A method for static clutter removal in long-term monitoring of urban bridges using ground-based radar

Abstract

This invention discloses a method for removing static clutter in long-term monitoring of urban bridges using ground-based radar. The method includes acquiring complex signals from long-term monitoring of urban bridges using ground-based radar; using a sliding window dynamic neighborhood parameter constraint local outlier factor method to dynamically identify outliers in the complex signals, obtaining non-uniformly distributed, high-density clusters of complex plane points resembling circular arcs; performing robust estimation of the non-uniformly distributed center parameters of the high-density clusters of complex plane points resembling circular arcs to obtain optimal center and radius parameters; and removing static clutter from the complex signals based on the optimal center parameters, converting the output into time-series radial displacement data. This invention reduces the impact of time window edge effects while compressing redundant calculations in overlapping areas, balancing the accuracy and efficiency of outlier identification; and reduces computational complexity by optimizing the weight update strategy, achieving real-time processing of static clutter and meeting the timeliness requirements of urban bridge dynamic deflection monitoring.

Description

Technical Field

[0001] This invention relates to the field of time-series monitoring data noise reduction technology, and in particular to a method for removing static clutter in long-term time-series monitoring of urban bridges using ground-based radar. Background Technology

[0002] Urban bridges, as vital transportation infrastructure, play a crucial role in connecting regions, alleviating congestion, and supporting logistics. As of 2024, my country had over 125,000 urban bridges, of which approximately 25% were over 30 years old. Affected by increasing traffic loads, material aging, and environmental erosion, bridge structures are prone to damage such as cracks and bearing failure, threatening operational safety. The degradation of urban bridge structural performance is a gradual process influenced by multiple coupled factors, and its damage evolution exhibits time-delay and nonlinear characteristics. This means that short-term monitoring is insufficient to meet the needs for accurate diagnosis and early warning of health status. Therefore, to ensure the safe operation of urban bridges, high-precision long-term dynamic deflection monitoring technology has become an urgent need for accurate analysis of the degradation trend of urban bridge structures and precise detection of their structural safety status in my country.

[0003] Traditional dynamic deflection monitoring technologies have significant limitations: contact sensors (such as strain gauges and accelerometers) require physical installation and have limited monitoring range, making it difficult to cover the entire span of long-span bridges; among non-contact methods, Global Navigation Satellite Systems (GNSS) are limited by low sampling rates and cannot capture high-frequency vibrations, while 3D laser scanning (TLS) and spaceborne interferometric synthetic aperture radar (InSAR) are difficult to achieve real-time dynamic monitoring due to long data update cycles. In contrast, ground-based synthetic aperture radar (GBSAR) integrates synthetic aperture imaging, stepped-frequency continuous wave (SFCW), and interferometry technologies, offering advantages such as non-contact deployment, sub-millimeter accuracy, and high sampling frequency. It can simultaneously acquire dynamic deformation data from high-density measurement points across the entire bridge area. Especially in densely populated urban bridge areas, ground-based radar does not require prism installation or wiring, can penetrate rain and fog interference, and adapt to complex electromagnetic environments, making it the optimal choice for high-resolution, all-weather dynamic deflection monitoring.

[0004] During bridge dynamic deflection monitoring, ground-based radar is susceptible to interference from radar wave reflections from other stationary reflectors (such as fixed structural components) within the same range cell of the monitored target. This interference can easily lead to static clutter in the target monitoring signal, reducing radar measurement accuracy. Currently, the main methods for static clutter processing are frequency nulling and circle fitting. Frequency nulling is based on the characteristic that static clutter spectral energy is concentrated in the zero-frequency or extremely low-frequency band. It uses a high-pass filter to suppress zero-frequency or extremely low-frequency data, reducing static clutter interference. This method is computationally simple and highly feasible, but it also filters out low-frequency information from bridge monitoring, resulting in the loss of useful monitoring information. Circle fitting processes the monitoring signal in the complex plane. The monitoring signal is often distributed in a circular arc-like pattern on the complex plane. Ideally, the center of the circular arc-like monitoring signal point is at the origin of the coordinate axis after circle fitting. However, the circular arc-like signal points affected by static clutter will experience a center offset after circle fitting. Therefore, static clutter can be processed by obtaining the center parameters and correcting this offset. The circle fitting method directly utilizes the spatial distribution characteristics of the monitoring signal in the complex plane to process static clutter, avoiding the loss of time-frequency domain information and making it suitable for static clutter processing in long-term monitoring by ground-based radar. However, long-term monitoring of urban bridges by ground-based radar easily leads to uneven distribution of signal points in the complex plane. Furthermore, as the monitoring time increases, the probability of hardware failures and abnormal environmental excitations increases, resulting in an increase in the number of outlier signal points in the complex plane, affecting the accuracy of circle center parameter estimation. These factors render traditional static clutter suppression methods based on short-term calibration ineffective, necessitating the development of dynamic filtering algorithms adapted to the characteristics of long-term data.

[0005] In summary, the circle fitting method faces two challenges in real-time removal of static clutter from the dynamic deflection signals of urban bridges monitored by ground-based radar over long time periods: 1) Long-term monitoring by ground-based radar increases the number of outliers in the complex plane, resulting in insufficient parameter estimation accuracy of traditional circle fitting methods; 2) The uneven distribution of long-term monitoring data from ground-based radar in the complex plane makes it difficult for traditional circle fitting methods to guarantee fitting accuracy. Therefore, a static clutter removal method for long-term monitoring of urban bridges using ground-based radar is needed. Summary of the Invention

[0006] The purpose of this invention is to provide a method for removing static clutter in long-term monitoring of urban bridges using ground-based radar, so as to solve the problems existing in the prior art.

[0007] To achieve the above objectives, the present invention is implemented according to the following technical solution:

[0008] On one hand, the present invention includes the following steps:

[0009] 1) Acquire complex signals from long-term monitoring of urban bridges using ground-based radar;

[0010] 2) The sliding window dynamic neighborhood parameter constraint local outlier factor method is used to dynamically identify outliers in the complex signal, resulting in non-uniformly distributed quasi-circular arc high-density cluster complex plane points;

[0011] 3) Robust estimation of the non-uniformly distributed center parameters is performed on the complex plane points of the high-density cluster of circular arcs to obtain the optimal center and radius parameters;

[0012] 4) Based on the optimal center parameters, remove static clutter from the complex signal and convert the output into time-series radial displacement data.

[0013] Furthermore, the method of using a sliding window dynamic neighborhood parameter constraint to identify local outliers in the complex signal includes the following sub-steps:

[0014] S201) Construct a sliding window, wherein the time window length of the sliding window satisfies the requirement of covering at least one complete natural vibration period of a city bridge, and adopts a sliding strategy with a 50% overlap rate;

[0015] S202) Calculate the LOF value of the dynamic neighborhood parameter constraint, determine the dynamic neighborhood quantity parameter k based on the local density distribution of the signal points in the sliding window, and calculate the LOF value of each signal point based on the dynamic neighborhood quantity parameter.

[0016] S203) Adaptive threshold for outlier identification: Based on the distribution characteristics of the LOF values ​​of the monitoring points within the current sliding window, an adaptive threshold is determined. Signal points with LOF values ​​greater than the adaptive threshold are identified as outliers and removed, while high-density clusters of complex plane points resembling circular arcs are retained.

[0017] Furthermore, robust estimation of the non-uniformly distributed center parameters of the complex plane points of the quasi-circular arc high-density cluster includes the following sub-steps:

[0018] S301) Obtain the initial center and radius parameters of non-uniformly distributed circular arc data;

[0019] S302) Calculate the residual between the complex plane coordinates of each monitoring point and the initial circle center and radius parameters;

[0020] S303) Optimizes the allocation of weights for each monitoring point based on the exponential decay forgetting factor;

[0021] S304) The center and radius parameters of the circle are updated iteratively using the weighted least squares method;

[0022] S305) Set a threshold and determine whether the center and radius parameters converge. If they converge, output the optimal center and radius parameters. If they do not converge, repeat steps S302-S304.

[0023] Furthermore, in step S202, the formula for calculating the dynamic k value is as follows:

[0024]

[0025] Where W is the time window length in formula (1), ρ local ρ is the average local density of all monitoring points in the current window. global This represents the average local density of all monitoring points up to the current time.

[0026] Further, in step S202, the complex form expression of the ground-based radar monitoring signal is:

[0027]

[0028] Where S(t) is the long-time monitoring signal of the ground-based radar, and A(t) is the signal amplitude. It is the signal phase, Ψ I and Ψ Q It is a static clutter present in the real and imaginary parts of a complex signal. In the complex plane, the ground-based radar monitoring signal exhibits a quasi-circular discrete point distribution; let each signal point be p. n Let n = 1, 2, ..., N, where N is the number of sampling points within each window, then the signal point p n The formula for calculating the LOF value is as follows:

[0029]

[0030] Among them, LOF k (p n ) represents point p n The local outlier value, where k is the value of point p. n The number of neighboring points is a parameter obtained by determining the value of k for point p. n Domain scope, N k (p n () represents the set of signal points within the neighborhood, LRD k (p n Let p be a point. n Based on N in the neighborhood k (p n Local density obtained from the set, LRD k (o) is point p n The local density of the farthest point o within the neighborhood, |N k (p n )| is N k (p n The number of points in the set.

[0031] Furthermore, the adaptive LOF threshold determination criteria are as follows:

[0032] LOF_Thre = LOF Q3+1.5·(LOF Q3 -LOF Q1 (5)

[0033] Among them, LOF Q1 LOF represents the 25th percentile of the LOF value for the monitoring points within the current time window. Q3 This represents the 75th quantile of the LOF value. When the LOF value of a monitoring point is greater than the threshold, it indicates that the density of that point is lower than that of its neighboring points, and it may be an outlier. When the LOF value of a monitoring point is less than the threshold, it indicates that the density of that point is similar to that of its neighboring points, and it can be judged as a normal point.

[0034] Furthermore, in step S301, the weights of all monitoring signal points in the complex plane are optimized and allocated as follows:

[0035]

[0036] in, This represents the weight of the nth monitoring point; φ(·) is the robust kernel function, which can be achieved using the Huber function. Calculate the residual between the complex plane coordinates of the nth monitoring point and the initial center and radius parameters, where λ∈(0,1] is the forgetting factor. Represents the number of decay forgetting factors, where w c Indicates the current time window number, w n The time window number of the nth monitoring point.

[0037] The beneficial effects of this invention are:

[0038] This invention provides a method for removing static clutter during long-term monitoring of urban bridges using ground-based radar. Compared with existing technologies, this invention offers the following technical advantages:

[0039] This invention employs a sliding window dynamic neighborhood parameter constrained local outlier factor (DN-LOF) method, combining dynamic neighborhood parameters with an adaptive threshold criterion, to accurately identify and remove outliers in the complex plane of long-term monitoring by ground-based radar. This solves the problem of misjudgment and omission of outliers caused by fixed parameters and thresholds in traditional LOF algorithms, effectively preserving useful signals from high-density clusters of quasi-circular arcs, providing a high-quality data foundation for subsequent circle fitting, and improving the accuracy of static clutter removal.

[0040] This invention employs the exponentially decaying forgetting factor iterative reweighted least squares (F-IRLS) method. By introducing an exponentially decaying forgetting factor to optimize the weight allocation of monitoring points, it strengthens the influence of the current signal and weakens the interference of historical data. Combined with the robust iterative advantage of iterative reweighted least squares, it achieves accurate estimation of the center parameters of non-uniformly distributed circular arc signals. This overcomes the shortcomings of traditional circle fitting methods in parameter estimation accuracy in long-term non-uniform data and further improves the accuracy of static clutter removal. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the adjustment system framework for a ground-based radar method for removing static clutter during long-term monitoring of urban bridges according to the present invention. Detailed Implementation

[0042] The present invention will be further described below through specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0043] like Figure 1 As shown, a method for removing static clutter in long-term monitoring of urban bridges using ground-based radar includes the following steps:

[0044] The dynamic neighborhood parameter constrained local outlier factor (DN-LOF) and exponential decay forgetting factor iterative reweighted least squares (F-IRLS) constrained circle fitting method for static clutter removal proposed in this invention includes the following key steps: including the following two core steps: (1) accurate identification of dynamic outliers by sliding window DN-LOF; (2) robust estimation of the center parameter of the non-uniform distribution of the complex plane signal by F-IRLS.

[0045] (1) Accurate identification of dynamic outliers using sliding window DN-LOF

[0046] The DN-LOF algorithm, by combining density and neighborhood information, can more accurately identify and remove outliers. Compared to the traditional LOF algorithm, DN-LOF considers the local density distribution of data points when calculating the outlier factor, and can better adapt to non-uniformly distributed circular arc-shaped data points. This allows for more accurate removal of noise points and retention of valid data in long-term monitoring by ground-based radar, thereby improving the accuracy of subsequent circle fitting.

[0047] Compared to isolated outliers dominated by transient interference in short-term monitoring, outliers in the complex plane monitoring signals caused by long-term anomaly excitation of ground-based radar have higher dispersion, more random distribution, and greater number. By quantifying the density deviation between the target point and its neighboring points, i.e., the LOF value, it is possible to accurately distinguish between useful signals in circular arc-like high-density clusters and random discrete low-density outliers. At the same time, to ensure real-time processing of static clutter in long-term monitoring of ground-based radar, it is also necessary to consider the balance between the accuracy of outlier identification and the real-time processing efficiency, given that the number and spatial distribution of outliers change in real time. Therefore, a sliding window DN-LOF dynamic outlier real-time identification method is proposed, which mainly includes the following key steps:

[0048] ① Construction of a sliding window for real-time identification of dynamic outliers: Designing a suitable time window and sliding strategy is an effective way to ensure real-time processing of dynamically changing outliers in long-term monitoring by ground-based radar. However, if the time window is too small, the monitoring data density will be insufficient, leading to inaccurate identification of LOF outliers; if the time window is too large, the data processing efficiency within the window will decrease, making it difficult to guarantee the efficiency of long-term dynamic outlier identification. Therefore, to simultaneously ensure the accuracy and efficiency of dynamic outlier identification, the time window length is designed to cover at least one complete natural vibration period of a city bridge, i.e.:

[0049]

[0050] Among them, W min f is the minimum length of the time window. s f is the sampling frequency of the ground-based radar. min This is the lowest frequency of the bridge's dominant vibration frequency.

[0051] Meanwhile, to reduce the impact of the time window edge effect, a sliding window architecture with a 50% overlap rate is designed, and the repeated calculation of LOF values ​​within the overlapping area data is compressed. This solves the problem of LOF value calculation deviation caused by the time window edge effect, while ensuring the real-time performance of ground-based radar for long-term dynamic outlier identification.

[0052] ② LOF Calculation Constrained by Dynamic Domain Quantity Parameters: In long-term monitoring by ground-based radar, by quantifying the density deviation between a target point and its neighboring points, i.e., the LOF value, accurate differentiation can be achieved between useful signals from circular arc-shaped high-density clusters and random discrete low-density outliers. The complex form expression of the ground-based radar monitoring signal is defined as follows:

[0053]

[0054] Where S(t) is the long-time monitoring signal of the ground-based radar, and A(t) is the signal amplitude. It is the signal phase, Ψ I and Ψ Q It is a static clutter present in the real and imaginary parts of a complex signal. In the complex plane, the ground-based radar monitoring signal exhibits a quasi-circular discrete point distribution; let each signal point be p. n Let n = 1, 2, ..., N, where N is the number of sampling points within each window, then the signal point p n The formula for calculating the LOF value is as follows:

[0055]

[0056] Among them, LOF k (p n ) represents point p n The local outlier value, where k is the value of point p. nThe number of neighboring points is a parameter obtained by determining the value of k for point p. n Domain scope, N k (p n () represents the set of signal points within the neighborhood, LRD k (p n Let p be a point. n Based on N in the neighborhood k (p n Local density obtained from the set, LRD k (o) is point p n The local density of the farthest point o within the neighborhood, |N k (p n )| is N k (p n The number of points in the set.

[0057] As can be seen from the formula for calculating the LOF value of a signal point, the k-value is a crucial fundamental parameter affecting the accuracy of LOF value calculation. Traditional LOF outlier identification often uses empirically fixed k-values. However, in the long-term monitoring process of ground-based radar, the number and spatial distribution of outliers on the complex plane of the monitoring signal change in real time. Fixed k-values ​​are insufficient to cope with the dynamic changes in the local density of the monitoring signal, leading to misidentification or missed detection of outliers. Therefore, this study proposes a dynamic k-value to accurately obtain the LOF value of monitoring points and improve the accuracy of identifying dynamically changing outliers. The formula for calculating the dynamic k-value is as follows:

[0058]

[0059] Where W is the time window length in formula (1), ρ local ρ is the average local density of all monitoring points in the current window. global This represents the average local density of all monitoring points up to the current time.

[0060] ③ Adaptive LOF Threshold Outlier Judgment: In long-term monitoring by ground-based radar, a fixed LOF threshold (e.g., LOF>1) is difficult to adapt to the real-time changes in the number and spatial distribution of outliers on the complex plane. An adaptive LOF threshold, however, can dynamically track the distribution characteristics of the LOF values ​​of monitoring points in different windows, automatically adjusting the outlier judgment boundary to achieve real-time and accurate differentiation between useful signals from high-density clusters resembling circular arcs and random discrete low-density outliers. The adaptive LOF threshold judgment criteria are established as follows:

[0061] LOF_Thre = LOF Q3 +1.5·(LOF Q3 -LOF Q1 (5)

[0062] Among them, LOF Q1LOF represents the 25th percentile of the LOF value for the monitoring points within the current time window. Q3 This represents the 75th quantile of the LOF value. When the LOF value of a monitoring point is greater than the threshold, it indicates that the density of that point is lower than that of its neighboring points, and it may be an outlier. When the LOF value of a monitoring point is less than the threshold, it indicates that the density of that point is similar to that of its neighboring points, and it can be judged as a normal point.

[0063] (2) Robust estimation of the center parameter of non-uniformly distributed complex plane signal in F-IRLS

[0064] The F-IRLS algorithm significantly reduces computational complexity by introducing a fast iterative reweighted least squares method, enabling real-time data processing in long-term monitoring. Compared to the traditional IRLS algorithm, F-IRLS reduces computational load and improves processing speed by optimizing the weight update strategy in each iteration. This allows the method to adapt to the high-frequency, large-data-volume monitoring needs of ground-based radar and achieve real-time processing. After outlier identification by the sliding window dynamic neighborhood parameter constraint, the remaining monitoring points mostly exhibit non-uniform circular arc distribution characteristics, making it difficult to accurately estimate the circle fitting parameters (center and radius), thus reducing the accuracy of static clutter processing in the complex plane of ground-based radar urban bridge dynamic deflection monitoring signals. Therefore, this project proposes to introduce an exponentially decaying forgetting factor to achieve optimal weight allocation of long-term complex plane signal points, reduce the impact of non-uniformly distributed signal points on the accuracy of center parameter estimation, and, based on the robust weighting and iterative optimization advantages of the iterative reweighted least squares method, achieve accurate estimation of the center parameters of the fitted circle for non-uniformly distributed circular arc monitoring signals. The main key steps include the following:

[0065] ① Optimization of Exponentially Decaying Forgetting Factor Weights: An exponentially decaying forgetting factor is introduced to weaken the influence of historical monitoring points and strengthen the role of the current monitoring point. When iterating the initial parameters at the current monitoring moment, the weights of all monitoring signal points in the complex plane are optimized as follows:

[0066]

[0067] in, This represents the weight of the nth monitoring point; φ(·) is the robust kernel function, which can be achieved using the Huber function. Calculate the residual between the complex plane coordinates of the nth monitoring point and the initial center and radius parameters, where λ∈(0,1] is the forgetting factor. Represents the number of decay forgetting factors, where w c Indicates the current time window number, w n The time window number of the nth monitoring point.

[0068] ②F-IRLS circle center parameter estimation: Based on the weight optimization allocation results of all monitoring signal points in the complex plane, an iterative reweighted least squares method is constructed to accurately estimate the circle center parameters of the non-uniform monitoring signal in the complex plane, which resembles a circular arc. The specific steps are as follows:

[0069] Step 1: Calculate the initial center and radius parameters. In the first iteration of the first window, first obtain the initial center and radius parameters θ of the current non-uniformly distributed circular arc data based on the least squares method. (0) =(a (0) ,b (0) ,R (0) );

[0070] Step 2: Calculate the residuals between the complex plane coordinates of the nth monitoring point and the center and radius parameters.

[0071] Step 3: Implement the weight optimization allocation of complex plane monitoring signal points for the exponential decay forgetting factor in formula (6);

[0072] Step 4: Based on the weight allocation results of the complex plane monitoring signal points in Step 3, update the center and radius parameters θ using the weighted least squares method. (1) =(a (1) ,b (1) ,R (1) );

[0073] Step 5: Set a threshold and determine whether the estimation of the center and radius parameters converges. If they do not converge, repeat steps 2-4. If they converge, output the optimal center and radius parameters to achieve accurate circle fitting of non-uniformly distributed circular arc signals, identify and eliminate static clutter in the monitoring data at the current moment, and use the optimal center and radius parameters as the initial parameters for the next time window. Iterate again to achieve real-time processing of static clutter in long-term monitoring of ground-based radar, obtain the monitoring complex signal with static clutter removed, and convert it into time-series radial displacement S′(t).

[0074] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for removing static clutter in long-term monitoring of urban bridges using ground-based radar, characterized in that, Includes the following steps: 1) Acquire complex signals from long-term time-series monitoring of urban bridges using ground-based radar; 2) The sliding window dynamic neighborhood parameter constraint local outlier factor method is used to dynamically identify outliers in the complex signal, resulting in non-uniformly distributed quasi-circular arc high-density cluster complex plane points; 3) Robust estimation of the non-uniformly distributed center parameters is performed on the complex plane points of the high-density cluster of circular arcs to obtain the optimal center and radius parameters; 4) Based on the optimal center parameters, remove static clutter from the complex signal and convert the output into time-series radial displacement data; The method of using a sliding window dynamic neighborhood parameter constraint to identify local outliers in the complex signal includes the following sub-steps: S201) Construct a sliding window, wherein the time window length of the sliding window satisfies the requirement of covering at least one complete natural vibration period of a city bridge, and adopts a sliding strategy with a 50% overlap rate; S202) Calculate the LOF value of the dynamic neighborhood parameter constraint, determine the dynamic neighborhood quantity parameter k based on the local density distribution of signal points within the sliding window, and calculate the LOF value of each signal point based on the dynamic neighborhood quantity parameter. S203) Adaptive threshold for outlier detection: Based on the distribution characteristics of the LOF values ​​of the monitoring points within the current sliding window, an adaptive threshold is determined. Signal points with LOF values ​​greater than the adaptive threshold are identified as outliers and removed, while high-density clusters of complex plane points resembling circular arcs are retained. Robust estimation of the non-uniformly distributed center parameters of the complex plane points of the high-density cluster of circular arcs includes the following sub-steps: S301) Obtain the initial center and radius parameters of non-uniformly distributed circular arc data; S302) Calculate the residual between the complex plane coordinates of each monitoring point and the initial circle center and radius parameters; S303) Based on the exponential decay forgetting factor and optimized allocation of weights for each monitoring point; S304) The center and radius parameters of the circle are updated iteratively using the weighted least squares method; S305) Set a threshold and determine whether the center and radius parameters converge. If they converge, output the optimal center and radius parameters. If they do not converge, repeat steps S302-S304. In step S202, dynamic The formula for calculating the value is as follows: in, The time window length in formula (1) is... This represents the average local density of all monitoring points within the current window. This represents the average local density of all monitoring points up to the current time. In step S303, the weights of all monitoring signal points in the complex plane are optimized and allocated as follows: in, It is the first The weight of each monitoring point; For a robust kernel function, use the Huber function. For the first The residuals were calculated using the complex plane coordinates of each monitoring point and the initial center and radius parameters. Forgetting factor, Represents the exponentially decaying forgetting factor, where, Indicates the current time window number. No. The time window number of each monitoring point.

2. The method for removing static clutter in long-term monitoring of urban bridges using ground-based radar according to claim 1, characterized in that, In step S202, the complex form expression of the ground-based radar monitoring signal is: in, It is a long-term monitoring signal from ground-based radar. It is the signal amplitude. It is the signal phase. and It is a static clutter existing in the real and imaginary parts of a complex signal; in the complex plane, the ground-based radar monitoring signal exhibits a quasi-circular arc discrete point distribution, let each signal point be... , , The number of sampling points within each window, then the signal points The formula for calculating the LOF value is as follows: in, Point The local outlier value, Value is a point The parameter for the number of neighboring points is based on Value acquisition point Scope of the field The set of signal points within this neighborhood. For point Based on the neighborhood range Local density obtained from the set For point farthest point within the neighborhood Local density, for The number of points in the set.

3. The method for removing static clutter in long-term monitoring of urban bridges using ground-based radar according to claim 1, characterized in that, The adaptive LOF threshold determination criteria are as follows: in, This represents the 25th quantile of the LOF value for the monitoring point within the current time window. This represents the 75th quantile of the LOF value. When the LOF value of a monitoring point is greater than the threshold, it indicates that the density of the point is lower than that of its neighboring points, and it may be an outlier. When the LOF value of a monitoring point is less than the threshold, it indicates that the density of the point is similar to that of its neighboring points, and it can be judged as a normal point.

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