Non-targeted structure displacement measurement method using data depth

Abstract

The present invention relates to a non-targeted structure displacement measurement method using a data depth, wherein a projection distance, which is a distance from one point to another point, is newly calculated from a three-dimensional point cloud acquired from LiDAR, so as to determine a structure through a difference in centrality or a change in the projection distance, or determine a displacement of the structure through dispersion using a Mahalanobis depth. The non-targeted structure displacement measurement method using a data depth according to the present invention comprises: a first step of calculating a projection depth by using three-dimensional point cloud data obtained from a structure in different time slots; a second step of obtaining a difference in centrality of two different data sets (X, Y) through the projection depth obtained in the first step, wherein a distance between points in one data set (X) and a center in the other data set (Y) is calculated and quantified; and a third step of determining the displacement of the structure on the basis of the change between the two data sets obtained through the second step, wherein the second step includes obtaining the centrality of each of the data sets through an equation, and the third step includes determining the displacement of the structure when a test value is smaller than a threshold value (crit) through the equation.

Description

Non-target structural displacement measurement method using data depth

[0001] The present invention relates to the measurement of structural displacement, and more specifically, to a non-target structural displacement measurement method using a data depth (projection depth, mahalanobis depth) that measures displacement over the entire structure without blind spots by utilizing a data depth obtained from a LiDAR without specifying the structure as a target.

[0002] Civil or architectural structures undergo deformation due to external factors such as aging, dynamic loads, and earthquakes. Furthermore, as the number of aging structures that have exceeded their service life (30 years) is rapidly increasing, Structural Health Monitoring (SHM), which examines the usability of structures over the long term, is becoming increasingly important.

[0003] Methods for monitoring structural safety include a method in which an inspector physically moves close to the structure and performs a visual inspection, and a method utilizing sensors (such as cameras) and programs (artificial intelligence). The former not only lacks accuracy but also poses a risk of safety accidents to the inspector during the inspection process, whereas the latter offers the advantages of being more convenient to operate and capable of making accurate judgments compared to the former.

[0004] Furthermore, structural displacement measurement technologies are classified into target-based and non-target technologies based on the presence or absence of a target. Since target-based displacement measurement technology tracks displacement using targets with known characteristic points, it is difficult to apply to bridges where installing targets is challenging and it cannot detect deformation in areas where targets are not attached, whereas the non-target method has the advantage of eliminating the target installation process.

[0005] Published Patent No. 10-2005-0097593 and Published Patent No. 10-2008-0021300, which utilize LiDAR as a technology for measuring displacement (structural integrity) of structures, use LiDAR information to extract 3D shape information and analyze behavior, but they take a long time and require large facilities due to the use of a vast amount of 3D shape information.

[0006] (Patent Document 1) Published Patent No. 10-2005-0097593

[0007] (Patent Document 2) Published Patent No. 10-2008-0021300

[0008] The present invention aims to solve the aforementioned problems by providing a non-target structural displacement measurement method using data depth, which newly calculates the projection distances of points (reference and comparison points) from a 3D point cloud acquired from LiDAR and determines the displacement of a structure without blind spots through changes in distance.

[0009] In addition, the present invention provides a non-target structural displacement measurement method using data depth that calculates centrality from points (reference and comparison points) from a 3D point cloud acquired from LiDAR at different times and determines the displacement of a structure without blind spots through the difference in centrality.

[0010] The present invention aims to solve the aforementioned problems by providing a non-target structural displacement measurement method using data depth, which calculates how far points (reference and comparison points) are from a 3D point cloud acquired from LiDAR using the Mahalanobis depth method and determines the displacement of a structure without blind spots based on data dispersion.

[0011] The non-target type structural displacement measurement method using data depth according to the present invention is characterized by setting one or more reference points among a plurality of point cloud data obtained from a structure and setting one or more comparison points among the remaining points and performing projection, obtaining a projection distance between the reference point and the comparison point and calculating a projection depth which is one of the data depth methods, and determining the displacement of the structure by comparing two projection depth values ​​calculated with a time difference (previous / postvous time difference) for comparison points at the same location.

[0012] A non-target method for measuring structural displacement using data depth according to the present invention comprises: a first step of acquiring three-dimensional point cloud data from a structure; and a second step of determining the displacement of a structure by checking the difference in centrality using three-dimensional point cloud data acquired at different times through the first step, wherein the second step comprises: a second-1 step of setting a reference point among the three-dimensional point cloud data; a second-2 step of calculating the projection distance between other points excluding the reference point among the three-dimensional point cloud data and the reference point belonging to the relative three-dimensional point cloud data; and calculating the projection depth from the value calculated in the second-2 step, calculating the average of the projection depths to calculate centrality, and then determining the displacement of the structure through the difference in centrality.

[0013] The non-target structural displacement measurement method using data depth according to the present invention determines the deformation of a structure by quantitatively analyzing the change between two data sets measured at different times or conditions through variance calculation, and is characterized by applying the Mahalanobis depth calculation method, which is one of the data depth methods, to compare the displacement between the two data sets.

[0014] According to the non-target structural displacement measurement method using data depth according to the present invention, the projection depth is processed from the values ​​of the LiDAR into the projection distance between a reference point (centrality) and a comparison point, and the displacement of the structure can be determined through changes in projection depth, differences in centrality, and dispersion, so a target is not required, and thus operations such as target installation are eliminated, making operation very easy. In addition, the condition of the structure can be evaluated without blind spots, thereby improving reliability. Furthermore, accurate judgment is possible through a method of calculating the distance between the reference point and the comparison point from the acquired values ​​of the LiDAR and statistically analyzing it, and it is highly effective in that it does not require large equipment or consume high power.

[0015] FIG. 1 is a flowchart of a non-target structural displacement measurement method using data depth according to Example 1 of the present invention.

[0016] FIG. 2 is a flowchart of a non-target structural displacement measurement method using data depth according to Example 2 of the present invention.

[0017] FIG. 3 is an example diagram visualizing the results of data depth in 2D according to the non-target structural displacement measurement method using data depth according to Embodiment 3 of the present invention.

[0018] In the following description of the present invention, specific descriptions of related known functions or configurations will be omitted if it is determined that such descriptions would unnecessarily obscure the essence of the invention. Furthermore, the terms described below are defined in consideration of their functions within the present invention, and these definitions may vary depending on the intentions or practices of the user or operator. Therefore, such definitions should be based on the content throughout this specification.

[0019] The present invention measures (determines) the displacement of a structure using data depth, which is a term of a concept different from the depth measured in LiDAR and is one of the robust statistical methods. While depth in LiDAR refers to the physical distance from the surface of the structure to the LiDAR, the data depth used in the present invention is a statistical concept that measures how close each point is to the center within the data distribution (evaluating the centrality between a reference point and a comparison point), and there are various methods such as projection depth and Mahalanobis depth.

[0020] Example 1 compares two projection depths with a parallax, Example 2 calculates the difference in centrality through projection depth and uses that difference, and Example 3 uses the variance based on Mahalanobis depth.

[0021] In other words, data depth is used as one of three main elements to evaluate deformation and changes in the state of a structure. First, projection distance values ​​are calculated for each point to evaluate how close the points are to the center within the data set (data obtained by 3D scanning the entire structure to be analyzed (such as a bridge) using LiDAR, i.e., all points acquired by LiDAR) (Example 1). Second, a center point representing the overall distribution of the data set is calculated through center point calculation, and then the change in centrality is evaluated (evaluation of centrality difference) (Example 2). Third, the change between two data sets measured at different times or conditions is quantitatively analyzed through variance calculation (Example 3) to determine whether the structure is deformed.

[0022] <Example 1>

[0023] As shown in FIG. 1, the non-target structural displacement measurement method using a data depth technique according to the present embodiment includes the following steps: 1. acquiring three-dimensional point cloud data from a structure, 2. setting a reference point and a comparison point, 3. calculating a projection distance between the reference point and the comparison point, and 4. determining the displacement of the structure by calculating and comparing two projection depths with a parallax. The specific steps are as follows.

[0024] 1. Acquire point cloud data from the structure.

[0025] A LiDAR is installed at a location away from the structure, and three-dimensional point cloud data is acquired from the structure through the LiDAR.

[0026] 3D point cloud data consists of 3D coordinate information that reflects the shape of the target structure, and through a preprocessing process, noise is removed and refined into a form suitable for analysis.

[0027] 2. Setting reference point and comparison point.

[0028] Among the numerous points configured in the 3D point cloud data, a reference point (centrality) is set to determine the displacement of the structure.

[0029] All points have x, y, and z coordinates, and a reference point must be established so that it can be verified even if displacement occurs in the structure; for example, it is desirable to set the point located at the center as the reference point. In other words, since the position of the reference point remains at the center even if its x, y, and z coordinates change due to structural displacement, it is desirable to set the reference point to the center. Of course, the present invention will also verify changes in the reference point's left and right coordinates and utilize this for determining structural displacement.

[0030] Comparison points are set from the remaining points excluding the reference point. It is also possible to set all points excluding the reference point as comparison points without setting a comparison point separately, or to set one or more comparison points by specifying a location that can be distinguished by the displacement of the structure (for example, a location based on the reference point).

[0031] In the case of point clouds, it is impossible or very difficult to set a reference point without using a target; however, the present invention enables displacement determination without using a target by using the center position (center point) as the reference point and setting a comparison point.

[0032] 3. Calculation of projection distance to evaluate the relative position between a reference point and a comparison point.

[0033] After projecting the point to be calculated (comparison point) and the center point (reference point) in various directions (which involves positioning 3D data on a 2D plane and is included in the process of converting to 1D by calculating the distance for this position), the projection distance is calculated. The projection distance value is used to determine the projection depth and represents the distance between the projected comparison point and the reference point (output in scalar form). This calculation process is expressed by the following mathematical formula 1.

[0034] ----------- (Mathematical Formula 1)

[0035] D ij : Projection distance

[0036] X j : Projected comparison points

[0037] C j : Reference point

[0038] Lidar periodically emits laser beams with a time delay to acquire 3D cloud point data with a time delay, that is, it calculates different projection distances at different times from reference points and comparison points at the same location.

[0039] 4. Determine displacement by calculating and comparing two projection depths with a parallax.

[0040] A projection distance, which is the distance from a reference point, is calculated by targeting a comparison point at the same location (coordinates may change), and displacement is determined by comparing the two projection distances calculated in this way. That is, if there is no difference between the preceding value and the succeeding value, it is determined that there is no displacement, whereas if there is a difference between the projection distances before and after, it is determined that there is displacement.

[0041] However, it is desirable to standardize the two projection distances so that the difference can be clearly compared, and the standardized depth (standardized projection distance) is calculated using the following mathematical formula 2. Here, q1 and q2 are quartiles used as criteria to compare distance values ​​more clearly.

[0042] ----------- (Mathematical Formula 2)

[0043] d ij : Standardized depth (standardized projection distance), q1,q3: quartiles

[0044] Since Dij and dij represent the physical distance between points, they are measured in units of length in the coordinate system.

[0045] Next, the projection depth is calculated.

[0046] Projection depth is calculated by projecting data in various directions relative to each point and measuring the distance from the center in those directions. The projection distance of each point indicates how close it is to the center, and the projection depth value is determined based on this distance. Points closer to the center have higher projection depth values, while the value decreases as they move further away.

[0047] Projection depth is based on the largest value among standardized projection distance values ​​(since many projection distance values ​​can be obtained from a single point due to the nature of projection, the largest (farthest) value among them is selected) and is expressed by the following mathematical formula 3. The projection depth value approaches 1 as the distance from the center decreases, and decreases as it moves further away from the center. This means that the closer a point is to the center, the higher the depth value it will have.

[0048] The aforementioned mathematical formulas 1 and 2 are intended to calculate the projection depth through mathematical formula 3.

[0049] ----------(Mathematical Formula 3)

[0050] The displacement is determined by comparing the two projection depth values ​​with the calculated parallax.

[0051] <Example 2>

[0052] This embodiment measures the displacement of a structure using the difference in centrality (see FIG. 2). The difference in centrality involves quantifying the change in the center point (reference point) between two data sets using projection depth.

[0053] Example 1 is a single process for calculating the j-th point of the X data set, and calculation is possible only if the center point is perfectly identical, that is, the movement of the center cannot be verified, whereas the present example has a difference in that the movement of the center point can be verified.

[0054] For example, if the projection depth is calculated using the median of a single data set (X), it is calculated in a scalar form, and the data is arranged in the form of a normal distribution, which can be said to have no change in centrality. However, when calculating using the median of a single data set (Y) and another data set, if it is assumed that the median of the other data set (Y) is skewed to one side, the result will be skewed to one side rather than in the form of a normal distribution, and through this, the displacement of the structure can be determined.

[0055] 1. Calculation of projection depth.

[0056] The evaluation of centrality differences quantifies the change in the center point between two datasets using projection depth. Projection depth is calculated by projecting data in various directions relative to each point and measuring the distance from the center in those directions. The projection distance of each point indicates how close it is to the center, and the projection depth value is determined based on this distance. Points closer to the center have higher projection depth values, while values ​​decrease as they move further away.

[0057] The projection depth is calculated using Equation 3 (calculating the distance by projecting the j-point included in the X data set) described in Example 1.

[0058] ----------(Mathematical Formula 3)

[0059] 2. Quantification of centrality differences.

[0060] To evaluate the difference in centrality between two datasets (3D point cloud data with anterior-posterior disparity), the projection depth is calculated to determine how close the points of each dataset are to the center of the relative dataset. This calculation process compares the points of the two datasets to produce a projection depth value that indicates how close each point is to the center point of the relative dataset.

[0061] In other words, if the X dataset and the X center point, and the Y dataset and the Y center point are compared respectively, they are highly likely to exhibit a normal distribution shape. However, such comparisons are not appropriate due to differences in shooting time, environmental conditions, and data characteristics. To address this, the center point of Y is set (as coordinates) on the X dataset, and the center point of X is set (as coordinates) on the Y dataset, allowing for the evaluation of the centrality difference between the two datasets under the assumption that they represent the same structure. This method enables the comparison of different datasets using the same criteria and allows for the measurement of structural changes by calculating how close each dataset is to the other's center point (Projection Depth).

[0062] Specifically, data set Each point of (for example, the first acquired 3D point cloud data) is a dataset Using the projection depth value calculated for the center point of the (second acquired 3D point cloud data), The points of the set It evaluates how close it is to the center. The value calculated in this process is as, Each of the points It is a value that indicates on average how deeply it is located relative to. It is expressed by mathematical formula 4.

[0063] ------------(Mathematical Formula 4)

[0064] Here, is a dataset It is the number of points, is a dataset The point of data set The center point of This is the projection depth value calculated for.

[0065] Conversely, to evaluate how close the points of dataset Y are to the center point of dataset X, the projection depth is calculated for the points in Y in the same way. This value It is expressed as and represented by mathematical formula 5.

[0066] -------------(Mathematical Formula 5)

[0067] Here is a dataset It is the number of points, is a dataset The point of data set The center point of This is the projection depth value calculated for.

[0068] At this time, is a dataset and dataset It represents the interaction with the centrality of the liver, Conversely, the dataset and dataset It represents the interaction with centrality between them.

[0069] 3. Evaluation of changes between data sets.

[0070] After quantifying the difference in centrality, test values ​​and critical values ​​are used to statistically evaluate the change between the two data sets.

[0071] The test value is calculated based on the larger of the two values ​​after evaluating how close the points of each data set are to the center of the relative data set. This is used as an indicator that best explains the difference in centrality between the two data sets and is calculated by Equation 6.

[0072] --------------(Mathematical Formula 6)

[0073] In addition, the critical value is determined based on the dimensions and sample size of the data set, and can determine whether there is a statistically significant difference between two data sets.

[0074] In this case, the threshold is an empirically set value representing the difference in centrality between the two groups, and is calculated, for example, by the following formula.

[0075] (Use the corresponding formula for 3D calculations)

[0076] The details of the verification can be confirmed through the paper below.

[0077] Wilcox, R. R. (2003). Two-Sample, Bivariate Hypothesis Testing Methods Based on Tukey's Depth. Multivariate Behavioral Research, 38(2), 225-246.

[0078] Subsequently, if the test value is smaller than the critical value, the difference between the two data sets is considered statistically significant, indicating that deformation or movement of the structure has occurred. Conversely, if the test value is larger than the critical value, the difference between the two data sets is not statistically significant, leading to the conclusion that there has been no change in the state of the structure. Through this process, changes in the structural state between two time points can be precisely evaluated using depth values ​​and statistical verification.

[0079] <Example 3>

[0080] This embodiment determines the deformation of a structure by quantitatively analyzing the change between two data sets measured at different times or conditions through the calculation of variance, and uses a calculation method different from the projection depth calculated earlier, in which projection depth is used to calculate the center point and Mahalanobis depth is used to calculate the variance.

[0081] To compare the displacement between two datasets, the Mahalanobis depth calculation method is applied. Mahalanobis depth calculates how far each point is from the mean of the dataset using the covariance matrix. The distance each point takes from the center is represented by the Mahalanobis distance; the closer the data point is to the center, the larger the Mahalanobis depth value becomes, and the further it is from the center, the smaller the value becomes. The Mahalanobis distance can be calculated using Equation 7, and the Mahalanobis depth can be calculated using Equation 8. Here is a dataset of The first point, is a dataset Calculated as the average value of all my coordinates, that is, the average value of the X-axis, Y-axis, and Z-axis, Σ - y 1 represents the inverse of the covariance matrix of the dataset Y.

[0082]

[0083] ----(Mathematical Formula 7)

[0084] -------(Mathematical Formula 8)

[0085] For the data set (Y), the Mahalanobis depth is calculated using the same formula as Equation 7.

[0086] The above mathematical formula is the default formula before Bootstrap is applied.

[0087] In addition, the bootstrap method is used in the variance calculation process to evaluate whether the difference in variance between the two datasets is statistically significant. Bootstrap generates a new dataset through multiple iterative samplings from each dataset, and then iteratively estimates the difference in variance by calculating the Mahalanobis depth for each sample. At this time, bootstrap is performed iteratively by randomly sampling from each dataset while maintaining the sample size.

[0088] In other words, new dataset samples were extracted through bootstrapping, Mahalanobis distance and Mahalanobis depth were calculated for the extracted samples, and the difference in Mahalanobis depth was used.

[0089]

[0090] This means that in the b-th bootstrap iteration, data Xb and Yb are randomly sampled to generate a new sample.

[0091] After calculating the Mahalanobis depth values ​​of the two datasets for each iteration sample, the difference in Mahalanobis depth between the two datasets △MD is calculated using Equation 9.

[0092] ----(Mathematical Formula 9)

[0093] Here and is the average Mahalanobis depth value of the X and Y datasets calculated from the bootstrap samples, respectively. This process is performed through b bootstrap iterations.

[0094] Points are randomly sampled using bootstrapping, and Mahalanobis depth is calculated for the selected points. The reason for selecting random numbers rather than calculating and using all the depth values ​​for every point is to reduce the influence of outliers, increase the reliability of the displacement, eliminate uncertainty, and ultimately calculate the confidence interval. Since random sampling can lead to biased selection, this can be addressed by increasing the number of bootstrap samples to ensure that the bias does not affect the overall result.

[0095] Once the bootstrap iterations are complete, the variance difference values ​​calculated in each iteration are sorted, and a confidence interval is set to evaluate whether the difference between the two datasets is significant. The confidence interval represents the range indicating how likely the bootstrap-estimated variance difference actually is to occur, and this interval is set to the values ​​corresponding to the top 2.5% and bottom 2.5%. Specifically, the top 2.5% and bottom 2.5% values ​​of the bootstrap-calculated variance difference are used as the boundaries of the confidence interval.

[0096] Finally, if the confidence interval does not include 0, it can be concluded that the difference in variance between the two data sets is statistically significant. This means that the displacements between the two data sets are significantly different, suggesting that a change in the state or deformation of the structure has occurred. On the other hand, if the confidence interval includes 0, it can be concluded that the difference between the two data sets is not statistically significant and that the difference in displacement is not large.

[0097] Figure 3 is an example of 2D visualization after calculating data depth. The polygon enclosed by black lines represents the variance calculated from the point cloud (T1) of the initial structure, and the red dot in the middle represents the calculated center of T1. The polygon enclosed by dotted lines represents the variance calculated from the point cloud (T2) of the currently scanned structure, and the blue dot represents the calculated center of T2. Looking at Figure 3, it can be seen that both the shift in the centers of T1 and T2 and the change in variance have been confirmed.

[0098] Deformation mode analysis plays a crucial role in evaluating the condition of a structure and identifying flexural and shear failures. Flexural failure is a phenomenon where a structure bends, characterized by large deformation observed at the center of the structure. The deformation caused by bending becomes zero relative to the neutral axis, where compressive deformation occurs at the top and tensile deformation at the bottom. When flexural failure occurs, the upper and lower parts of the structure move in opposite directions, causing it to bend. The cracks that develop at this time typically originate at the center of the structure and propagate vertically. To detect flexural failure, centrality displacement analysis can be used; if displacement is detected at the centrality of the structure, it indicates that the entire structure has bent.

[0099] Shear failure is a type of failure caused by stress that causes adjacent faces of structural elements to slide against each other, characterized by the observation of large displacements at specific points. When shear failure occurs, a portion of the structure moves horizontally relative to other parts, leading to the formation of shear cracks. To detect shear failure, the occurrence of large localized displacements at specific points can be considered an indication.

[0100] If displacement of the dispersion before and after is detected through data depth analysis, shear failure can be suspected. Flexural and shear failures can be identified by analyzing the structural point cloud data using a data depth algorithm. Specifically, the presence of flexural failure is determined by detecting changes in the overall position or movement of the structure; if the center point shifts significantly, this can be interpreted as a flexural failure where the entire structure is bent. Through this analysis, flexural and shear failures can be accurately identified and structural safety evaluated, enabling the prompt implementation of necessary maintenance measures and ensuring the long-term stability of the structure.

Claims

1. A first step of calculating projection depth using 3D point cloud data acquired from a structure at different times; A second step of calculating the difference in centrality between two different data sets (X,Y) using the projection depth obtained in the first step, and quantifying the distance between points in one data set (X) and centers in the other data set (Y); It includes a third step of determining the displacement of the structure based on the change between the two data sets obtained through the second step above, and The above second step (Mathematical Formula 4), (Mathematical Formula 5) Calculate the centrality of each data set using the above mathematical formulas 4 and 5, and The above third step (Mathematical Formula 6) A non-target structural displacement measurement method using data depth, characterized by obtaining a test value through the above mathematical formula 6 and determining the displacement of the structure when the test value is smaller than the above critical value.

2. A method for measuring non-target structural displacement using data depth according to claim 1, wherein the first step comprises: a first-1 step of setting a reference point among three-dimensional point cloud data; a first-2 step of calculating a projection distance between other points excluding the reference point among the three-dimensional point cloud data and a reference point belonging to relative three-dimensional point cloud data; and a first-3 step of calculating a projection depth from the projection distance value calculated in the second-2 step.

3. In claim 2, the first-2 steps (Mathematical Formula 1) The projection distance is calculated using the above mathematical formula 1, and The above steps 1-3 (Mathematical Formula 2) After calculating the depth standardized by the above mathematical formula 2, (Mathematical Formula 3) A non-target structural displacement measurement method using data depth, characterized by calculating the projection depth using the above mathematical formula 3.

4. (Mathematical Formula 7) ( is a dataset of The first point, is a dataset Calculated as the average value of all my coordinates, that is, the average value of the X-axis, Y-axis, and Z-axis, Σ - y 1 represents the inverse of the covariance matrix of the dataset Y. Calculate the Mahalanobis distance using the above mathematical formula 7, and -------(Mathematical Formula 8) Calculate the Mahalanobis depth using the above mathematical formula 8, and ----(Mathematical Formula 9) A non-target structural displacement measurement method using data depth, characterized by calculating the difference in Mahalanobis depth (△ MD) between two data sets using the above mathematical formula 9 and determining the displacement of the structure through comparison.

5. A first step of acquiring three-dimensional point cloud data from a structure; A second step of setting one or more of the points obtained through the first step above as reference points and setting one or more of the remaining points as comparison points; A third step of calculating the projection distance between the above reference point and the comparison point; A non-target structural displacement measurement method using data depth, characterized by calculating a projection depth from the projection distance obtained through the third step above and determining the displacement of a structure by comparing data depths calculated with a time difference before and after for comparison points at the same location.

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