Construction method of dam multi-measuring-point deformation deep learning monitoring model

Abstract

The invention discloses a construction method of a dam multi-measuring-point deformation deep learning monitoring model, and the method comprises the steps: carrying out the clustering analysis of dam deformation data through employing a K-means algorithm, so as to recognize a spatial mode of a monitoring region; in each clustering region, based on the interaction of dependent variables between the monitoring points, a long-short-term memory network of a coupling attention mechanism is adopted to construct a deformation prediction model; sequencing and evaluating the measuring points and the influence factors of the measuring points in different areas by applying an interpretability analysis technology; according to the method, clustering analysis, an attention mechanism, deep learning and other algorithms are effectively integrated, and a dam multi-measuring-point deformation monitoring model which is high in prediction precision and high in explanation capacity is successfully constructed. The model provides a new thought and method for reasonably analyzing and predicting the overall deformation characteristics of the dam. The application of the method not only improves the prediction accuracy, but also enhances the transparency and credibility of the model.

Description

Technical Field

[0001] The present invention relates to the technical field of water conservancy dam deformation monitoring, and specifically to a method for constructing a dam multi-measuring point deformation deep learning monitoring model. Background Art

[0002] In water conservancy projects, deformation is one of the key observation indicators that directly reflects the service performance of dam structures under the influence of internal and external environments. The deformation monitoring model has become one of the most widely used methods in dam safety monitoring by exploring the internal connection between external environmental factors and deformation observation values. A reasonable and effective deformation monitoring model can quantitatively explain the impact of external factors on the response of dam structures, predict the service state of dams, and provide protection for dam safety during the operation and maintenance period. Statistical models are currently the most commonly used methods in dam deformation monitoring due to their simple formulas and fast execution speed. With the development of artificial intelligence technology, a variety of machine learning algorithms such as artificial neural networks, support vector machines, extreme learning machines, and random forests have gradually been applied to deformation monitoring analysis, effectively improving the prediction accuracy of traditional statistical models. In addition, traditional dam deformation monitoring models are mainly established for single measuring points, and it is difficult to reasonably characterize the spatial deformation field of dams with internal correlations. In order to more accurately reflect the overall deformation state of dams, many achievements have also emerged in the prediction of deformation at multiple measuring points of dams in recent years. The above research has promoted the development of dam safety monitoring theory. However, through comparative analysis, it can be seen that most of the existing studies are aimed at improving the prediction accuracy of single-point models. Multi-point deformation monitoring models that can comprehensively consider prediction accuracy, spatial location and interpretability are still relatively scarce.

[0003] Therefore, at this stage, there is an urgent need for a method to construct a deep learning monitoring model for dam multi-measurement point deformation. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a method for constructing a deep learning monitoring model for deformation of multiple measuring points of a dam to solve the problems raised in the background technology.

[0005] To achieve the above object, the present invention provides the following technical solution: a method for constructing a deep learning monitoring model for dam multi-measurement point deformation, comprising the following steps:

[0006] S1. Cluster analysis of dam deformation data was performed using K-means algorithm to identify spatial patterns in the monitoring area.

[0007] S2. In each clustering area, based on the interaction of dependent variables between monitoring points, a long short-term memory network with coupled attention mechanism is used to build a deformation prediction model to enhance the model's ability to process time series data;

[0008] S3. Use interpretable analysis techniques to sort and evaluate measurement points and their influencing factors in different regions to ensure the transparency and explanatory power of the monitoring model.

[0009] Preferably, in step S1, cluster analysis of dam deformation data is performed using a K-means algorithm, comprising the following steps:

[0010] During the dam monitoring process, deformation data from multiple measuring points were collected. The data showed obvious spatial and temporal characteristics. In order to effectively analyze the distribution and characteristics of these data, the K-means clustering analysis method was used to systematically classify the deformation characteristics of the measuring points. K-means is a widely used clustering algorithm that evaluates the similarity of samples by calculating the distance between them and divides the sample set into K clusters based on the similarity. Each cluster C i The center of i This vector is also called the centroid of the cluster.

[0011]

[0012] The purpose of the Kmeans algorithm is to find K centroids to minimize the square error E:

[0013]

[0014] The smaller the square error E is, the higher the similarity of samples in the cluster is.

[0015] Preferably, the specific process of the K-means algorithm is as follows:

[0016] ① Randomly select k different measurement point sample data from all the measurement point displacement sample data to be clustered and generate the initial cluster centroid [μ1,μ2,…,μ k ];

[0017] ② Calculate the Euclidean distance from each sample to each initial cluster centroid, form k clusters based on the cluster centroid with the closest distance, and update the k clusters according to the distance formula. The distance formula is formula (2);

[0018] ③ Recalculate the cluster centroids for the new k clusters using formula (1), and repeat processes ② and ③ until the termination condition is met and the square error E reaches the preset value or the preset number of iterations is reached.

[0019] Preferably, in step S2, establishing a prediction model using a long short-term memory network coupled with an attention mechanism comprises the following steps:

[0020] 1) The water level-season-time effect model is selected as the dam deformation monitoring statistical model. The water level-season-time effect model expresses the displacement change with three components: water pressure, temperature and time effect:

[0021]

[0022] Where, δ is the horizontal displacement; H is the water depth in front of the dam; t is the cumulative number of days from the observation day to the observation base day; θ = t / 100; a1, a2, a3, a4, b1, b2, b3, b4, c1, c2 are all model regression coefficients; d is the constant term;

[0023] 2) According to the measurement point sample partitioning result of step S1, the data of each measurement point in the same area are analyzed, with the independent variable in formula (3) as input and the displacement as output, and the displacement data of other measurement points in the same area are introduced as new independent variables; based on the above data, a long short-term memory artificial neural network model integrating coupled attention mechanism is established for prediction; and the prediction results of this model are compared with the prediction results of the model using only single measurement point data; which helps to evaluate the effect of coupled attention mechanism in improving prediction accuracy.

[0024] Preferably, the principle of the attention mechanism is as follows:

[0025] In the attention mechanism, input data is usually represented as <key, value> pairs. In the calculation process, the weight coefficient is first determined by the similarity between the query and the key. Specifically, let the query, key, and value be Q, K, and V respectively, then the attention weight W is calculated by the following formula:

[0026]

[0027] Where, d k is the dimension of the key, which is used to scale the dot product to prevent the inner product value from being too large; by applying the softmax function, the weight coefficient W ensures that the sum of all weights is 1, thus forming a probability distribution;

[0028] Then, by multiplying the weight coefficient W by the corresponding value V,

[0029] a=W·V (5)

[0030] Calculate the final output a.

[0031] Preferably, the principle of the long short-term memory artificial neural network model is as follows:

[0032] The calculation formulas of LSTM internal structure are as follows:

[0033] f t =σ(W f ·[h t-1 ,x t ]+b f ) (6)

[0034] it =σ(W i ·[h t-1 ,x t ]+b i ) (7)

[0035] c t =σ(W c ·[h t-1 ,x t ]+b c ) (8)

[0036]

[0037] o t =σ(W o ·[h t-1 ,x t ]+b o ) (10)

[0038]

[0039] h t =o t ·tanh(c t ) (12)

[0040] Where W f , W i , W c and W o is the weight matrix, b f 、b i 、b c and b o is the bias term; c t-1 、h t-1 Respectively represent the unit state and output at the previous time point, x t represents the input at this moment, and the three together constitute the input at the current moment; f t 、i t and c t They represent the forget gate, input gate, and output gate structures respectively. The three gate structures work together to control the LSTM unit to selectively store and update the memory content at the current time point; σ represents the Sigmoid activation function; tanh represents the hyperbolic tangent activation function; c t 、h t They represent the unit state and output at the current time point, and will also serve as the input at the next moment.

[0041] Preferably, in step S3, interpretability analysis is used to rank and evaluate the influencing factors of each regional measurement point, which specifically includes the following steps:

[0042] 1) Utilizing the characteristics of the attention mechanism, the attention mechanism automatically identifies and assigns corresponding importance weights to different input features when processing data;

[0043] 2) For each measuring point, the importance of each influencing factor is evaluated before and after the displacement of other measuring points in the same area is introduced as an influencing factor; in this way, the contribution of different factors to the model output can be clarified, thereby optimizing the model's interpretability and prediction accuracy.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1. In the present invention, cluster analysis, attention mechanism, deep learning and other algorithms are organically combined to construct a dam multi-point deformation monitoring model with high predictive ability and strong interpretability. This model provides new ideas and methods for rationally analyzing and predicting the overall deformation characteristics of the dam. The application of this method not only improves the accuracy of the prediction, but also enhances the transparency and credibility of the model.

[0046] 2. In the present invention, an interpretable dam multi-point deformation monitoring model is constructed to improve the analysis and prediction capabilities of the overall deformation characteristics of the dam. The model fully considers the spatial correlation between the dam monitoring points and can more accurately reflect the deformation of the measuring points in the same area by clustering and partitioning the deformation monitoring data. In addition, the long short-term memory artificial neural network (LSTM) with coupled attention mechanism effectively captures the mutual influence of the dependent variables of the measuring points and enhances the prediction accuracy. Finally, through interpretability analysis, the model can rank and evaluate the influencing factors of the measuring points in different regions, thereby providing a more scientific and effective decision-making basis for dam safety monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0048] In the attached picture:

[0049] Figure 1 It is a schematic diagram of the internal structure of the LSTM unit of the present invention;

[0050] Figure 2 It is a specific implementation flow chart of the present invention;

[0051] Figure 3 It is a schematic diagram of the clustering results of the dam measurement points of the present invention;

[0052] Figure 4 It is a schematic diagram of the prediction results of the displacement of the measuring point 1 of the present invention before and after considering the mutual influence of the dependent variables of the measuring points;

[0053] Figure 5 It is a schematic diagram of the prediction results of the displacement of the measuring point 2 of the present invention before and after considering the mutual influence of the dependent variables of the measuring points;

[0054] Figure 6 It is a schematic diagram of the prediction results before and after the displacement of the measuring point 3 of the present invention is considered the mutual influence of the dependent variables of the measuring points;

[0055] Figure 7 This is a schematic diagram of the impact factor scores of measuring point 1 before and after considering the influence of the displacement factor of the present invention;

[0056] Figure 8 Schematic diagram of the impact score of the displacement factors of other measuring points in the same area on measuring point 1 in the present invention;

[0057] Fig. 9 This is a schematic diagram of the impact factor scores of measuring point 2 of the present invention before and after considering the influence of the displacement factor;

[0058] Fig.10 This is a schematic diagram of the impact of other displacement factors in the same area on the score of measuring point 2 in the present invention;

[0059] Fig.11 This is a schematic diagram of the impact factor scores of measuring point 3 of the present invention before and after considering the impact of the displacement factor;

[0060] Fig.12 This is a schematic diagram of the impact of other displacement factors in the same area on the score of measuring point 3 in the present invention. DETAILED DESCRIPTION

[0061] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0062] A method for constructing a deep learning monitoring model for deformation of multiple measuring points of a dam is proposed. The deformation monitoring data is clustered and partitioned by considering the spatial correlation of the dam monitoring points. Further, for the measuring points in the same area, a long short-term memory artificial neural network (LSTM) coupled with an attention mechanism is used to establish a prediction model based on the mutual influence of the dependent variables of the measuring points. Finally, the ranking of the influencing factors of the measuring points in different regions is evaluated by interpretability analysis. The specific steps include the following:

[0063] Step 1: Considering the spatial relationship between the dam monitoring points, the deformation monitoring data are first clustered and partitioned to identify the spatial pattern of the monitoring area.

[0064] Step 2: In each cluster area, based on the interaction of dependent variables between monitoring points, a long short-term memory (LSTM) network integrated with a coupled attention mechanism is used to build a deformation prediction model to enhance the model's ability to process time series data.

[0065] Step 3: Apply interpretable analysis techniques to sort and evaluate the measurement points and their influencing factors in different regions to ensure the transparency and explanatory power of the monitoring model.

[0066] This is achieved through the following technical methods:

[0067] Step 1: Use K-means algorithm to perform cluster analysis on dam deformation data:

[0068] In the process of dam monitoring, deformation data of multiple measuring points can usually be collected, and these data show obvious spatial and temporal characteristics. In order to effectively analyze the distribution and characteristics of these data, the K-means clustering analysis method is used to systematically classify the deformation characteristics of the measuring points. K-means is a widely used clustering algorithm that evaluates the similarity of samples by calculating the distance between them and divides the sample set into K clusters based on this similarity. Each cluster C i The center of i This vector is also called the centroid of the cluster.

[0069]

[0070] The purpose of the Kmeans algorithm is to find K centroids to minimize the square error E. The smaller the square error E, the higher the similarity of the samples in the cluster.

[0071]

[0072] The specific K-means algorithm process is as follows.

[0073] ① Randomly select k different measurement point sample data from all the measurement point displacement sample data to be clustered and generate the initial cluster centroid [μ1,μ2,…,μ k ].

[0074] ② Calculate the Euclidean distance from each sample to each initial cluster centroid, form k clusters based on the cluster centroid with the closest distance, and update the k clusters according to the distance formula. The distance formula is formula (2).

[0075] ③ Recalculate the cluster centroids for the new k clusters using formula (1), and repeat processes ② and ③ until the termination condition is met and the square error E reaches the preset value or the preset number of iterations is reached.

[0076] Step 2: Use the long short-term memory (LSTM) network coupled with the attention mechanism to build a prediction model:

[0077] Dam displacement is the result of multiple factors. The water level-season-time (HST) model is the most widely used statistical model for dam deformation monitoring. This model represents displacement changes using three components: water pressure, temperature, and time:

[0078]

[0079] Where, δ is the horizontal displacement; H is the water depth in front of the dam; t is the cumulative number of days from the observation day to the observation base day; θ = t / 100; a1, a2, a3, a4, b1, b2, b3, b4, c1, c2 are all model regression coefficients; d is the constant term.

[0080] According to the sample partitioning results of the measuring points in step 1, the data of each measuring point in the same area are analyzed, with the independent variable in formula (3) as input and the displacement as output, and the displacement data of other measuring points in the same area are introduced as new independent variables. Based on these data, a long short-term memory artificial neural network model integrating coupled attention mechanism is established for prediction. In addition, the prediction results of this model are compared with the prediction results of the model using only single measuring point data (without considering the displacement data of other measuring points in the same area). Such a comparison helps to evaluate the effect of coupled attention mechanism in improving prediction accuracy. The principle of the attention mechanism is as follows:

[0081] In the attention mechanism, input data is usually represented as a <Key, Value> pair. In the calculation process, the weight coefficient is first determined by the similarity between the query and the key. Specifically, let the query, key, and value be Q, K, and V respectively, then the attention weight W can be calculated by the following formula:

[0082]

[0083] Where, d k Is the dimension of the key, used to scale the dot product to prevent the inner product value from being too large. By applying the softmax function, the weight coefficient W ensures that the sum of all weights is 1, thus forming a probability distribution.

[0084] Then, by multiplying the weight coefficient W by the corresponding value V, the final output a can be calculated:

[0085] a=W·V (5)

[0086] The principle of the long short-term memory artificial neural network model is as follows:

[0087] The LSTM unit structure is as follows Figure 1 As shown in the figure, c t-1 、h t-1 Respectively represent the unit state and output at the previous time point, x trepresents the input at this moment, and the three together constitute the input at the current moment; f t 、i t and c t They represent the forget gate, input gate, and output gate structures respectively. The three gate structures work together to control the LSTM unit to selectively store and update the memory content at the current time point; σ represents the Sigmoid activation function; tanh represents the hyperbolic tangent activation function; c t 、h t They represent the unit state and output at the current time point, and will also serve as the input at the next moment. The calculation formulas for the LSTM internal structure are as follows:

[0088] f t =σ(W f ·[h t-1 ,x t ]+b f ) (6)

[0089] i t =σ(W i ·[h t-1 ,x t ]+b i ) (7)

[0090] c t =σ(W c ·[h t-1 ,x t ]+b c ) (8)

[0091]

[0092] o t =σ(W o ·[h t-1 ,x t ]+b o ) (10)

[0093]

[0094] h t =o t ·tanh(c t ) (12)

[0095] Where W f , W i , W c and W o is the weight matrix, b f , b i , b c and b o is the bias term.

[0096] Step 3: Use interpretability analysis to rank and evaluate the influencing factors of the measurement points in each region.

[0097] By utilizing the characteristics of the attention mechanism, the mechanism can automatically identify and assign corresponding importance weights to different input features when processing data. For each measuring point, the importance of each influencing factor is evaluated before and after the displacement of other measuring points in the same area is introduced as an influencing factor. In this way, the contribution of different factors to the model output can be clarified, thereby optimizing the model's interpretability and prediction accuracy. The specific implementation process of all steps is as follows: Figure 2 shown.

[0099] In this example, the displacement data of 18 measuring points of the dam are used as clustering objects, and the K-means clustering method is used for analysis. Figure 3 As shown in the figure, the clustering results classify measuring points 1-3 as region 1, measuring points 4, 5, and 7 as region 2, measuring points 9-13 as region 3, and measuring points 14-20 as region 4. Taking region 1 as an example, based on the displacement monitoring data of all measuring points in the region, a prediction model considering the long short-term memory (LSTM) network with coupled attention mechanism was established. The prediction results are shown in Figures 4 to 6 In addition, according to whether a single measuring point considers the displacement of other measuring points in the same area as an influencing factor, the prediction result evaluation index of each model is obtained, as shown in Table 1

[0100] Table 1 Evaluation indicators of model prediction results

[0101]

[0102] from Figures 4 to 6 From the data in Table 1, we can see that clustering the dam measurement points and considering the mutual influence between the measurement points significantly improves the prediction performance of the model. 2 Taking the evaluation index as an example, the analysis of measuring points 1, 2, and 3 shows that when the model considers the displacement of other measuring points as influencing factors, the R 2 The value increased from 0.845 to 0.930, and the R 2 The value increased from 0.914 to 0.936, and the R 2 The value increased from 0.840 to 0.907. These results clearly show that introducing the displacement of other measuring points as an influencing factor can greatly enhance the prediction accuracy of the model.

[0103] In addition, through the explanatory analysis of the attention mechanism, the ranking results of the influencing factors of the measurement points in different regions are obtained and displayed in Figures 7 to 12 These graphs provide the interpretability of the deep learning model for deformation at multiple measurement points on the dam.

[0104] According to the above example analysis, the present invention successfully constructs a dam multi-point deformation monitoring model with high prediction accuracy and strong explanatory power by effectively integrating algorithms such as cluster analysis, attention mechanism and deep learning. This model provides new ideas and methods for the reasonable analysis and prediction of the overall deformation characteristics of the dam. The application of this method not only improves the accuracy of the prediction, but also enhances the transparency and credibility of the model.

[0105] Finally, it should be noted that the above description is only a preferred example of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for constructing a deep learning monitoring model for dam multi-measurement point deformation, characterized in that: The following steps are involved: S1. Cluster analysis of dam deformation data was performed using K-means algorithm to identify spatial patterns in the monitoring area. S2. In each clustering area, based on the interaction of dependent variables between monitoring points, a long short-term memory network with coupled attention mechanism is used to construct a deformation prediction model. S3. Use interpretable analysis techniques to sort and evaluate measurement points and their influencing factors in different regions to ensure the transparency and explanatory power of the monitoring model.

2. The method for constructing a deep learning monitoring model for dam multi-measurement point deformation according to claim 1, characterized in that: In step S1, the K-means algorithm is used to perform cluster analysis on the dam deformation data, including the following steps: During the dam monitoring process, deformation data of multiple measuring points were collected. The above data showed obvious spatial and temporal characteristics. The K-means clustering analysis method was used to systematically classify the deformation characteristics of the measuring points. The similarity between samples was evaluated by calculating the distance between them, and the sample set was divided into K clusters based on the above similarity. Each cluster C i The center of i This vector is also called the centroid of the cluster. The purpose of the Kmeans algorithm is to find K centroids to minimize the square error E: The smaller the square error E is, the higher the similarity of samples in the cluster is.

3. The method for constructing a dam multi-measurement point deformation deep learning monitoring model according to claim 2, characterized in that: The specific process of the K-means algorithm is as follows: ① Randomly select k different measurement point sample data from all the measurement point displacement sample data to be clustered and generate the initial cluster centroid [μ1,μ2,…,μ k ]; ② Calculate the Euclidean distance from each sample to each initial cluster centroid, form k clusters based on the cluster centroid with the closest distance, and update the k clusters according to the distance formula. The distance formula is formula (2); ③ Recalculate the cluster centroids for the new k clusters using formula (1), and repeat processes ② and ③ until the termination condition is met and the square error E reaches the preset value or the preset number of iterations is reached.

4. The method for constructing a deep learning monitoring model for dam multi-measurement point deformation according to claim 1 is characterized in that: In step S2, a prediction model is established using a long short-term memory network coupled with an attention mechanism, including the following steps: 1) The water level-season-time effect model is selected as the dam deformation monitoring statistical model. The water level-season-time effect model expresses the displacement change with three components: water pressure, temperature and time effect: Where, δ is the horizontal displacement; H is the water depth in front of the dam; t is the cumulative number of days from the observation day to the observation base day; θ = t / 100; a1, a2, a3, a4, b1, b2, b3, b4, c1, c2 are all model regression coefficients; d is the constant term; 2) According to the measurement point sample partitioning result of step S1, the data of each measurement point in the same area are analyzed, the independent variable in formula (3) is used as input, the displacement is used as output, and the displacement data of other measurement points in the same area are introduced as new independent variables; based on the above data, a long short-term memory artificial neural network model with integrated coupled attention mechanism is established for prediction; The prediction results of this model are compared with those of the model using only single-point data; this helps to evaluate the effectiveness of the coupled attention mechanism in improving prediction accuracy.

5. The method for constructing a dam multi-measurement point deformation deep learning monitoring model according to claim 4, characterized in that: The principle of the attention mechanism is as follows: In the attention mechanism, input data is usually represented as <key, value> pairs. In the calculation process, the weight coefficient is first determined by the similarity between the query and the key. Specifically, let the query, key, and value be Q, K, and V respectively, then the attention weight W is calculated by the following formula: Where, d k is the dimension of the key, which is used to scale the dot product to prevent the inner product value from being too large; by applying the softmax function, the weight coefficient W ensures that the sum of all weights is 1, thus forming a probability distribution; Then, by multiplying the weight coefficient W by the corresponding value V, a=W·V (5) Calculate the final output a.

6. The method for constructing a deep learning monitoring model for dam multi-measurement point deformation according to claim 5 is characterized in that: The principle of the long short-term memory artificial neural network model is as follows: The calculation formulas of LSTM internal structure are as follows: f t =σ(W f ·[h t-1 ,x t ]+b f ) (6) i t =σ(W i ·[h t-1 ,x t ]+b i ) (7) c t =σ(W c ·[h t-1 ,x t ]+b c ) (8) the t =σ(W o ·[h t-1 ,x t ]+b o ) (10) h t =o t ·tanh(c t ) (12) Where W f , W i , W c and W o is the weight matrix, b f , b i , b c and b o is the bias term; c t-1 、h t-1 Respectively represent the unit state and output at the previous time point, x t represents the input at this moment, and the three together constitute the input at the current moment; f t 、i t and c t They represent the forget gate, input gate, and output gate structures respectively. The three gate structures work together to control the LSTM unit to selectively store and update the memory content at the current time point; σ represents the Sigmoid activation function; tanh represents the hyperbolic tangent activation function; c t 、h t They represent the unit state and output at the current time point, and will also serve as the input at the next moment.

7. The method for constructing a dam multi-measurement point deformation deep learning monitoring model according to claim 1, characterized in that: In step S3, interpretability analysis is used to rank and evaluate the influencing factors of each regional measurement point, which specifically includes the following steps: 1) Utilizing the characteristics of the attention mechanism, the attention mechanism automatically identifies and assigns corresponding importance weights to different input features when processing data; 2) For each measuring point, the importance of each influencing factor is evaluated before and after the displacement of other measuring points in the same area is introduced as an influencing factor.

Images