normalized forward memory potential, quasi-static tilt component and vibration coupling component to obtain the driving vector corresponding to each historical moment. S434. Introduce the sampling interval power coefficient, multiply the power law weight coefficients of each order with the corresponding historical moment driving vectors and sum them to obtain the state increment; S435. Add the state increment to the state vector of the previous time step to complete the update of the state vector at the current time step.

[0016] Furthermore, S5 includes: S51. Use the multi-order memory kernel function at the current moment to perform weighted calculation on the historical instantaneous vibration inertia, and output the predicted value of the instantaneous vibration inertia; S52. Subtract the predicted value from the actual instantaneous vibration inertia to calculate the prediction error; S53. The partial derivatives corresponding to each kernel parameter are obtained by numerical difference approximation, and the exponential decay rate, the magnitude coefficient of each power-law term and the order of each power-law term are updated by gradient descent algorithm. S54. After the update is complete, the amplitude coefficients of each power-law term are re-normalized so that the sum of all amplitude coefficients equals one, and the orders of each power-law term are reordered in ascending order.

[0017] According to another aspect of the present invention, a structural tilt angle signal processing system for highway bridges in strong dynamic environments is also provided, the system comprising: The signal acquisition module is used to acquire the original tilt angle signal and triaxial acceleration signal of the highway bridge structure; A multi-order memory kernel construction module is used to calculate instantaneous vibration inertia based on triaxial acceleration signals; and to construct multi-order memory kernel functions; wherein, the multi-order memory kernel function includes exponential decay rate, the order of each power-law term and amplitude coefficient; The forward memory potential calculation module is used to use the multi-order memory kernel function at the current moment to predict the influence intensity of several future sampling points on the current instantaneous vibration inertia and accumulate them to obtain the forward memory potential. The forward memory potential is then normalized to a preset interval to obtain the normalized forward memory potential. The multi-order state evolution module is used to construct a state vector containing quasi-static tilt components and vibration coupling components; dynamically adjust the order of each power-law term according to the forward memory potential, and use the power-law weight coefficients of each order to perform weighted recursion on the historical state vector to update the state vector; add the error between the original tilt signal and the current reconstructed tilt angle to the quasi-static tilt component for correction to obtain the current output tilt signal. The parameter adaptive module is used to predict the current instantaneous vibration inertia by weighting the historical instantaneous vibration inertia with the multi-order memory kernel function at the current moment, and to update the multi-order memory kernel function using the gradient descent method according to the prediction error. The output module is used to output the tilt angle signal of the current sampling point and store or transmit it.

[0018] The beneficial effects of this invention are as follows: 1. This invention proposes the concept of a multi-order memory tensor field and constructs a multi-order memory kernel function composed of a weighted superposition of an exponential decay term and multiple power-law decay terms of different orders, which can accurately characterize the differences in memory intensity at different time scales in real highway bridge structures.

[0019] 2. This invention designs a multi-order memory kernel function, which is composed of multiple power-law terms of different orders with weighted synthesis, and the weight coefficients of each order can be dynamically adjusted according to the environmental state, thereby realizing a multi-scale description of the dissipative behavior of the structure.

[0020] 3. This invention proposes the concept of forward memory potential, which enables quantitative assessment of the continuous impact of vibration and allows the processing parameters to be dynamically adjusted with the memory potential.

[0021] 4. This invention designs a multi-order memory tensor operator as the core mathematical structure of state evolution, replacing the conventional state transition matrix, so that the signal processing process has real multi-order history dependency characteristics.

[0022] 5. This invention does not require a pre-set noise statistical model, does not rely on the first-order Markov assumption, and does not require known external excitation. Through adaptive modulation of the multi-order memory tensor field, it simultaneously achieves the maintenance of the true attitude and the physical separation of vibration disturbance within a single dynamic framework, effectively overcoming the systematic defects of Kalman filtering in strong dynamic non-stationary environments where the accuracy decreases or even diverges.

[0023] 6. This invention utilizes an active prediction mechanism based on forward memory potential to pre-modulate the memory kernel parameters before the impact arrives, avoiding phase lag caused by insufficient steady-state gain in Kalman filtering. Simultaneously, the joint recursion of multiple power-law terms endows the algorithm with parallel tracking capabilities across multiple time scales. Experimental data shows that in the initial impact phase of a heavy-load vehicle entering the bridge surface, this invention significantly shortens the output lag time compared to conventional Kalman filtering, ensuring the real-time performance and accuracy of tilt angle output under strong dynamic conditions. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a flowchart of a method for processing the tilt angle signal of a highway bridge in a strong dynamic environment according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a highway bridge in a strong dynamic environment structural tilt angle signal processing system according to an embodiment of the present invention. Figure 3 These are waveforms of the original tilt angle signals collected during actual bridge monitoring according to an embodiment of the present invention, wherein (a), (b), and (c) are waveforms of the original tilt angle signals of the X-axis, Y-axis, and Z-axis, respectively. Figure 4 These are the original tilt angle signal waveforms of the three axes collected during an approximately 90° rotation test using an actual rotation sensor according to an embodiment of the present invention, wherein (d), (e), and (f) are the original tilt angle signal waveforms of the X-axis, Y-axis, and Z-axis, respectively; Figure 5 This is an output waveform diagram obtained after processing the acquired triaxial raw tilt angle signals according to an embodiment of the present invention, wherein (g), (h), and (i) are the output tilt angle signals of the X-axis, Y-axis, and Z-axis, respectively, and... Figure 3 (a), (b), and (c) in the text correspond to respectively; Figure 6 This is an output waveform diagram obtained after processing the triaxial original tilt angle signals of the sensor rotation test according to an embodiment of the present invention, wherein (j), (k), and (l) are the output tilt angle signals of the X-axis, Y-axis, and Z-axis, respectively, and... Figure 4 (d), (e), and (f) in the text correspond to respectively.

[0026] In the picture: 1. Signal acquisition module; 2. Multi-level memory kernel construction module; 3. Forward memory potential calculation module; 4. Multi-level state evolution module; 5. Parameter adaptive module; 6. Output module. Detailed Implementation

[0027] To further illustrate the various embodiments, the present invention provides accompanying drawings, which are part of the disclosure of the present invention. These drawings are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these drawings, those skilled in the art should be able to understand other possible implementation methods and the advantages of the present invention.

[0028] According to an embodiment of the present invention, a method and system for processing the tilt angle signal of a highway bridge in a strong dynamic environment are provided.

[0029] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments, such as... Figure 1 As shown, the method for processing the tilt angle signal of a highway bridge in a strong dynamic environment according to an embodiment of the present invention includes: Step S1: Collect the original tilt angle signal and triaxial acceleration signal of the highway bridge structure; Step S2: Calculate the instantaneous vibration inertia based on the triaxial acceleration signal; construct a multi-order memory kernel function; wherein, the multi-order memory kernel function includes the exponential decay rate, the order of each power-law term, and the amplitude coefficient; Step S3: Use the multi-order memory kernel function at the current moment to predict the influence intensity of several future sampling points on the current instantaneous vibration inertia and accumulate them to obtain the forward memory potential. Then, normalize the forward memory potential to a preset interval to obtain the normalized forward memory potential. Step S4: Construct a state vector containing quasi-static tilt angle components and vibration coupling components; dynamically adjust the order of each power-law term according to the forward memory potential, and use the power-law weight coefficients of each order to perform weighted recursion on the historical state vector to update the state vector; add the error between the original tilt angle signal and the current reconstructed tilt angle to the quasi-static tilt angle component for correction, and obtain the current output tilt angle signal. Step S5: Use the multi-order memory kernel function at the current moment to weight the historical instantaneous vibration inertia to predict the current instantaneous vibration inertia, and update the multi-order memory kernel function using the gradient descent method based on the prediction error; Step S6: Output the tilt angle signal of the current sampling point and store or send it.

[0030] In this optional embodiment, S2 includes: S21, obtaining the sensitivity coefficient of offline calibration; calculating the square of the acceleration vector magnitude based on the triaxial acceleration signal of the current sampling point; calculating the magnitude of the jerk term based on the acceleration vectors of the current sampling point and the previous sampling point; multiplying the square of the acceleration vector magnitude and the magnitude of the jerk term by the sensitivity coefficient and then adding them together to obtain the instantaneous vibration inertia of the current sampling point; S22, obtaining the inherent value of the exponential decay rate, the inherent order of each power-law term, and the inherent amplitude coefficient of the offline calibration; for each historical moment within a preset range, constructing a multi-order memory kernel function composed of the weighted superposition of the exponential decay term and multiple power-law decay terms of different orders; S23, calculating the magnitude of the difference between the acceleration vectors of the current sampling point and the previous sampling point as the acceleration change; if the change is greater than a preset threshold, increasing the exponential decay rate, decreasing the order of each power-law term, and redistributing the amplitude coefficient to enhance the weight of lower-order terms; otherwise, restoring to the inherent value of offline calibration.

[0031] In this optional embodiment, S3 includes: S31, obtaining the offline calibration prediction window length, the prediction window length being used to limit the number of sampling points for forward prediction; S32, at the current sampling point, obtaining the multi-order memory kernel function and instantaneous vibration inertia at the current moment; for each future sampling point within a preset range, using the multi-order memory kernel function parameters at the current moment, calculating the influence intensity of the current instantaneous vibration inertia on each future sampling point; summing all predicted influence intensities to obtain the forward memory potential of the current sampling point; S33, obtaining the offline calibration forward memory potential reference value, dividing the forward memory potential by the forward memory potential reference value, if the obtained value is greater than one, then taking one, and normalizing the forward memory potential to a preset range of zero to one to obtain a normalized forward memory potential.

[0032] In this optional embodiment, S4 includes: S41, initializing the state vector by setting the initial vibration coupling component to zero and assigning the quasi-static tilt component to the acquired original tilt signal; S42, calculating the weighted average of the normalized forward memory potential and the trend of memory potential change, and adaptively updating the order of each power-law term based on the weighted average and the trend of change; S43, calculating the power-law weight coefficients corresponding to each order, weighting the historical state vector, solving for the state increment, and updating the state vector; S44, calculating the error between the original tilt signal and the current reconstructed tilt, multiplying the error by the learning rate, and correcting only the quasi-static tilt component while keeping the vibration coupling component unchanged; S45, adding the corrected quasi-static tilt component to the vibration coupling component to obtain the currently output tilt signal.

[0033] In this optional embodiment, S42 includes: S421, using weights isomorphic to the multi-order memory kernel function to perform a weighted operation on the historical normalized forward memory potential to obtain the weighted average value of the normalized forward memory potential; S422, taking the difference between the current weighted average value and the weighted average value at the previous moment to obtain the trend of the memory potential; S423, based on the inherent order of each power-law term, and combining the exponential compression relationship determined by the weighted average value and the trend modulation relationship determined by the trend of change, calculating the updated order of each power-law term; S424, verifying the value range of each updated power-law term order, and sorting each power-law term order in ascending order.

[0034] In this optional embodiment, S43 includes: S431, reading the order and sampling interval of each power law term; S432, according to the preset definition of fractional calculus, recursively solving the power law weight coefficients corresponding to each order according to each historical delay time; S433, calling the preset driving function, combining the normalized forward memory potential, quasi-static tilt component and vibration coupling component, to obtain the driving vector corresponding to each historical time; S434, introducing the sampling interval power coefficient, multiplying the power law weight coefficients of each order and the corresponding historical time driving vector and summing them to obtain the state increment; S435, superimposing the state increment onto the state vector of the previous time to complete the update of the state vector at the current time.

[0035] In this optional embodiment, S5 includes: S51, using the multi-order memory kernel function at the current moment to perform a weighted operation on the historical instantaneous vibration inertia, and outputting the predicted value of the instantaneous vibration inertia; S52, subtracting the predicted value from the actual instantaneous vibration inertia to calculate the prediction error; S53, using numerical difference approximation to obtain the partial derivatives corresponding to each kernel parameter, and updating the exponential decay rate, the amplitude coefficient of each power-law term, and the order of each power-law term respectively through the gradient descent algorithm; S54, after the update is completed, re-normalizing the amplitude coefficient of each power-law term so that the sum of all amplitude coefficients equals one, and reordering the order of each power-law term in ascending order.

[0036] According to another embodiment of the invention, such as Figure 2 As shown, a structural tilt angle signal processing system for highway bridges in strong dynamic environments is also provided. This system includes: Signal acquisition module 1 is used to acquire the original tilt angle signal and triaxial acceleration signal of the highway bridge structure; Multi-order memory kernel construction module 2 is used to calculate instantaneous vibration inertia based on triaxial acceleration signals and construct multi-order memory kernel functions; wherein, the multi-order memory kernel function includes exponential decay rate, the order of each power-law term and amplitude coefficient; The forward memory potential calculation module 3 is used to use the multi-order memory kernel function at the current moment to predict the influence intensity of several future sampling points on the current instantaneous vibration inertia and accumulate them to obtain the forward memory potential. The forward memory potential is then normalized to a preset interval to obtain the normalized forward memory potential. The multi-order state evolution module 4 is used to construct a state vector containing quasi-static tilt angle components and vibration coupling components; dynamically adjust the order of each power law term according to the forward memory potential, and use the power law weight coefficient of each order to perform weighted recursion on the historical state vector to update the state vector; add the error between the original tilt angle signal and the current reconstructed tilt angle to the quasi-static tilt angle component for correction, and obtain the current output tilt angle signal. The parameter adaptive module 5 is used to predict the current instantaneous vibration inertia by weighting the historical instantaneous vibration inertia with the multi-order memory kernel function at the current moment, and to update the multi-order memory kernel function by gradient descent method according to the prediction error. Output module 6 is used to output the tilt angle signal of the current sampling point and store or send it.

[0037] To facilitate understanding of the above technical solutions of the present invention, the following provides a detailed description of the structural tilt angle signal processing of highway bridges in strong dynamic environments during actual operation.

[0038] This invention uses the tilt monitoring of highway beam bridges as an application scenario, with heavy-load vehicle traffic as a typical strong dynamic excitation condition, and a sampling frequency of 128Hz. However, this invention is not limited to this scenario and parameters. Specifically, it includes the following steps: I. System hardware configuration and offline parameter calibration.

[0039] 1. Hardware Configuration: An integrated MEMS six-axis sensor is installed at the mid-span of the highway bridge and connected to an STM32H743 embedded processor via an SPI interface. The sensor simultaneously reads signals from the tilt sensor and accelerometer installed on the bridge structure at a fixed sampling frequency of 128Hz to obtain the raw tilt angle value and X / Y / Z-axis acceleration values ​​at the current sampling moment, and then proceeds to the following processing flow.

[0040] ; In the formula: The sampling point number, The time interval between two adjacent sampling points is denoted as ; For the first The original tilt angle signal of each sampling point is expressed in radians (rad). For the first The triaxial acceleration signals at each sampling point are in m / s². The axis is usually in the vertical direction.

[0041] It needs to be explained that the original triaxial tilt angle signals collected in actual bridge monitoring are as follows: Figure 3 As shown, where, Figure 3 (a), (b), and (c) in the figure represent the original tilt angle signal waveforms of the X-axis, Y-axis, and Z-axis, respectively. Together, they constitute the three-axis original tilt angle signal waveform diagram under bridge monitoring conditions.

[0042] In addition, a rotation test of approximately 90° was conducted using an actual rotation sensor, and the original triaxial tilt angle signals were collected as follows: Figure 4 As shown, where, Figure 4 In the diagram, (d), (e), and (f) represent the original tilt angle signal waveforms of the X-axis, Y-axis, and Z-axis, respectively. Together, these three waveforms constitute the triaxial original tilt angle signal waveform diagram under the sensor rotation test conditions. Figure 3 and Figure 4 The horizontal axis represents the sampling point number, and the vertical axis represents the angle value of the corresponding axis, in degrees (°). It should be noted that the acceleration signal includes a static gravity component of 9.8 m / s². In subsequent calculations of this invention, this component is not deliberately removed, but its amplitude change is used to reflect the vibration energy.

[0043] 2. Offline parameter calibration: Collect 10 minutes of data during a static period with no heavy vehicles and no wind, and calculate the basis noise of acceleration to set the sensitivity coefficient. The inherent exponential decay rate of the structure was obtained through hammer impact tests. and inherent multi-order order A momentary impact is applied at the sensor location, and the acceleration decay curve is recorded. The exponential decay over a short period and the power-law decay over a long period are fitted separately to obtain... The three inherent orders are taken (Long memory) (Medium memory) (Short memory), inherent amplitude coefficient , , .

[0044] 2.1 During a static period when there are no heavy vehicles, no wind, and no construction or other external stimuli on the bridge, data should be collected continuously for at least 10 minutes. The triaxial acceleration signal is sampled at 128Hz from 1 sampling point. Record each sampling point. acceleration vector For each sampling point Calculate the square of the magnitude of the acceleration vector. Then calculate its average value. In the formula Proportional to instantaneous vibrational energy, under static conditions The value remains essentially constant, serving as a benchmark for subsequent comparisons. If the structure is completely stationary and only gravity exists, However, actual noise will cause it to fluctuate slightly. Then, the magnitude of the jerk is calculated for adjacent sampling points: , ,in This is the sampling interval. Take all. The arithmetic mean is To ensure that the average contribution of the jerk term to the moment of inertia under static conditions does not exceed one-third of the square term of the acceleration modulus, let... To prevent the coefficient from becoming too large when the denominator is too small, an upper limit is added. If the calculated value exceeds 0.5, then take 0.5 and prompt the user to check the data quality.

[0045] In this embodiment, the mean square of the acceleration modulus at static time The average jerk is ,but Verify the ratio of static standard deviation to mean. ,in, The standard deviation of static acceleration. The mean static acceleration and the peak contribution of the acceleration term under impact conditions account for approximately 25%, which meets the design requirements. Therefore, the sensitivity coefficient is determined. .

[0046] 2.2. Apply an instantaneous impact load at the mid-span of the bridge, at the same location as the tilt sensor, and synchronously record the triaxial acceleration response at a sampling frequency of 128Hz. Repeat the experiment 3-5 times, and take the average value to eliminate random interference. Select data from the free decay period of the structure after impact, with a length of not less than 10 seconds. Compare the measured acceleration modulus... Performing a Hilbert transform or connecting the peaks yields a smooth, decaying envelope. To facilitate fitting, the logarithmic domain is used for analysis.

[0047] 2.3. Take the envelope data within 0~0.5s after the impact, time window =0.5s, corresponding to Assume that the decay during this period follows a certain pattern. Take the natural logarithm of both sides ,right The negative of the slope of a linear least-squares fit with time t is... In this embodiment, of and Perform linear regression to obtain the slope Therefore, the fitting result .

[0048] 2.4. Obtain envelope data within 1-10 seconds after the impact, time window. , In practical engineering structures, the long-tail decay often exhibits the superposition of multiple power-law effects. Therefore, a multi-order power-law model is used for fitting: ; in, For amplitude coefficients, satisfying The parameters were fitted using the nonlinear least squares method. .Will The intervals are roughly divided into three segments, representing typical central values ​​for long, medium, and short memories, respectively. Statistical results from numerous bridge structure hammer tests show that the convergence order of multi-order power-law fitting commonly falls within three sub-intervals: 0.1–0.3, 0.4–0.6, and 0.7–0.9. Taking the interval midpoints of 0.2, 0.5, and 0.8 as initial guesses can cover the vast majority of cases. Amplitude coefficients satisfy ,and In the absence of any empirical data, the fairest assumption is that the contributions of each power-law term are equal.

[0049] It should be noted that, in order to avoid initial bias towards a certain order, which could lead to local optima, the initial value in this invention is set to... Furthermore, nonlinear least squares is very sensitive to the amplitude coefficients; even if the initial values ​​are equal, it can quickly converge to the true value after several iterations.

[0050] The final fitting result obtained in this embodiment is: , , In actual coding, a multi-starting-point initialization strategy can also be adopted, randomly perturbing the initial value and fitting it multiple times, taking the result with the smallest residual, to further reduce the dependence on a single initial value.

[0051] 3. Reference value calibration: Calculate the maximum value of the forward memory potential under the strong impact condition of a heavy-load vehicle passing through, and take... .

[0052] 3.1 Collect synchronous raw tilt angle and triaxial acceleration signals of heavy-duty vehicles crossing the bridge, covering the entire process from vehicle entry to exit. Select data from at least three different heavy-duty freight trucks and high-speed buses to ensure coverage of varying impact intensities. For each heavy-duty vehicle, collect data from all sampling points. Calculate the forward memory potential For each heavy-load vehicle data, calculate The sequence records the maximum value of that pass. Then take the maximum value from all passes. ,in, For all trips.

[0053] In this embodiment, the maximum value obtained from multiple trials is To prevent the forward memorpotential from exceeding the limit during actual online operation, i.e., causing the normalized value to... Multiplying the maximum value by a safety factor of 1.1, then If there is a more extreme impact such as an earthquake at the scene, the 99.9th percentile can be multiplied by 1.05 based on historical data.

[0054] 4. Driving function coefficients: , , , .

[0055] The driving function is used to describe the quasi-static tilt components. Vibration coupling component The dynamic coupling relationship between them can be generally expressed as follows: ; In the formula, To standardize the forward memory potential; For quasi-static tilt component; It is a vibration coupling component; , , , All of these are driving function coefficients.

[0056] 4.1. Isolate the vibration component by utilizing the free decay section of the hammer impact test. By fitting its envelope attenuation curve, we obtain From the data on heavy-load vehicles passing through, the section with the strongest impact is selected. When the value approaches 1, the instantaneous decay rate of the vibration component is measured, combined with... Reverse push ; and Calibration is achieved by minimizing the long-term error between the reconstructed tilt angle and the original tilt angle: in static or slowly varying segments. It should be guaranteed Slowly track the original value; during the impact phase, Should be avoided Follow Violent fluctuations.

[0057] 5. Learning rate: , .

[0058] It should be noted that, in the laboratory, the tilt sensor was fixed to a rotating platform, and a step change of 0.01 rad in the actual tilt angle was applied. Simultaneously, ambient noise was simulated, and small-amplitude random vibrations were applied, while the original tilt angle was recorded. With the algorithm output .calculate Time from the start of the step jump to 90% of the final value The quasi-static deformation time constant of real bridge structures is typically between 0.5 and 2 seconds. Requirements Match this. Use empirical references and common values ​​from literature. Test and draw separately and The comparison curves. Simultaneously calculate the static segment. The standard deviation of . Choose to make The maximum value falling within the 1~1.5s range and with a noise standard deviation less than 0.0005rad. .

[0059] In this embodiment hour, The noise standard deviation is 0.0003 rad, which meets the requirements. If... , The noise standard deviation is 0.0008 rad (too large); if , (Too slow).

[0060] It should be noted that, using long-term monitoring data, a scenario of linear degradation of structural stiffness was artificially constructed: the actual exponential decay rate was expressed every 12 hours. Increase by 0.01. Use a fixed value. Run the online update algorithm and observe the estimated values. The tracking error relative to the true value. First, define the mean absolute tracking error. , For the first The true value of the exponential decay rate at each sampling time; and the parameter volatility. (Standard deviation per 100 points). Then take... Test them separately. Then when hour, , The parameter variation range remains within And it can track daily changes. When hour, It slightly decreased to 0.002, but volatility increased to 0.003, indicating significant fluctuations. When hour, There is a significant lag. Taking all factors into consideration, this embodiment selects... .

[0061] II. Steps for recursive processing of each sampling point.

[0062] 1. Calculate a scalar of instantaneous vibration inertia based on the current triaxial acceleration signal. The mathematical expression for calculating the instantaneous vibration inertia is as follows: ; in .

[0063] In the formula: This is a sensitivity coefficient, ranging from 0.1 to 0.5, used to adjust the contribution strength of the jerk term; The sampling interval; For the first Instantaneous vibration inertia at each sampling point; Indicates the first The magnitude of the triaxial acceleration vector at each sampling point; It represents the magnitude of the difference in acceleration vectors between adjacent sampling points.

[0064] It should be noted that for MEMS accelerometers, at a sampling frequency of 128Hz, about , Approximately 96~100, therefore To ensure that the contribution of the accelerometer term under static conditions does not exceed 30% to 50% of the squared modulus term, we take... This meets the requirements. If During the static period, the moment of inertia will fluctuate significantly, leading to instability in subsequent forward memory potential calculations. If the jerk term is required to contribute at least 20% of the squared modulus term, then... Considering the actual sensor noise and the impact characteristics of different bridges, to ensure sensitivity, a value is typically taken as... .

[0065] Numerical calculations in this embodiment: Magnitude of acceleration vector: .

[0066] but .

[0067] Assume the acceleration at the previous sampling point is ,and Then the acceleration term is: ;therefore, .

[0068] 2. Construct a multi-order memory kernel function that describes the weight of the influence of historical vibrations on the current state, and update the parameters in the kernel function online according to the rate of change of acceleration.

[0069] ; In the formula, The value of the multi-order memory kernel function represents the value of the first... The moment of inertia of vibration at time t on the first The impact weight of time; Indicates time delay, in units of sampling periods; The number of power-law terms is taken in this embodiment. ; Indicates the first Time-varying exponential decay rate at each sampling point; Indicates the first The amplitude coefficients of each power-law term, with values ​​ranging from (0, 1); Indicates the first The sampling point at the th sampling point The order of each power-law term.

[0070] It should be noted that the multi-order memory kernel contains three power-law terms of different orders, which can describe the recent (high) memory respectively. ), mid-term (medium ) and long term (low) The memory contribution of the index term. Mainly used for small This causes the memory nucleus to quickly forget short-term disturbances after the impact; while the power-law term exist When the size is large, it plays a dominant role, producing a long tail effect and simulating the multi-scale dissipation of real structures.

[0071] It should be noted that in actual programming, due to Maximum retrieved memory truncation length Each can be calculated in advance The corresponding power law value is stored in a lookup table to improve operating efficiency.

[0072] It should be noted that, based on actual hammer impact tests, even the most flexible bridge exhibits an equivalent exponential decay rate greater than 0.2 within 0.5 seconds of acceleration envelope. This was statistically analyzed for the inherent exponential decay rate of multiple bridges under unmodulated conditions. The minimum value is 0.23, so a lower limit of 0.2 is taken as the safety boundary. At the start of the impact, the algorithm will... Temporary augmentation is used to "forget" unrelated history prior to the impact. Based on statistical data from numerous heavy-duty vehicles, even under the most intense impact, the temporary augmentation... It rarely exceeds 1.5. If it exceeds 1.5, the forward memory potential's response to shocks becomes too short, making it unable to effectively predict future vibration effects. The maximum transient response in actual measurements... Approximately 1.4, with an upper limit of 1.5 to leave a margin.

[0073] The parameter values ​​in this embodiment are:

[0074] ; Furthermore, the memory kernel function is .

[0075] 3. Detect the change in acceleration between the current moment and the previous moment. If the change is large, it indicates the onset of an impact, and temporary adjustments should be made. , and Otherwise, revert to the default value.

[0076] Specifically, define the change in acceleration. .

[0077] like (The threshold can be calibrated according to the actual environment), then it is determined as the onset of the impact: ; ; ; otherwise: .

[0078] It should be noted that at the initial moment of the impact, the temporary increase It can accelerate the forgetting of irrelevant history prior to the shock, while reducing... To enhance long-term memory, enabling the system to better track the slow decay process after an impact. Amplitude coefficient. The redistribution is intended to give lower-order terms a larger weight, as vibrations decay slowly after an impact, making long-term memory more important.

[0079] In this embodiment: due to Therefore, parameters for the steady state are adopted.

[0080] 4. Using the multi-order memory kernel function at the current moment, predict the intensity of the influence of the current vibration inertia on several future sampling moments, and sum these influences to obtain a scalar of the forward memory potential. Finally, normalize it to the interval of 0 to 1. The specific expression is as follows: ; ; In the formula, To predict the window length, this embodiment takes... This corresponds to 0.5 seconds in the future; Indicates from the first Time Rewind At this moment (i.e., returning to the first moment) The memory weights at each time step (in time). However, in the recursive implementation, the parameters at future time steps are unknown, so the parameters at the current time step are used as an approximation: ; In the formula, Forward memory potential, unit is seconds; The reference value obtained through offline calibration is used in this embodiment. ; For normalized forward memory potential, the range is [0, 1].

[0081] It should be noted that the parameters in the memory kernel function are regarded as the weights of the influence on the past, while when calculating the forward memory potential, the current moment is regarded as the "source" to predict the influence forward, and the same kernel function form is still used in practice.

[0082] Specifically, because the future cannot be predicted... This invention approximates future parameters using current parameters, which is reasonable when the impact changes are not too drastic. For greater accuracy, short-time linear extrapolation can be introduced, but this would increase computational complexity.

[0083] It should be noted that, in Real-time calculation under strong impact conditions And record its maximum value, and set that value as... Leave a 10% margin.

[0084] In this embodiment, the summation is calculated using stationary state parameters: ; Assuming it has been obtained through a pre-computed lookup table: ,but .

[0085] 5. Define the state vector, update each order, use multi-order memory weights to perform weighted summation of historical states to obtain the state increment, update the state, correct it with the original tilt angle signal, and finally output the current tilt angle.

[0086] 5.1 Define and initialize the state vector. Since the sum of the two components is the reconstructed tilt angle signal, but they have different physical sources, they need to be processed separately; and at the initial time... Since there is no history, the vibration component is set to 0, and the quasi-static component is directly taken as the original tilt angle.

[0087] ; Initialization expression: .

[0088] In the formula, The quasi-static tilt component (rad) represents the actual long-term attitude change of the bridge. The vibration coupling component (rad) represents the transient response caused by external excitation.

[0089] 5.2. Based on the normalized forward memory potential and its changing trend, dynamically adjust each order. This enables it to respond to changes in environmental stimuli, as shown in the following formula: ; Among them, weight .

[0090] ; ; In the formula, The number of historical points used to calculate the weighted average; Weights that are isomorphic to multi-order kernel functions use intrinsic parameters and do not change with the state; It is a weighted average of the forward memory potential; This represents the first-order trend of the memory potential. For the first The sensitivity coefficient of the order controls the compressibility of the memory potential on the order; For the first The trend modulation coefficient of the order.

[0091] It should be noted that the exponential function in the formula When When it increases, This reduces the likelihood of loss, thereby enhancing long-term memory. (Second Factor) This achieves a feedforward effect: if the memory potential is rapidly increasing, even if the current value is not high, the order will temporarily decrease, allowing the system to enhance its memory ahead of time. Must meet If the order is disordered after the update, a forced sorting will be required.

[0092] In this embodiment, it is assumed that the calculation is obtained. , ,but ;for : Therefore Similarly , .

[0093] 5.3 For each order Calculate the corresponding historical delays Weighting coefficients These coefficients will be used to weight and sum the historical states.

[0094] ; ; In the formula, Indicates a historical delay. Indicates the previous moment, This indicates the two previous moments, and so on. This indicates the memory truncation length; in this embodiment, it is taken as... ; Indicates the first The memory weight coefficient of the order.

[0095] It should be noted that these weighting coefficients are not arbitrary; they are derived from the GL definition in fractional calculus (i.e., the pre-defined definition of fractional calculus) and exhibit power-law decay characteristics. When When the weight is small, the weight decays slowly; when When the value is large, the decay is rapid. The signs in the recursive formula alternate (negative, positive, negative, positive…), which is an inherent characteristic of the power-law weight sequence. During the final summation, the positive and negative signs cancel each other out, creating an effect similar to "damped oscillations." In actual programming, it is only necessary to calculate up to… Because when When very big The absolute value is already very small (e.g., less than). ), can be truncated.

[0096] In this embodiment, , For example, , , And so on, continuing the calculation until... .

[0097] 5.4 For each historical delay Based on the quasi-static component, vibrational component, and forward memory potential at that time, a two-dimensional driving vector is calculated. Since all orders in this embodiment use the same driving function form, the calculation can be simplified: ; In the formula, 、 、 、 All are driving function coefficients; This serves as a standardized forward memory potential for this historical moment; This represents the state component at that historical moment.

[0098] It should be noted that the first component of the driving function is only related to... and It is related and negative. This means the vibration component... Energy will "leak" into the quasi-static component, but the leakage intensity varies with the memory potential. The second component increases with increasing; the second component contains two terms: the first term is a self-decaying term, which increases with increasing... The increase strengthens as the quasi-static component grows; the second term is the reverse coupling from the quasi-static component to the vibrational component, which increases with... The asymmetric coupling design ensures the stability of the quasi-static component under strong vibrations.

[0099] In this embodiment, historical delay is used. =1; Take values ​​of 0.05, 0.2, and 0.01 respectively; Take 2.0: Given , First component: Second component: ; The second portion totals... ,therefore Similarly, for =2, assuming , The calculation yields: Continue calculating to .

[0100] 5.5 Multiply the memory weights of each order by their corresponding driving functions, sum them, and then multiply by . , obtain the state increment Then add it to the state from the previous time step. In actual programming, the values ​​for each order are pre-calculated. Values ​​should be used to avoid repeated calls to the exponentiation function.

[0101] ; ; In the formula, Indicates the sampling interval Powers are used to adjust time scales of different orders; Indicates the first The memory weight coefficient of the order; It is a two-dimensional driving vector; For state increments; This is the state vector.

[0102] It needs to be made clear that, exist When it approaches 0, it approaches 1. When it approaches 1, it approaches That is, 0.01. Therefore, lower-order long-memory terms contribute more to the increment, which is consistent with physical expectations; during programming, the increments of each order can be pre-calculated. Values ​​should be used to avoid repeated calls to the exponentiation function.

[0103] In this embodiment, the calculations for each order are first performed. : , , Similarly Assuming the weighted sums of each order have been calculated, the sum of the first component is: The second component totals: ,therefore After the status update .

[0104] 5.6. The error between the current original tilt angle measurement and the current reconstructed tilt angle (the sum of the two components) is added to the quasi-static component according to a certain learning rate to ensure that the processing result does not deviate from the true measurement value. Finally, the reconstructed tilt angle is summed and output. .

[0105] ; ; constant; In the formula, This represents the reconstruction error; The learning rate is 0.01 to 0.05.

[0106] It should be noted that in the fields of adaptive signal processing and structural health monitoring, commonly used learning rate values ​​for online correction include 0.01, 0.02, and 0.05, such as the normalized step size of the LMS algorithm. This scan set includes these classic values, with additional values ​​of 0.005 and 0.03 added to refine the trend of change. 0.005 is half of 0.01, used to verify whether... Too small and it lacks tracking; 0.03 is between 0.02 and 0.05 and is used to confirm whether the optimal value falls at a point in the 0.02~0.05 range.

[0107] It's important to clarify that the correction is applied only to the quasi-static component, not the vibration component. This is because the vibration component should be determined by historical driving forces and adaptive decay, and should not be directly "pulled back" by the original signal; otherwise, high-frequency noise would be introduced. (Learning rate) The value cannot be too large, otherwise the quasi-static component will follow the vibration disturbance; nor can it be too small, otherwise the tracking of real long-term changes will be too slow. In this embodiment, 0.02 is an empirical value. In practical applications, it can be... Follow Adaptive: Decrease when memory potential is high To avoid mistaking disturbances for real changes; increase when memory potential is low. For simplicity, this embodiment uses fixed values.

[0108] In this embodiment, the tilt angle is reconstructed. Original tilt angle ,but: ; After substituting into the formula and correcting... , Keep it unchanged at 0.000500; finally and Summation yields rad.

[0109] It needs to be explained that, for Figure 3 The above correction method is applied to each sample point of the original triaxial tilt signal shown, and the resulting output tilt signal is as follows: Figure 5 As shown, where, Figure 5 In the diagram, (g), (h), and (i) represent the output tilt angle signal waveforms for the X, Y, and Z axes, respectively. Figure 3 (a), (b), and (c) in the text correspond to respectively.

[0110] In addition, for Figure 4 The sensor rotation test data shown is processed in the same way, and the resulting output tilt angle signal is as follows: Figure 6 As shown, where, Figure 6 In the figure, (j), (k), and (l) represent the output tilt angle signal waveforms of the X-axis, Y-axis, and Z-axis, respectively. Figure 4 (d), (e), and (f) in the text correspond to respectively. Figure 5 and Figure 6 The horizontal axis represents the sampling point number, and the vertical axis represents the corresponding angle value after processing, in degrees (°).

[0111] 6. Utilize the current instantaneous vibration inertia Compared with the predicted value obtained by weighting the historical vibration inertia with memory kernels The error between them.

[0112] ; ; In the formula, Predicted values ​​obtained by weighting historical vibrational inertia with the current memory kernel; This represents the prediction error.

[0113] It should be noted that here The parameters used are those at the current time, and the prediction window length L is set to 50.

[0114] In this embodiment, it is assumed that the calculation is performed using historical data. In reality ,but: .

[0115] 6.1 Update using gradient descent method , and This enables the memory core to adapt to changes in the dynamic characteristics of the bridge structure.

[0116] ; in, ; Approximation via numerical difference: .

[0117] In the formula, The learning rate is set to 0.001 in this embodiment; The difference step size is set to 0.01.

[0118] It should be noted that, due to Need to meet After the update, re-normalization is required. Update The sorting must be maintained afterwards. If the condition is not met, the value will be swapped or reassigned.

[0119] In this embodiment, partial derivatives are calculated using: respectively... and Calculate, and let the results be 97.78 and 97.82 respectively, then: Note: In actual physics... Increasing the gradient should shorten the memory span, potentially reducing the predicted value, thus making a negative gradient reasonable. The calculated result is 0.6, which is a very small change, indicating that the system is stable.

[0120] 7. Set the output tilt angle of the current sampling point. Store or send, then sample point sequence number Increment 1, return to the original tilt angle and triaxial acceleration signal acquisition process for the highway bridge structure, and repeat the above process to achieve recursive processing of the continuous sampling stream. All historical states and and The data needs to be stored in a circular queue, and each time a new sampling point enters, it overwrites the oldest data.

[0121] It should be noted that this invention does not rely on any future data; all calculations use only current and historical information. Therefore, it can be run point-by-point, making it suitable for embedded real-time systems. If processor resources are limited, the size can be appropriately reduced. For example, if we take 100, it corresponds to 1 second of history, but it can still maintain good performance.

[0122] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for processing the tilt angle signal of a highway bridge in a strong dynamic environment, characterized in that, include: S1. Collect the original tilt angle signal and triaxial acceleration signal of the highway bridge structure; S2. Calculate the instantaneous vibration inertia based on the triaxial acceleration signal; construct a multi-order memory kernel function; wherein, the multi-order memory kernel function includes the exponential decay rate, the order of each power-law term, and the amplitude coefficient; S3. Using the multi-order memory kernel function at the current moment, predict the influence intensity of several future sampling points on the current instantaneous vibration inertia and accumulate them to obtain the forward memory potential. Then, normalize the forward memory potential to a preset interval to obtain the normalized forward memory potential. S4. Construct a state vector containing quasi-static tilt angle components and vibration coupling components; dynamically adjust the order of each power law term according to the forward memory potential, and use the power law weight coefficient of each order to perform weighted recursion on the historical state vector to update the state vector; add the error between the original tilt angle signal and the current reconstructed tilt angle to the quasi-static tilt angle component for correction, and obtain the current output tilt angle signal. S5. Use the multi-order memory kernel function at the current moment to weight the historical instantaneous vibration inertia to predict the current instantaneous vibration inertia, and use the gradient descent method to update the multi-order memory kernel function according to the prediction error. S6. Output the tilt angle signal of the current sampling point and store or send it.

2. The method for processing the tilt angle signal of a highway bridge in a strong dynamic environment according to claim 1, characterized in that, S2 includes: S21. Obtain the sensitivity coefficient of the offline calibration; calculate the square of the acceleration vector magnitude based on the triaxial acceleration signal of the current sampling point; calculate the magnitude of the jerk term based on the acceleration vector of the current sampling point and the previous sampling point; multiply the square of the acceleration vector magnitude and the magnitude of the jerk term by the sensitivity coefficient and add them together to obtain the instantaneous vibration inertia of the current sampling point. S22. Obtain the inherent value of the exponential decay rate, the inherent order and inherent amplitude coefficient of each power law term, and construct a multi-order memory kernel function for each historical moment within a preset range, which is a weighted superposition of the exponential decay term and multiple power law decay terms of different orders. S23. Calculate the magnitude of the difference between the acceleration vector of the current sampling point and the previous sampling point as the acceleration change; if the change is greater than the preset threshold, increase the exponential decay rate, decrease the order of each power-law term, and redistribute the amplitude coefficient to enhance the weight of the lower-order terms; otherwise, restore to the inherent value of the offline calibration.

3. The method for processing the tilt angle signal of a highway bridge in a strong dynamic environment according to claim 2, characterized in that, The formula for obtaining the instantaneous vibration inertia of the current sampling point is: ； In the formula, Indicates the first Instantaneous vibration inertia at each sampling point; Indicates the first The magnitude of the triaxial acceleration vector at each sampling point; Indicates the sensitivity coefficient; This represents the magnitude of the difference in acceleration vectors between adjacent sampling points; Indicates the sampling interval.

4. The method for processing the tilt angle signal of a highway bridge in a strong dynamic environment according to claim 2, characterized in that, The formula for constructing a multi-order memory kernel function, which is a weighted superposition of an exponentially decaying term and multiple power-law decaying terms of different orders, is as follows: ； In the formula, Indicates the first Multi-order memory kernel function under each sampling point; Indicates a time delay; Indicates the number of power-law terms; Indicates the first Time-varying exponential decay rate at each sampling point; Indicates the first The amplitude coefficient of each power-law term; Indicates the first The sampling point at the th sampling point The order of each power-law term.

5. The method for processing the tilt angle signal of a highway bridge in a strong dynamic environment according to claim 1, characterized in that, S3 includes: S31. Obtain the length of the offline calibration preview window, wherein the preview window length is used to limit the number of sampling points for forward prediction; S32. At the current sampling point, obtain the multi-order memory kernel function and instantaneous vibration inertia at the current moment; for each future sampling point within the preset range, use the parameters of the multi-order memory kernel function at the current moment to calculate the influence intensity of the current instantaneous vibration inertia on each future sampling point; sum up all the predicted influence intensities to obtain the forward memory potential of the current sampling point. S33. Obtain the reference value of the forward memory potential calibrated offline, divide the forward memory potential by the reference value, if the obtained value is greater than one, take one, and normalize the forward memory potential to a preset range of zero to one to obtain the normalized forward memory potential.

6. The method for processing the tilt angle signal of a highway bridge in a strong dynamic environment according to claim 1, characterized in that, S4 includes: S41. Initialize the state vector, set the initial vibration coupling component to zero, and assign the quasi-static tilt component to the acquired original tilt signal. S42. Calculate the weighted average of the normalized forward memory potential and the trend of memory potential change, and adaptively update the order of each power-law term based on the weighted average and the trend of change. S43. Calculate the power-law weight coefficients corresponding to each order, perform weighted processing on the historical state vector, solve for the state increment and update the state vector. S44. Calculate the error between the original tilt angle signal and the current reconstructed tilt angle. Multiply the error by the learning rate and correct only the static tilt angle component, while keeping the vibration coupling component unchanged. S45. Add the corrected quasi-static tilt component to the vibration coupling component to obtain the current output tilt signal.

7. The method for processing the tilt angle signal of a highway bridge in a strong dynamic environment according to claim 6, characterized in that, S42 includes: S421. Using weights isomorphic to the multi-order memory kernel function, perform weighted operations on the historical normalized forward memory potential to obtain the weighted average value of the normalized forward memory potential. S422. Take the difference between the current weighted average and the weighted average at the previous moment to obtain the trend of the memory potential. S423. Based on the inherent order of each power-law term, and combining the exponential compression relationship determined by the weighted average and the trend modulation relationship determined by the trend of change, the updated order of each power-law term is calculated. S424. Verify the value range of each power-law term after the update, and sort each power-law term in ascending order.

8. The method for processing the tilt angle signal of a highway bridge in a strong dynamic environment according to claim 6, characterized in that, S43 includes: S431. Read the order and sampling interval of each power-law term; S432. According to the preset definition of fractional calculus, solve the power law weight coefficients corresponding to each order in turn according to each historical delay time. S433. Call the preset driving function, and combine the normalized forward memory potential, quasi-static tilt component and vibration coupling component to obtain the driving vector corresponding to each historical moment. S434. Introduce the sampling interval power coefficient, multiply the power law weight coefficients of each order with the corresponding historical moment driving vectors and sum them to obtain the state increment; S435. Add the state increment to the state vector of the previous time step to complete the update of the state vector at the current time step.

9. The method for processing the tilt angle signal of a highway bridge in a strong dynamic environment according to claim 1, characterized in that, S5 includes: S51. Use the multi-order memory kernel function at the current moment to perform weighted calculation on the historical instantaneous vibration inertia, and output the predicted value of the instantaneous vibration inertia; S52. Subtract the predicted value from the actual instantaneous vibration inertia to calculate the prediction error; S53. The partial derivatives corresponding to each kernel parameter are obtained by numerical difference approximation, and the exponential decay rate, the magnitude coefficient of each power-law term and the order of each power-law term are updated by gradient descent algorithm. S54. After the update is complete, the amplitude coefficients of each power-law term are re-normalized so that the sum of all amplitude coefficients equals one, and the orders of each power-law term are reordered in ascending order.

10. A system for processing the tilt angle signal of a highway bridge in a strong dynamic environment, used to implement the method for processing the tilt angle signal of a highway bridge in a strong dynamic environment as described in any one of claims 1-9, characterized in that, The system includes: The signal acquisition module is used to acquire the original tilt angle signal and triaxial acceleration signal of the highway bridge structure; A multi-order memory kernel construction module is used to calculate instantaneous vibration inertia based on triaxial acceleration signals and construct a multi-order memory kernel function; wherein, the multi-order memory kernel function includes an exponential decay rate, the order of each power-law term, and the amplitude coefficient; The forward memory potential calculation module is used to use the multi-order memory kernel function at the current moment to predict the influence intensity of several future sampling points on the current instantaneous vibration inertia and accumulate them to obtain the forward memory potential. The forward memory potential is then normalized to a preset interval to obtain the normalized forward memory potential. The multi-order state evolution module is used to construct a state vector containing quasi-static tilt components and vibration coupling components; dynamically adjust the order of each power-law term according to the forward memory potential, and use the power-law weight coefficients of each order to perform weighted recursion on the historical state vector to update the state vector; add the error between the original tilt signal and the current reconstructed tilt angle to the quasi-static tilt component for correction to obtain the current output tilt signal. The parameter adaptive module is used to predict the current instantaneous vibration inertia by weighting the historical instantaneous vibration inertia with the multi-order memory kernel function at the current moment, and to update the multi-order memory kernel function using the gradient descent method according to the prediction error. The output module is used to output the tilt angle signal of the current sampling point and store or transmit it.

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