Bridge dynamic deflection measurement method and system based on photoelectric calibration and response recognition

Abstract

The present application relates to the technical field of structural health monitoring and deformation measurement, and particularly relates to a bridge dynamic deflection measurement method and system based on photoelectric calibration and response identification, comprising: in the calibration stage, photoelectric reference displacement signals and acceleration signals are synchronously acquired and time-aligned, response feature vectors are extracted and response types are identified, reconstruction parameters are determined based on the photoelectric reference displacement signals and a mapping relationship is established; in the online monitoring stage, only single acceleration signals are acquired, feature vectors are extracted and reconstruction parameters are matched; recursive least squares method is used for pretreatment, a forgetting factor is determined based on a dominant time scale and a baseline change time scale to estimate and deduct baseline bias; after pretreatment, the signals are adaptively decomposed to screen reconstruction effective vibration components, after noise suppression, integral operation and response type related residual trend compensation, dynamic deflection time courses are output. The present application realizes low-cost and high-precision dynamic deflection reconstruction.

Description

Technical Field

[0001] This invention relates to the field of structural health monitoring and deformation measurement technology, and in particular to a method and system for measuring dynamic deflection of bridges based on photoelectric calibration and response recognition. Background Technology

[0002] Bridge dynamic deflection reflects the deformation state of a structure under vehicle loads, environmental excitations, and other dynamic forces, and is an important indicator in bridge service performance evaluation and dynamic response testing. Current bridge displacement or deflection measurements typically employ methods such as total stations, linear displacement gauges, laser displacement sensors, electromagnetic ranging, satellite positioning, or visual measurement. Among these, laser displacement, laser ranging, and other photoelectric displacement measurement methods offer advantages such as non-contact operation, fast response, and high measurement accuracy. They can directly or quasi-directly obtain structural displacement information, making them suitable for model testing, short-term inspections, and parameter calibration.

[0003] Existing technologies have significant drawbacks in long-term online monitoring applications: they are highly and continuously dependent on fixed optical reference points, good line-of-sight distances, and stable lighting and weather conditions, resulting in extremely high long-term deployment and maintenance costs for monitoring systems in complex field environments, making it difficult to meet the actual needs of long-term, low-cost, and highly reliable online monitoring of large-scale engineering structures. Summary of the Invention

[0004] To overcome the above shortcomings, this invention provides a method and system for measuring bridge dynamic deflection based on photoelectric calibration and response recognition, aiming to improve the problem that existing technologies cannot meet the actual needs of long-term, low-cost and highly reliable online monitoring of large-scale engineering structures.

[0005] In a first aspect, the present invention provides the following technical solution: a method for measuring the dynamic deflection of bridges based on photoelectric calibration and response recognition, comprising:

[0006] S1. During the calibration phase, the photoelectric reference displacement signal and acceleration signal of the structural target measurement point are acquired synchronously and time-aligned. The response feature vector of the acceleration signal is extracted and the response type is identified. The dynamic deflection reconstruction parameters under the corresponding response type are determined based on the photoelectric reference displacement signal, and the mapping relationship between the response features and the dynamic deflection reconstruction parameters is established.

[0007] S2. During the online monitoring phase, only a single acceleration signal of the target measuring point is acquired, the current response feature vector is extracted, and the corresponding dynamic deflection reconstruction parameters are configured according to the mapping relationship.

[0008] S3. According to the configured dynamic deflection reconstruction parameters, the single acceleration signal is preprocessed including recursive least squares baseline correction to obtain the baseline-corrected acceleration signal, wherein the forgetting factor of the recursive least squares method is determined according to the dominant time scale of the current response and the baseline change time scale.

[0009] S4. Adaptively decompose and filter the baseline-corrected acceleration signal to reconstruct the effective vibration components, and sequentially perform noise suppression, integral operation, and residual trend compensation related to response type on the effective vibration components to output the dynamic deflection time history of the target measurement point.

[0010] Preferably, in S1, the photoelectric reference displacement signal is acquired by at least one of a laser displacement sensor, a laser rangefinder, an optical displacement measuring device, or a visual photoelectric displacement measuring device.

[0011] The time alignment is achieved through a unified sampling clock, hardware triggering, timestamp matching, or offline alignment based on response correlation.

[0012] Preferably, in S1, the response feature vector is composed of spectral concentration, interpeak periodic stability, and envelope decay characteristics, wherein the spectral concentration is the ratio of the sum of squares of amplitudes in a local narrow band near the dominant frequency to the sum of squares of amplitudes in the full effective analysis band, the interpeak periodic stability is the variance or standard deviation of the time interval between adjacent response peaks, and the envelope decay characteristics are the decay rate of the response amplitude envelope over time.

[0013] Based on the response feature vector, the response type is divided into periodically dominant response and transient decay response.

[0014] Preferably, in S1, the steps for establishing the mapping relationship include:

[0015] Multiple sets of candidate dynamic deflection reconstruction parameters are set for the same response type, and the candidate reconstruction displacements are calculated from the acceleration signals respectively.

[0016] Calculate the normalized root mean square error, correlation coefficient, amplitude deviation, or phase deviation between the candidate reconstructed displacement and the time-aligned photoelectric reference displacement. Select the set of candidate parameters with the smallest error evaluation index as calibration parameters, and associate and store the response characteristics with the calibration parameters to form a mapping relationship.

[0017] Preferably, in S1, the dynamic deflection reconstruction parameters include the target frequency band, baseline change time scale, effective vibration component screening conditions, noise suppression parameters, integral frequency band, and residual trend compensation parameters.

[0018] The baseline change timescale configured when the identification result is a periodically dominant response is greater than the baseline change timescale configured when the identification result is a transient decay response.

[0019] Preferably, in S3, the recursive least squares baseline correction uses a zero-order polynomial baseline model to estimate the locally slowly varying DC bias.

[0020] The dominant timescale is the reciprocal of the dominant frequency of the current response, i.e., the dominant period, and the baseline change timescale is the timescale allowed by the recursive least squares method and is greater than the dominant period.

[0021] The forgetting factor of the recursive least squares method is calculated by a negative exponential function of the ratio of the inverse of the sampling frequency to the time scale of the baseline change.

[0022] Preferably, in S4, the adaptive decomposition and filtering steps are as follows:

[0023] The baseline-corrected acceleration signal is decomposed into several intrinsic mode components and residual terms using a complete set empirical mode decomposition adaptive noise algorithm. The set of retained components is determined based on whether the dominant frequency of the intrinsic mode component is within the target frequency band, the correlation coefficient between the intrinsic mode component and the bandpass reference signal, and the energy ratio of the intrinsic mode component. The effective vibration components are obtained by summing and reconstructing the set of retained components.

[0024] Preferably, in S4, the noise suppression steps are as follows:

[0025] When the response type is a periodic dominant response, a second-level wavelet soft thresholding denoising is performed using a sixth-order compactly supported orthogonal wavelet.

[0026] When the response type is transient decay response, a three-level wavelet soft thresholding denoising is performed using fourth-order orthogonal wavelets.

[0027] Preferably, in S4, the steps of integration and residual trend compensation include:

[0028] The effective acceleration after noise suppression is integrated once in the time domain to obtain the velocity time history. The velocity time history is then transformed to the frequency domain after linear detrending and band filtering. The velocity spectrum is divided by the product of the imaginary unit and the angular frequency within the integration band to complete the frequency domain integration. The initial dynamic deflection is obtained by inverse transformation.

[0029] When the response type is periodic dominant response, the displacement mean sequence of the complete vibration period is calculated according to the dominant period and then subtracted as the residual slow trend.

[0030] When the response type is transient decay response, the time history estimate of the residual slow-changing trend of the low-amplitude segment of the decay tail is extracted and subtracted.

[0031] Secondly, the present invention provides the following technical solution: a bridge dynamic deflection measurement system based on photoelectric calibration and response recognition, the system comprising:

[0032] The calibration and mapping module is used to synchronously acquire the photoelectric reference displacement signal and acceleration signal of the structural target measurement point and perform time alignment during the calibration stage, extract the response feature vector of the acceleration signal and identify the response type, determine the dynamic deflection reconstruction parameters under the corresponding response type based on the photoelectric reference displacement signal, and establish the mapping relationship between the response features and the dynamic deflection reconstruction parameters.

[0033] The parameter configuration module is used to acquire a single acceleration signal of the target measuring point during the online monitoring phase, extract the current response feature vector, and configure the corresponding dynamic deflection reconstruction parameters according to the mapping relationship.

[0034] The baseline correction preprocessing module is used to perform preprocessing including recursive least squares baseline correction on the single acceleration signal according to the configured dynamic deflection reconstruction parameters to obtain the baseline-corrected acceleration signal, wherein the forgetting factor of the recursive least squares method is determined according to the dominant time scale of the current response and the baseline change time scale.

[0035] The reconstruction and trend compensation module is used to adaptively decompose and filter the baseline-corrected acceleration signal, reconstruct the effective vibration components, and sequentially perform noise suppression, integral operation, and response type-related residual trend compensation on the effective vibration components, and output the dynamic deflection time history of the target measurement point.

[0036] The present invention has the following beneficial effects:

[0037] 1. In this invention, a two-stage technical approach of "photoelectric reference calibration - response recognition - parameter mapping - single acceleration online reconstruction" is adopted to transform high-precision photoelectric displacement measurement from a long-term continuous monitoring link to a calibration or on-demand verification link. The online stage relies only on a single acceleration input, which realizes a deep integration of the high reference accuracy of photoelectric measurement and the convenience of long-term deployment of acceleration sensors. This solves the problem that traditional photoelectric or laser displacement measurement relies excessively on fixed optical reference points, line-of-sight distance and optical path conditions, resulting in high long-term outdoor deployment costs and difficult maintenance.

[0038] 2. In this invention, a response feature vector is constructed by comprehensively extracting spectral concentration, inter-peak periodic stability and envelope attenuation characteristics, and an adaptive mapping relationship between the vector and the complete set of reconstruction parameters is established based on photoelectric reference error evaluation. This realizes the objective traceability and adaptive adjustment of reconstruction parameter configuration, and solves the problem that traditional reconstruction algorithms rely heavily on repeated manual experience-based parameter tuning under different working conditions, are highly subjective and lack certainty.

[0039] 3. In this invention, by adaptively calling calibration parameters based on the response characteristics of the current single acceleration signal during the online monitoring stage, the recursive least squares baseline correction, effective vibration component screening, and integral frequency band selection are precisely matched with the current true response of the structure. This enables real-time tracking and precise control of the complex dynamic changes of the structure during the reconstruction process, and solves the problem that traditional fixed parameter algorithms are prone to falsely weakening the true vibration components or causing integral divergence due to insufficient control of residual drift.

[0040] 4. In this invention, by combining a time-domain-frequency-domain hybrid integration mechanism and introducing a targeted residual trend compensation strategy that is deeply compatible with the response type, a high-precision steady-state reconstruction of the dynamic deflection time history of the entire process is achieved. This solves the problem that traditional quadratic integration is prone to time history instability, drift and distortion when dealing with low-amplitude response segments and transient decay tail segments. Attached Figure Description

[0041] Figure 1 This is a flowchart of the bridge dynamic deflection measurement method based on photoelectric calibration and response recognition proposed in this invention;

[0042] Figure 2 This is a schematic diagram of the experimental system and data connection for acquiring photoelectric reference displacement and acceleration signals of the bridge dynamic deflection measurement method and system based on photoelectric calibration and response recognition proposed in this invention;

[0043] Figure 3 The flowchart shows the response identification, photoelectric reference error evaluation, and dynamic deflection reconstruction parameter mapping of the bridge dynamic deflection measurement method based on photoelectric calibration and response identification proposed in this invention.

[0044] Figure 4 This is a flowchart of the dynamic deflection reconstruction process of a single acceleration signal in the online monitoring stage of the bridge dynamic deflection measurement method based on photoelectric calibration and response recognition proposed in this invention.

[0045] Figure 5 This is a comparison diagram of the reconstructed displacement and the photoelectric reference measured displacement of the bridge dynamic deflection measurement method based on photoelectric calibration and response recognition proposed in this invention.

[0046] Figure 6 This is an architecture diagram of the bridge dynamic deflection measurement system based on photoelectric calibration and response recognition proposed in this invention.

[0047] Reference numerals: 1. Laptop computer receiving displacement signals; 2. Vibrator; 3. Accelerometer; 4. Model beam; 5. Photoelectric displacement measurement module; 6. Signal amplifier; 7. Signal generator; 8. NI data acquisition card; 9. Laptop computer receiving acceleration signals; 10. Acceleration integrated acquisition system. Detailed Implementation

[0048] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] Example 1:

[0050] In the first embodiment of the present invention, the present invention provides a method for measuring the dynamic deflection of bridges based on photoelectric calibration and response recognition, such as... Figures 1-5 As shown, it includes the following steps:

[0051] S1. During the calibration phase, the photoelectric reference displacement signal and acceleration signal of the structural target measurement point are acquired synchronously and time-aligned. The response feature vector of the acceleration signal is extracted and the response type is identified. The dynamic deflection reconstruction parameters under the corresponding response type are determined based on the photoelectric reference displacement signal, and the mapping relationship between the response features and the dynamic deflection reconstruction parameters is established.

[0052] Furthermore, in S1, the photoelectric reference displacement signal is acquired by at least one of a laser displacement sensor, a laser rangefinder, an optical displacement measuring device, or a visual photoelectric displacement measuring device.

[0053] Time alignment is achieved through a unified sampling clock, hardware triggering, timestamp matching, or offline alignment based on response correlation.

[0054] Furthermore, in S1, the response feature vector is composed of spectral concentration, interpeak periodic stability, and envelope decay characteristics. The spectral concentration is the ratio of the sum of squares of amplitudes in a local narrow band near the dominant frequency to the sum of squares of amplitudes in the full effective analysis band. The interpeak periodic stability is the variance or standard deviation of the time interval between adjacent response peaks. The envelope decay characteristics are the decay rate of the response amplitude envelope over time.

[0055] Based on the response feature vector, the response type is divided into periodically dominant response and transient decay response.

[0056] Furthermore, in S1, the steps for establishing the mapping relationship include:

[0057] Multiple sets of candidate dynamic deflection reconstruction parameters are set for the same response type, and the candidate reconstruction displacements are calculated from the acceleration signals respectively.

[0058] Calculate the normalized root mean square error, correlation coefficient, amplitude deviation, or phase deviation between the candidate reconstructed displacement and the time-aligned photoelectric reference displacement. Select the set of candidate parameters with the smallest error evaluation index as the calibration parameters, and associate the response characteristics with the calibration parameters to form a mapping relationship.

[0059] Furthermore, in S1, the dynamic deflection reconstruction parameters include the target frequency band, baseline change time scale, effective vibration component screening conditions, noise suppression parameters, integral frequency band, and residual trend compensation parameters.

[0060] The baseline change timescale configured when the identification result is a periodically dominant response is greater than the baseline change timescale configured when the identification result is a transient decay response.

[0061] Specifically, in order to obtain photoelectric reference displacement and acceleration signals under real dynamic response and establish a calibration mapping database, this embodiment sets up an experimental testing and data acquisition system.

[0062] The system includes a model beam 4, a vibrator 2 positioned below the model beam 4, an accelerometer 3 deployed at the target measurement point on the model beam 4, and a photoelectric displacement measurement module 5 (in this embodiment, a laser displacement sensor is specifically selected). The signal input terminal of the vibrator 2 is connected sequentially through a signal amplifier 6 and a signal generator 7. The signal generator 7 generates an excitation signal with a set frequency and amplitude, which, after being amplified by the signal amplifier 6, drives the vibrator 2 to apply dynamic excitation to the model beam 4, causing the model beam 4 to produce a dynamic response.

[0063] At the data acquisition and receiving end, the photoelectric displacement measurement module 5 is aligned with the target measurement point of the model beam 4. Its signal output end is connected to the laptop computer 1, which receives displacement signals, through the NI data acquisition card 8. This is used to acquire and record the real displacement of the target measurement point of the model beam 4 in real time, as a photoelectric reference displacement signal. Accelerometer 3, deployed at the same target measurement point, has its signal output connected to a laptop computer 9 that receives acceleration signals via an integrated acceleration acquisition system 10, for real-time acquisition of acceleration signals from the target measurement point of the model beam 4. The laptop 1 receiving the displacement signal and the laptop 9 receiving the acceleration signal achieve time synchronization alignment of the two signals through hardware triggering or timestamp alignment, and then synchronize the aligned photoelectric reference displacement signal. With acceleration signal The signal is transmitted to the algorithm processing unit for subsequent response feature extraction, type identification, and reconstruction parameter calibration. The raw acceleration signal acquired by the sensor physically comprises the true dynamic response component, random noise component, and slowly varying baseline component, as shown below:

[0064] ;

[0065] In the formula, for The raw acceleration signal acquired by the time sensor. for The acceleration component corresponding to the actual dynamic response of the structure at any given moment. for High-frequency random noise and local disturbance components at all times. for The system uses a slowly varying baseline component caused by sensor bias or temperature drift. To eliminate time discrepancies between the photoelectric measurement channel and the acceleration measurement channel, time alignment is implemented. This alignment is achieved through a unified sampling clock, hardware triggering, timestamp matching, or offline alignment based on response correlation. In hardware alignment mode, the system uses a unified timing clock source to perform multi-channel synchronous sampling of the laser displacement sensor and accelerometer 3, or applies a hardware pulse trigger signal at the start of sampling to synchronously activate both acquisition channels. In software alignment mode, the system adds high-precision timestamps to each sampling point of the two signals for timestamp alignment, or calculates the cross-correlation function between the initial displacement obtained by the second integral of the acceleration signal and the photoelectric reference displacement signal, searches for the time delay corresponding to the peak value of the cross-correlation function as the offset correction, adjusts the time axis sequence of the two signals in the time domain, and outputs the time-aligned photoelectric reference displacement signal. With acceleration signal .

[0066] After time alignment, the system extracts the response feature vector of the acceleration signal and identifies the current response type of the structure. The response feature vector consists of spectral concentration, inter-peak periodic stability, and envelope attenuation characteristics, and is expressed as follows:

[0067] ;

[0068] In the formula, In response to the feature vector, For spectral concentration, For inter-peak periodic stability, This involves identifying envelope attenuation characteristics. Specifically, during extraction, the system performs a Discrete Fourier Transform on the acceleration signal sequence to calculate the single-sided amplitude spectrum, and searches for the frequency corresponding to the amplitude maxima as the dominant frequency. The system has a local narrow frequency band near the dominant frequency. The sum of squared amplitudes is accumulated within the entire effective analysis frequency band. Calculate the spectral concentration by summing the squared amplitude values. The calculation formula is:

[0069] ;

[0070] In the formula, For acceleration signals at frequency The discrete spectral amplitude at that location. In this embodiment, the local narrow frequency band... Set the frequency band to 0.5 Hz on either side of the dominant frequency. to ), full effective analysis frequency band The frequency was set to 0.1 Hz to 50 Hz. Subsequently, the system used a peak detection algorithm to locate positive local maxima in the acceleration signal time history, calculated the time interval sequence between adjacent maxima, and calculated the standard deviation or variance of this time interval sequence as the inter-peak periodic stability. When expressed as standard deviation, the calculation formula is:

[0071] ;

[0072] In the formula, It is the arithmetic mean of the time interval sequence between adjacent maxima. This represents the total number of positive local maxima points extracted. For the first The peak point and the first The actual time interval between each peak point. Next, the system analyzes the acceleration signal. Perform a Hilbert transform to generate an analytic signal, and calculate the magnitude of the analytic signal to obtain the time-domain amplitude envelope. For the envelope After taking the natural logarithm, a linear fit is performed using the least squares method, and the fitting equation is: The absolute value of the slope of the fitted straight line is determined as the envelope decay characteristic. , is used to characterize the decay rate of the response amplitude envelope over time.

[0073] The system will construct the response feature vector The input judgment logic module classifies response types into periodically dominant responses and transiently decaying responses based on response feature vectors. The system sets judgment thresholds: spectral concentration threshold. Set to 0.65, the interpeak periodic stability threshold. Set to 0.05 seconds, envelope decay characteristic threshold Set to 0.02 per second. When the condition is met. and When the condition is met, the system will determine the response type as a periodic dominant response; or At that time, the system will determine the response type as a transient decay response.

[0074] In the step of establishing the mapping relationship, the system discretizes and sets multiple sets of candidate dynamic deflection reconstruction parameters in the parameter space for the same identified response type. The dynamic deflection reconstruction parameters include the target frequency band and the baseline change time scale. Effective vibration component screening conditions, noise suppression parameters, integration bandwidth, and residual trend compensation parameters. Assume the sampling frequency of the acceleration acquisition system is... The dominant frequency of the current acceleration signal is The dominant period of the structural response is The recursive least squares algorithm is used to estimate slowly varying baselines. At that time, the forgetting factor it used The calculation formula is:

[0075] ;

[0076] In the formula, The baseline variation timescale is configured adaptively. To prevent the baseline subtraction process from unduly weakening the true low-frequency vibrations of the structure, the baseline variation timescale is configured when the identification result indicates a periodic dominant response. (Preferred configuration is) (This is greater than the baseline change timescale configured when the identification result is a transient decay response). (Preferred configuration is) Under the periodic dominant response, a narrow target frequency band around the dominant frequency, sym6 wavelet and 2-level decomposition denoising parameters, a narrow integral frequency band, and residual trend correction for the periodic mean are configured. Under the transient decay response, a wide target frequency band covering the main decay modes, db4 wavelet and 3-level decomposition denoising parameters, a wide integral frequency band, and decay tail trend compensation are configured. The system substitutes the acceleration signal into the preset reconstruction algorithm flow corresponding to each group of candidate parameters, which includes bandpass filtering, recursive least squares baseline subtraction, complete ensemble empirical mode decomposition, wavelet soft thresholding denoising, frequency domain integration, and residual trend subtraction, respectively, to calculate the corresponding candidate reconstruction displacement time history. The system will calculate the time histories of each candidate reconstructed displacement. Photoelectric reference displacement time history aligned with time The input error evaluation module calculates the normalized root mean square error between the candidate reconstructed displacement and the time-aligned photoelectric reference displacement. The calculation formula is:

[0077] ;

[0078] In the formula, The total number of sampling points. and The first The system calculates the candidate reconstructed displacement and photoelectric reference displacement values ​​at each sampling point. It can also calculate at least one of the correlation coefficient, amplitude deviation, or phase deviation between the candidate reconstructed displacement and the photoelectric reference displacement as an error evaluation index. The system selects the set of candidate parameters with the smallest error evaluation index as calibration parameters and uses the response feature vector... A mapping database is formed by storing the calibration parameters together.

[0079] S2. During the online monitoring phase, only a single acceleration signal of the target measuring point is acquired, the current response feature vector is extracted, and the corresponding dynamic deflection reconstruction parameters are configured according to the mapping relationship.

[0080] Specifically, during the calibration phase, the photoelectric displacement measurement module 5 stops working or switches to standby mode, and the monitoring system only deploys the acceleration sensor 3 at the target measurement point on the structure to collect a single acceleration signal along the direction of the deflection to be measured in real time. The acceleration signal The physical composition model follows the description from the calibration stage above.

[0081] Received real-time acceleration signal Then, following the methods and processes described in the aforementioned calibration phase, the spectral concentration of the current acceleration signal is extracted sequentially. Interpeak periodic stability and envelope attenuation characteristics This allows us to construct the current response feature vector. The system will extract the current response feature vector. The mapping database established during the input calibration phase is used to adaptively retrieve dynamic deflection reconstruction parameters corresponding to the current response feature vector through retrieval and matching. These parameters include the target frequency band and the baseline change time scale. Effective vibration component screening conditions, noise suppression parameters, integral frequency band, and residual trend compensation parameters.

[0082] After retrieving the corresponding reconstruction parameters, the system will display the real-time acceleration signal. Input reconstruction algorithm flow:

[0083] Will The input bandpass filter applies a band constraint based on the modulated target frequency band parameters, and the output is a band-constrained acceleration signal. ;

[0084] Based on the timescale of baseline changes The forgetting factor is determined according to the forgetting factor calculation formula in the aforementioned calibration stage. The slowly varying baseline was estimated by recursively estimating it using a recursive least squares algorithm. and from After subtraction, the output acceleration signal is baseline corrected. Next, regarding A complete ensemble empirical mode decomposition is performed. Based on the effective vibration component selection criteria, qualified intrinsic mode components are retained and then superimposed for reconstruction. Next, wavelet soft thresholding denoising is applied to the reconstructed signal according to the noise suppression parameters, outputting an effective acceleration signal with a high signal-to-noise ratio. ;

[0085] For effective acceleration signals Perform frequency domain integration, solve for the complex frequency domain displacement spectrum based on the retrieved integration frequency band, and then perform an inverse transform back to the time domain to obtain the initial dynamic deflection time history. And based on the retrieved residual trend compensation parameters, the residual slow-varying trend is subtracted. The final output is a high-precision dynamic deflection time history. .

[0086] S3. According to the configured dynamic deflection reconstruction parameters, perform preprocessing on the single acceleration signal including recursive least squares baseline correction to obtain the baseline-corrected acceleration signal. The forgetting factor of the recursive least squares method is determined according to the dominant time scale of the current response and the time scale of the baseline change.

[0087] Furthermore, in S3, the recursive least squares baseline correction uses a zero-order polynomial baseline model to estimate the locally slowly varying DC bias.

[0088] The dominant timescale is the reciprocal of the dominant frequency of the current response, i.e., the dominant period. The baseline change timescale is the timescale allowed by the recursive least squares method and is greater than the dominant period.

[0089] The forgetting factor of the recursive least squares method is calculated by a negative exponential function of the ratio of the inverse of the sampling frequency to the time scale of the baseline change.

[0090] Specifically, the system uses the aforementioned dynamic deflection reconstruction parameters to process the single acceleration signal acquired during the online monitoring phase. Preprocessing including recursive least squares baseline correction is performed to obtain the baseline-corrected acceleration signal. The system first processes the input single acceleration signal. The input bandpass filter applies a target frequency band constraint, filters out out-of-band high-frequency noise and extremely low-frequency interference, and outputs a bandpass-filtered acceleration signal. Subsequently, the system employs the Recursive Least Squares (RLS) algorithm to estimate the locally varying DC bias. The RLS baseline correction uses a zero-order polynomial baseline model to estimate the locally varying DC bias in real time; that is, the baseline model is set as follows:

[0091] ;

[0092] In the formula, Let be the local DC bias constant to be recursively estimated. During the recursive solution process, the forgetting factor of the recursive least squares method... Based on the dominant timescale of the current response and the timescale of baseline change Determined. The dominant time scale is the dominant frequency of the current acceleration signal. The calculated reciprocal is the dominant cycle. The calculation is expressed as:

[0093] ;

[0094] Baseline change time scale The allowed time scale for recursive least squares tracking must satisfy the constraints. Forgetting factor Based on sampling frequency The reciprocal of the baseline change time scale The ratio is calculated using a negative exponential function, and the formula is as follows:

[0095] ;

[0096] The system will calculate the forgetting factor. Substituting into the recursive least squares solver, through The memory length of the control algorithm is used to recursively estimate the locally varying DC bias caused by sensor zero bias or ambient temperature drift in real time. and from the bandpass filtered acceleration signal The deduction is calculated using the following formula:

[0097] ;

[0098] The final output is a baseline-corrected acceleration signal that eliminates low-frequency baseline drift and fully preserves the true low-frequency dynamic response. .

[0099] S4. Adaptively decompose and filter the baseline-corrected acceleration signal to reconstruct the effective vibration components. Then, perform noise suppression, integral operation, and residual trend compensation related to the response type on the effective vibration components in sequence, and output the dynamic deflection time history of the target measurement point.

[0100] Furthermore, in S4, the adaptive decomposition and filtering steps are as follows:

[0101] The baseline-corrected acceleration signal is decomposed into several intrinsic mode components and residual terms using a complete set empirical mode decomposition adaptive noise algorithm. The set of retained components is determined based on whether the dominant frequency of the intrinsic mode component is within the target frequency band, the correlation coefficient between the intrinsic mode component and the bandpass reference signal, and the energy ratio of the intrinsic mode component. The effective vibration components are obtained by summing and reconstructing the retained component set.

[0102] Furthermore, in S4, the noise suppression steps are as follows:

[0103] When the response type is a periodic dominant response, a second-level wavelet soft thresholding denoising is performed using a sixth-order compactly supported orthogonal wavelet.

[0104] When the response type is transient decay response, a three-level wavelet soft thresholding denoising is performed using fourth-order orthogonal wavelets.

[0105] Furthermore, in S4, the steps of integration and residual trend compensation include:

[0106] The effective acceleration after noise suppression is integrated once in the time domain to obtain the velocity time history. The velocity time history is then transformed to the frequency domain after linear detrending and band filtering. The velocity spectrum is divided by the product of the imaginary unit and the angular frequency within the integration band to complete the frequency domain integration. The initial dynamic deflection is obtained by inverse transformation.

[0107] When the response type is periodic dominant response, the displacement mean sequence of the complete vibration period is calculated according to the dominant period and then subtracted as the residual slow trend.

[0108] When the response type is transient decay response, the time history estimate of the residual slow-changing trend of the low-amplitude segment of the decay tail is extracted and subtracted.

[0109] Specifically, in the adaptive decomposition, reconstruction, and final dynamic deflection solution stages, the system processes the baseline-corrected acceleration signal. Adaptive decomposition and filtering are performed to reconstruct the effective vibration components. Noise suppression, integration, and residual trend compensation related to the response type are then sequentially applied to these effective vibration components, ultimately outputting a high-precision dynamic deflection time history of the target measurement point. The specific implementation process is as follows:

[0110] The system first processes the baseline-corrected acceleration signal. Adaptive decomposition and filtering are performed. The system employs the Complete Ensemble Empirical Mode Decomposition Adaptive Noise (CEEMDAN) algorithm to perform... Decomposed into Individual intrinsic mode components (IMF) and residual terms , expressed as:

[0111] ;

[0112] After decomposition, the system uses each intrinsic mode component... dominant frequency Whether it is within the aforementioned target frequency band, and the intrinsic mode components and bandpass reference signal The system comprehensively evaluates an intrinsic mode component based on its cross-correlation coefficient and the energy proportion of its intrinsic mode components. When an intrinsic mode component's dominant frequency falls within the target frequency band, its correlation coefficient with the bandpass reference signal exceeds a preset correlation threshold (e.g., 0.6), and its energy proportion reaches a preset ratio, that intrinsic mode component is included in the reserved component set. Conversely, components belonging to out-of-band high-frequency noise or low-frequency drift interference are removed. The system retains the set of components. By summing and reconstructing the intrinsic modal components, preliminary effective vibrational components are obtained. The calculation formula is:

[0113] ;

[0114] Next, the system analyzes the preliminary effective vibration components. Adaptive wavelet soft thresholding denoising is performed to match the response type. When the response type corresponding to the currently extracted response feature vector is a periodic dominant response, the system uses a sixth-order compactly supported orthogonal wavelet (sym6) as the wavelet basis pair. A two-level wavelet decomposition is performed, and the high-frequency wavelet coefficients of each level are denoised using a soft threshold before reconstruction. When the response type is a transient decay response, the system uses a fourth-order orthogonal wavelet (db4) as the wavelet basis pair. A three-level wavelet decomposition is performed, followed by three-level wavelet soft thresholding for denoising. After wavelet denoising and secondary bandpass filtering, a high signal-to-noise ratio effective acceleration signal is output. .

[0115] Obtaining high signal-to-noise ratio effective acceleration signals Then, the system performs integration and residual trend compensation. The system first... Perform a first integration in the time domain to obtain the preliminary velocity time history. and to Perform linear detrending and band filtering to obtain the constrained velocity time history. Then, the system sets the time history for the constrained velocity. Perform a Fast Fourier Transform to switch to the frequency domain, and obtain the complex frequency spectrum of the velocity. Within the selected integration frequency band, the system will display the velocity complex spectrum. Divide by the imaginary unit With angular frequency The product of the two elements is used to perform a second-order integral operation in the frequency domain, and the complex frequency-domain shift spectrum is calculated. :

[0116] ;

[0117] The frequency domain displacement complex spectrum obtained by the solution Perform an inverse Fourier transform back to the time domain to obtain the initial dynamic deflection time history. Finally, the system combines the response type with the initial dynamic deflection time history. Apply targeted residual trend compensation: When the response type is a periodic dominant response, the system follows the dominant periodicity. The time history is divided into several complete vibration periods. The displacement mean sequence within each complete vibration period is calculated to construct the residual slow-varying trend. And subtract it; when the response type is a transient decay response, the system extracts the low-amplitude segment of the response decay tail and fits and evaluates the residual slow-changing trend. And deduct it. The final dynamic deflection time history after deducting the residual slow-varying trend. The calculation formula is:

[0118] ;

[0119] The system will calculate The final dynamic deflection time history of the target measurement point is output and stored.

[0120] Example 2:

[0121] To address the technical challenges of long-term operation of large cross-river / sea bridges, where the large spans and open waters beneath them pose significant obstacles, including the lack of fixed reference points, severe interference from diffuse reflection of light from the water surface and fog, and extremely high maintenance costs for long-term deployment of photoelectric or laser displacement sensors, while relying solely on bridge deck accelerometers for direct integration is prone to zero-point drift and integral divergence, making it difficult to accurately obtain the true dynamic deflection of the bridge under heavy train / vehicle crossings and strong wind loads, this invention provides a bridge dynamic deflection measurement system based on photoelectric calibration and response recognition. The structure of this system is as follows: Figure 6 As shown. The specific implementation process of this system is as follows:

[0122] The calibration and mapping module is used to synchronously acquire the photoelectric reference displacement signal and acceleration signal of the structural target measurement point and perform time alignment during the calibration stage, extract the response feature vector of the acceleration signal and identify the response type, determine the dynamic deflection reconstruction parameters under the corresponding response type based on the photoelectric reference displacement signal, and establish the mapping relationship between the response features and the dynamic deflection reconstruction parameters.

[0123] The parameter configuration module is used to acquire a single acceleration signal of the target measuring point during the online monitoring phase, extract the current response feature vector, and configure the corresponding dynamic deflection reconstruction parameters according to the mapping relationship.

[0124] The baseline correction preprocessing module is used to perform preprocessing including recursive least squares baseline correction on a single acceleration signal according to the configured dynamic deflection reconstruction parameters, so as to obtain the baseline-corrected acceleration signal. The forgetting factor of the recursive least squares method is determined according to the dominant time scale of the current response and the baseline change time scale.

[0125] The reconstruction and trend compensation module is used to adaptively decompose and filter the baseline-corrected acceleration signal, reconstruct the effective vibration components, and sequentially perform noise suppression, integral operation, and residual trend compensation related to the response type on the effective vibration components, and output the dynamic deflection time history of the target measurement point.

[0126] Specifically, addressing the challenges of long-term deployment of photoelectric equipment due to the lack of a fixed reference benchmark under the bridge and the difficulties posed by water surface diffuse reflection and fog obstruction, the calibration and mapping module employs short-term calibration during load tests or periodic maintenance windows before the bridge opens to traffic. The module controls a laser displacement sensor temporarily installed under the bridge and an accelerometer deployed at a mid-span measurement point on the bridge deck to synchronously acquire displacement and acceleration signals and perform time alignment. The module extracts response feature vectors from the acceleration signals, including spectral concentration, inter-peak periodic stability, and envelope attenuation characteristics, accurately identifying the bridge's periodically dominant response during continuous passage of heavy-load trains / vehicles, as well as its transient attenuation response under strong winds or sudden impact loads. Using a high-precision photoelectric reference displacement as a benchmark, the module performs inverse optimization to determine an adaptive parameter set covering the target frequency band, baseline change time scale, wavelet basis and decomposition level, integral frequency band, and residual trend compensation mode, and establishes a mapping database. Once calibration is complete, the photoelectric equipment under the bridge can be removed, eliminating the continuous dependence on the optical path and fixed reference points for long-term monitoring.

[0127] To address the issue that a single bridge deck acceleration signal is prone to divergence distortion due to temperature drift and zero-point bias, making it difficult to obtain the true deflection, the parameter configuration module receives only the single bridge deck acceleration signal during long-term online monitoring. It extracts response features in real time and adaptively retrieves matching reconstruction parameters. Subsequently, the baseline correction preprocessing module applies target frequency band filtering to the acceleration signal and adaptively calculates the forgetting factor using recursive least squares based on the dominant period of the current response. A zero-order polynomial model is then used to estimate and subtract the locally varying baseline caused by sensor zero bias and temperature changes in real time. This process accurately eliminates low-frequency DC bias and zero-point drift while fully preserving the bridge's true low-frequency large deformation response under heavy vehicle loads and strong winds.

[0128] To address the significant differences in heterogeneous vibration characteristics under complex conditions such as heavy-load vehicle crossings and strong wind loads, and the potential for filtering distortion or residual trends due to traditional fixed parameters, the reconstruction and trend compensation module performs complete ensemble empirical mode decomposition and effective component screening on the baseline-corrected signal, and then applies targeted processing based on the operating conditions: when identified as a periodically dominant response such as continuous crossings of heavy-load trains or vehicles, the module uses a longer baseline time scale and a second-level denoising layer with sixth-order compactly supported orthogonal wavelets, and after frequency domain integration, subtracts the displacement mean trend of the complete vibration cycle according to the dominant period; when identified as a transient attenuated response such as strong wind excitation or sudden impact, the module switches to a shorter baseline time scale and a third-level denoising layer with fourth-order orthogonal wavelets, and after frequency domain integration, truncates the low-amplitude segment of the attenuation tail and fits it to subtract the residual slow-changing trend. Through this adaptive matching mechanism for specific bridge defects and operating conditions, the module ultimately outputs the true dynamic deflection time history of the bridge mid-span under complex conditions with high accuracy.

[0129] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. 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 measuring dynamic deflection of bridges based on photoelectric calibration and response recognition, characterized in that, include: S1. During the calibration phase, the photoelectric reference displacement signal and acceleration signal of the structural target measurement point are acquired synchronously and time-aligned. The response feature vector of the acceleration signal is extracted and the response type is identified. The dynamic deflection reconstruction parameters under the corresponding response type are determined based on the photoelectric reference displacement signal, and the mapping relationship between the response features and the dynamic deflection reconstruction parameters is established. S2. During the online monitoring phase, only a single acceleration signal of the target measuring point is acquired, the current response feature vector is extracted, and the corresponding dynamic deflection reconstruction parameters are configured according to the mapping relationship. S3. According to the configured dynamic deflection reconstruction parameters, the single acceleration signal is preprocessed including recursive least squares baseline correction to obtain the baseline-corrected acceleration signal, wherein the forgetting factor of the recursive least squares method is determined according to the dominant time scale of the current response and the baseline change time scale. S4. Adaptively decompose and filter the baseline-corrected acceleration signal to reconstruct the effective vibration components, and sequentially perform noise suppression, integral operation, and residual trend compensation related to response type on the effective vibration components to output the dynamic deflection time history of the target measurement point.

2. The bridge dynamic deflection measurement method based on photoelectric calibration and response recognition according to claim 1, characterized in that, In S1, the photoelectric reference displacement signal is acquired by at least one of a laser displacement sensor, a laser rangefinder, an optical displacement measuring device, or a visual photoelectric displacement measuring device. The time alignment is achieved through a unified sampling clock, hardware triggering, timestamp matching, or offline alignment based on response correlation.

3. The method for measuring bridge dynamic deflection based on photoelectric calibration and response recognition according to claim 1, characterized in that, In S1, the response feature vector is composed of spectral concentration, interpeak periodic stability, and envelope decay characteristics. The spectral concentration is the ratio of the sum of squares of amplitudes in a local narrow band near the dominant frequency to the sum of squares of amplitudes in the full effective analysis band. The interpeak periodic stability is the variance or standard deviation of the time interval between adjacent response peaks. The envelope decay characteristics are the decay rate of the response amplitude envelope over time. Based on the response feature vector, the response type is divided into periodically dominant response and transient decay response.

4. The bridge dynamic deflection measurement method based on photoelectric calibration and response recognition according to claim 1, characterized in that, In S1, the steps to establish the mapping relationship include: Multiple sets of candidate dynamic deflection reconstruction parameters are set for the same response type, and the candidate reconstruction displacements are calculated from the acceleration signals respectively. Calculate the normalized root mean square error, correlation coefficient, amplitude deviation, or phase deviation between the candidate reconstructed displacement and the time-aligned photoelectric reference displacement. Select the set of candidate parameters with the smallest error evaluation index as calibration parameters, and associate and store the response characteristics with the calibration parameters to form a mapping relationship.

5. The bridge dynamic deflection measurement method based on photoelectric calibration and response recognition according to claim 3, characterized in that, In S1, the dynamic deflection reconstruction parameters include the target frequency band, baseline change time scale, effective vibration component screening conditions, noise suppression parameters, integral frequency band, and residual trend compensation parameters. The baseline change timescale configured when the identification result is a periodically dominant response is greater than the baseline change timescale configured when the identification result is a transient decay response.

6. The method for measuring bridge dynamic deflection based on photoelectric calibration and response recognition according to claim 1, characterized in that, In S3, recursive least squares baseline correction uses a zero-order polynomial baseline model to estimate the locally slowly varying DC bias; The dominant timescale is the reciprocal of the dominant frequency of the current response, i.e., the dominant period, and the baseline change timescale is the timescale allowed by the recursive least squares method and is greater than the dominant period. The forgetting factor of the recursive least squares method is calculated by a negative exponential function of the ratio of the inverse of the sampling frequency to the time scale of the baseline change.

7. The method for measuring bridge dynamic deflection based on photoelectric calibration and response recognition according to claim 1, characterized in that, In S4, the adaptive decomposition and filtering steps are as follows: The baseline-corrected acceleration signal is decomposed into several intrinsic mode components and residual terms using a complete set empirical mode decomposition adaptive noise algorithm. The set of retained components is determined based on whether the dominant frequency of the intrinsic mode component is within the target frequency band, the correlation coefficient between the intrinsic mode component and the bandpass reference signal, and the energy ratio of the intrinsic mode component. The effective vibration components are obtained by summing and reconstructing the set of retained components.

8. The method for measuring bridge dynamic deflection based on photoelectric calibration and response recognition according to claim 3, characterized in that, In S4, the noise suppression steps are as follows: When the response type is a periodic dominant response, a second-level wavelet soft thresholding denoising is performed using a sixth-order compactly supported orthogonal wavelet. When the response type is transient decay response, a three-level wavelet soft thresholding denoising is performed using fourth-order orthogonal wavelets.

9. The bridge dynamic deflection measurement method based on photoelectric calibration and response recognition according to claim 3, characterized in that, In S4, the steps for integration and residual trend compensation include: The effective acceleration after noise suppression is integrated once in the time domain to obtain the velocity time history. The velocity time history is then transformed to the frequency domain after linear detrending and band filtering. The velocity spectrum is divided by the product of the imaginary unit and the angular frequency within the integration band to complete the frequency domain integration. The initial dynamic deflection is obtained by inverse transformation. When the response type is periodic dominant response, the displacement mean sequence of the complete vibration period is calculated according to the dominant period and then subtracted as the residual slow trend. When the response type is transient decay response, the time history estimate of the residual slow-changing trend of the low-amplitude segment of the decay tail is extracted and subtracted.

10. A bridge dynamic deflection measurement system based on photoelectric calibration and response recognition, characterized in that, The system for the bridge dynamic deflection measurement method based on photoelectric calibration and response recognition as described in any one of claims 1-9 comprises: The calibration and mapping module is used to synchronously acquire the photoelectric reference displacement signal and acceleration signal of the structural target measurement point and perform time alignment during the calibration stage, extract the response feature vector of the acceleration signal and identify the response type, determine the dynamic deflection reconstruction parameters under the corresponding response type based on the photoelectric reference displacement signal, and establish the mapping relationship between the response features and the dynamic deflection reconstruction parameters. The parameter configuration module is used to acquire a single acceleration signal of the target measuring point during the online monitoring phase, extract the current response feature vector, and configure the corresponding dynamic deflection reconstruction parameters according to the mapping relationship. The baseline correction preprocessing module is used to perform preprocessing including recursive least squares baseline correction on the single acceleration signal according to the configured dynamic deflection reconstruction parameters to obtain the baseline-corrected acceleration signal, wherein the forgetting factor of the recursive least squares method is determined according to the dominant time scale of the current response and the baseline change time scale. The reconstruction and trend compensation module is used to adaptively decompose and filter the baseline-corrected acceleration signal, reconstruct the effective vibration components, and sequentially perform noise suppression, integral operation, and response type-related residual trend compensation on the effective vibration components, and output the dynamic deflection time history of the target measurement point.

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