Method and system for monitoring cracks of small and medium span bridges based on multi-dimensional enhanced OFDR

Abstract

This invention belongs to the field of fiber optic distributed sensing and bridge structural health monitoring technology. It discloses a crack monitoring system and method for small-to-medium span bridges based on multidimensional enhanced OFDR. The method includes the following steps: acquiring Rayleigh scattering interferometry signals; converting the time-domain signal to a frequency-domain signal and processing the time-domain signal to obtain suspected crack regions; precisely aligning the frequency-domain signal to the time axis; for suspected crack regions, performing sparse decomposition on the normalized frequency-domain signal, and then reconstructing it using an orthogonal matching pursuit algorithm and wavelet inverse transform to obtain a denoised frequency-domain signal; segmenting the denoised frequency-domain signal and calculating the first frequency shift value through cross-correlation; constructing a search interval centered on the first frequency shift value, and performing global optimization using a particle swarm optimization algorithm to obtain an optimized second frequency shift value; and demodulating to obtain the crack width. This invention can balance measurement speed, measurement distance, and positioning accuracy.

Description

Technical Field

[0001] This invention belongs to the field of fiber optic distributed sensing and bridge structural health monitoring technology, specifically involving a crack monitoring system for small and medium-span bridges based on multidimensional enhanced OFDR (Optical Frequency Domain Reflectometry). Background Technology

[0002] Small and medium-span bridges, due to their widespread distribution, large number, and complex service environments, have become critical nodes in transportation networks. Cracks in concrete structures are the most direct manifestation of bridge defects, often indicating a decrease in structural stiffness and a degradation of load-bearing capacity. Due to long-term exposure to vehicle loads, environmental erosion, and material aging, small and medium-span bridges are highly susceptible to developing hidden cracks. If these cracks are not detected and repaired in time, their expansion will lead to steel corrosion, concrete spalling, and in severe cases, even bridge collapse, causing enormous economic losses and casualties. Therefore, monitoring and diagnosing cracks in small and medium-span bridges throughout their entire lifecycle is crucial. Traditional bridge crack monitoring typically employs manual inspection methods, using bridge inspection vehicles or scaffolding to subjectively inspect the bridge structure surface through visual inspection and crack gauge measurements. This primitive inspection method is not only labor-intensive, has many blind spots, and is inefficient, but also often requires closed traffic conditions, significantly impacting traffic flow. More importantly, manual inspections are intermittent, point-based checks with significant time lag, making it impossible to capture the dynamic expansion process of bridge cracks in real time. In contrast, fiber optic sensing technology has advantages such as strong resistance to electromagnetic interference, corrosion resistance, small size, and ease of embedding or surface installation. It can convert minute deformations on the structural surface into changes in optical signals, enabling long-distance, distributed, continuous monitoring, which is very suitable for structural health monitoring of small and medium-span bridges.

[0003] Chinese patent publication CN120948558A discloses a method for monitoring cracks on bridges using conductive fiber bundles. This method uses the resistance change or open-circuit characteristics of the conductive material as the crack propagates to trigger an alarm. While this method is low-cost and simple to install, the conductive fiber bundles are susceptible to interference from the external electromagnetic environment and typically only provide "on / off" switching signals or coarse resistance changes, making it difficult to accurately quantify crack width changes and specific strain distributions. The positioning accuracy is also limited by the wiring density, failing to meet the requirements for high-precision quantitative analysis. Chinese patent publication CN121147164A discloses a method for monitoring bridge cracks using drone inspections. This method uses a drone equipped with a high-definition camera to photograph the bridge surface and extracts crack features using image recognition technology. However, this method is greatly affected by weather conditions (such as sunlight, rain, fog, and wind speed) and can only detect cracks on the visible surface of the bridge, leaving blind spots for hidden parts such as the bottom of the beam and the inside of the box girder. At the same time, the drone has a short flight time, a large amount of image data to process, and recognition errors, making it difficult to achieve all-weather, high-frequency real-time monitoring.

[0004] While existing optical frequency domain reflectance (OFDR) technologies offer high spatial resolution, they still face numerous challenges in practical applications. Traditional OFDR techniques often sacrifice measurement distance and speed in pursuit of high spatial resolution, resulting in low data refresh rates that fail to meet the real-time capture requirements of dynamic cracks. Furthermore, in the complex traffic environment of actual bridge operations, vibration and noise severely impact the signal-to-noise ratio. Additionally, traditional Rayleigh scattering demodulation algorithms are prone to computational errors when handling large or non-uniform strains. Therefore, to overcome these shortcomings and achieve accurate quantification and rapid diagnosis of cracks in small-to-medium span bridges, it is necessary to provide a new bridge crack monitoring technology that addresses the issues of low positioning accuracy, poor real-time performance, and insufficient anti-interference capabilities inherent in traditional methods. Summary of the Invention

[0005] To address the technical challenges of existing distributed fiber optic sensing solutions for monitoring microcracks in bridges, such as limited spatial resolution leading to low positioning accuracy, slow data sampling and processing resulting in insufficient real-time performance, low signal-to-noise ratio in complex traffic environments leading to poor anti-interference capabilities, and large strain calculation errors in traditional demodulation algorithms, this invention proposes a multidimensional enhanced OFDR-based crack monitoring system and method for small- and medium-span bridges. This system aims to achieve high-precision positioning, rapid capture, and accurate quantitative diagnosis and monitoring of microstrain cracks in small- and medium-span bridges.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for monitoring cracks in small and medium-span bridges based on multidimensional enhanced OFDR, comprising: Step 1: Scan the laser frequency and acquire the Rayleigh scattering interference signal; Step 2: Convert the time-domain signal of the collected Rayleigh scattering interferometry signal into a frequency-domain signal, and process the time-domain signal using the sliding window threshold method to obtain the suspected crack region; Step 3: Through timestamp synchronization and linear interpolation, the frequency domain signal is precisely aligned to the time axis in the time domain, and then normalized to obtain the normalized frequency domain signal; Step 4: For suspected crack regions, the normalized frequency domain signal is sparsely decomposed using wavelet basis, and then the optimal sparse coefficients are obtained by combining the orthogonal matching pursuit algorithm. The denoised frequency domain signal is then reconstructed by wavelet inverse transform using the obtained optimal sparse coefficients. Step 5: After segmenting the denoised frequency domain signal, the first frequency shift value is obtained by cross-correlation calculation. Where p represents the segment index and k represents the spatial location index; Step 6: Construct a search interval centered on the first frequency shift value, and perform global optimization using the particle swarm optimization algorithm to obtain the optimized second frequency shift value. ; Step 7: Demodulate the crack width based on the second frequency shift value.

[0007] The method for monitoring cracks in small-to-medium span bridges based on multidimensional enhanced OFDR further includes the following steps: Step 8: Compare the crack width with the set warning thresholds at each level, and issue a warning based on the comparison results.

[0008] Step 2 specifically includes: Step 2.1: Convert the time-domain signal of the acquired Rayleigh scattering interference signal into a frequency-domain signal using Fast Fourier Transform; Step 2.2: Set up a sliding window, process the time-domain signal through the sliding window, and calculate the signal mean within each window; Step 2.3: Determine if any sampling points meet the threshold condition. If so, mark the location corresponding to the sampling point as a suspected crack area. The threshold condition is: ; in, The acquired time-domain signal, where n represents the time sampling point index and k represents the spatial location index. This represents the signal mean, and i represents the window index. This indicates an adaptive threshold.

[0009] In step 2.2, the sliding window function is set as follows: in, This represents the sliding window function. This indicates the window length, with a window overlap rate of 50%. In step 2.3, the adaptive threshold is set as follows: ; in, To represent standard deviation, we have: ; .

[0010] Step 3 specifically includes the following steps: Step 3.1: For discrete-time domain signals Assign a unified timestamp to the frequency domain signal F[k,m]. , This establishes a precise correspondence between the sampling points of the frequency domain signal and the time axis of the time domain signal; n represents the index of the time sampling point. Indicates the sampling rate; Step 3.2: Using the time axis in the time domain as the target reference, resample the frequency domain signal using linear interpolation to obtain the time-aligned frequency domain signal. The linear interpolation formula is as follows: ; in, This represents the aligned frequency domain signal, where n represents the time sampling point index and k represents the spatial location index. and Represents frequency domain timestamp index +1 and The corresponding original frequency domain signal; and Represents frequency domain timestamp index +1 and Corresponding frequency domain signal timestamp; Represents the timestamp of a time-domain signal; Represents time-domain timestamps The closest frequency domain timestamp index; Step 3.3: Process the time-aligned frequency domain signal Normalization is performed to obtain the normalized frequency domain signal. The normalization formula is: ; in, Represents a normalized frequency domain signal; , These represent the minimum and maximum values ​​of the frequency domain signal at position k, respectively.

[0011] Step 4 specifically includes the following steps: Step 4.1: For the suspected crack region, perform sparse decomposition on the normalized frequency domain signal using a wavelet basis. The decomposition formula is as follows: ; in, This represents the normalized frequency domain signal at position k; This represents the db4 wavelet basis matrix, which is used to transform the original signal into the sparse domain through wavelet transform. Represents a sparse coefficient vector; Represents the noise vector; Step 4.2: Calculate the observation vector using the following formula: ; in, This represents a Gaussian random observation matrix (dimension M×N); The column vector representing the normalized frequency domain signal at position k; Step 4.3: Use the orthogonal matching pursuit algorithm to obtain the optimal sparsity coefficients. ; Step 4.4: Reconstruct the denoised frequency domain signal using inverse wavelet transform of the solved sparse coefficients. The reconstruction formula is as follows: ; in, This indicates the reconstructed and denoised frequency domain signal.

[0012] Step 5 specifically includes the following steps: Step 5.1: Transfer the reference signal acquired under unstrained conditions Reconstructed noise-reduced frequency domain signal corresponding to the measurement state Segmented according to spatial resolution; Step 5.2: Calculate the cross-correlation function. The formula is as follows: ; in, This represents the cross-correlation function value at position k in segment p. Indicates the amount of spectrum shift; express The p-th segment after segmentation Indicates time sampling point The corresponding reconstructed and denoised frequency domain signal The pth segment, and Representing the time sampling points n and respectively The corresponding Hamming window function, where n represents the index of the time sampling point; L represents the number of sampling points in each segment; Step 5.3: Determine the displacement corresponding to the peak position of the cross-correlation function. ,according to The first frequency shift value is calculated using the following formula: ; in, This represents the first frequency shift value at position k in segment p; This represents the displacement corresponding to the peak value of the cross-correlation; This represents the frequency domain resolution, where L represents the number of sampling points in each segment, and c represents the speed of light. Indicates wavelength.

[0013] In step 6, the particle swarm optimization algorithm uses a composite evaluation function as the fitness value, and its calculation formula is as follows: ; in, Represents the evaluation function. This represents the frequency shift to be optimized. Indicates the weighting coefficient. Indicates mean square error. This represents the correlation coefficient value; ; ; in, The sampling rate is represented by n, the index of the time sampling point is represented by k, and the spatial location index is represented by k. and These represent the reconstructed and denoised frequency domain signals corresponding to the reference Rayleigh scattering spectrum, respectively. Reconstructed and denoised frequency domain signal corresponding to the measurement spectrum The p-th segment, where L represents the number of sampling points in each segment. , They represent and The mean; In step 7, the formula for calculating the crack width is: ; ; ; in, This represents the crack width at position k; Indicates the length of the seam-affected zone; Poisson's ratio for concrete This represents the axial strain of the optical fiber at position k. This represents the average frequency shift, and P represents the number of segments.

[0014] Furthermore, this invention also provides a crack monitoring system for small-to-medium span bridges based on multidimensional enhanced OFDR, comprising a tunable laser, a first coupler, a main interferometer, a first balanced detector, a second balanced detector, a data acquisition system, and a computer; the main interferometer comprises a fourth coupler, a polarization controller, a fifth coupler, a circulator, and the optical fiber under test; the auxiliary interferometer comprises a second coupler, a delay fiber, and a third coupler; The output of the tunable laser is connected to the input of the first coupler, the first output of the first coupler is connected to the input of the second coupler, the first output of the second coupler is connected to the first input of the third coupler, the second output of the second coupler is connected to the second input of the third coupler via a delay fiber, and the first and second outputs of the third coupler are connected to the two inputs of the first balanced detector. The second output of the first coupler is connected to the input of the fourth coupler; the first output of the fourth coupler is connected to the first input of the fifth coupler via a polarization controller; the second output of the fourth coupler is connected to the input of the circulator; the output of the circulator is connected to the optical fiber under test; the reflecting end of the circulator is connected to the second input of the fifth coupler; the first and second outputs of the fifth coupler are connected to the two inputs of the second balanced detector. The outputs of the first and second balance detectors are connected to a computer via a data acquisition system. A computer is used to execute the aforementioned method for monitoring cracks in small-to-medium span bridges based on multidimensional enhanced OFDR.

[0015] The tunable laser outputs light with a wavelength range of 1530-1630nm, and the scanning power is adjustable. The third and fifth couplers are 2×2 fiber optic couplers.

[0016] Compared with the prior art, the present invention has the following advantages: (1) This invention employs a time-domain and frequency-domain fusion sampling method, breaking the constraint between the scanning cycle and measurement distance of traditional OFDR systems. By processing the impulse response in the time domain and the beat frequency signal in the frequency domain in parallel, the data acquisition and processing cycle is significantly shortened, and the real-time measurement speed of the system is significantly improved. This enables the system to capture the instantaneous crack propagation behavior of bridges under dynamic vehicle loads. Moreover, this invention retains the high spatial resolution characteristic of OFDR technology, breaking through the spatial resolution bottleneck of traditional OTDR or BOTDA technology in short-distance monitoring. Through high-precision optical frequency tuning and phase analysis, it can accurately capture minute Rayleigh scattering changes along the optical fiber, thereby achieving millimeter-level precise positioning of bridge cracks and effectively solving the problem of difficulty in detecting and locating minute cracks. Therefore, this invention can balance measurement speed, measurement distance, and positioning accuracy.

[0017] (2) In terms of improving the signal-to-noise ratio, the present invention performs noise reduction based on the principle of compressed sensing. By utilizing the sparsity of crack signals in the transform domain and constructing a targeted observation matrix and reconstruction algorithm, it can accurately restore the effective strain signal from the signal containing a large amount of traffic vibration noise under under-sampling conditions, which greatly improves the signal-to-noise ratio and anti-interference ability of the system in complex bridge operation environment.

[0018] (3) Regarding strain accuracy, this invention utilizes the optimal solution algorithm of the Rayleigh scattering light correlation evaluation function to calculate the strain magnitude. This algorithm improves upon the traditional cross-correlation peak search strategy, avoids demodulation errors caused by local extrema through global optimization, and can more accurately quantify the linear relationship between light frequency shift and strain, thereby significantly improving the measurement accuracy of strain magnitude and realizing the quantitative diagnosis of crack width.

[0019] In summary, this invention proposes a crack monitoring system for small-to-medium span bridges based on multidimensional enhanced OFDR. By integrating a high spatial resolution OFDR architecture, a time-frequency fusion sampling mechanism, a compressed sensing noise reduction algorithm, and an optimal solution correlation demodulation algorithm, it achieves high signal-to-noise ratio detection, high-precision positioning, rapid response, and accurate quantification of bridge cracks, providing reliable technical support for the structural health diagnosis of small-to-medium span bridges. Attached Figure Description

[0020] Figure 1 A schematic diagram of a crack monitoring system for small-to-medium span bridges based on multidimensional enhanced OFDR technology is provided for an embodiment of the present invention. Figure 2 This is a data processing flowchart of a crack monitoring system for small- and medium-span bridges based on multidimensional enhanced OFDR technology, used as an example of the present invention.

[0021] In the figure: 1 is a tunable laser, 2 is the first coupler, 3 is the second coupler, 4 is a delay fiber, 5 is the third coupler, 6 is the first balanced detector, 7 is the fourth coupler, 8 is the polarization controller, 9 is the fifth coupler, 10 is a circulator, 11 is the fiber under test, and 12 is the second balanced detector. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are some embodiments of the present invention, but 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.

[0023] Example 1 like Figure 1 As shown, Embodiment 1 of the present invention provides a method for monitoring cracks in small-to-medium span bridges based on multidimensional enhanced OFDR, comprising: Step 1: Scan the laser frequency and acquire the Rayleigh scattering interference signal.

[0024] Specifically, such as Figure 2 As shown, in this embodiment, the OFDR measurement device includes a tunable laser 1, a first coupler 2, a main interferometer, a first balanced detector 6, a second balanced detector 12, a data acquisition system 13, and a computer 14. The main interferometer includes a fourth coupler 7, a polarization controller 8, a fifth coupler 9, a circulator 10, and the fiber under test 11. The auxiliary interferometer includes a second coupler 3, a delay fiber 4, and a third coupler 5. The output of the tunable laser 1 is connected to the input of the first coupler 2. The first output of the first coupler 2 is connected to the input of the second coupler 3. The first output of the second coupler 3 is connected to the first input of the third coupler 5. The second output of the second coupler 3 is connected to the second input of the third coupler 5 via the delay fiber 4. The first and second outputs of the third coupler 5 are connected to the two inputs of the first balanced detector 6.

[0025] The second output terminal of the first coupler 2 is connected to the input terminal of the fourth coupler 7. The first output terminal of the fourth coupler 7 is connected to the first input terminal of the fifth coupler 9 via the polarization controller 8. The second output terminal of the fourth coupler 7 is connected to the input terminal of the circulator 10. The output terminal of the circulator 10 is connected to the optical fiber 11 under test. The reflecting terminal of the circulator 10 is connected to the second input terminal of the fifth coupler 9. The first and second output terminals of the fifth coupler 9 are connected to the two input terminals of the second balanced detector 12.

[0026] The laser output from the tunable laser 1 is split into two beams after passing through the first coupler 2. One beam enters the auxiliary interferometer section, and the other enters the main interferometer section. The light from the auxiliary interferometer section is split into a reference path and a delay path by the second coupler 3. After passing through the delay fiber 4, a signal light with a fixed known optical path difference is generated, which beats with the reference path inside the third coupler 5. Then, it is received by the first balanced detector 6 for photoelectric conversion. The light entering the main interferometer is split into a reference path and a detector path by the fourth coupler 7. The optical signal of the reference path passes through the polarization controller 8 for controlling and optimizing parameters. The polarization state of the light is matched with that of the probe path to suppress polarization fading noise to the greatest extent and improve the stability of the interference signal. The light signal of the probe path enters the fiber under test 11 through the circulator 10, and Rayleigh scattering effect is generated in the fiber under test 11. The generated backscattered Rayleigh signal is emitted through the circulator 10 and beats with the reference light at the fifth coupler 9. It is received by the second balanced detector 12 for photoelectric conversion. The data acquisition system 13 collects and processes the signals of the first balanced detector 6 and the second balanced detector 12 to obtain the Rayleigh scattering spectrum, and the computer 14 performs subsequent signal processing.

[0027] Specifically, in the monitoring device used in this embodiment, the wavelength range of the light output by the tunable laser 1 is 1530-1630 nm, the scanning power is adjustable, and the output end is connected to the input end of the first coupler 2, which has two output ends, through a single-mode fiber optic patch cord. In the monitoring device used in this embodiment, the first coupler 2, the second coupler 3, and the fourth coupler 7 are all fiber optic couplers. One output end of the first coupler 2 is connected to the input end of the second coupler 3 through a single-mode fiber optic patch cord, one output end of the second coupler 3 is connected to one input end of the third coupler 5 through a single-mode fiber optic patch cord, the other output end of the second coupler 3 is connected to a delay fiber 4, the output end of the delay fiber 4 is connected to the other input end of the third coupler 5, and the output end of the third coupler 5 is connected to the input end of the first balanced detector 6 through a single-mode fiber optic patch cord. The other output end of the first coupler 2... The emitter is connected to the input of the fourth coupler 7 via a single-mode fiber optic patch cord. One of the outputs of the fourth coupler 7 is connected to the input of the polarization controller 8 via a single-mode fiber optic patch cord. The output of the polarization controller 8 is connected to one of the inputs of the fifth coupler 9 via a single-mode fiber optic patch cord. The other output of the fourth coupler 7 is connected to the input of the circulator 10 via a single-mode fiber optic patch cord. The reflector of the circulator 10 is input to the fiber under test 11 via a single-mode fiber optic patch cord. The output of the circulator 10 is connected to the other input of the fifth coupler 9 via a single-mode fiber optic patch cord. The output of the first balanced detector 6 is connected to the input of the data acquisition system via an RF cable. The output of the second balanced detector 12 is connected to the input of the data acquisition system via an RF cable.

[0028] In this embodiment, the master interferometer signal carries strain information distributed along the optical fiber, directly reflecting the minute deformation and potential crack characteristics of the bridge structure. When the laser propagates in the optical fiber 11 under test, it couples with the deformation of the bridge structure to generate backscattered Rayleigh light. This scattered light interferes with the reference light to form an interference signal containing strain information, the expression of which is: (1) in, The signal strength is a binary function of time t and the spatial position z of the optical fiber. The signal changes at different locations correspond to the strain state of different areas of the bridge. Indicates the reference light intensity; This represents the intensity of the backscattered Rayleigh light at point z; It represents the frequency difference between the reference light and the scattered light, including information on the frequency shift caused by crack strain; The initial phase difference between the reference light and the scattered light at point z is represented; z represents the spatial position of the optical fiber.

[0029] Data acquisition system 13 acquires the aforementioned interference signals and converts the analog signals into discrete digital signals. (where n is the index of the time sampling point and k is the index of the spatial location), and store it in the cache unit to provide raw data support for subsequent time-frequency domain processing.

[0030] Step 2: Convert the time-domain signal of the collected Rayleigh scattering interferometry signal into a frequency-domain signal, and process the time-domain signal using the sliding window threshold method to obtain the suspected crack region.

[0031] The raw acquired signals contain a large amount of redundant information and noise. Directly performing high-precision processing would result in excessive computation and insufficient real-time performance. In this embodiment, suspected crack areas are rapidly screened and marked in the time domain to reduce the amount of data for subsequent processing; at the same time, accurate positioning information is obtained through high-resolution sampling in the frequency domain.

[0032] Step 2 specifically includes the following steps: Step 2.1: Convert the time-domain signal of the acquired Rayleigh scattering interference signal into a frequency-domain signal using Fast Fourier Transform.

[0033] Since time-domain signals cannot directly reflect the relationship between frequency and spatial location, they need to be converted into frequency-domain signals using Fast Fourier Transform (FFT). The expression for this is: (2) in, The frequency domain amplitude of the interference signal at position k is represented by its peak position, which corresponds to the signal's beat frequency and has a linear relationship with the spatial position of the optical fiber. This is the core basis for positioning. N represents the number of FFT points; m represents the frequency domain sampling point index, corresponding to a frequency range from 0 to the sampling rate. .

[0034] Step 2.2: Set up a sliding window to process the time-domain signal and calculate the signal mean within each window.

[0035] The time-domain sampling response is fast, allowing for rapid screening of suspected crack regions and reducing the computational load of subsequent high-frequency domain processing. Crack formation causes abrupt changes in signal amplitude; therefore, a sliding window thresholding method is used to capture this abrupt change. In step 2.2, the sliding window function is set as follows: (3) in, This represents the sliding window function. This indicates the window length, with a window overlap rate of 50%.

[0036] Step 2.3: Determine if any sampling points meet the threshold condition. If so, mark the location corresponding to the sampling point as a suspected crack area. The threshold condition is: (4) in, The acquired time-domain signal, where n represents the time sampling point index and k represents the spatial location index. Let represent the signal mean at position k in the i-th window, where i represents the window index, which serves as the benchmark for judging signal abrupt changes. This indicates an adaptive threshold.

[0037] Specifically, in step 2.3, the adaptive threshold is set as follows: (5) in, The standard deviation of the signal at position k within the i-th window can be used to quantify the noise level within the window; we have: (6) in, This represents the signal mean, reflecting the baseline level of the signal within the window and eliminating the influence of the DC component; the specific expression is: ; (7) In this embodiment, the adaptive threshold is dynamically adjusted based on the noise level of the signal within the window, which can adapt to noise changes in different monitoring environments. When any sampling point within the window meets the threshold condition, it indicates that there is a significant abrupt change in the signal at that location, which is likely caused by a crack. Therefore, location k is marked as a suspected crack area; otherwise, it is marked as a non-suspected area.

[0038] Step 3: Through timestamp synchronization and linear interpolation, the frequency domain signal is precisely aligned to the time axis in the time domain, and then normalized to obtain the normalized frequency domain signal.

[0039] Frequency domain signal obtained by FFT transform There is a time reference difference between the frequency domain signal and the synchronously acquired time domain signal. Direct joint analysis would lead to spatiotemporal information misalignment. To solve this problem, in this embodiment, the time axis of the time domain signal is used as the reference. Through timestamp synchronization and linear interpolation, the frequency domain signal is precisely aligned to the time axis of the time domain, resulting in a time-aligned frequency domain signal. The normalized frequency domain signal is then obtained through normalization. This provides high-quality frequency domain data for subsequent compressed sensing reconstruction and spectral analysis.

[0040] Specifically, step 3 includes the following steps: Step 3.1: For discrete-time domain signals Assign a unified timestamp to the frequency domain signal F[k,m]. , This establishes a precise correspondence between the sampling points of the frequency domain signal and the time axis of the time domain signal; n represents the index of the time sampling point. This indicates the sampling rate.

[0041] Timestamp synchronization is fundamental for providing a time-domain reference for frequency-domain signals. The data acquisition system incorporates a high-precision clock chip, which can provide a time-domain reference for discrete time-domain signals. Assign a unified timestamp to the frequency domain signal F[k,m]. .

[0042] Step 3.2: Using the time axis in the time domain as the target reference, resample the frequency domain signal using linear interpolation to obtain the time-aligned frequency domain signal. The linear interpolation formula is as follows: (8) in, This represents the aligned frequency domain signal, where n represents the time sampling point index and k represents the spatial location index. and Represents frequency domain timestamp index +1 and The corresponding original frequency domain signal; and Represents frequency domain timestamp index +1 and Corresponding frequency domain signal timestamp; Represents the timestamp of a time-domain signal; Represents time-domain timestamps The closest frequency domain timestamp index; Step 3.3: Process the time-aligned frequency domain signal Normalization is performed to obtain the normalized frequency domain signal. The normalization formula is: (9) in, Represents a normalized frequency domain signal; , These represent the minimum and maximum values ​​of the frequency domain signal at position k, respectively.

[0043] Step 4: For suspected crack regions, the normalized frequency domain signal is sparsely decomposed using wavelet basis, and then the optimal sparse coefficients are obtained by combining the orthogonal matching pursuit algorithm. The denoised frequency domain signal is then reconstructed by wavelet inverse transform using the obtained optimal sparse coefficients.

[0044] The bridge operating environment contains a large amount of clutter such as traffic vibration noise and electromagnetic interference. This clutter can overwhelm the weak strain signals generated by cracks, leading to a decrease in the signal-to-noise ratio and affecting the subsequent demodulation accuracy. Crack strain signals have sparse characteristics in the wavelet transform domain, meaning the signal can be characterized by a small number of non-zero coefficients. This step only targets the suspected crack regions identified in step 2.2.3, extracting the frequency domain signals corresponding to each suspected location. Utilizing the sparsity of crack signals in the wavelet domain, a sparse basis and observation matrix are constructed. Combined with the Orthogonal Matching Pursuit (OMP) algorithm, high-precision reconstruction and noise suppression of local signals are achieved in the frequency domain, providing high-quality frequency domain input for subsequent quantitative crack analysis.

[0045] Specifically, step 4 includes the following steps: Step 4.1: For the suspected crack region, perform sparse decomposition on the normalized frequency domain signal using a wavelet basis. The decomposition formula is as follows: (10) in, This represents the normalized frequency domain signal at position k; This represents the db4 wavelet basis matrix. Dimensions N×N; Represents a sparse coefficient vector; The noise vector represents traffic vibration noise and electromagnetic interference, which do not exhibit significant sparsity characteristics in the sparse domain, facilitating subsequent separation. For non-suspected regions, the sparse decomposition and reconstruction process in this step is omitted, and the original frequency domain signal can be directly used to save computational resources.

[0046] The choice of sparse basis directly determines the effectiveness of the sparse representation of the frequency domain signal in the suspected region. It needs to possess good time-frequency localization characteristics to accurately capture the abrupt changes in the crack signal. The db4 wavelet basis performs well in terms of the sparsity of crack strain signals and has strong time-frequency localization capabilities, effectively distinguishing signals from noise in the frequency domain. Therefore, the db4 wavelet basis is selected for each suspected crack location. Sparse decomposition is performed on the normalized frequency domain signal.

[0047] Step 4.2: Calculate the observation vector using the following formula: (11) in, The observation vector has a dimension that is only 30%-50% of the original signal, which greatly reduces the data processing pressure. This represents a Gaussian random observation matrix (dimension M×N); The column vector (dimension N×1) represents the normalized frequency domain signal at position k.

[0048] The core function of the observation matrix is ​​to undersample the signal in the sparse domain, preserving the core information of the signal with fewer observations while reducing data storage and processing pressure. To ensure that the observation matrix effectively preserves the geometric properties of the sparse coefficients, the Restricted Isometry Point (RIP) condition must be satisfied: (12) in, Let RIP be a constant, satisfying In this embodiment, To ensure the reliability of the observation matrix, a Gaussian random observation matrix is ​​selected. This matrix has good randomness and uncorrelatedness, and is easy to satisfy the RIP condition.

[0049] Step 4.3: Use the Orthogonal Matching Pursuit (OMP) algorithm to obtain the optimal sparse coefficients. .

[0050] In this embodiment, the OMP algorithm, which has fast convergence speed and strong engineering feasibility, is used to solve for the optimal sparse coefficients for signal reconstruction from the observation vector, and to restore the effective frequency domain signal. The specific steps are as follows: Step 4.3.1: Set initialization parameters. In this embodiment, the residual is set. Atomic index set The number of iterations t=0, the convergence threshold Maximum number of iterations .

[0051] Step 4.3.2: Calculate the correlation value between the residual and each wavelet atom. The calculation formula is as follows: (13) in, This indicates the relationship between the wavelet atom and the wavelet atom in the t-th iteration. The relevant values, This represents the residual obtained in the t-th iteration. Represents the Gaussian random observation matrix. Represents the db4 wavelet basis matrix The j-th atom (column vector) in the array.

[0052] Step 4.3.3: Select the atom update index set with the largest correlation value, and estimate the optimal sparsity coefficients using least squares. The residual is updated synchronously; when the residual obtained in the t-th iteration is less than the threshold, or the number of iterations reaches the maximum number of iterations, i.e. or When the iteration terminates, the frequency domain signal is gradually approximated in the sparse domain through the above iterative process, and the optimal sparse coefficients are obtained. .

[0053] Step 4.4: Reconstruct the denoised frequency domain signal using inverse wavelet transform of the solved sparse coefficients. The reconstruction formula is as follows: (14) in, This indicates the reconstructed and denoised frequency domain signal.

[0054] Step 5: After segmenting the denoised frequency domain signal, the first frequency shift value is obtained by cross-correlation calculation. , where p represents the segment index and k represents the spatial location index.

[0055] The denoised frequency domain signal still contains frequency shift information corresponding to crack strain. First, a coarse frequency shift is obtained through cross-correlation analysis as the first frequency shift value, providing a reasonable search range for subsequent high-precision optimization. Then, the accurate frequency shift is obtained through global optimization. Directly performing global optimization would lead to a surge in computational load and low efficiency due to the excessively large search range.

[0056] Step 5 specifically includes the following steps: Step 5.1: Transfer the signals acquired under no-strain conditions Reconstructed noise-reduced frequency domain signal corresponding to the measurement state Segmented according to spatial resolution.

[0057] When the bridge is not under stress, the Rayleigh scattering spectrum collected under the unstrained state is used as the reference signal. In this embodiment, the sampling points corresponding to each segment length are L=256, corresponding to an optical fiber length of approximately 0.5mm. This length ensures that each signal segment contains sufficient frequency domain characteristics while also reflecting the differences in local frequency shifts, avoiding the loss of local frequency shift information due to excessively long segments. The segmented signal expression is: (15) in P is the number of segments. , where n represents the sampling point index, .

[0058] Step 5.2: Calculate the cross-correlation function. The formula is as follows: (16) in, This represents the cross-correlation function value at position k in segment p. The larger the value, the higher the similarity between the reference spectrum and the measured spectrum. It represents the amount of frequency spectrum shift, which is linearly related to the frequency shift and corresponds to the displacement. express The p-th segment after segmentation Indicates time sampling point The corresponding reconstructed and denoised frequency domain signal The pth segment, and Representing the time sampling points n and respectively The corresponding Hamming window function, where n represents the index of the time sampling point; L represents the number of sampling points in each segment.

[0059] The cross-correlation function measures the similarity between the reference spectrum and the measured spectrum. The peak position corresponds to the optimal matching shift between the two signals, which is directly related to the frequency shift. To suppress the influence of spectral leakage on the cross-correlation results, a Hamming window is applied to the segmented signal before calculating the cross-correlation function. The Hamming window can effectively reduce abrupt changes in signal boundaries and decrease spectral leakage. In this embodiment, the window function expression of the Hamming window is: .

[0060] Step 5.3: Determine the displacement corresponding to the peak position of the cross-correlation function. ,according to The first frequency shift value is calculated using the following formula: (17) in, This represents the first frequency shift value at position k in segment p; This represents the displacement corresponding to the peak value of the cross-correlation. ; The frequency domain resolution is determined by the number of FFT points and the sampling rate; L represents the number of sampling points in each segment, and c represents the speed of light. Indicates wavelength.

[0061] The peak position of the cross-correlation function directly corresponds to the optimal matching displacement between the reference spectrum and the measured spectrum. This peak position can be accurately located using parabolic interpolation. .

[0062] Step 6: Construct a search interval centered on the first frequency shift value, and perform global optimization using the particle swarm optimization algorithm to obtain the optimized second frequency shift value. .

[0063] In this embodiment, an evaluation function is constructed that integrates mean square error (MSE) and correlation coefficient (CC). MSE reflects the amplitude difference between two signals, while CC reflects the degree of linear correlation between the two signals. The combination of the two can comprehensively characterize the signal matching degree, avoid misjudgment caused by a single index, and comprehensively measure the matching degree between the reference spectrum and the frequency-shifted measurement spectrum. At the same time, the particle swarm optimization (PSO) algorithm is used for global optimization to ensure that the true optimal frequency shift is found and improve the frequency shift measurement accuracy.

[0064] Specifically, in step 6, the particle swarm optimization algorithm uses a composite evaluation function value as the fitness value, and its calculation formula is as follows: (18) in, This represents a composite evaluation function. The smaller the value, the higher the matching degree between the reference spectrum and the frequency-shifted measured spectrum. It is the objective function for optimization. This represents the frequency shift to be optimized. This represents the weighting coefficient, calibrated through multiple experiments. Indicates mean square error. This represents the correlation coefficient value.

[0065] The smaller the mean square error, the smaller the amplitude difference between the reference spectrum and the frequency-shifted measured spectrum, and the higher the matching degree. The expression is: (19) The closer the correlation coefficient is to 1, the higher the linear correlation between the two signals and the better the match. The expression is: (20) in, The sampling rate is represented by n, the index of the time sampling point is represented by k, and the spatial location index is represented by k. and These represent the reconstructed and denoised frequency domain signals corresponding to the reference Rayleigh scattering spectrum, respectively. Reconstructed and denoised frequency domain signal corresponding to the measurement spectrum The p-th segment, where L represents the number of sampling points in each segment. , They represent and The mean value is used to eliminate the influence of the DC component on the correlation coefficient calculation.

[0066] Specifically, in this embodiment, the specific steps of the particle swarm optimization algorithm for global optimization are as follows: Step 6.1: Set initialization parameters: number of particles Too many particles will increase the computational load, while too few may lead to insufficient searching. This embodiment selects 40 particles; particle positions... That is, the initial positions of the particles are randomly distributed within the search range of the first frequency shift value; the particle velocity... ,in To avoid unstable search due to excessively high particle speeds; inertial weights. To balance global and local search capabilities, this embodiment uses 0.7; the learning factor c1=c2=2 guides the particle to move towards the individual optimal and global optimal positions.

[0067] Step 6.2: Calculate the composite evaluation function value of each particle as the fitness value using the above evaluation function formula. The smaller the fitness value, the closer the particle position is to the optimal frequency shift.

[0068] Step 6.3: Record the position corresponding to the optimal fitness in the history position of each particle, i.e., the individual's optimal position. : ( (The historical position of particle q). Step 6.4: Record the position corresponding to the best fitness among all individual particle optimal positions, i.e., the global optimal position. : Step 6.5: Update the particle position and velocity as follows: ;(twenty one) ;(twenty two) in Using random numbers increases the randomness of the search and avoids getting trapped in local optima. and These represent the velocity values ​​before and after the iteration, respectively. and These represent the positions before and after the iteration, respectively.

[0069] Step 6.6: Repeat the iteration until the difference between the global optimal fitness of two consecutive iterations is less than a threshold, at which point the iteration terminates. For example, . and This represents the fitness value corresponding to the global optimum position before and after the iteration, where the global optimum position is now... This is the high-precision second frequency shift value. .

[0070] Step 7: Demodulate the crack width based on the second frequency shift value.

[0071] Based on the elasto-optic effect of OFDR technology, the frequency shift and the axial strain of the optical fiber have a strict linear relationship; combined with the elastic mechanical properties of concrete, the strain and crack width have a clear correlation. Through these two mappings, the accurate inversion from the frequency shift to the crack width can be achieved.

[0072] When an optical fiber is subjected to strain, its refractive index changes, causing a frequency shift in the Rayleigh scattered light. This frequency shift exhibits a strictly linear relationship with the strain. The expression for this linear relationship is: ;(twenty three) in, This represents the axial strain of the optical fiber at position k; K is the frequency shift-strain proportionality coefficient, which is related to the type of optical fiber and material properties, and is calibrated through a standard tensile test. The average frequency shift at position k is expressed as follows: ;(twenty four) Where P represents the number of segments. This represents the second frequency shift value at position k calculated from the p-th segment of the signal. By averaging the frequency shifts of multiple segments, the influence of random errors on the measurement results can be reduced.

[0073] Crack width needs to be inverted based on strain distribution and the elastic mechanical properties of concrete. Assuming the crack is open and the strain is uniformly distributed within the crack's influence zone, and considering the Poisson's ratio of the concrete, the inversion formula for crack width is: (25) in, This represents the crack width at position k; The length of the affected area is determined by the fiber optic laying density and the concrete strength grade. The Poisson's ratio for concrete.

[0074] Crack width is graded: when When, it is determined that there are no effective cracks; when At that time, it was determined to be a minor crack; when When a crack is identified as requiring attention, it provides a basis for setting subsequent early warning thresholds.

[0075] Furthermore, the crack monitoring method for small-to-medium span bridges based on multidimensional enhanced OFDR in this embodiment also includes the following steps: Step 8: Compare the crack width with the set warning thresholds at each level, and issue a warning based on the comparison results.

[0076] Specifically, in this embodiment, the crack width is graded: when When, it is determined that there are no effective cracks; when At that time, it was determined to be a minor crack; when When a crack is identified as requiring attention, it provides a basis for setting subsequent early warning thresholds.

[0077] Specifically, based on the operational characteristics of small and medium-span bridges, a three-level early warning threshold is set to adapt to bridges in different service conditions, as follows: Level 1 Early Warning Threshold (Emergency Early Warning): The corresponding crack width has reached the standard limit, posing a serious risk to the bridge structure's safety, requiring immediate closure for repairs; Level II warning threshold (key warning): The corresponding crack width is close to the limit, indicating a risk of further crack expansion. Monitoring frequency needs to be increased and a maintenance plan developed. Level 3 warning threshold (general warning): When the cracks begin to expand significantly, it is necessary to record the crack change trend to provide data support for subsequent maintenance. The aforementioned thresholds can be dynamically adjusted based on the bridge's design load, service life, and importance level.

[0078] Specifically, the monitoring data was organized into a structured format, including the location of cracks. (Converted to actual bridge coordinates based on coordinate calibration during fiber optic cable installation), strain Crack width To ensure data integrity.

[0079] Specifically, in this embodiment, the early warning method is as follows: (1) If : Triggering a Level 1 warning, the system immediately generates an emergency warning report, which includes the precise location of the crack, its real-time width, strain value, and propagation rate (average of the width differences from the last 5 measurements). (2) If Trigger a Level II early warning, generate a key early warning report, reduce the sampling cycle, and continuously and intensively monitor the crack expansion. (3) If Triggering a Level 3 early warning triggers a general early warning report and generates a weekly monitoring report, recording crack changes. (4) If If the status is determined to be safe, no warning report will be generated; only the monitoring data will be stored in the health monitoring database.

[0080] After completing all alarm tasks and data storage, the system waits for the trigger signal of the next laser scanning cycle, returns to step 1, and begins a new round of monitoring cycle.

[0081] Example 2 Embodiment 2 of the present invention provides a crack monitoring system for small and medium span bridges based on multidimensional enhanced OFDR, the structure of which is as follows: Figure 2 As shown, it includes a tunable laser 1, a first coupler 2, a main interferometer, a first balanced detector 6, a second balanced detector 12, a data acquisition system 13, and a computer 14; the main interferometer includes a fourth coupler 7, a polarization controller 8, a fifth coupler 9, a circulator 10, and an optical fiber under test 11; the auxiliary interferometer includes a second coupler 3, a delay optical fiber 4, and a third coupler 5.

[0082] Specifically, the output of the tunable laser 1 is connected to the input of the first coupler 2, the first output of the first coupler 2 is connected to the input of the second coupler 3, the first output of the second coupler 3 is connected to the first input of the third coupler 5, the second output of the second coupler 3 is connected to the second input of the third coupler 5 via the delay fiber 4, and the first and second outputs of the third coupler 5 are connected to the two inputs of the first balanced detector 6. The second output terminal of the first coupler 2 is connected to the input terminal of the fourth coupler 7. The first output terminal of the fourth coupler 7 is connected to the first input terminal of the fifth coupler 9 via the polarization controller 8. The second output terminal of the fourth coupler 7 is connected to the input terminal of the circulator 10. The output terminal of the circulator 10 is connected to the optical fiber 11 under test. The reflecting terminal of the circulator 10 is connected to the second input terminal of the fifth coupler 9. The first and second output terminals of the fifth coupler 9 are connected to the two input terminals of the second balanced detector 12. The output terminals of the first balance detector 6 and the second balance detector 12 are connected to the computer 14 via the data acquisition system 13; the computer 14 is used to execute the method for monitoring cracks in small and medium-span bridges based on multidimensional enhanced OFDR as described in Embodiment 1.

[0083] Specifically, in this embodiment, the wavelength range of the light output by the tunable laser 1 is 1530-1630 nm, and the scanning power is adjustable; the third coupler 5 and the fifth coupler 9 are 2×2 fiber couplers.

[0084] In this embodiment, the measurement requires driving a tunable laser to begin a linear frequency scan. Because nonlinear deviations exist during laser frequency scanning, they disrupt the linear mapping between the beat frequency and the spatial position of the optical fiber, affecting positioning accuracy. In this embodiment, the auxiliary interferometer signal is used as a calibration reference to perform nonlinear compensation on the main interferometer signal.

[0085] The auxiliary interferometer introduces a fixed optical path difference through a delay fiber, and its output signal can be expressed as: (26) in, To enhance the light intensity of the interferometer, The delay introduced by the delay fiber This represents the instantaneous phase of the laser. (For) Perform Hilbert transform to extract phase information: (27) in, For Hilbert transform operators, To perform complex phase operations, This is the phase expansion function. It remaps the sampling axis of the master interferometer signal from time t to a new sampling axis with an equal phase step. : (28) in, For phase The minimum value, The phase step size is equiphase, and N is the number of sampling points. After this resampling, the nonlinear sweep error of the main interferometer signal is effectively eliminated, ensuring the linear mapping relationship between the beat frequency and the spatial position of the fiber. The auxiliary interferometer signal, after completing the calibration function, is no longer involved in subsequent processing.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for monitoring cracks of small and medium span bridges based on multi-dimensional enhanced OFDR, characterized in that, include: Step 1: Scan the laser frequency and acquire the Rayleigh scattering interference signal; Step 2: Convert the time-domain signal of the collected Rayleigh scattering interferometry signal into a frequency-domain signal, and process the time-domain signal using the sliding window threshold method to obtain the suspected crack region; Step 3: Through timestamp synchronization and linear interpolation, the frequency domain signal is precisely aligned to the time axis in the time domain, and then normalized to obtain the normalized frequency domain signal; Step 4: For suspected crack regions, the normalized frequency domain signal is sparsely decomposed using wavelet basis, and then the optimal sparse coefficients are obtained by combining the orthogonal matching pursuit algorithm. The denoised frequency domain signal is then reconstructed by wavelet inverse transform using the obtained optimal sparse coefficients. Step 5: After segmenting the noise-reduced frequency-domain signal, the first frequency shift value is obtained by cross-correlation calculation where p represents the segment index, and k represents the spatial position index. Step 6: build a search interval centered on the first frequency shift value, and perform global optimization by combining a particle swarm optimization algorithm to obtain an optimized second frequency shift value ; Step 7: Demodulate the crack width based on the second frequency shift value.

2. The method according to claim 1, wherein, It also includes the following steps: Step 8: Compare the crack width with the set warning thresholds at each level, and issue a warning based on the comparison results.

3. The method according to claim 1, wherein, Step 2 specifically includes: Step 2.1: Convert the time-domain signal of the acquired Rayleigh scattering interference signal into a frequency-domain signal using Fast Fourier Transform; Step 2.2: Set up a sliding window, process the time-domain signal through the sliding window, and calculate the signal mean within each window; Step 2.3: Determine if any sampling points meet the threshold condition. If so, mark the location corresponding to the sampling point as a suspected crack area. The threshold condition is: ； in, The acquired time-domain signal, where n represents the time sampling point index and k represents the spatial location index. This represents the signal mean, and i represents the window index. This indicates an adaptive threshold.

4. The method for monitoring cracks in small-to-medium span bridges based on multidimensional enhanced OFDR according to claim 3, characterized in that, In step 2.2, the sliding window function is set as follows: in, This represents the sliding window function. This indicates the window length, with a window overlap rate of 50%. In step 2.3, the adaptive threshold is set as follows: ； in, To represent standard deviation, we have: ； 。 5. The method for monitoring cracks in small-to-medium span bridges based on multidimensional enhanced OFDR according to claim 1, characterized in that, Step 3 specifically includes the following steps: Step 3.1: For discrete-time domain signals Assign a unified timestamp to the frequency domain signal F[k,m]. , This establishes a precise correspondence between the sampling points of the frequency domain signal and the time axis of the time domain signal; n represents the index of the time sampling point. Indicates the sampling rate; Step 3.2: Using the time axis in the time domain as the target reference, resample the frequency domain signal using linear interpolation to obtain the time-aligned frequency domain signal. The linear interpolation formula is as follows: ； in, This represents the aligned frequency domain signal, where n represents the time sampling point index and k represents the spatial location index. and Represents frequency domain timestamp index +1 and The corresponding original frequency domain signal; and Represents frequency domain timestamp index +1 and Corresponding frequency domain signal timestamp; Represents the timestamp of a time-domain signal; Represents time-domain timestamps The closest frequency domain timestamp index; Step 3.3: Process the time-aligned frequency domain signal Normalization is performed to obtain the normalized frequency domain signal. The normalization formula is: ； in, Represents a normalized frequency domain signal; , These represent the minimum and maximum values ​​of the frequency domain signal at position k, respectively.

6. The method for monitoring cracks in small-to-medium span bridges based on multidimensional enhanced OFDR according to claim 1, characterized in that, Step 4 specifically includes the following steps: Step 4.1: For the suspected crack region, perform sparse decomposition on the normalized frequency domain signal using a wavelet basis. The decomposition formula is as follows: ； in, This represents the normalized frequency domain signal at position k; This represents the db4 wavelet basis matrix, which is used to transform the original signal into the sparse domain through wavelet transform. Represents a sparse coefficient vector; Represents the noise vector; Step 4.2: Calculate the observation vector using the following formula: ； in, Represents the Gaussian random observation matrix; The column vector representing the normalized frequency domain signal at position k; Step 4.3: Use the orthogonal matching pursuit algorithm to obtain the optimal sparsity coefficients. ; Step 4.4: Reconstruct the denoised frequency domain signal using inverse wavelet transform of the solved sparse coefficients. The reconstruction formula is as follows: ； in, This indicates the reconstructed and denoised frequency domain signal.

7. The method for monitoring cracks in small-to-medium span bridges based on multidimensional enhanced OFDR according to claim 1, characterized in that, Step 5 specifically includes the following steps: Step 5.1: Transfer the reference signal acquired under unstrained conditions Reconstructed noise-reduced frequency domain signal corresponding to the measurement state Segmented according to spatial resolution; Step 5.2: Calculate the cross-correlation function. The formula is as follows: ； in, This represents the cross-correlation function value at position k in segment p. Indicates the amount of spectrum shift; express The p-th segment after segmentation Indicates time sampling point The corresponding reconstructed and denoised frequency domain signal The pth segment, and Representing the time sampling points n and respectively The corresponding Hamming window function, where n represents the index of the time sampling point; L represents the number of sampling points in each segment; Step 5.3: Determine the displacement corresponding to the peak position of the cross-correlation function. ,according to The first frequency shift value is calculated using the following formula: ； in, This represents the first frequency shift value at position k in segment p; This represents the displacement corresponding to the peak value of the cross-correlation; This represents the frequency domain resolution, where L represents the number of sampling points in each segment, and c represents the speed of light. Indicates wavelength.

8. A method for monitoring cracks in small-to-medium span bridges based on multidimensional enhanced OFDR according to claim 1, characterized in that, In step 6, the particle swarm optimization algorithm uses a composite evaluation function as the fitness value, and its calculation formula is as follows: ； in, Represents the evaluation function. This represents the frequency shift to be optimized. Indicates the weighting coefficient. Indicates mean square error. This represents the correlation coefficient value; ； ； in, The sampling rate is represented by n, the index of the time sampling point is represented by k, and the spatial location index is represented by k. and These represent the reconstructed and denoised frequency domain signals corresponding to the reference Rayleigh scattering spectrum, respectively. Reconstructed and denoised frequency domain signal corresponding to the measurement spectrum The p-th segment, where L represents the number of sampling points in each segment. , They represent and The mean; In step 7, the formula for calculating the crack width is: ； ； ； in, This represents the crack width at position k; Indicates the length of the seam-affected zone; Poisson's ratio for concrete This represents the axial strain of the optical fiber at position k. This represents the average frequency shift, and P represents the number of segments.

9. A crack monitoring system for small-to-medium span bridges based on multidimensional enhanced OFDR, characterized in that, The system includes a tunable laser (1), a first coupler (2), a main interferometer, a first balanced detector (6), a second balanced detector (12), a data acquisition system (13), and a computer (14); the main interferometer includes a fourth coupler (7), a polarization controller (8), a fifth coupler (9), a circulator (10), and the fiber under test (11); the auxiliary interferometer includes a second coupler (3), a delay fiber (4), and a third coupler (5). The output of the tunable laser (1) is connected to the input of the first coupler (2), the first output of the first coupler (2) is connected to the input of the second coupler (3), the first output of the second coupler (3) is connected to the first input of the third coupler (5), the second output of the second coupler (3) is connected to the second input of the third coupler (5) via the delay fiber (4), and the first and second outputs of the third coupler (5) are connected to the two inputs of the first balanced detector (6). The second output of the first coupler (2) is connected to the input of the fourth coupler (7). The first output of the fourth coupler (7) is connected to the first input of the fifth coupler (9) via the polarization controller (8). The second output of the fourth coupler (7) is connected to the input of the circulator (10). The output of the circulator (10) is connected to the fiber under test (11). The reflecting end of the circulator (10) is connected to the second input of the fifth coupler (9). The first and second outputs of the fifth coupler (9) are connected to the two inputs of the second balanced detector (12). The output terminals of the first balance detector (6) and the second balance detector (12) are connected to the computer (14) via the data acquisition system (13); The computer (14) is used to execute the method for monitoring cracks in small and medium-span bridges based on multidimensional enhanced OFDR as described in any one of claims 1-8.

10. A crack monitoring system for small-to-medium span bridges based on multidimensional enhanced OFDR according to claim 9, characterized in that, The tunable laser (1) outputs light with a wavelength range of 1530-1630 nm and the scanning power is adjustable; The third coupler (5) and the fifth coupler (9) are 2×2 fiber optic couplers.

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