Method for predicting failure point by reconstructing displacement field of ancient city wall

Abstract

The invention discloses a method for predicting a damage point by reconstructing an ancient city wall displacement field. The method comprises the following steps: carrying out grid division on a target structure to be detected by an ancient city wall, carrying out sub-region division on a grid, selecting a grid point where the center position of a sub-region is located as a sampling point, and collecting displacement information of the point position; the obtained displacement information is processed into a data format in one-to-one correspondence with row coordinates, column coordinates and plane positions, and normalization processing is carried out; sending the processed data into a deep learning model for training; using the trained model to obtain non-sampling point coordinates and displacement values, and obtaining a reconstructed ancient city wall displacement field image; and predicting a damage point according to the displacement field image of the ancient city wall, and performing preventive protection on the ancient city wall. According to the method, the health information of the cultural relics is obtained under the condition that intervention on the fragile ancient city wall cultural relics is reduced as much as possible, possible potential damage points are predicted, prevention measures are taken, and a scientific decision basis is provided for cultural relic protection workers.

Description

Technical Field

[0001] The invention relates to the technical field of ancient city wall protection and structural health monitoring, and in particular to a method for predicting damage points of an ancient city wall displacement field reconstruction. Background Art

[0002] The ancient city wall is an important part of the ancient architectural heritage. As a knowledge medium connecting history and modern times, it witnesses the development of ancient society and reflects the development process of ancient social and economic levels and urban construction. [1] , which has important value to modern society.

[0003] In terms of monitoring of ancient city walls, currently, professionals are mostly responsible for manual inspection and evaluation and issuing analysis reports to predict potential damage points in ancient city walls and conduct pre-reinforcement. However, because some ancient city walls are very old and have relatively fragile structures, excessive human intervention may lead to secondary damage. Using a small amount of test data to predict the overall health of ancient city walls has become the mainstream method.

[0004] In the prior art, a patent document with publication number CN114581449B proposes a method for extracting the swelling of a city wall. The method collects data of part of the city wall and uses a fitting plane equation to obtain the swelling range and degree of the city wall, thereby achieving the purpose of investigating the faults and diseases of the city wall. There are also similar prediction methods such as interpolation algorithms in the prior art, but such methods only perform interpolation operations based on adjacent points, lack learning predictions for all sampling points in space, and lack sampling of data in the peripheral area. The accuracy of the reconstruction and fitting of the ancient city wall cannot reach the optimal state, and some faults and damage points may be ignored, which may lead to the generation of hidden dangers. Summary of the invention

[0005] Purpose of the invention: To solve the problems raised in the background technology, the present invention provides a method for reconstructing the displacement field of an ancient city wall and predicting the damage points. The method collects and preprocesses sample data of some ancient city wall structures, uses an ANN artificial neural network model to match the ancient city wall reconstruction scene and configures the matching model hidden layer parameters, inputs sample data for training, and uses the final model to reconstruct the complete ancient city wall displacement field data and visualize it. The method aims to observe and predict potential damage points of the ancient city wall and prevent reinforcement with higher accuracy and edge expansion capability.

[0006] Technical solution:

[0007] The present invention discloses a method for predicting damage points by reconstructing displacement fields of ancient city walls, the method comprising the following steps:

[0008] S1 obtains and preprocesses the sample data of the ancient city wall structure;

[0009] S1.1 Divide the ancient city wall structure samples to be monitored into grids, divide the grids into sub-regions, and select the grid points at the center of the sub-regions as sampling points;

[0010] S1.2 collect displacement data of each sampling point;

[0011] The displacement data acquired by S1.3 format is processed into a data format in which row coordinates, column coordinates and the plane position correspond one to one;

[0012] S1.4 normalizes the displacement data and waits to be sent to the machine learning model;

[0013] S2 puts the pre-processed ancient city wall structure sample data into the artificial neural network ANN for training to obtain the final model after training;

[0014] S3 reconstructs the displacement field through the final model;

[0015] S3.1 Input the spatial coordinates of the non-sampling points into the final model to obtain the displacement values ​​of the corresponding points;

[0016] S3.2 further organizes the data into a two-dimensional data format, and performs contrast imaging processing on the grid displacement values ​​and different colors to obtain the reconstructed displacement field image of the ancient city wall;

[0017] S3.4 analyzes the reconstructed displacement field image, predicts the damage points of the ancient city wall based on the visualization image and the grid point positions, and performs preventive reinforcement in advance.

[0018] Furthermore, the sample data of the ancient city wall structure described in S1 is obtained by sampling the displacement data of the ancient city wall to be monitored using a three-dimensional measuring instrument XTDIC.

[0019] Furthermore, after selecting the grid point at the center of the sub-area as the sampling point in S1.1, the key area is selected for encryption processing according to the different ancient city wall structures. The encryption processing method is: random sampling is performed in the specified small area to simulate the real ancient city wall structure.

[0020] Furthermore, the displacement data obtained by S1.3 format processing is processed separately according to different plane conditions:

[0021] Two-dimensional plane case:

[0022] Process the data into a data format in which the row coordinates and column coordinates correspond to the plane position one by one. If the grid point is a monitoring point, it will be a specific value. If it is not a monitoring point, it will be None, waiting for the trained model to predict it.

[0023] Three-dimensional space surface situation:

[0024] The data is organized into a data format where X, Y, Z correspond to the displacement value of the point. If the grid point is a monitoring point, it is a specific value. If it is not a monitoring point, fill in None and wait for the trained model to predict it.

[0025] Furthermore, S1.4 performs normalization processing on the displacement data, and the processing formula is:

[0026]

[0027] Among them, x norm is the standardized value, x is the actual value, and x max is the maximum value, x min is the minimum value.

[0028] Furthermore, the artificial neural network ANN model parameters are set in S2: the Adam optimizer is selected and the learning rate is configured as 0.0001;

[0029] All hidden layers use the ReLU activation function. The formula of the ReLU activation function in the hidden layer is as follows:

[0030]

[0031] Among them, N i is the parameter, w x and b x are the calculated values, weight parameters and bias factors of the hidden layer nodes respectively, z represents the neuron output and the summation result is connected according to the weight;

[0032] MSE is selected as the loss function to measure the difference between the displacement value predicted by the model and the actual displacement value. The formula is as follows:

[0033]

[0034] Where N is the number of samples, y i is the actual displacement value of the ith sample, is the displacement value predicted by the model. By minimizing MSE, the model can gradually learn the mapping relationship from the input coordinates to the accurate displacement value.

[0035] Furthermore, the hidden layer network structure has four layers, and the number of neurons in the first to fourth hidden layers are 32, 128, 64, and 32, respectively.

[0036] Furthermore, S3.2 matches the grid displacement values ​​with different colors for imaging processing, with blue representing the area with zero displacement and red representing the area with the largest displacement value. The closer to red, the larger the grid displacement value, and the higher the possibility of a potential damage point; the closer to blue, the smaller the grid displacement value, or even close to 0, and the lower the possibility of a potential damage point.

[0037] Beneficial effects:

[0038] 1. The present invention divides the grids into sub-areas and selects the grid points at the center of the sub-areas as the monitoring point arrangement mode of the sampling points, so as to maximize the uniform distribution of the sampling points, so that the model can better fit the displacement field, and the reconstructed displacement field image of the ancient city wall is more accurate.

[0039] 2. Compared with the traditional fitting plane equation and interpolation algorithm prediction, the present invention selects the ANN artificial neural network model for training and uses the machine learning model for global data learning. It has higher accuracy and edge expansion capability, so that it can generate data images that are closer to the real displacement field of the ancient city wall to check the damage points of the ancient city wall, and is more suitable for complex ancient city wall construction conditions.

[0040] 3. Through multiple groups of experimental comparisons, the present invention finally adopts a network structure of 4 hidden layers in the ANN artificial neural network, and obtains the optimal number of neurons in each layer, so that the ANN artificial neural network model reaches the optimal threshold of convergence speed and model reconstruction accuracy. This threshold is more in line with the needs of reconstruction and analysis of the displacement field of the ancient city wall in real scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a specific flow chart of the present invention;

[0042] Figure 2 This is a flow chart of the idea of ​​building and verifying the displacement field reconstruction model of the present invention;

[0043] Figure 3 This is a schematic diagram of grid division and monitoring point arrangement of the present invention;

[0044] Figure 4 It is a schematic diagram of the hierarchical structure of the neural network model of the present invention;

[0045] Figure 5 This is a displacement field data imaging result diagram of the present invention;

[0046] Figure 6 This is the cloud diagram of the real displacement field of the target sample of the present invention;

[0047] Figure 7 Comparison of displacement field images reconstructed for each method;

[0048] Figure 8 This is a schematic diagram of the effect of sample quantity on the reconstruction results of the present invention. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0050] This example takes the ancient city wall of Hailongtun in Guizhou as the research target, and prepares the experimental model according to the results of the field investigation. Before loading, the plane needs to be sprayed with speckle, which is equivalent to meshing the plane and giving spatial position information. This is a necessary step to record data using the XTDIC device.

[0051] The soil-filled wall model loading experiment took about 4.5 hours from loading to failure, and the whole process was monitored by DIC image measurement technology. The displacement field data of one frame was recorded every 8 seconds, and a total of 2030 frames of data were collected, each frame containing 38×51=1938 grid data points. The data of the 2000th frame collected are shown in Table 1. (During the experiment, a small amount of speckle fell off on the wall surface, resulting in some points in the upper left corner area not being monitored by the DIC device, so it is sufficient not to sample these positions)

[0052] Table 1

[0053]

[0054] Step 1: Obtain and preprocess the ancient city wall structure sample data

[0055] like Figure 3 As shown in the figure, the plane area to be measured is divided into 25 sub-areas, and the center points of these 25 sub-areas are selected as part of the training data set. Then, considering that in actual projects, some locations on the plane of some city walls may not be sampled to obtain data, the encryption processing of this embodiment is set to: randomly select in a specified part of the small area to simulate the actual situation as much as possible. Finally, 50 sampling points were selected, accounting for less than 3% of the total data volume. A three-dimensional measuring instrument (XTDIC) is used to sample and acquire the displacement data of the ancient city wall that needs to be monitored.

[0056] The displacement data obtained by format processing is processed into a data format in which the row coordinates, column coordinates and the plane position correspond one to one. The displacement data obtained by format processing are processed separately according to different plane conditions:

[0057] Two-dimensional plane case:

[0058] The data is processed into a data format in which the row coordinates and column coordinates correspond to the plane position. If the grid point is a monitoring point, it is a specific value. If it is not a monitoring point, it is None, waiting for the trained model to predict it. The data format for the two cases is shown in Table 2.

[0059] Table 2

[0060]

[0061]

[0062] Three-dimensional space surface situation:

[0063] The data is organized into a data format where X, Y, and Z correspond to the displacement value of the point. If the grid point is a monitoring point, it is a specific value. If it is not a monitoring point, fill in None and wait for the trained model to predict it. The data format for the three-dimensional situation is shown in Table 3:

[0064] Table 3

[0065]

[0066] The final sampling point data format of this embodiment is shown in Table 4:

[0067] Table 4

[0068]

[0069]

[0070] The displacement data is normalized and the processing formula is:

[0071]

[0072] Among them, x norm is the standardized value, x is the actual value, and x max is the maximum value, x min is the minimum value.

[0073] Step 2: The preprocessed ancient city wall structure sample data is put into the artificial neural network ANN for training to obtain the final model after training.

[0074] Set the artificial neural network ANN model parameters: select Adam optimizer and configure a learning rate of 0.0001;

[0075] All hidden layers use the ReLU activation function. The formula of the ReLU activation function in the hidden layer is as follows:

[0076]

[0077] Among them, N i is the parameter, w x and b x are the calculated values, weight parameters and bias factors of the hidden layer nodes respectively, z represents the neuron output and the summation result is connected according to the weight;

[0078] MSE is selected as the loss function to measure the difference between the displacement value predicted by the model and the actual displacement value. The formula is as follows:

[0079]

[0080] Where N is the number of samples, y i is the actual displacement value of the ith sample, is the displacement value predicted by the model. By minimizing MSE, the model can gradually learn the mapping relationship from the input coordinates to the accurate displacement value.

[0081] This embodiment uses multiple groups of experiments on the displacement field data of the soil-filled wall, keeps other parameters unchanged, adopts a network structure with 1-5 hidden layers, increases the number of neurons in the middle (when there are multiple hidden layers, the number of neurons set in each layer is the same), and explores the optimal number of neurons corresponding to different hidden layers.

[0082] When the number of neurons is small, the learning ability of the model is weak, and the reconstruction result is quite different from the real result. As the number of neurons increases, the learning and fitting ability of the model is enhanced, and the RMSE error decreases, which means that the reconstructed displacement field cloud map is closer to the real displacement field cloud map. However, the more neurons the better. If the number of neurons continues to increase, the RMSE will no longer decrease, but will show an upward trend. This is because too many neurons make the model structure too complex, resulting in overfitting, which increases the RMSE in the prediction stage and reduces the reconstruction accuracy. Finally, the optimal number of neurons under the 1-5 hidden layer structure is listed, as shown in Table 5:

[0083] Table 5

[0084]

[0085] like Figure 4 As shown in FIG. 1 , the RMSE error of the model with four hidden layers is minimized the earliest, and the number of neurons required is the least. Therefore, based on this conclusion, the optimal model structure diagram determined in this embodiment is as follows: Figure 8As shown in Figure 1, the input layer of the model receives the row and column coordinates (ROW and COL) of the grid points, while the output layer predicts the principal displacement (Displacement E) of the corresponding grid points. The number of neurons in each hidden layer is 32, 128, 64, and 32, respectively.

[0086] After the parameters are set, the ANN artificial neural network model is put into training. The input of the model is the row and column coordinates of the grid points, and the output layer predicts the main displacement (Displacement E) of the corresponding grid points, and fits the spatial displacement field of the structure based on 50 sampling points.

[0087] Step 3: Reconstruct the displacement field through the final model.

[0088] After obtaining the trained model, the spatial coordinates XY (Z) of the non-monitoring points are input into the trained model to obtain the displacement values ​​of the corresponding points, and the complete displacement field data is obtained as shown in Table 6 (this embodiment takes two dimensions as an example).

[0089] Table 6

[0090]

[0091] Then the data is further organized into a two-dimensional data format, as shown in Table 7. Finally, the displacement value of each grid is contrasted with the color, with blue representing the area with zero displacement and red representing the area with the largest displacement value, for imaging processing, as shown in Table 7. Figure 5 As shown, the reconstructed displacement field image is obtained.

[0092] Table 7

[0093]

[0094] Finally, through the analysis of the reconstructed displacement field image, it can be found that due to the soil structure filled inside, the deformation of the upper part is the largest under the top loading, and the displacement field image is presented in an inverted trapezoidal distribution. This is consistent with the "inverted trapezoidal" distribution presented in the displacement field cloud map, such as Figure 6 As shown in the figure, it is shown that the monitoring of displacement field helps to understand the most likely damage points of the structural plane in advance, thereby guiding people on how to strengthen the key parts of the structure in a targeted manner and implement precise reinforcement.

[0095] The present invention reconstructs the displacement field of the ancient city wall and predicts the damage points of the city wall by training a machine learning model, and also conducts a quantitative evaluation on the selection of the reconstruction method.

[0096] Quantitative evaluation results:

[0097] Four quantitative indicators are used to quantitatively evaluate the results, namely: mean absolute error (MAE), root mean square error (RMSE), structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR). The calculation formulas of these indicators are as follows.

[0098] MAE

[0099]

[0100] Among them, y i represents the true displacement value, represents the predicted displacement value, and n is the total number of observation points.

[0101] RMSE

[0102]

[0103] Where n is the number of samples, y i is the actual displacement value of the ith sample, is the displacement value predicted by the model. By minimizing MSE, the model can gradually learn the mapping relationship from input coordinates to accurate displacement values.

[0104] SSIM

[0105]

[0106] The meanings of the parameters in the formula are as follows:

[0107] x and y represent the displacement field image data in the two windows respectively.

[0108] μ x and μ y is the average of x and y.

[0109] σ x and σ y is the standard deviation of x and y.

[0110] σ xy is the covariance of x and y.

[0111] c 1 and c 2 A small constant added to avoid division by zero errors, usually c 1 =(k 1 ·L) 2 and c 2 =k 2 ·L) 2 , where L is the maximum displacement in the displacement field, k 1 = 0.01 and k 2 =0.03 is the default value

[35] .

[0112] PSNR

[0113]

[0114] Among them, peakval represents the peak value, corresponding to the maximum displacement value in the displacement field at this time, and MSE is the mean square error between the real displacement field and the predicted displacement field.

[0115] For MAE and RMSE, lower values ​​indicate better performance because they measure the error between the actual image and the reconstructed image. On the contrary, for SSIM and PSNR, higher values ​​are better because they measure the similarity between the actual image and the reconstructed image. The average values ​​of each indicator under different wall types are listed in Table 8. The conclusions obtained by the four indicators are consistent, and the reconstructed displacement field image of the neural network model is closest to the real displacement field image.

[0116] Table 8

[0117]

[0118] An example analysis is given for the quantization results of the neural network.

[0119] RMSE is an error indicator. The lower the error, the better the result. The unit is mm, which means that the average error of each point is 0.873mm. Since the average displacement of the entire plane is 18.472mm, the RMSE relative error is

[0120] The value range of SSIM is from -1 to 1. The closer to 1, the higher the similarity between the two. This index can well quantify the similarity between the original displacement field image and the reconstructed displacement field image. If the SSIM value can reach 0.7, it means that the two images are relatively similar. In the results obtained in this study, SSIM can reach 0.928, indicating that the displacement field reconstructed image obtained by this method is very similar to the actual image.

[0121] The reconstruction results of each method are as follows Figure 7 As shown in the figure, (a) is the displacement field image obtained by plotting 100% data acquired by DIC monitoring, (b)-(f) are the displacement field images reconstructed based on 2.6% sample data, among which the reconstruction result obtained by the ANN model is the best, which is consistent with the real image. Figure 6 It is closest, so it is selected as the target model of the present invention, which is more in line with the actual implementation environment of the present invention.

[0122] Analysis of the impact of sampling points on reconstruction accuracy:

[0123] The present invention divides the ancient city wall structure samples to be monitored into grids, and divides the grids into sub-areas, selects the grid points at the center of the sub-areas as sampling points, and then selects key areas for encryption processing according to different ancient city wall structures. The encryption processing method is: random sampling is performed in designated small areas to simulate the real ancient city wall structure.

[0124] In order to explore the influence of sampling points on reconstruction accuracy, this study adopts random sampling to sample from the displacement field data of soil filling wall, and increases the number of sampling points from 1% to 5%, with an increase of 0.1% each time, to check the RMSE between the reconstruction result and the true result. Figure 8 As shown, the larger the number of samples, the smaller the error between the reconstructed result and the true result, showing an exponential downward trend.

[0125] There is a significant disadvantage in the case of random arrangement of sampling points, which is that it is easy to cause uneven distribution of samples on the surface of the structure, making it difficult for the model to fit the spatial displacement field well, and the reconstructed effect is more volatile. Therefore, it is possible that the RMSE error will increase instead of decrease with the increase of sampling points. Although the data sampling ratio has reached 3.5% and 3.7%, their RMSE errors have increased significantly due to uneven distribution, and are even only comparable to the RMSE obtained by reconstruction with a 1.5% sampling ratio under a more uniform distribution.

[0126] The relationship between the RMSE error percentage and the number of sampling points can be expressed as y = e -0.27x +1.79 means that if you want to reduce the RMSE error to below 5%, 4.2% of the sampling points are needed. However, if the method mentioned in the present invention is adopted (first divide the grid into sub-regions, and then take the center position of the sub-region to ensure that the samples are evenly distributed), only 2.6% of the sampling points can reduce the RMSE relative error to 4.7% (0.873mm / 18.472mm=4.7%).

[0127] As a further extension of this embodiment, the reconstruction method is also applicable to data reconstruction of strain or stress fields in other fields.

[0128] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting damage points by reconstructing displacement fields of ancient city walls, characterized in that: The method comprises the following steps: S1 obtains and preprocesses the sample data of the ancient city wall structure; S1.1 Divide the ancient city wall structure samples to be monitored into grids, divide the grids into sub-regions, and select the grid points at the center of the sub-regions as sampling points; S1.2 collect displacement data of each sampling point; The displacement data acquired by S1.3 format is processed into a data format in which row coordinates, column coordinates and the plane position correspond one to one; S1.4 normalizes the displacement data and waits to be sent to the machine learning model; S2 puts the pre-processed ancient city wall structure sample data into the artificial neural network ANN for training to obtain the final model after training; S3 reconstructs the displacement field through the final model; S3.1 Input the spatial coordinates of the non-sampling points into the final model to obtain the displacement values ​​of the corresponding points; S3.2 further organizes the data into a two-dimensional data format, and performs contrast imaging processing on the grid displacement values ​​and different colors to obtain the reconstructed displacement field image of the ancient city wall; S3.4 analyzes the reconstructed displacement field image, predicts the damage points of the ancient city wall based on the visualization image and the grid point positions, and performs preventive reinforcement in advance.

2. The method for predicting damage points by reconstructing displacement fields of ancient city walls according to claim 1 is characterized in that: The sample data of the ancient city wall structure described in S1 is obtained by sampling the displacement data of the ancient city wall to be monitored using the three-dimensional measuring instrument XTDIC.

3. The method for predicting damage points by reconstructing displacement fields of ancient city walls according to claim 1 is characterized in that: After selecting the grid point at the center of the sub-area as the sampling point in S1.1, the key area is selected for encryption processing according to the different ancient city wall structures. The encryption processing method is: random sampling is performed in the specified small area to simulate the real ancient city wall structure.

4. The method for predicting damage points by reconstructing displacement fields of ancient city walls according to claim 1 is characterized in that: The displacement data obtained by S1.3 format processing are processed separately according to different plane conditions: Two-dimensional plane case: Process the data into a data format in which the row coordinates and column coordinates correspond to the plane position one by one. If the grid point is a monitoring point, it will be a specific value. If it is not a monitoring point, it will be None, waiting for the trained model to predict it. Three-dimensional space surface situation: The data is organized into a data format where X, Y, Z correspond to the displacement value of the point. If the grid point is a monitoring point, it is a specific value. If it is not a monitoring point, fill in None and wait for the trained model to predict it.

5. The method for predicting damage points by reconstructing displacement fields of ancient city walls according to claim 1 is characterized in that: S1.4 performs normalization processing on the displacement data, and the processing formula is: Among them, x norm is the standardized value, x is the actual value, and x max is the maximum value, x min is the minimum value.

6. The method for predicting damage points by reconstructing displacement fields of ancient city walls according to claim 1 is characterized in that: In S2, set the ANN model parameters: select the Adam optimizer and configure a learning rate of 0.0001; All hidden layers use the ReLU activation function. The formula of the ReLU activation function in the hidden layer is as follows: Among them, N i is the parameter, w x and b x are the calculated values, weight parameters and bias factors of the hidden layer nodes respectively, z represents the neuron output and the summation result is connected according to the weight; MSE is selected as the loss function to measure the difference between the displacement value predicted by the model and the actual displacement value. The formula is as follows: Where N is the number of samples, y i is the actual displacement value of the ith sample, is the displacement value predicted by the model. By minimizing MSE, the model can gradually learn the mapping relationship from the input coordinates to the accurate displacement value.

7. The method for predicting damage points by reconstructing displacement fields of ancient city walls according to claim 6 is characterized in that: The hidden layer network structure consists of four layers, and the number of neurons in the first to fourth hidden layers are 32, 128, 64, and 32, respectively.

8. The method for predicting damage points by reconstructing displacement fields of ancient city walls according to claim 1 is characterized in that: S3.2 uses different colors to contrast the grid displacement values ​​for imaging processing, with blue representing the area with zero displacement and red representing the area with the largest displacement value. The closer to red, the larger the grid displacement value, and the higher the possibility of a potential damage point; the closer to blue, the smaller the grid displacement value or even approaches 0, and the lower the possibility of a potential damage point.

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