Comprehensive evaluation analysis and application method based on dam safety monitoring principal component analysis technology

Abstract

The invention discloses a comprehensive evaluation analysis and application method based on a dam safety monitoring principal component analysis technology, and the method comprises the following steps: sample data is checked, and the data quantity requires that the object number / index number is greater than 1; performing KMO and Butt sphere inspection on the sample data, wherein the inspection results meet the conditions that KMO is greater than 0.6 and sig is less than 0.05; performing Z-score standardization on the sample data; calculating a correlation coefficient matrix; calculating a principal component eigenvalue and an eigenvector; calculating a principal component variance contribution rate and an accumulated variance contribution rate; extracting principal components of which the characteristic values are greater than 1 and the cumulative variance contribution rate is greater than about 85%, and determining the number of the principal components; calculating the score of the principal component; carrying out minimum and maximum normalization processing on the score of the principal component; calculating the weights of the first K principal components; calculating a comprehensive score; and drawing a characteristic value macadam diagram and a comprehensive score histogram in a data visualization manner, and completing the comprehensive analysis of the principal components. According to the invention, the efficiency of engineering safety monitoring comprehensive analysis and evaluation is improved.

Description

Technical Field

[0001] The present invention belongs to the field of engineering safety monitoring, and specifically relates to a comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring. Background Art

[0002] In the construction of hydropower station projects, safety is the basic guarantee for personal life and health. In particular, the safety of hydropower station dams is of crucial importance. The accuracy and reliability of dam safety monitoring data play a vital role in the safety prediction of dams. To ensure the safety of dams, the construction unit will entrust a qualified third-party inspection unit to conduct safety monitoring on the dam. At the same time, to ensure the reliability of the monitoring data, the monitoring unit often recommends that the construction unit arrange a large number of monitoring points inside and outside the dam. In theory, the reliability of dam safety monitoring data can be ensured. However, it will also cause a large amount of economic waste for the construction unit. Similarly, the monitoring unit cannot analyze the results in a short time in the face of massive data and cannot quickly find the main factors affecting the dam safety, resulting in economic losses and potential safety hazards for the construction unit, making it impossible for decision-makers to make rapid decisions.

[0003] In dam safety monitoring, after on-site monitoring personnel collect the monitoring data, professional personnel analyze the data to form a process line chart and analysis results. In the face of massive data, the monitoring unit often invests a large number of personnel to process the data, which is likely to cause a lag in monitoring information and low efficiency. Practice has proved that through the analysis of dam safety monitoring data, several key components often play a decisive role in the safety of the dam. Therefore, it is particularly important to find a method to transform multiple indicators to be analyzed into several comprehensive indicators (i.e., principal components) under the premise of losing less information among the numerous indicators in dam safety monitoring. Summary of the Invention

[0004] The purpose of the present invention is to provide a comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring, so as to improve the efficiency of comprehensive analysis and evaluation of engineering safety monitoring.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0006] A comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring includes the following steps:

[0007] S1, Prepare the sample data to be subjected to principal component analysis, and check the sample data. The requirement for the number of data is that the number of objects / number of indicators > 1. If the requirement is met, proceed to the next step; otherwise, principal component analysis cannot be carried out.

[0008] S2. Perform the KMO and Bartlett sphericity tests on the sample data in S1. If the test results satisfy KMO > 0.6 and sig < 0.05, proceed to the next step; otherwise, principal component analysis cannot be performed. Here, KMO is an index for testing the sampling suitability, and sig is the significance level.

[0009] S3. Perform Z-score standardization on the sample data in S1.

[0010] S4. Calculate the correlation coefficient matrix based on S3.

[0011] S5. Calculate the principal component eigenvalues and eigenvectors based on S4.

[0012] S6. Calculate the principal component variance contribution rate and cumulative variance contribution rate based on S5.

[0013] S7. Extract the principal components with eigenvalues > 1 and cumulative variance contribution rate > 85% approximately based on S5 and S6, and determine the number of principal components.

[0014] S8. Calculate the principal component scores based on S3 and S5.

[0015] S9. Perform min-max normalization on the principal component scores based on S8.

[0016] S10. Calculate the weights of the first K principal components based on S6.

[0017] S11. Calculate the comprehensive score based on S9 and S10.

[0018] S12. Draw a scree plot of eigenvalues and a bar chart of comprehensive scores for data visualization based on S5 and S11 to complete the principal component comprehensive analysis.

[0019] Preferably, in S1, the sample data matrix is represented in the form of:

[0020]

[0021] where n is the number of object information and p is the number of index information.

[0022] Preferably, in S3, when performing Z-score standardization on the sample data, the standardized matrix z ij has the following calculation formula:

[0023]

[0024] where μ j and σ j are respectively the mean and standard deviation of the variables in the j-th column of matrix X, and X′ ij is the sample in matrix X, and j = 1, 2,... p.

[0025] Preferably, in the step S4, the correlation coefficient matrix r ij is calculated as follows:

[0026]

[0027] where z ki is the sample at the i-th column and k-th row in the standardized matrix z ij , is the mean value at the i-th column and k-th row in the standardized matrix z ij , z kj is the sample at the j-th column and k-th row in the standardized matrix z ij , is the mean value at the j-th column and k-th row in the standardized matrix z ij .

[0028] Preferably, in the step S5, the correlation coefficient matrix is subjected to eigenvalue decomposition to obtain eigenvalues λ p : λ1≥λ2≥...≥λ p ≥0 and eigenvectors u ij , where i represents the row, j represents the column, i = 1, 2,..., p; j = 1, 2,... p.

[0029] Preferably, in the step S6, the variance contribution rate f i of the i-th principal component is calculated as follows:

[0030]

[0031] where λ i , λ j are all eigenvalues, i = 1, 2,..., p;

[0032] The cumulative variance contribution rate F k of the first k principal components is calculated as follows:

[0033]

[0034] where f i is the variance contribution rate of the i-th principal component, k = 1, 2,..., p.

[0035] Preferably, in the step S8, the calculation formula of the principal component score is as follows:

[0036]

[0037] where u kj is the principal component coefficient, z ik is the sample at the k-th column and i-th row in the standardized matrix z ij , k = 1, 2,..., p.

[0038] Preferably, in S9, the principal component scores are processed by min-max normalization, and the min-max normalization result t of the principal component scores ij is calculated by the formula:

[0039]

[0040] where s ij is the principal component score, and s j is the principal component score matrix.

[0041] Preferably, in S10, the calculation formula for the weights of the first K principal components is as follows:

[0042]

[0043] where f i is the variance contribution rate of the i-th principal component, and i = 1, 2,..., k.

[0044] Preferably, in S11, the calculation formula for the comprehensive score of the object is as follows:

[0045]

[0046] where w i is the weight of the first K principal components, and t ij is the min-max normalization result of the principal component scores.

[0047] The beneficial effects of the present invention are as follows: The principle of the present invention is a multivariate statistical analysis method that uses the idea of principal component analysis (PCA) for dimensionality reduction. Under the premise of losing less information, multiple indicators in the dam engineering safety monitoring are transformed into several comprehensive indicators (i.e., principal components). Each principal component is a linear combination of the sample data variables, and the principal components should be independent of each other. This makes the principal components have more excellent performance than the original variables. With the help of the SPSS statistical analysis software, the accuracy of the analysis results is ensured, and the efficiency of the comprehensive analysis and evaluation of engineering safety monitoring is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is a flowchart of the present invention.

[0049] Figure 2 is a scree plot of the present invention.

[0050] Figure 3 is a bar chart of the comprehensive scores of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0051] To make the objectives, technical solutions and advantages of the invention more clear, the following will clearly and completely describe the technical solutions of the present invention in conjunction with the drawings and embodiments of the present invention.

[0052] As Figures 1 - 3 shown, a comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring includes the following steps:

[0053] S1. Prepare the sample data that needs to be subjected to principal component analysis (PCA), and check the sample data. The requirement for the number of data is the number of objects / the number of indicators > 1. If the requirement is met, proceed to the next step; otherwise, principal component analysis (PCA) cannot be performed.

[0054] Assume that the number of object information and the number of indicator information in the sample data that needs to be subjected to comprehensive evaluation analysis are represented by n and p respectively. Then, the matrix representation form of the sample data for principal component analysis is:

[0055]

[0056] Among them, n is the number of object information, and p is the number of indicator information.

[0057] S2. Perform the KMO and Bartlett spherical tests on the sample data. If the test results meet KMO > 0.6 and sig (significance) < 0.05, proceed to the next step; otherwise, principal component analysis (PCA) cannot be performed. Among them, KMO is an index for testing the sampling suitability, and sig is the significance.

[0058] Usually, the SPSS statistical analysis software is used to perform the KMO and Bartlett spherical tests on the data. If the test results meet KMO > 0.6 and sig (significance) < 0.05, proceed to the next step; otherwise, principal component analysis (PCA) cannot be performed.

[0059] S3. Perform Z-score standardization on the sample data in S1 to obtain the standardized matrix.

[0060] Perform Z-score standardization on the sample data. The calculation formula for the standardized matrix z ij is as follows:

[0061]

[0062] Among them, μ j and σ j are respectively the mean and standard deviation of the variables in the j-th column of the matrix X, and X′ ij is the sample in the X matrix.

[0063] S4. Calculate the correlation coefficient matrix according to S3.

[0064] Calculate the correlation coefficient matrix r for the standardized matrix ij , the correlation coefficient matrix r ij has the following calculation formula:

[0065]

[0066] where z ki is the sample at the i-th column and k-th row in the standardized matrix z ij , is the mean value at the i-th column and k-th row in the standardized matrix z ij , z kj is the sample at the j-th column and k-th row in the standardized matrix z ij , is the mean value at the j-th column and k-th row in the standardized matrix z ij .

[0067] S5. According to S4, calculate the principal component eigenvalues and eigenvectors.

[0068] Perform eigen decomposition on the correlation coefficient matrix to obtain eigenvalues λ p : λ1 ≥ λ2 ≥... ≥ λ p ≥ 0 and eigenvectors u ij (i = 1, 2,..., p; j = 1, 2,... p), where i is the row and j is the column.

[0069] S6. According to S5, calculate the principal component variance contribution rate and cumulative variance contribution rate.

[0070] The calculation formula for the variance contribution rate f i of the i-th principal component is as follows:

[0071]

[0072] where λ i , λ j are both eigenvalues.

[0073] The calculation formula for the cumulative variance contribution rate F k of the first k principal components is as follows:

[0074]

[0075] where f i is the variance contribution rate of the i-th principal component.

[0076] S7. According to S5 and S6, extract the principal components with eigenvalues > 1 and cumulative variance contribution rate > 85% or so, and determine the number of principal components K.

[0077] The k in S6 is in lowercase (is an integer), and the K in S7 is in uppercase (is a numerical value), and the two are different.

[0078] S8. Calculate the principal component scores according to S3 and S5.

[0079] The calculation formula for the principal component scores is as follows:

[0080]

[0081] where u kj is the principal component coefficient (eigenvector), and z ik is the sample at the i-th row and k-th column in the standardized matrix z ij , where k = 1, 2,..., p.

[0082] S9. Perform min-max normalization on the principal component scores according to S8.

[0083] For the min-max normalization of the principal component scores, the calculation formula for the min-max normalization result t ij is as follows:

[0084]

[0085] where s ij is the principal component score, and s j is the principal component score matrix.

[0086] S10. Calculate the weights of the first K principal components according to S6.

[0087] The calculation formula for the weights of the first K principal components is as follows:

[0088]

[0089] where f i is the variance contribution rate of the i-th principal component.

[0090] S11. Calculate the comprehensive score of the object according to S9 and S10.

[0091] The calculation formula for the comprehensive score of the object is as follows:

[0092]

[0093] where w i is the weight of the first K principal components, and t ij is the min-max normalization result of the principal component scores.

[0094] S12. Draw a scree plot of the eigenvalues and a bar chart of the comprehensive scores for data visualization according to S5 and S11, and complete the principal component comprehensive analysis.

[0095] The following further verifies and explains the present invention in combination with specific embodiments.

[0096] In this example, a certain hydropower engineering project is taken to conduct safety monitoring on the dam body of this project. A total of 31 cross-sections are arranged on the dam body, and there are 12 indicators on each cross-section (crack indicators 1 and 2, seepage pressure indicators 1 and 2, strain indicators 1 and 2, spirit level indicators 1 and 2, seepage flow indicators 1 and 2, anchoring force indicators 1 and 2). Through the method of dimensionality reduction by principal component analysis (PCA), on the premise of not losing less information, a multivariate statistical analysis method that transforms multiple indicators to be analyzed into several comprehensive indicators (i.e., principal components) is used to conduct comprehensive analysis and evaluation of the dam safety monitoring. Combine formulas (1) to (9). The results are shown in Tables 1 to 10 below.

[0097] Table 1: Data Sheet of Dam Safety Monitoring Samples

[0098]

[0099] Table 2: KMO and Bartlett Sphericity Test Table

[0100]

[0101] Table 3: Matrix Table after Z-score Standardization of Sample Data

[0102]

[0103] Table 4: Correlation Coefficient Matrix Table

[0104]

[0105] Table 5: Principal Component Eigenvalue and Eigenvector Table

[0106]

[0107] Table 6: Principal Component Variance Contribution Rate and Cumulative Variance Contribution Rate Table

[0108] Principal component K Variance contribution rate % Cumulative variance contribution rate % 1 37.1553 37.1553 2 15.6439 52.7992 3 12.0870 64.8862 4 9.7676 74.6538

[0109] Table 7: Calculation of Principal Component Score Table

[0110]

[0111] Table 8: Table of Results after Min-Max Normalization of Component Scores

[0112]

[0113] Table 9: Calculation of the Weights of the First K Principal Components

[0114] <![CDATA[w1]]> <![CDATA[w2]]> <![CDATA[w3]]> <![CDATA[w4]]> 0.4419 0.2060 0.1921 0.1599

[0115] Table 10: Calculation of Comprehensive Score Table

[0116] Cross-section Score Rank Cross-section Score Rank Cross-section Score Rank DM01 0.23582 29 DM12 0.54956 10 DM23 0.58176 9 DM02 0.25095 28 DM13 0.60530 8 DM24 0.63869 7 DM03 0.26180 26 DM14 0.50119 20 DM25 0.65819 6 DM04 0.22084 30 DM15 0.52261 16 DM26 0.71159 1 DM05 0.17339 31 DM16 0.52173 17 DM27 0.68073 4 DM06 0.25946 27 DM17 0.54071 12 DM28 0.66891 5 DM07 0.34239 25 DM18 0.50551 19 DM29 0.71103 2 DM08 0.35839 24 DM19 0.52638 14 DM30 0.69260 3 DM09 0.40794 23 DM20 0.50577 18 DM31 0.54494 11 DM10 0.44890 21 DM21 0.52284 15 DM11 0.44110 22 DM22 0.53291 13

[0117] According to Table 5 and Table 10, the eigenvalue scree plot and the bar chart of the comprehensive scores are drawn for data visualization to complete the comprehensive principal component analysis. The scree plot is shown in Figure 2 , and the bar chart of the comprehensive scores is shown in Figure 3 .

Claims

1. A comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring, characterized in that, It includes the following steps: S1. Prepare the sample data for principal component analysis and check the sample data. The requirement for the number of data is the number of objects / the number of indicators > 1. If the requirement is met, proceed to the next step; otherwise, principal component analysis cannot be performed. S2. Conduct the KMO and Bartlett sphericity tests on the sample data in S1. If the test results meet KMO > 0.6 and sig < 0.05, proceed to the next step; otherwise, principal component analysis cannot be performed. Here, KMO is the index for testing the sampling suitability, and sig is the significance. S3. Perform Z - score standardization on the sample data in S1. S4. Calculate the correlation coefficient matrix according to S3. S5. Calculate the principal component eigenvalues and eigenvectors according to S4. S6. Calculate the principal component variance contribution rate and cumulative variance contribution rate according to S5. S7. Extract the principal components with eigenvalues > 1 and cumulative variance contribution rate > 85% approximately according to S5 and S6, and determine the number of principal components. S8. Calculate the principal component scores according to S3 and S5. S9. Perform min - max normalization on the principal component scores according to S8. S10. Calculate the weights of the first K principal components according to S6. S11. Calculate the comprehensive score according to S9 and S10. S12. Draw the eigenvalue scree plot and the comprehensive score bar chart for data visualization according to S5 and S11 to complete the comprehensive principal component analysis.

2. The comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring according to claim 1, wherein In S1, the sample data matrix representation form is: where n is the number of object information and p is the number of index information.

3. The comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring according to claim 1, characterized in that In S3, perform Z-score normalization on the sample data, and the matrix z after normalization ij has the following calculation formula: where μ j and σ j are the mean and standard deviation of the variables in the j-th column of matrix X, respectively, and X′ ij is the sample in matrix X, and j = 1, 2,... p.

4. The comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring according to claim 1, characterized in that In S4, the correlation coefficient matrix r ij is calculated as follows: Among them, z ki is the sample at the i-th column and k-th row in the standardized matrix z ij , is the mean value at the i-th column and k-th row in the standardized matrix z ij , z kj is the sample at the j-th column and k-th row in the standardized matrix z ij , is the mean value at the j-th column and k-th row in the standardized matrix z ij .

5. The comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring according to claim 1, characterized in that, In S5, the correlation coefficient matrix is subjected to eigenvalue decomposition to obtain eigenvalues λ p : λ1 ≥ λ2 ≥... ≥ λ p ≥ 0 and eigenvectors u ij , where i is the row, j is the column, i = 1, 2,..., p; j = 1, 2,... p.

6. The comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring according to claim 1, characterized in that, In S6, the variance contribution rate f of the i-th principal component i is calculated as follows: Among them, λ i , λ j are all eigenvalues, where i = 1, 2,..., p; Cumulative variance contribution rate F of the first k principal components k The calculation formula is as follows: where, f i is the variance contribution rate of the i-th principal component, and k = 1, 2,..., p.

7. The comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring according to claim 1, characterized in that, In S8, the calculation formula for the principal component score is as follows: where, u kj is the principal component coefficient, z ik is the sample at the i-th row and k-th column in the standardized matrix z ij , where k = 1, 2, ..., p.

8. The comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring according to claim 1, characterized in that In the above S9, the principal component scores are processed by min-max normalization, and the min-max normalization result t of the principal component scores ij has the following calculation formula: Among them, s ij is the principal component score, and s j is the principal component score matrix.

9. The comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring according to claim 1, characterized in that In S10, the calculation formula for the weights of the first K principal components is as follows: where, f i is the contribution rate of variance of the i-th principal component, i = 1, 2, ..., k.

10. The comprehensive evaluation analysis and application method based on the principal component analysis technology for dam safety monitoring according to claim 1, characterized in that, In S11, the calculation formula for the object comprehensive score is as follows: where w i is the weight of the first K principal components, and t ij is the result of min-max normalization of the principal component scores.

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