A method for monitoring spatial non-continuous deformation based on InSAR technology

Abstract

The application relates to a space non-continuous deformation monitoring method based on a time-series InSAR technology, and specifically comprises the following steps: firstly, an arc network is constructed based on selected coherent points, and an arc segment solving model without a deformation mode constraint is used to perform time-series solving on all arc segments in the network; then, based on a phase jump mechanism at a non-continuous deformation position, an arc segment mean square error threshold method is used to detect the displacement discontinuous position and divide the coherent network into multiple independent subnetworks; based on the mechanical deformation characteristics of the structure, a center point in each subnetwork is selected as a reference point, and then multi-reference-point and adaptive unwrapping of all subnetworks are completed, and finally, relatively reliable deformation monitoring results are obtained. The method provided by the application can automatically detect the displacement discontinuous position and perform adaptive segmented unwrapping, can overcome the inapplicability of existing time-series InSAR algorithms in space non-continuous deformation monitoring, and improves the reliability of the deformation monitoring results.

Description

Technical Field

[0001] This invention relates to the field of time-series data processing in interferometric synthetic aperture radar (InSAR) technology, and in particular to a method for monitoring the deformation of spatial discontinuous structures such as bridges based on time-series InSAR technology. Background Technology

[0002] Multi-temporal interferometric synthetic aperture radar (MTInSAR) technology, with its advantages of all-weather, all-time capability, high spatial resolution, and high accuracy, has been widely used in bridge structural health monitoring in recent years. In contrast, traditional deformation monitoring methods currently in use have several limitations. For example: ① GNSS, leveling, and sensor monitoring methods are all single-point monitoring with low spatial resolution, making it difficult to effectively assess the overall health of the bridge structure; ② GPS receivers and various sensors are not only expensive but also have short lifespans due to long-term operation in harsh environments; ③ Accelerometers are effective for high-frequency dynamic measurements of bridges but are ineffective for slow deformations caused by factors such as temperature changes; ④ Total stations, levels, and laser interferometers are easily limited by line-of-sight and weather conditions, and their sampling rates are difficult to meet the requirements of dynamic measurements, often requiring road closures during the measurement process, resulting in high costs.

[0003] While MTI-InSAR technology offers numerous advantages in bridge monitoring, the complexity and unique characteristics of bridge structures also present significant challenges. Expansion joints, also known as temperature joints, are a key structural element of bridges, typically installed between the ends of two beams. Their primary purpose is to prevent damage to the bridge structure caused by temperature stresses resulting from thermal expansion and contraction, as well as vehicle loads. When the bridge structure is affected by thermal expansion and contraction, the movement directions of the box girders on both sides of the expansion joint are always opposite; for example, they move towards each other when expanding and in opposite directions when contracting. This causes a phase jump in the interference at the expansion joint.

[0004] Research has found that when the length of the box girder or the temperature difference exceeds a certain threshold, the phase jump value on both sides of the expansion joint will be greater than πradian. The prerequisite for correct phase unwrapping is that the absolute value of the interference phase difference between neighboring pixels is not greater than πradian. Therefore, this phase jump will invalidate the prerequisite for phase unwrapping, ultimately leading to errors in phase unwrapping. Phase unwrapping is an unavoidable and crucial step in MTISAR data processing; correctly achieving phase unwrapping is essential for ensuring the reliability of deformation results. The presence of expansion joints in bridge structures renders existing mature MTISAR techniques inapplicable. Therefore, a new MTISAR bridge monitoring scheme is needed to perform spatial discontinuous deformation calculation based on the phase jump on both sides of the expansion joint. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a spatial discontinuous deformation monitoring method based on time-series InSAR technology.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A method for monitoring spatial discontinuous deformation based on time-series InSAR technology, the method comprising the following steps:

[0008] Acquire SAR image data, preprocess the image data, and select coherent points;

[0009] An arc network is constructed based on the selected coherent points, and a temporal solution model without deformation mode constraints is used to perform time-series solution on all arcs in the network.

[0010] Based on the phase jump mechanism at discontinuous deformation, the arc segment mean square error threshold method is used to detect the displacement discontinuity and the coherent point arc segment network is divided into multiple independent subnets.

[0011] Based on the mechanical deformation characteristics of the structure, reference points are selected in each subnet, and then the adaptive unwrapping of multiple reference points in all subnets is completed, finally obtaining the deformation monitoring results.

[0012] Furthermore, the data preprocessing includes image registration, geocoding, temporal interferogram generation, and permanent scatterer selection, with the selected permanent scatterer points serving as coherence points.

[0013] Furthermore, the amplitude deviation index method is used when selecting the permanent scattering point, and the amplitude deviation value D A Defined as:

[0014]

[0015] In the formula, σ A With μ AThese are the standard deviation and mean of the amplitude time series of a certain pixel, respectively;

[0016] For each pixel in the image, the amplitude deviation index is calculated based on the pixel amplitude time series. If the amplitude deviation index value is less than the given amplitude deviation index threshold, the pixel is considered to be a permanent scattering point, i.e., a coherent point.

[0017] Furthermore, the arc segment network uses KNN nearest neighbor search to select coherent points and uses Deloni triangulation to establish the initial arc segment network.

[0018] Furthermore, the specific steps for calculating the arc segment timing are as follows:

[0019] For each adjacent time period, the network is solved for each arc segment, and N+1 images covering the study area are arranged in chronological order (t0, t1, ..., t). N From the SAR image, M differential interferograms are generated. For the arc segment i formed by points x and y, the observation equation is expressed as follows:

[0020]

[0021] In the formula, For observations of the arc segment; elevation difference error Δh i and the relative displacement Δd between each adjacent time period i The quantity to be estimated is λ; λ is the radar wavelength. The variables related to the vertical baseline are represented in matrix form:

[0022]

[0023] In the formula, y represents the observed value of the arc segment, and A is the coefficient matrix. The parameter to be estimated;

[0024] Based on the least squares principle, we get:

[0025]

[0026] In the formula, P is the weight matrix of the observations, and the mean square error of the arc segment is:

[0027]

[0028] In the formula, v is the correction for the observed value.

[0029] Based on the above steps, all arc segments in the network are solved.

[0030] Furthermore, the specific steps for the independent subnet segmentation are as follows:

[0031] Based on the phase jump mechanism at discontinuous deformation, the arc segment mean square error threshold method is used to detect the displacement discontinuity. By setting the arc segment mean square error threshold, arc segments crossing the expansion joint are eliminated, and the originally connected arc segment network is divided into multiple independent sub-networks.

[0032] Furthermore, the specific steps for untangling the reference points of the subnet include:

[0033] For each subnetwork, the coherent point at its center is set as the reference point, and the unwrapping model is as follows:

[0034]

[0035]

[0036] In the formula, m is the number of arc segments; n is the number of coherent points; and s is the number of reference points. Let be the relative displacement value of the endpoints of the arc segment during the j-th time period. For the quantity to be estimated, let V be the displacement value of the coherent point in the j-th time period, V be the residual matrix, W be the deformation value of the reference point, and B and C be the design matrices.

[0037] The parametric solution obtained using the least squares method with additional constraints is as follows:

[0038]

[0039] In the formula, N bb =B T PB, Z = B T PL, P is the observation weight matrix;

[0040] After the reference point of the subnet is unwrapped, the displacement value of the reference point in each adjacent time period is obtained; the initial displacement is recorded as 0, and the displacement values ​​of the coherent points are accumulated in time order to recover the displacement time sequence relative to the starting time.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] 1) This invention is based on the phase jump mechanism at discontinuous deformation sites. It employs the arc segment mean square error threshold method to detect displacement discontinuities and divides the coherent point arc segment network into multiple independent subnets. Based on the mechanical deformation characteristics of the structure, reference points are selected within each subnet, thereby completing the adaptive unwrapping of multiple reference points across all subnets. This invention fills the gap in the field of space discontinuous deformation monitoring based on MTISAR technology, greatly improving the applicability and reliability of this technology.

[0043] 2) The phase unwrapping scheme and unwrapping model proposed in this invention result in a clear and continuous unwrapped phase trend for each subnet, with no abnormal phase jumps at the expansion joints. Compared to traditional unwrapping methods, the unwrapping results show a higher degree of agreement with the actual situation.

[0044] 3) This invention overcomes the difficulties and low reliability of bridge deformation monitoring based on MTI InSAR technology. Compared with traditional monitoring methods, it has advantages such as all-day, all-weather, high precision, low cost, and high spatial and temporal resolution. Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating the selection of interferograms and the construction of the spatial network of coherent points in this invention.

[0046] Figure 2 The diagram shows the expansion joints of the Shanghai Yangtze River Bridge; (a) shows the location of the expansion joints and their corresponding numbers; (b) shows actual photos of expansion joints #16, #10, #8 and #5.

[0047] Figure 3 This is a schematic diagram of the arc segment spanning the expansion joint and its mean square error. The ellipse in the diagram indicates the location of the expansion joint.

[0048] Figure 4 The figures are comparison diagrams of the unwrapping results; (a), (c), (e), and (g) are the unwrapping results of ASU (the present invention); (b), (d), (f), and (h) are the unwrapping results of MCF. Detailed Implementation

[0049] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0050] Example 1

[0051] This invention provides a method for calculating spatial discontinuous deformation based on InSAR technology. This method can automatically detect displacement discontinuities and perform adaptive segmented unwrapping. Specifically, it includes the following steps: First, an arc segment network is constructed based on selected coherent points, and a time-series calculation of all arc segments in the network is performed using an arc segment calculation model without deformation mode constraints. Then, based on the phase jump mechanism at discontinuous deformation locations, the arc segment mean square error threshold method is used to detect displacement discontinuities and divide the coherent network into multiple independent subnets. Based on the mechanical deformation characteristics of the structure, a center point is selected as a reference point within each subnet, thereby completing multi-reference point, adaptive unwrapping of all subnets, ultimately obtaining relatively reliable deformation monitoring results. Using this invention, the inapplicability of existing time-series InSAR algorithms in monitoring spatial discontinuous deformation can be overcome, improving the reliability of deformation monitoring results.

[0052] The technical process of the entire solution is as follows: Figure 1 As shown, the process can be mainly divided into three steps: data preprocessing, arc segment time series calculation, and adaptive segmented unwrapping, as described in detail below:

[0053] 1.1 Data Preprocessing

[0054] Data preprocessing mainly includes image registration, geocoding, temporal interferogram generation, and permanent scatterer (PS) selection. The amplitude deviation index method is used when selecting PS points, and the amplitude deviation value is defined as...

[0055]

[0056] In the formula, σ A With μ A These are the standard deviation and mean of the amplitude time series of a certain pixel, respectively. For each pixel in the image, an amplitude deviation index can be calculated based on its amplitude time series. If the value is less than a given amplitude deviation index threshold (e.g., 0.25), the point is considered a PS point.

[0057] 1.2 Arc Segment Timing Solution

[0058] After selecting the PS point, an initial network for the PS point is established using KNN nearest neighbor search and Deloni triangulation. Then, in each adjacent time period, the network is solved for each arc segment. There are N+1 images covering the study area, arranged in chronological order (t0, t1, ..., t...). N From the SAR imagery, a total of M differential interferograms are generated. For the arc segment i formed by points x and y, the following observation equation can be obtained:

[0059]

[0060] The left side of the equation represents the observed values ​​of the arc segment, and the right side represents the elevation difference error Δh.i and the relative displacement Δd between each adjacent time period i The quantity to be estimated is λ, where λ is the radar wavelength. This represents variables related to the vertical baseline. It can be written in matrix form as follows:

[0061]

[0062] In the formula, y represents the observed value of the arc segment, and A is the coefficient matrix. The parameter to be estimated;

[0063] Based on the least squares principle, we can solve for...

[0064]

[0065] In the formula, P is the weight matrix of the observations, and the mean square error of the arc segment is:

[0066]

[0067] In the formula, v is the correction for the observed value.

[0068] Based on formulas (2) to (5), the solution is completed for all arc segments in the network.

[0069] 1.3 Adaptive Segmented Untangling

[0070] Due to the phase entanglement characteristic, when the phase jump at the expansion joint is greater than π, the phase difference between the two endpoints of the arc segment cannot be accurately obtained. In short, for arc segments crossing expansion joints, the gross errors in the observed values ​​are large. After calculating the arc segment based on the principle in Section 2.2, the corresponding mean square error will be abnormally large. Therefore, arc segments crossing expansion joints can be removed by setting a mean square error threshold. At this point, the originally connected arc segment network will be divided into multiple independent sub-networks, and then a reference point is set in each sub-network to complete the displacement calculation.

[0071] During phase unwrapping, a point with the most stable spatial position is generally chosen as the reference point. Based on the linear expansion characteristics of materials, the displacement caused by thermal expansion of a linear structure is proportional to its length; that is, the displacement is greatest at both ends of the box girder (corresponding to expansion joints) and smallest in the middle. Therefore, for each sub-network, the PS point located at its center is set as the reference point, and the unwrapping model is as follows:

[0072]

[0073] In the formula, m is the number of arc segments, n is the number of PS points, and s is the number of reference points; Let be the relative displacement value of the endpoints of the arc segment during the j-th time period. For the quantity to be estimated, represents the displacement value of point PS in the j-th time period, V is the residual matrix, W is the deformation value of the reference point, which is set to 0 here; B and C are both design matrices.

[0074] The parametric solution can be obtained using the least squares method with additional constraints:

[0075]

[0076] In the formula, N bb =B T PB, Z = B T PL, P is the observation weight matrix.

[0077] Based on model (7), after unwrapping in all adjacent time periods, the displacement value of PS point in each adjacent time period is obtained. Assuming the initial displacement is 0, the displacement value can be accumulated in time order to recover the displacement time sequence relative to the starting time.

[0078] 2. Experimental verification

[0079] The experimental subject in this embodiment is the Shanghai Yangtze River Bridge, located at the mouth of the Yangtze River in China. This bridge is the world's longest combined road and rail bridge. The Shanghai Yangtze River Bridge spans the river and consists of 17 independent box girder structures. The longest box girder is 1430m, the shortest is 280m, and the average length is approximately 480.5m. The box girders are connected by expansion joints; there are a total of 18 expansion joints (corresponding to #1, #2…#18). Figure 2 As shown. The data used consists of 23 descending TerraSAR-X images, spanning from October 3, 2011 to July 26, 2012.

[0080] After estimating the arc segments using the spatial discontinuous deformation temporal InSAR technique described above, the estimation accuracy for each arc segment can be obtained, such as... Figure 3 The figure shows the calculated mean square error for the arc segment near each expansion joint. Figure 3 It is known that the mean square error of the arc segment across the expansion joint is relatively large, generally greater than 1.2 rad. After removing the arc segments with a mean square error greater than a certain threshold (e.g., 0.5 rad), the coherent network will be divided into multiple subnets, each subnet corresponding to a box girder structure.

[0081] The method proposed in this invention is used to untangle each subnet, and some untangling results are as follows: Figure 4 As shown. Meanwhile, to compare the advantages of this invention, the untangling results obtained using the classic minimum cost flow (MCF) method are compared, for example... Figure 4 As shown.

[0082] Figure 4This indicates that the results obtained using the MCF method contain numerous errors, with abnormal phase jumps on both sides of the expansion joint, which clearly do not conform to reality. In contrast, the unwrapping phase trend of each subnet obtained by this invention is obvious and continuous, with no abnormal phase jumps at the expansion joint, and the unwrapping results are in high agreement with the actual situation.

[0083] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for monitoring spatial discontinuous deformation based on time-series InSAR technology, characterized in that, The method steps include: Acquire SAR image data, preprocess the image data, and select coherent points; An arc network is constructed based on the selected coherent points, and a temporal solution model without deformation mode constraints is used to perform time-series solution on all arcs in the network. Based on the phase jump mechanism at discontinuous deformation, the arc segment mean square error threshold method is used to detect the displacement discontinuity and divide the coherent point arc segment network into multiple independent subnets. The specific implementation of the independent subnet division is as follows: Based on the phase jump mechanism at discontinuous deformation, the arc segment mean square error threshold method is used to detect the displacement discontinuity. By setting the arc segment mean square error threshold, the arc segments crossing the expansion joint are eliminated, and the originally connected arc segment network is divided into multiple independent sub-networks. Based on the mechanical deformation characteristics of the structure, reference points are selected within each subnet, and then adaptive unwrapping of multiple reference points in all subnets is completed to finally obtain the deformation monitoring results. The specific implementation of unwrapping the reference points of the subnets is as follows: For each subnetwork, the coherent point at its center is set as the reference point, and the unwrapping model is as follows: In the formula, The number of arc segments; This represents the number of coherent points. Number of reference points; For the first j The relative displacement values ​​of the endpoints of the arc segment during each time period. "To be estimated" indicates the first... j Displacement values ​​of coherent points in each time period The residual matrix is... The deformation value at the reference point. and For designing the matrix; The parametric solution obtained using the least squares method with additional constraints is as follows: In the formula, , , , The observation weight matrix; After the reference point of the subnet is unwrapped, the displacement value of the reference point in each adjacent time period is obtained; the initial displacement is recorded as 0, and the displacement time sequence relative to the starting time can be recovered by accumulating the displacement values ​​of the coherent points in time order.

2. The spatial discontinuous deformation monitoring method based on time-series InSAR technology according to claim 1, characterized in that, The data preprocessing includes image registration, geocoding, temporal interferogram generation, and permanent scatterer selection, with the selected permanent scatterer points serving as coherence points.

3. The spatial discontinuous deformation monitoring method based on time-series InSAR technology according to claim 2, characterized in that, The amplitude deviation index method was used to select the permanent scattering point, and the amplitude deviation value was... Defined as: In the formula, and These are the standard deviation and mean of the amplitude time series of a certain pixel, respectively; For each pixel in the image, the amplitude deviation index is calculated based on the pixel amplitude time series. If the amplitude deviation index value is less than the given amplitude deviation index threshold, the pixel is considered to be a permanent scattering point, i.e., a coherent point.

4. The spatial discontinuous deformation monitoring method based on time-series InSAR technology according to claim 1, characterized in that, The arc segment network uses KNN nearest neighbor search to select coherent points and uses Deloni triangulation to establish the initial arc segment network.

5. A spatial discontinuous deformation monitoring method based on time-series InSAR technology according to claim 1, characterized in that, The specific steps for calculating the arc segment timing are as follows: For each adjacent time period, the network is solved for each arc segment, and N+1 images covering the study area are arranged in chronological order. SAR images are used to generate M differential interferograms for... x,y Arc segment formed by two points The observation equation is expressed as follows: In the formula, For arc segment observations; elevation difference error and the relative displacement of each adjacent time period To be estimated; The radar wavelength; The variables related to the vertical baseline are represented in matrix form: In the formula, For arc segment observations, The coefficient matrix, The parameter to be estimated; Based on the least squares principle, we get: In the formula, Let be the weight matrix of the observations, and the mean square error of the arc segment be: In the formula, For the correction of the observations, ; Based on the above steps, all arc segments in the network are solved.

Images