Method for identifying abnormal data of multi-directional stress meter based on svm and pca confidence interval analysis

Abstract

The application relates to a multi-directional stress meter monitoring abnormal data identification method based on SVM and PCA confidence interval analysis, and relates to the field of multi-directional stress meter monitoring data analysis.The specific steps of the application include data and PCA dimension reduction, n confidence circles generation, confidence circle center coordinate generation, final confidence circle radius, final confidence circle and abnormality detection; the application uses SVM to analyze the monitoring data of multiple time periods, analyzes the confidence circle center coordinates obtained after PCA dimension reduction analysis, selects support vectors and averages the support vectors to obtain the final circle center.The application can focus on the key points of determining the data distribution boundary to a greater extent, improves the sensitivity to abnormal values and boundary points, reduces the influence of the solution of the optimal circle center under the condition that abnormal points are more in the overall data or the data distribution is multimodal, and finally obtains the circle center and the radius obtained through average calculation to form a global confidence circle, so that abnormality detection is realized.

Description

Technical Field

[0001] This invention relates to the field of multi-dimensional stress gauge monitoring data analysis, and in particular to a method for identifying anomaly data in multi-dimensional stress gauge monitoring based on SVM and PCA confidence interval analysis, which accurately identifies new anomaly data by learning the distribution of historical data. Background Technology

[0002] Multi-directional stress gauges are widely used in the safety monitoring of dams in hydropower projects, providing crucial mechanical monitoring data. However, with the increasing volume of monitoring data, noise and outliers gradually affect the accuracy of monitoring analysis. Therefore, accurately and efficiently detecting and identifying anomalous data points has become a key issue in monitoring operations. The key characteristics of the monitoring data distribution are often determined by samples at the data boundaries. Using SVM, especially one-class SVM, can help determine the decision boundaries of the data, thereby selecting representative support vectors. These support vectors have higher discriminative power when forming the center of the final confidence circle, and can perform better in data anomaly analysis. Summary of the Invention

[0003] The present invention aims to solve the problem that noise and outliers in existing data affect the accuracy of monitoring business analysis. It provides a method for identifying anomaly data in multi-directional stress gauge monitoring based on SVM and PCA confidence interval analysis, which can accurately identify new anomalies by learning the distribution of historical data.

[0004] The present invention provides a method for identifying anomaly data from multi-directional stress gauge monitoring based on SVM and PCA confidence interval analysis, characterized by the following specific steps:

[0005] I. Data and PCA Dimensionality Reduction

[0006] Suppose there are n time slices, t=1,2,...,n, and each time slice has a k-dimensional vector data:

[0007]

[0008] T represents The transpose of , where R represents the data matrix, i.e., the dataset, and k represents the dimension of the vector data in each time slice.

[0009] Construct a matrix from all the data:

[0010] X

[0011] Centering: Calculating the mean vector

[0012]

[0013] X t X in n*k dimensional vector data t ;

[0014] Centralize X:

[0015]

[0016] Where 1 is an n-dimensional column vector of all 1s;

[0017] Covariance matrix:

[0018]

[0019] Where 1 is an n-dimensional column vector of all 1s, X c It is a centered matrix, where X represents the data matrix. C represents the transpose of the centered matrix, where C is the covariance matrix.

[0020] Eigenvalue decomposition: Find the eigenvalue decomposition of C:

[0021]

[0022] Where λ1≥λ2≥λ3≥λ4≥λ5 are eigenvalues, and v1,v2,…,v5 are the corresponding eigenvectors;

[0023] Select the first two principal components: take the eigenvectors v1 and v2 corresponding to the first two eigenvalues ​​to form a matrix.

[0024]

[0025] Data projected into two-dimensional space:

[0026]

[0027] We obtain n two-dimensional points:

[0028] t=1,…,n

[0029] II. Generate n confidence circles

[0030] For each time point t, there is a two-dimensional coordinate Z. t Let the confidence circle at each time point t be Z. t The radius is chosen based on the degree of dispersion of the local data, with the center as the center.

[0031] The radius r of each circle t The variation at local points within that time slice determines that there are n sub-data points within time t.

[0032]

[0033] After projecting it onto a two-dimensional coordinate system, we get

[0034] ,

[0035] The radius of the circle is the distance between these points and its center, i.e. Average Euclidean distance:

[0036] ;

[0037] III. Generating the coordinates of the center of the confidence circle

[0038] Given dataset {zt} t=1 n The following optimization problem is solved:

[0039]

[0040] Constraints:

[0041]

[0042] in It is a mapping function, with ν∈(0,1] as the parameter. After solving, we obtain the Lagrange multiplier α. t ;

[0043] The set of vectors is:

[0044]

[0045] Final center calculation:

[0046] After obtaining the set of support vectors S, the final center of the circle is defined as the arithmetic mean of the support vectors:

[0047] =

[0048] Obtain the coordinates of the center of the circle;

[0049] IV. Radius of the final confidence circle

[0050] The final confidence circle radius is obtained by taking the arithmetic mean of all n ellipse radii {rt}.

[0051]

[0052] V. Final Confidence Circle

[0053] Based on the above calculations, the final confidence circle is defined as follows:

[0054] Center: z final And radius: R;

[0055] VI. Anomaly Detection

[0056] Given new data x^, the PCA process described above is as follows:

[0057] Centralization: =

[0058] projection:

[0059] judge Is it within the final confidence circle?

[0060] ≤R normal

[0061] >R abnormal

[0062] Complete the calculation process.

[0063] This invention relates to the field of multi-dimensional stress gauge monitoring data analysis. It utilizes SVM (Support Vector Machine) to analyze the coordinates of the center of confidence circles obtained after PCA dimensionality reduction analysis of monitoring data from multiple time periods. This analysis selects support vectors and averages these support vectors to obtain the final circle center. This method can focus more on key points that determine the data distribution boundary, improving sensitivity to outliers and boundary points, and reducing the impact of numerous outliers or multimodal data distribution on finding the optimal circle center. The final circle center, together with the radius calculated by averaging, constitutes a global confidence circle, achieving anomaly detection. Attached Figure Description

[0064] Figure 1 This is a screenshot of the results for test data 1.

[0065] Figure 2 Screenshot of the results for test data 2.

[0066] Figure 3 Screenshot of the results for test data 3. Detailed Implementation

[0067] Example 1: A method for identifying anomaly data from multi-directional stress gauge monitoring based on SVM and PCA confidence interval analysis, characterized by the following specific steps:

[0068] I. Data and PCA Dimensionality Reduction

[0069] 1. Data Acquisition:

[0070] In the inclinometer monitoring system, data from nine measuring points are collected at regular intervals to form an n×9 data matrix. The following is the monitoring data of a multi-directional stress gauge for a power station dam:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] I. PCA Dimensionality Reduction:

[0085] Suppose there are n time slices, t=1,2,...,n, and each time slice has an n-dimensional vector data:

[0086]

[0087] Construct a matrix from all the data:

[0088] X

[0089] Centering: Calculating the mean vector

[0090]

[0091] Centralize X:

[0092]

[0093] Where 1 is an n-dimensional column vector of all 1s;

[0094] Covariance matrix:

[0095]

[0096] Eigenvalue decomposition: Find the eigenvalue decomposition of C:

[0097]

[0098] Where λ1≥λ2≥λ3≥λ4≥λ5 are eigenvalues, and v1,v2,…,v5 are the corresponding eigenvectors;

[0099] Select the first two principal components:

[0100] Take the eigenvectors v1 and v2 corresponding to the two largest eigenvalues ​​to form a matrix.

[0101]

[0102] Data projected into two-dimensional space:

[0103]

[0104] We obtain n two-dimensional points:

[0105] t=1,…,n

[0106] The data obtained after standardization is as follows:

[0107] [[-5.1700e-01 -1.6050e+00 -2.6100e+00 -9.3100e-01 2.1540e+00 3.4810e+00 2.4500e-01 3.6110e+00 1.0140e+01] [-8.7400e-01 -1.9400e+00 -2.6050e+00 -1.2720e+00 2.1540e+00 3.4610e+00 -1.4400e-01 2.9580e+00 1.0165e+01] [-1.2170e+00 -2.2730e+00 -2.9290e+00 -1.2690e+00 2.4640e+00 2.4300e+00 2.3000e-012.9460e+00 9.8270e+00] [-1.1970e+00 -2.3080e+00 -3.3110e+00 -1.6450e+003.1630e+00 2.4400e+00 -4.6800e-01 2.5600e+00 9.8270e+00] [-2.3600e-01 -2.0050e+00 -2.6460e+00 -1.2970e+00 3.1770e+00 3.0520e+00 5.2800e-01 3.2190e+00 9.5510e+00] [-1.3000e-01 -1.9650e+00 -2.9480e+00 -1.5420e+00 2.1690e+003.4810e+00 -4.8300e-01 3.5800e+00 1.0246e+01] [-8.6300e-01 -1.6260e+00 -2.6310e+00 -1.3220e+00 3.5560e+00 4.1420e+00 8.1200e-01 3.5850e+00 1.0215e+01] [-5.1800e-01 -2.0040e+00 -2.9940e+00 -1.5850e+00 2.1500e+00 2.7580e+00 -1.5400e-01 3.2470e+00 9.6000e+00] [-1.5500e-01 -1.6560e+00 -2.6660e+00 -6.6000e-01 2.8120e+00 3.0860e+00 5.4800e-01 3.2340e+00 9.9130e+00] [1.3800e-01 -9.6300e-01 -1.9200e+00 -9.7400e-01 3.5200e+00 3.8030e+00 9.2200e-013.9240e+00 1.0332e+01] [-1.5550e+00 -1.9680e+00 -3.3170e+00 -1.2620e+001.8060e+00 3.1320e+00 -8.0100e-01 3.2500e+00 9.6140e+00] [-1.2470e+00 -2.3340e+00 -3.0650e+00 -1.3750e+00 2.4590e+00 2.7220e+00 -1.6400e-01 3.5680e+00 9.9830e+00] [-8.8700e-01 -2.2770e+00 -3.0260e+00 -1.6630e+00 2.1200e+002.3740e+00 -4.8800e-01 2.8680e+00 9.3120e+00] [-5.3700e-01 -1.5860e+00 -2.6160e+00 -6.2000e-01 2.4330e+00 3.1160e+00 1.9400e-01 2.9230e+00 9.7370e+00] [-5.9200e-01 -1.3670e+00 -2.6910e+00 -1.3170e+00 2.8220e+00 3.3790e+00 -1.6500e-01 3.2290e+00 1.0014e+01] [-8.3600e-01 -2.3630e+00 -3.6900e+00 -1.3320e+00 2.4900e+00 2.4040e+00 -4.8300e-01 2.5270e+00 8.6920e+00] [-1.8500e-01 -1.5960e+00 -2.6660e+00 -9.9100e-01 2.4730e+00 3.4790e+00 -1.3000e-01 3.2340e+00 9.4450e+00] [-2.0300e-01 -5.8300e-01 -2.3230e+00 -6.4800e-01 3.8540e+00 3.7770e+00 5.6300e-01 3.2510e+00 9.4660e+00] [-1.2430e+00 -1.6840e+00 -3.3730e+00 -1.3620e+00 2.8240e+00 2.7270e+00 -8.6700e-012.8990e+00 8.7380e+00] [-5.7900e-01 -1.6150e+00 -2.6920e+00 -9.1800e-012.4640e+00 2.7620e+00 2.0500e-01 3.2420e+00 9.4840e+00] [-9.1200e-01 -2.3280e+00 -3.0610e+00 -1.3370e+00 2.4690e+00 2.7620e+00 -5.0800e-01 2.9090e+008.8540e+00] [-5.4800e-01 -2.0300e+00 -3.0300e+00 -1.3500e+00 2.7620e+002.7060e+00 -2.0500e-01 2.8760e+00 9.1320e+00] [-5.6000e-01 -1.9530e+00 -3.0460e+00 -9.5100e-01 2.1300e+00 3.1200e+00 1.3000e-01 3.1950e+00 8.8940e+00] [4.4800e-01 -1.3770e+00 -2.0370e+00 -1.0520e+00 3.4300e+00 3.3880e+00 -5.9500e-01 2.8420e+00 9.1780e+00] [-1.2940e+00 -1.6690e+00 -2.7090e+00 -9.8600e-01 2.4290e+00 2.3170e+00 -8.7700e-01 2.8680e+00 7.8610e+00] [-1.8600e-01 -1.6600e+00 -2.3800e+00 -6.7300e-01 2.7720e+00 2.6510e+00 -1.9000e-01 2.8860e+00 8.6070e+00] [-9.3700e-01 -1.6790e+00 -2.7290e+00 -1.0070e+00 2.4590e+00 1.6650e+00 -5.4300e-01 2.5370e+00 8.2640e+00] [-5.7800e-01 -1.3460e+00 -2.3700e+00 -6.8300e-01 2.4180e+00 2.3070e+00 -2.0000e-01 2.8500e+00 8.6380e+00] [-1.2830e+00 -1.3700e+00 -2.3770e+00 -1.0470e+00 1.6950e+00 1.6600e+00 -5.8400e-01 2.4770e+00 7.9620e+00] [-1.6190e+00 -2.3910e+00 -3.0180e+00 -1.3420e+00 1.3930e+00 1.2870e+00 -1.2300e+001.8350e+00 7.6130e+00] [-5.9300e-01 -6.4700e-01 -2.0030e+00 -3.1700e-012.4380e+00 2.7200e+00 -5.3900e-01 3.1820e+00 8.0480e+00] [-9.5700e-01 -9.8100e-01 -2.0650e+00 -1.0470e+00 2.0840e+00 2.0080e+00 8.9000e-02 2.1760e+00 8.3850e+00] [-6.5200e-01 -1.0600e+00 -2.0410e+00 -1.0850e+00 2.3790e+001.6440e+00 -1.6100e+00 2.0980e+00 7.3870e+00] [-5.6500e-01 -1.3400e+00 -2.3770e+00 -6.9100e-01 3.1430e+00 2.0030e+00 -9.0800e-01 2.8480e+00 8.8030e+00] [-1.0090e+00 -2.0380e+00 -2.4430e+00 -1.4260e+00 2.7740e+00 1.5990e+00 -1.5950e+00 2.4600e+00 8.7770e+00] [-5.4600e-01 -2.0130e+00 -2.0400e+00 -1.3500e+00 2.7890e+00 1.6740e+00 -9.2200e-01 2.5500e+00 8.4700e+00] [-9.5000e-01 -1.4030e+00 -2.7970e+00 -1.7940e+00 2.4000e+00 1.2500e+00 -9.6700e-01 1.1180e+00 7.7940e+00] [-1.2950e+00 -1.0100e+00 -2.3780e+00 -7.1900e-01 2.7690e+00 1.6390e+00 -9.3200e-01 1.7720e+00 8.1980e+00] [-6.5200e-01 -7.6600e-01 -2.0910e+00 -1.4010e+00 3.0880e+00 8.9200e-01 -1.3010e+00 1.7870e+00 7.5530e+00] [-9.8700e-01 -4.1800e-01 -1.3850e+00 -1.1230e+003.0420e+00 1.2050e+00 -2.4500e-01 2.1000e+00 7.8410e+00] [-1.0090e+00 -1.3640e+00 -2.1160e+00 -1.7970e+00 1.6800e+00 9.0100e-01 -6.1900e-01 1.7620e+00 6.5000e+00] [-3.6200e-01 -4.1900e-01 -1.1420e+00 -4.1800e-01 3.7450e+001.8760e+00 6.8000e-02 1.7560e+00 7.5850e+00] [-6.2700e-01 -1.3590e+00 -1.3360e+00 -1.0700e+00 2.4300e+00 9.2600e-01 -9.2200e-01 1.1150e+00 6.9430e+00] [-1.0340e+00 -1.1010e+00 -1.8440e+00 -8.0400e-01 2.6630e+00 1.1540e+00 -1.0480e+00 1.3450e+00 5.8750e+00] [-9.8400e-01 -1.0300e+00 -1.4270e+00 -7.2900e-01 2.0850e+00 8.7100e-01 -9.6800e-01 1.4810e+00 6.6610e+00] [-7.4600e-01 -4.2300e-01 -1.1690e+00 -8.3200e-01 2.6770e+00 1.1090e+00 3.1700e-01 2.0650e+00 6.6110e+00] [-2.6700e-01 -1.4440e+00 -2.1380e+00 -1.4990e+002.6540e+00 5.1700e-01 -9.6700e-01 3.6400e-01 5.9650e+00] [-2.4790e+00 -3.3000e-02 -1.0780e+00 -7.4200e-01 3.0720e+00 1.5780e+00 -3.1100e-01 1.8700e+00 6.4250e+00] [1.8000e-02 -4.3300e-01 -7.4100e-01 -8.0200e-01 2.7420e+001.5520e+00 3.3000e-02 4.2700e-01 6.0120e+00] [3.6500e-01 -2.3000e-02 -1.0880e+00 -4.2600e-01 2.6970e+00 1.1590e+00 9.5900e-01 1.0810e+00 6.4200e+00] [-4.9000e-02 -1.1310e+00 -1.1550e+00 -1.1610e+00 2.6730e+00 8.1000e-01 -7.1000e-01 1.0490e+00 5.3410e+00] [-3.4900e-01 -6.3000e-02 -7.7100e-01 -1.3500e-01 2.6620e+00 1.1680e+00 3.4200e-01 2.0650e+00 6.0870e+00] [3.6000e-02 -1.0800e-01 -7.5700e-01 -5.1400e-01 2.7030e+00 7.8500e-01 3.4700e-011.7670e+00 6.0870e+00] [-7.1400e-01 -4.7600e-01 -8.6400e-01 -8.1700e-012.6130e+00 8.0400e-01 -1.4120e+00 3.0400e-01 5.4560e+00] [-6.4000e-022.2200e-01 -8.2800e-01 -1.1510e+00 2.6070e+00 7.9400e-01 -7.5000e-01 1.7010e+00 5.1090e+00] [-6.5500e-01 -7.2400e-01 -1.4290e+00 -1.4560e+00 2.0210e+008.9000e-01 -1.0120e+00 4.1300e-01 5.2030e+00] [-1.1130e+00 -8.1000e-01 -8.3500e-01 -1.1960e+00 1.5560e+00 7.7000e-02 -1.0480e+00 3.1200e-01 5.1780e+00] [-1.3890e+00 -1.1640e+00 -1.4740e+00 -1.2210e+00 1.2570e+00 -5.9500e-01 -1.0630e+00 3.0700e-01 4.1500e+00] [-7.5900e-01 -7.8000e-01 -4.5600e-01 -8.7700e-01 2.2990e+00 1.1530e+00 -1.0430e+00 1.0820e+00 4.7610e+00] [-7.8100e-01 -8.1000e-01 -8.2000e-01 -1.6020e+00 1.9060e+00 -3.1600e-01 -1.4420e+00 6.6800e-01 4.1910e+00] [-7.1900e-01 -5.6000e-02 -4.2600e-01 -8.4200e-01 2.4000e+00 1.5200e-01 -6.8900e-01 1.0620e+00 4.9470e+00] [-2.0910e+00 -7.8700e-01 -1.8590e+00 -1.5520e+00 9.8500e-01 -8.7800e-01 -2.3870e+003.7000e-02 3.9320e+00] [-1.1210e+00 1.5200e-01 -8.5400e-01 -5.2200e-012.2640e+00 3.9500e-01 -7.1400e-01 6.3000e-01 4.5690e+00] [-1.1130e+00 -4.7500e-01 -8.6500e-01 -9.2000e-01 1.9560e+00 1.1700e-01 -1.0880e+00 6.4300e-01 4.3010e+00] [-7.3400e-01 -1.8700e-01 -8.8900e-01 -1.2140e+00 2.2240e+002.7000e-02 -7.3400e-01 2.9400e-01 4.3380e+00] [-1.1660e+00 -1.1750e+00 -4.9700e-01 -5.4200e-01 1.9500e+00 4.2000e-02 -4.3600e-01 6.5000e-01 4.3680e+00] [-1.4460e+00 -8.3400e-01 -8.7100e-01 -1.2230e+00 1.2580e+00 -2.5700e-01 -1.4510e+00 -2.6000e-02 4.0340e+00] [-4.5100e-01 5.3600e-01 1.5900e-01 -2.0300e-01 2.9520e+00 4.2000e-01 -3.2000e-02 1.6910e+00 5.1240e+00] [-1.7170e+00 -4.4400e-01 -1.5260e+00 -1.5240e+00 1.3080e+00 -5.2000e-01 -1.4010e+009.0000e-03 4.4220e+00] [-1.1140e+00 -1.4500e-01 -1.2340e+00 -1.2280e+001.5670e+00 4.2000e-02 -1.4560e+00 2.9000e-01 4.0840e+00] [-8.2200e-01 -4.6500e-01 -8.5000e-01 -1.2360e+00 1.5910e+00 -2.5700e-01 -3.9000e-016.2800e-01 4.4780e+00] [-1.1560e+00 1.8700e-01 -5.2700e-01 -6.1200e-012.5430e+00 4.4400e-01 -4.8600e-01 2.2900e-01 4.4280e+00] [-1.0900e-015.4600e-01 -5.4600e-01 -2.0800e-01 1.8780e+00 3.6500e-01 2.2600e-01 9.4300e-01 5.1700e+00] [-7.8600e-01 -1.7100e-01 -8.7600e-01 -9.1500e-01 1.5610e+003.6000e-02 -3.8000e-01 3.1700e-01 4.5530e+00] [2.1700e-01 1.5600e-01 -1.9900e-01 1.1200e-01 2.1970e+00 -3.5300e-01 2.1100e-01 9.5900e-01 5.2000e+00] [-4.2600e-01 2.2100e-01 5.1100e-01 -1.9800e-01 2.2880e+00 1.6000e-02 -7.5000e-01 6.5800e-01 5.2300e+00] [-8.1600e-01 -2.0600e-01 -8.8600e-01 -6.6000e-01 2.2190e+00 -3.4300e-01 -1.1580e+00 2.2600e-01 3.8580e+00] [-4.2900e-01 1.9300e-01 1.2600e-01 -5.5400e-01 1.9250e+00 1.0600e-01 -7.6400e-01 -6.4000e-02 4.2260e+00] [2.5100e-01 1.3200e-01 -2.2000e-01 -2.0600e-011.8740e+00 5.1000e-02 -4.4600e-01 -6.7000e-02 3.5820e+00] [-1.1950e+00 -1.8500e-01 -2.4200e-01 -6.4200e-01 1.5370e+00 -6.8600e-01 -8.2400e-01 -4.4300e-01 3.2070e+00] [-4.4900e-01 5.1800e-01 -2.2600e-01 -2.5400e-011.8850e+00 -7.2100e-01 -8.0400e-01 2.4100e-01 3.9590e+00] [-1.2000e+00 -2.0000e-01 -2.4700e-01 -3.4100e-01 1.5110e+00 -3.5800e-01 -1.5820e+00 -7.8900e-01 3.2630e+00] [-1.1300e-01 -9.6000e-02 -9.0600e-01 -2.5900e-011.5460e+00 -1.0500e+00 -7.6900e-01 2.4700e-01 3.9540e+00] [-1.1500e+00 -1.4500e-01 -1.9200e-01 -5.8200e-01 1.6120e+00 -9.6000e-01 -4.1500e-016.6600e-01 3.3890e+00] [-1.1970e+00 -5.7400e-01 -6.1100e-01 -9.8600e-018.1900e-01 -1.7070e+00 -1.1520e+00 -8.0700e-01 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-1.0740e+00 -6.3380e+00] [1.7560e+00 5.9500e-011.6300e-01 1.1360e+00 -1.4860e+00 -5.5700e-01 -3.2000e-02 -6.5700e-01 -5.6880e+00] [9.8700e-01 2.2100e-01 4.5500e-01 8.3500e-01 -1.8910e+00 -1.6900e-01 2.7700e-01 -7.0700e-01 -6.1110e+00] [6.6500e-01 -1.2400e-011.7300e-01 8.3000e-01 -1.1870e+00 -5.4700e-01 -3.1000e-02 -6.8700e-01 -5.7230e+00] [6.9900e-01 -4.3200e-01 -1.4000e-01 1.8600e-01 -2.1440e+00 -1.0400e-01 -3.4500e-01 -2.0540e+00 -6.1570e+00] [6.6900e-01 -4.7200e-01 -5.0800e-01 5.0700e-01 -1.8300e+00 -5.1200e-01 2.8800e-01 -1.0250e+00 -6.1220e+00] [9.9700e-01 -8.1800e-01 -1.0900e-01 4.7900e-01 -1.4810e+00 -1.0400e-01 -1.1000e-02 -3.1600e-01 -5.4610e+00] [1.4510e+00 -4.1900e-01 -1.2800e-015.2700e-01 -1.4370e+00 -8.3600e-01 7.2600e-01 -3.1900e-01 -4.7950e+00][6.2700e-01 -4.6400e-01 1.2400e-01 7.9700e-01 -1.1730e+00 -2.3400e-01 -3.9100e-01 -3.9900e-01 -4.8350e+00] [9.9900e-01 2.2000e-01 -5.4100e-018.3700e-01 -1.4670e+00 -1.9900e-01 2.6700e-01 -9.8600e-01 -4.5230e+00] [-1.0000e-03 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1.0170e+00 6.7000e-01 4.5090e+00] [3.8200e-01 -1.7780e+00 -2.5380e+00 2.2000e-01 -7.9400e-01 2.5990e+00 1.7800e+00 1.7920e+00 5.2150e+00] [-3.5200e-01 -4.2210e+00 -4.5700e+00 -8.3000e-01 -1.4850e+00 1.5880e+002.7500e-01 3.2500e-01 5.1270e+00] [-6.8000e-02 -2.5770e+00 -3.2340e+00 -1.6900e-01 -8.2400e-01 1.8860e+00 5.9800e-01 1.3280e+00 6.4390e+00] [-4.1900e-01 -2.8560e+00 -3.8980e+00 -4.8000e-01 -8.1300e-01 1.8670e+006.1800e-01 1.3730e+00 6.1160e+00] [-3.1700e-01 -2.1070e+00 -3.5140e+00 -9.1000e-02 -1.4530e+00 2.2600e+00 1.0420e+00 1.4110e+00 6.8380e+00] [-3.8900e-01 -2.8860e+00 -4.5980e+00 -4.4900e-01 -1.5420e+00 1.8320e+006.3300e-01 1.6640e+00 7.4510e+00] [-3.8200e-01 -2.5220e+00 -3.9070e+00 -4.1700e-01 -4.4500e-01 2.2350e+00 1.3610e+00 1.3800e+00 7.4220e+00] [-3.5700e-01 -2.7910e+00 -3.8970e+00 -5.0700e-01 -4.7500e-01 2.2750e+00 1.3150e+00 1.7220e+00 8.0570e+00] [2.7200e-01 -2.8380e+00 -3.8860e+00 -4.4500e-01 -4.3600e-01 2.2650e+00 1.3900e+00 1.4230e+00 8.0830e+00] [-6.5300e-01 -3.1760e+00 -4.1840e+00 -3.4600e-01 -1.1030e+00 2.2600e+00 1.4260e+00 1.3700e+008.4250e+00] [-1.3500e+00 -3.4930e+00 -4.5080e+00 -1.8160e+00 -1.5060e+001.6540e+00 3.8500e-01 7.4900e-01 8.0500e+00] [-6.8900e-01 -3.4700e+00 -4.2140e+00 -7.2800e-01 -7.7400e-01 2.6440e+00 1.7500e+00 1.7010e+00 8.7270e+00] [-3.4500e-01 -2.2090e+00 -3.5890e+00 -1.3900e-01 -4.9100e-01 2.9370e+001.7790e+00 2.0100e+00 9.3270e+00] [-3.8200e-01 -3.2310e+00 -4.2190e+00 -8.4300e-01 -8.4000e-01 2.5840e+00 1.0270e+00 1.3850e+00 9.3260e+00] [-2.9000e-01 -3.1620e+00 -3.8050e+00 -3.3900e-01 -9.6000e-02 3.0170e+00 1.4860e+00 1.7540e+00 9.6950e+00] [-6.7700e-01 -2.8280e+00 -4.1880e+00 -4.3900e-01 -4.4100e-01 2.6390e+00 1.0460e+00 2.1460e+00 9.6400e+00] [-3.2500e-01 -2.8280e+00 -4.1880e+00 -7.5000e-01 -4.8600e-01 2.9820e+00 1.7190e+00 2.0500e+009.9270e+00] [-7.9100e-01 -2.5750e+00 -3.9300e+00 -8.4400e-01 -1.4300e-013.6140e+00 1.3140e+00 2.3530e+00 1.0920e+01] [-3.8900e-01 -2.4890e+00 -3.5070e+00 -4.0700e-01 2.4200e-01 3.3250e+00 1.4000e+00 3.1510e+00 1.0578e+01] [-1.0490e+00 -2.8180e+00 -4.1930e+00 -1.1520e+00 -9.7000e-02 3.3310e+001.3850e+00 2.4110e+00 1.0572e+01] [-6.3600e-01 -3.8110e+00 -4.8780e+00 -1.7830e+00 -1.0200e-01 3.3360e+00 1.7240e+00 2.4570e+00 1.0914e+01] [-6.4000e-01 -2.7680e+00 -3.4420e+00 -1.0640e+00 -9.2000e-02 3.3760e+00 1.0910e+00 2.7750e+00 1.0905e+01] [-1.0480e+00 -2.8230e+00 -4.1630e+00 -1.1170e+00 -8.7000e-02 2.9070e+00 1.3900e+00 2.0200e+00 1.0506e+01] [-6.3800e-01 -2.8300e+00 -3.1840e+00 -7.2000e-01 2.4600e-01 3.2950e+00 1.7530e+00 3.0880e+001.1551e+01] [-1.3300e+00 -2.4330e+00 -3.7900e+00 -1.4420e+00 3.2300e-012.6490e+00 1.4000e+00 2.1460e+00 1.1534e+01] [-7.4200e-01 -3.1520e+00 -4.1830e+00 -1.4370e+00 -5.6000e-02 2.6530e+00 1.0710e+00 2.1200e+00 1.1191e+01] [-6.7300e-01 -2.4960e+00 -3.5160e+00 -1.4480e+00 1.2840e+00 3.2850e+002.0010e+00 2.7670e+00 1.1803e+01] [-7.3000e-01 -2.8190e+00 -3.7940e+00 -1.4600e+00 2.5700e-01 3.6940e+00 1.7490e+00 2.7750e+00 1.1787e+01] [-1.0180e+00 -2.8330e+00 -4.1880e+00 -2.1240e+00 -1.0200e-01 3.3350e+00 1.7190e+002.4470e+00 1.0411e+01] [-1.0820e+00 -2.4940e+00 -4.2220e+00 -1.8260e+001.7600e-01 3.3000e+00 1.3740e+00 2.7550e+00 1.1762e+01] [-3.2600e-01 -2.0550e+00 -3.4210e+00 -1.3970e+00 1.2840e+00 4.0270e+00 2.1220e+00 3.1430e+001.1737e+01] [-6.7800e-01 -2.7900e+00 -3.8240e+00 -1.3870e+00 9.8000e-013.6940e+00 2.1270e+00 3.1580e+00 1.1112e+01] [-1.3750e+00 -2.4730e+00 -4.1330e+00 -1.4480e+00 2.4800e-01 2.6230e+00 1.4150e+00 2.1510e+00 1.0703e+01] [-1.0060e+00 -2.8090e+00 -3.8200e+00 -1.0840e+00 9.5100e-01 3.0110e+001.7130e+00 2.8000e+00 1.1041e+01] [-9.9100e-01 -2.8190e+00 -3.5070e+00 -1.4250e+00 5.3100e-01 3.7140e+00 1.4100e+00 2.7900e+00 1.1424e+01] [-1.3450e+00 -2.4580e+00 -4.1430e+00 -1.4370e+00 6.4700e-01 3.3950e+00 7.3700e-012.1360e+00 1.1338e+01] [-6.8500e-01 -2.1700e+00 -3.8450e+00 -1.4850e+002.3700e-01 3.6430e+00 1.3440e+00 3.4120e+00 1.0910e+01] [-1.2760e+00 -2.7460e+00 -4.8190e+00 -1.7260e+00 -3.6000e-01 3.0520e+00 1.0870e+00 2.4800e+001.0334e+01] [-3.7500e-01 -2.8330e+00 -4.5510e+00 -1.7890e+00 5.9700e-013.3100e+00 1.0310e+00 2.6970e+00 1.0617e+01] [-3.3600e-01 -2.1160e+00 -3.4960e+00 -7.7100e-01 6.1000e-01 4.3650e+00 1.4040e+00 3.1590e+00 1.1319e+01] [-1.0380e+00 -3.1770e+00 -3.8910e+00 -1.4780e+00 6.5200e-01 3.3350e+007.6700e-01 3.0480e+00 1.0950e+01] [-9.9400e-01 -2.4300e+00 -3.1340e+00 -1.1170e+00 1.3090e+00 4.0470e+00 2.1420e+00 3.7960e+00 1.1027e+01] [-6.9500e-01 -2.4850e+00 -3.5180e+00 -1.4450e+00 5.8600e-01 3.6830e+00 2.0820e+003.1360e+00 1.0981e+01] [3.1000e-02 -1.4270e+00 -3.7880e+00 -3.9000e-015.6000e-01 3.6930e+00 2.0770e+00 2.8220e+00 1.0291e+01] [-1.0670e+00 -2.5150e+00 -3.8350e+00 -1.8110e+00 5.6600e-01 4.0410e+00 2.3460e+00 3.4120e+001.0547e+01] [-9.7800e-01 -3.1620e+00 -3.8060e+00 -1.7740e+00 2.6300e-013.3450e+00 1.4150e+00 3.1240e+00 1.0275e+01] [-6.7000e-01 -1.7800e+00 -4.1720e+00 -1.0790e+00 1.2800e+00 4.0220e+00 1.0760e+00 2.8100e+00 1.1308e+01] [-6.2600e-01 -2.7980e+00 -4.1330e+00 -1.7940e+00 5.9200e-01 3.3650e+001.0860e+00 3.1140e+00 1.0617e+01] [-1.7110e+00 -2.4680e+00 -3.8060e+00 -1.7840e+00 -5.7000e-02 3.3350e+00 7.1200e-01 2.8080e+00 1.0265e+01] [-1.7690e+00 -3.1970e+00 -3.7970e+00 -2.2080e+00 2.6900e-01 3.0210e+00 1.0570e+002.4440e+00 9.2210e+00] [-1.0430e+00 -2.1140e+00 -3.5090e+00 -1.4430e+002.2700e-01 3.3740e+00 7.0700e-01 2.7880e+00 1.0587e+01] [-5.9900e-01 -2.0600e+00 -2.7170e+00 -1.0290e+00 9.8100e-01 3.3550e+00 1.4700e+00 3.1410e+001.0950e+01] [-1.3110e+00 -3.1510e+00 -3.4650e+00 -2.0970e+00 -6.6000e-022.9460e+00 4.0900e-01 2.0980e+00 9.2560e+00] [-1.0330e+00 -2.3930e+00 -3.4940e+00 -1.3930e+00 9.5600e-01 3.6780e+00 1.1060e+00 2.7980e+00 1.0244e+01] [-6.9600e-01 -2.4740e+00 -3.5590e+00 -1.1070e+00 -1.1700e-01 3.2840e+006.6700e-01 3.0940e+00 1.0527e+01] [-3.7500e-01 -2.8580e+00 -3.8810e+00 -7.4100e-01 5.7200e-01 3.6420e+00 1.0210e+00 2.7730e+00 1.0531e+01] [-1.0730e+00 -2.4640e+00 -3.5040e+00 -7.6100e-01 2.2700e-01 3.3590e+00 7.0200e-013.7760e+00 1.0557e+01] [-3.3300e-01 -1.7660e+00 -3.1350e+00 -1.0490e+009.6500e-01 4.0360e+00 1.1060e+00 3.4930e+00 1.0991e+01] [-3.3000e-01 -2.1640e+00 -3.1670e+00 -1.7940e+00 2.6700e-01 2.9550e+00 1.0360e+00 3.4550e+009.8510e+00] [-7.2500e-01 -1.8010e+00 -3.4980e+00 -1.1500e+00 9.7500e-013.3090e+00 1.3790e+00 3.4470e+00 1.0568e+01] [-1.4170e+00 -2.8370e+00 -4.2300e+00 -1.8520e+00 -1.5600e-01 2.5810e+00 6.7200e-01 2.3740e+00 9.8860e+00] [-1.3280e+00 -2.7910e+00 -4.1860e+00 -2.4760e+00 -4.4500e-01 2.9800e+003.6900e-01 2.3820e+00 8.9280e+00] [-1.0250e+00 -3.1620e+00 -3.8370e+00 -2.1680e+00 6.0300e-01 3.0250e+00 3.6300e-01 2.4040e+00 9.5830e+00] [-3.8200e-01 -2.4880e+00 -3.8520e+00 -1.4300e+00 -9.1000e-02 3.0000e+00 3.5800e-012.7350e+00 8.9490e+00] [-9.7400e-01 -2.8020e+00 -3.8320e+00 -1.7910e+002.9900e-01 3.0450e+00 7.1200e-01 2.4490e+00 9.6090e+00] [-1.4110e+00 -2.1640e+00 -3.5450e+00 -1.8020e+00 2.6300e-01 2.9740e+00 6.6700e-01 2.3790e+008.5610e+00] [-2.9200e-01 -1.4010e+00 -2.4410e+00 -3.5200e-01 9.8000e-013.3480e+00 1.4290e+00 3.8240e+00 9.6410e+00] [-9.9200e-01 -2.0940e+00 -3.4790e+00 -1.7740e+00 6.2200e-01 3.3280e+00 1.0710e+00 3.1040e+00 8.9850e+00] [-3.5800e-01 -1.0920e+00 -2.1340e+00 -1.1400e+00 9.0000e-01 3.3180e+001.0250e+00 3.1110e+00 9.2580e+00] [-6.6800e-01 -2.1330e+00 -3.8120e+00 -1.4560e+00 2.3300e-01 2.9450e+00 3.5300e-01 2.4390e+00 8.6010e+00] [-9.5400e-01 -2.1030e+00 -2.8510e+00 -1.0690e+00 5.8800e-01 2.9400e+00 1.0860e+002.8060e+00 8.5610e+00] [-7.3800e-01 -1.8590e+00 -3.2480e+00 -1.5310e+001.9800e-01 3.3130e+00 6.9200e-01 2.7450e+00 8.5560e+00] [-3.6100e-01 -1.7740e+00 -2.8160e+00 -1.1200e+00 6.0200e-01 2.9440e+00 7.1200e-01 2.7760e+008.2840e+00] [3.1000e-02 -1.7690e+00 -3.1230e+00 -8.0400e-01 5.6700e-012.9940e+00 3.6300e-01 2.4550e+00 8.6670e+00] [-3.7100e-01 -1.8290e+00 -2.8660e+00 -1.1500e+00 5.6700e-01 2.2320e+00 5.9000e-02 2.4290e+00 8.9490e+00] [-3.5300e-01 -1.7930e+00 -3.4710e+00 -1.1020e+00 -6.5000e-02 2.2820e+00 -2.8900e-01 2.4320e+00 8.3690e+00] [-1.0660e+00 -1.7980e+00 -3.5470e+00 -1.5130e+00 2.7400e-01 2.2870e+00 2.9800e-01 2.0760e+00 7.6030e+00] [-7.6500e-01 -2.2030e+00 -3.5170e+00 -1.8600e+00 1.9900e-01 2.2660e+00 -4.1000e-022.3870e+00 7.9150e+00] [-7.1000e-01 -1.8080e+00 -3.1990e+00 -1.1720e+002.3900e-01 2.2020e+00 -2.6000e-02 1.7200e+00 7.1950e+00] [3.7400e-01 -7.0600e-01 -2.4220e+00 -4.0000e-01 6.5700e-01 3.0440e+00 7.2200e-01 2.8080e+00 7.6900e+00] [-1.0380e+00 -1.7570e+00 -3.2150e+00 -1.4350e+00 2.7500e-012.3420e+00 -6.6800e-01 1.7430e+00 6.3420e+00] [-3.8800e-01 -1.4540e+00 -2.8920e+00 -5.0600e-01 2.3900e-01 1.9230e+00 -6.6000e-02 2.3620e+00 6.9020e+00] [-3.2300e-01 -1.4230e+00 -3.1540e+00 -1.1320e+00 5.9800e-01 2.2920e+00 -3.2400e-01 2.3920e+00 6.3280e+00] [-5.0000e-02 -1.1050e+00 -2.1560e+00 -7.7900e-01 2.5300e-01 3.0180e+00 7.3200e-01 2.4290e+00 6.3440e+00] [-7.3000e-01 -1.8430e+00 -2.5000e+00 -1.4830e+00 5.9300e-01 2.6050e+00 3.8400e-011.7090e+00 6.3530e+00] [-7.5200e-01 -1.7820e+00 -2.8580e+00 -1.4960e+002.5000e-01 2.6450e+00 -1.5000e-02 1.3460e+00 5.6470e+00] [9.0000e-03 -1.1190e+00 -2.4500e+00 -1.1630e+00 2.0800e-01 2.3110e+00 -3.6000e-02 2.0310e+005.6930e+00] [3.1700e-01 -1.1200e+00 -2.4690e+00 -3.9800e-01 2.6800e-012.6590e+00 3.7300e-01 2.1380e+00 5.7550e+00]].

[0108] The data after PCA dimensionality reduction is as follows:

[0109] [[-1.1811e+01 -1.8300e-01] [-1.1805e+01 -4.4300e-01] [-1.1509e+01 -6.8800e-01] [-1.1656e+01 -1.2410e+00] [-1.1361e+01 -5.8300e-01] [-1.2083e+01-2.2400e-01] [-1.2291e+01 -5.2800e-01] [-1.1352e+01 -3.5500e-01] [-1.1503e+01-4.9700e-01] [-1.1941e+01 -8.7600e-01] [-1.1517e+01 -2.6700e-01] [-1.1895e+01-5.5800e-01] [-1.1020e+01 -5.9700e-01] [-1.1230e+01 -5.1900e-01] [-1.1699e+01-8.5200e-01] [-1.0630e+01 -3.5800e-01] [-1.1153e+01 -3.0000e-01] [-1.1108e+01-1.0780e+00] [-1.0669e+01 -8.6800e-01] [-1.1069e+01 -5.5800e-01] [-1.0746e+01-4.3100e-01] [-1.0921e+01 -6.3100e-01] [-1.0752e+01 1.4800e-01] [-1.0660e+01-1.2240e+00] [-9.5270e+00 -8.5700e-01] [-1.0096e+01 -7.6300e-01] [-9.6540e+00-1.1550e+00] [-9.9630e+00 -9.1700e-01] [-9.1530e+00 -9.8800e-01] [-9.0100e+00-7.6800e-01] [-9.3320e+00 -9.6800e-01] [-9.4140e+00 -1.1550e+00] [-8.4290e+00-1.7590e+00] [-1.0109e+01 -1.7330e+00] [-1.0115e+01 -1.9200e+00] [-9.7400e+00-1.6370e+00] [-8.8930e+00 -1.7250e+00] [-9.2240e+00 -1.9730e+00] [-8.4310e+00-2.5700e+00] [-8.5650e+00 -2.4630e+00] [-7.5500e+00 -1.1950e+00] [-8.3190e+00-2.3480e+00] [-7.5470e+00 -2.1090e+00] [-6.8480e+00 -1.7740e+00] [-7.2770e+00-1.9220e+00] [-7.3280e+00 -1.8090e+00] [-6.7450e+00 -1.9470e+00] [-7.2850e+00-2.4500e+00] [-6.3760e+00 -1.9180e+00] [-6.7560e+00 -1.6400e+00] [-6.0270e+00-1.8490e+00] [-6.5940e+00 -1.7660e+00] [-6.4670e+00 -1.9740e+00] [-5.7450e+00-2.6350e+00] [-5.6060e+00 -2.1960e+00] [-5.7850e+00 -1.7990e+00] [-5.3480e+00-2.2050e+00] [-4.5440e+00 -1.7750e+00] [-5.3070e+00 -1.9220e+00] [-4.5300e+00-2.3590e+00] [-5.1110e+00 -2.5870e+00] [-4.2960e+00 -2.3290e+00] [-4.8080e+00-2.3330e+00] [-4.6320e+00 -2.1860e+00] [-4.5710e+00 -2.3600e+00] [-4.6750e+00-1.9080e+00] [-4.2050e+00 -2.1320e+00] [-5.1720e+00 -2.7700e+00] [-4.6700e+00-2.2970e+00] [-4.3740e+00 -2.1350e+00] [-4.6790e+00 -1.9520e+00] [-4.5640e+00-2.5660e+00] [-5.0900e+00 -1.9610e+00] [-4.6540e+00 -1.9270e+00] [-4.9080e+00-2.4020e+00] [-4.8040e+00 -3.1090e+00] [-3.9910e+00 -2.5240e+00] [-3.9130e+00-2.6170e+00] [-3.3650e+00 -2.0370e+00] [-2.9680e+00 -2.4660e+00] [-3.5640e+00-2.8030e+00] [-2.9620e+00 -2.6200e+00] [-3.7310e+00 -2.2510e+00] [-3.2880e+00-2.3480e+00] [-2.2610e+00 -2.3380e+00] [-2.0660e+00 -3.4180e+00] [-1.7670e+00-2.9080e+00] [-2.2210e+00 -2.4750e+00] [-2.1110e+00 -3.2630e+00] [-2.0810e+00-2.8340e+00] [-1.3950e+00 -2.0930e+00] [-3.2900e-01 -2.4010e+00] [-8.1100e-01-2.7620e+00] [3.6700e-01 -2.4990e+00] [1.7400e-01 -2.4490e+00] [1.3800e-01 -2.7830e+00] [9.9000e-02 -1.8250e+00] [-2.7200e-01 -3.0590e+00] [6.8600e-01 -2.1330e+00] [3.0000e-01 -2.1230e+00] [6.5000e-01 -2.2780e+00] [8.1900e-01 -2.5870e+00] [1.0830e+00 -2.2590e+00] [1.8110e+00 -2.6000e+00] [2.2350e+00 -3.1730e+00] [1.5120e+00 -3.0230e+00] [2.1050e+00 -2.8440e+00] [2.4470e+00 -2.9050e+00] [2.1850e+00 -2.9860e+00] [3.2540e+00 -2.7090e+00] [3.3790e+00 -2.5670e+00] [4.0470e+00 -2.9590e+00] [3.9040e+00 -2.8120e+00] [4.6330e+00 -2.1490e+00] [4.7530e+00 -2.8660e+00] [5.1190e+00 -2.0260e+00] [4.7940e+00 -2.2390e+00] [4.8470e+00 -2.6540e+00] [5.4660e+00 -2.0710e+00] [5.7380e+00 -2.5800e+00] [6.1580e+00 -1.7220e+00] [6.2210e+00 -2.4700e+00] [6.5170e+00 -2.4850e+00] [7.2630e+00 -2.5930e+00] [6.8810e+00 -2.5330e+00] [6.8160e+00 -2.0650e+00] [7.1120e+00 -2.3270e+00] [7.8540e+00 -2.2920e+00] [6.9470e+00 -2.8160e+00] [7.5040e+00 -2.2180e+00] [8.6880e+00 -2.7370e+00] [7.9990e+00 -2.9240e+00] [7.8710e+00 -1.8530e+00] [8.3630e+00 -8.8700e-01] [8.3870e+00 -2.2150e+00] [9.1070e+00 -1.5250e+00] [9.0820e+00 -1.5870e+00] [9.3570e+00 -1.5020e+00] [9.3090e+00 -1.7250e+00] [9.6250e+00 -1.1690e+00] [1.0137e+01 -1.3490e+00] [1.0240e+01 -1.1770e+00] [1.0629e+01 -1.5970e+00] [1.0217e+01 -1.6220e+00] [1.0991e+01 -1.3330e+00] [1.0333e+01 -1.3910e+00] [1.0891e+01 -1.2880e+00] [1.1149e+01 -6.0900e-01] [1.0677e+01 -1.4430e+00] [1.0577e+01 -1.0750e+00] [1.0567e+01 -1.3060e+00] [1.0950e+01 -8.8900e-01] [1.1240e+01 -7.8300e-01] [1.0828e+01 -1.4880e+00] [1.1218e+01 -8.8000e-01] [1.1226e+01 -1.5200e+00] [1.1578e+01 -8.7200e-01] [1.1712e+01 -1.3300e+00] [1.2708e+01 -2.9600e-01] [1.2479e+01 -7.7000e-02] [1.2095e+01 -8.3400e-01] [1.2722e+01 -2.2000e-01] [1.3314e+01 -3.4600e-01] [1.3205e+01 -2.7500e-01] [1.2727e+012.1800e-01] [1.1954e+01 -3.2600e-01] [1.2460e+01 -1.6900e-01] [1.3354e+01 -6.3000e-02] [1.4669e+01 -6.1000e-02] [1.4275e+01 -3.3200e-01] [1.4651e+012.6000e-02] [1.5666e+01 2.7300e-01] [1.5269e+01 -3.5300e-01] [1.6112e+014.0000e-03] [1.4659e+01 -2.9600e-01] [1.5420e+01 -4.6000e-01] [1.5417e+01 -2.2000e-02] [1.5753e+01 1.7900e-01] [1.4447e+01 -4.8500e-01] [1.5362e+012.3100e-01] [1.4868e+01 3.6900e-01] [1.4332e+01 -1.7500e-01] [1.3940e+01 -4.5000e-02] [1.4489e+01 -1.8300e-01] [1.4757e+01 5.6600e-01] [1.5114e+015.9900e-01] [1.3874e+01 3.9000e-01] [1.4320e+01 1.9300e-01] [1.3922e+011.4090e+00] [1.4430e+01 2.2000e-01] [1.4325e+01 1.2480e+00] [1.4794e+011.4250e+00] [1.3399e+01 6.4200e-01] [1.3824e+01 4.7100e-01] [1.3594e+011.0970e+00] [1.3012e+01 7.7900e-01] [1.4178e+01 1.4910e+00] [1.2693e+018.1700e-01] [1.3059e+01 1.1500e+00] [1.2511e+01 1.2690e+00] [1.3161e+011.1400e+00] [1.3229e+01 1.2290e+00] [1.3204e+01 1.3860e+00] [1.3366e+018.1400e-01] [1.2278e+01 1.1980e+00] [1.3205e+01 1.7000e+00] [1.3236e+011.5950e+00] [1.2332e+01 2.0610e+00] [1.2659e+01 1.6410e+00] [1.3201e+012.0940e+00] [1.3128e+01 1.0660e+00] [1.2828e+01 2.3380e+00] [1.2634e+011.8420e+00] [1.2714e+01 2.2910e+00] [1.2059e+01 1.3140e+00] [1.2358e+011.4620e+00] [1.3329e+01 1.7800e+00] [1.2592e+01 1.6250e+00] [1.2178e+011.7640e+00] [1.1649e+01 2.0460e+00] [1.1899e+01 1.4040e+00] [1.1909e+011.8570e+00] [1.1533e+01 1.8600e+00] [1.1623e+01 2.2770e+00] [1.2273e+011.4960e+00] [1.1566e+01 1.5130e+00] [1.0803e+01 1.2840e+00] [1.0694e+011.7480e+00] [1.0921e+01 1.8880e+00] [1.1070e+01 1.5640e+00] [1.0453e+011.8070e+00] [1.0151e+01 1.5200e+00] [9.6260e+00 1.8750e+00] [9.3150e+001.6840e+00] [9.8360e+00 1.9610e+00] [9.6330e+00 1.8330e+00] [9.7030e+002.6100e+00] [9.6370e+00 1.5190e+00] [9.4080e+00 1.4220e+00] [1.0121e+012.0330e+00] [9.7180e+00 2.1780e+00] [9.8080e+00 2.1350e+00] [9.6360e+002.0350e+00] [9.6370e+00 1.1060e+00] [9.2110e+00 2.1140e+00] [8.9890e+002.4810e+00] [8.4450e+00 1.5150e+00] [8.4130e+00 1.3340e+00] [7.7620e+002.1730e+00] [7.6970e+00 2.2880e+00] [7.7520e+00 2.3350e+00] [6.3800e+002.3560e+00] [7.6390e+00 3.0290e+00] [6.1020e+00 2.0200e+00] [6.3120e+001.9170e+00] [5.8000e+00 2.0690e+00] [6.0540e+00 2.5260e+00] [5.5480e+001.9300e+00] [6.0240e+00 2.5630e+00] [5.7300e+00 2.7890e+00] [4.9530e+002.6460e+00] [4.6240e+00 2.3310e+00] [4.5720e+00 1.8690e+00] [4.4040e+002.1890e+00] [4.0670e+00 2.7000e+00] [2.8840e+00 3.0070e+00] [1.7090e+001.9700e+00] [5.9500e-01 2.7270e+00] [-3.7000e-02 3.0270e+00] [-2.1590e+003.5360e+00] [-2.2640e+00 2.8780e+00] [-3.4570e+00 3.2710e+00] [-4.4180e+002.7180e+00] [-5.5720e+00 2.6590e+00] [-6.4450e+00 2.7740e+00] [-6.9220e+003.2310e+00] [-7.6390e+00 2.0410e+00] [-7.6740e+00 2.3880e+00] [-8.0240e+002.5390e+00] [-8.9960e+00 2.7460e+00] [-8.8860e+00 2.1830e+00] [-9.5680e+002.1700e+00] [-9.4820e+00 2.2290e+00] [-9.8920e+00 2.5650e+00] [-9.5950e+002.1100e+00] [-1.0470e+01 2.7260e+00] [-1.0649e+01 2.0890e+00] [-1.0828e+012.2280e+00] [-1.1231e+01 2.0370e+00] [-1.1215e+01 1.9520e+00] [-1.1543e+012.3090e+00] [-1.2566e+01 1.7990e+00] [-1.2205e+01 1.6470e+00] [-1.2397e+011.8830e+00] [-1.3137e+01 2.5130e+00] [-1.2497e+01 1.5470e+00] [-1.2151e+011.6230e+00] [-1.3062e+01 1.3960e+00] [-1.2940e+01 7.0200e-01] [-1.2784e+011.3490e+00] [-1.3467e+01 7.6000e-01] [-1.3558e+01 1.6060e+00] [-1.2385e+011.9860e+00] [-1.3556e+01 1.3170e+00] [-1.3519e+01 1.1180e+00] [-1.3147e+011.6240e+00] [-1.2317e+01 1.0960e+00] [-1.2833e+01 1.1080e+00] [-1.3209e+011.2990e+00] [-1.3065e+01 8.2900e-01] [-1.2803e+01 1.6310e+00] [-1.2353e+012.0030e+00] [-1.2697e+01 1.6260e+00] [-1.3094e+01 1.5890e+00] [-1.2953e+011.2580e+00] [-1.3055e+01 1.3500e+00] [-1.2838e+01 1.6250e+00] [-1.1879e+011.7500e+00] [-1.2775e+01 2.1000e+00] [-1.2357e+01 1.8420e+00] [-1.3202e+019.7500e-01] [-1.2691e+01 1.5370e+00] [-1.2148e+01 1.3660e+00] [-1.1332e+011.5620e+00] [-1.2225e+01 1.0560e+00] [-1.2405e+01 6.6800e-01] [-1.1060e+011.3470e+00] [-1.2142e+01 1.1270e+00] [-1.2190e+01 1.4720e+00] [-1.2401e+011.6580e+00] [-1.2393e+01 1.3950e+00] [-1.2705e+01 1.0270e+00] [-1.1546e+011.2570e+00] [-1.2327e+01 9.6800e-01] [-1.1722e+01 1.4030e+00] [-1.0982e+011.8250e+00] [-1.1605e+01 1.1700e+00] [-1.0779e+01 1.7220e+00] [-1.1497e+011.3900e+00] [-1.0386e+01 1.2480e+00] [-1.1110e+01 9.2600e-01] [-1.0975e+011.4070e+00] [-1.0547e+01 4.9600e-01] [-1.0390e+01 1.3860e+00] [-1.0189e+011.1360e+00] [-1.0303e+01 1.4420e+00] [-9.8250e+00 1.0470e+00] [-1.0107e+011.0100e+00] [-1.0173e+01 2.9900e-01] [-9.7560e+00 9.2100e-01] [-9.2010e+009.6800e-01] [-9.5980e+00 9.9000e-01] [-8.5740e+00 8.3300e-01] [-8.8960e+009.3100e-01] [-7.9090e+00 8.0000e-01] [-8.1380e+00 7.6900e-01] [-7.9050e+008.6800e-01] [-7.6660e+00 1.3490e+00] [-7.8300e+00 9.1100e-01] [-7.1920e+001.2080e+00] [-6.9590e+00 9.7700e-01] [-7.0270e+00 1.3720e+00]];.

[0110] 1. Train an SVM model using the center coordinates {zt} of n confidence circles;

[0111] For each time point t, there is a two-dimensional coordinate Z. t Let the confidence circle at each time point t be Z. t The radius is chosen based on the degree of dispersion of the local data, with the center as the center.

[0112] The radius r of each circle t The variation at local points within this time slice determines that there are n sub-data points within time t. ,

[0113] After projecting it into two dimensions, we get

[0114] ,

[0115] The radius of the circle is the distance between these points and its center, i.e. Average Euclidean distance:

[0116] ;

[0117] III. Generating the coordinates of the center of the confidence circle

[0118] Given dataset {zt} t=1 n The following optimization problem is solved:

[0119]

[0120] Constraints:

[0121]

[0122] Where ϕ() is the mapping function, ν∈(0,1] is the parameter, and after solving, the Lagrange multiplier α is obtained. t ;

[0123] The set of vectors is:

[0124]

[0125] Final center calculation:

[0126] After obtaining the set of support vectors S, the final center of the circle is defined as the arithmetic mean of the support vectors:

[0127] =

[0128] Obtain the coordinates of the center of the circle;

[0129] Obtain the support vector set S, generating 182 support vectors:

[0130] [-1.18106297e+01 -1.83129591e-01] [-1.18052873e+01 -4.43179393e-01] [-1.15085833e+01 -6.87824207e-01] [-1.16555611e+01 -1.24117879e+00] [-1.20828006e+01 -2.24450378e-01] [-1.22908909e+01 -5.27603086e-01] [-1.19407704e+01 -8.75914800e-01] [-1.18954313e+01] [-5.58343837e-01] [-1.16986706e+01 -8.52384060e-01] [-1.11080854e+01 -1.07777155e+00] [-1.01147463e+01 -1.91969738e+00] [-8.43104891e+00 -2.56992850e+00] [-8.56511386e+00 -2.46279044e+00] [-5.74549745e+00 -2.63492864e+00] [-5.11097150e+00 -2.58702730e+00] [-5.17211569e+00 -2.76982190e+00] [-4.56423772e+00 -2.56586655e+00] [-4.80391103e+00 -3.10940323e+00] [-3.99084885e+00 -2.52403512e+00] [-3.91307031e+00 -2.61739785e+00] [-2.96774524e+00 -2.46612252e+00] [-3.56380035e+00 -2.80279579e+00] [-2.96201012e+00 -2.61955158e+00] [-2.26093797e+00 -2.33783555e+00] [-2.06648535e+00 -3.41753290e+00] [-1.76667717e+00 -2.90755935e+00] [-2.22055246e+00 -2.47549964e+00] [-2.11074216e+00 -3.26273100e+00] [-2.08085728e+00 -2.83410944e+00] [-3.[28889227e-01 -2.40079170e+00] [-8.10614825e-01 -2.76244525e+00] [3.67209311e-01 -2.49929301e+00] [1.74410276e-01 -2.44902915e+00] [1.37737038e-01 -2.78295813e+00] [-2.71821186e-01 -3.05913311e+00] [6.85663362e-01 -2.13346863e+00] [2.99608794e-01] [ -2.12310563e+00] [ 6.49644716e-01 -2.27766338e+00] [8.18574444e-01 -2.58725792e+00] [ 1.08287310e+00 -2.25948713e+00] [ 1.81126536e+00 -2.59989242e+00] [ 2.23543534e+00 -3.17344045e+00] [ 1.51213441e+00 -3.02262384e+00] [ 2.10531658e+00 -2.84399343e+00] [2.44686018e+00 -2.90509715e+00] [2.18535314e+00 -2.98618185e+00] [3.25385587e+00 -2.70900399e+00] [3.37918233e+00 -2.56745228e+00] [4.04725694e+00 -2.95921396e+00] [3.90368973e+00 -2.81167604e+00] [4.75276270e+00 -2.86558400e+00] [4.84685933e+00] [-2.65388539e+00] [5.73846470e+00 -2.58032898e+00] [7.26345776e+00 -2.59303494e+00] [6.88087602e+00 -2.53278709e+00] [6.94696859e+00 -2.81596989e+00] [8.68848510e+00 -2.73736826e+00] [7.99909551e+00 -2.92420205e+00] [1.27083148e+01 -2.[95977544e-01] [1.27222442e+01 -2.20284466e-01] [1.33140790e+01 -3.45589757e-01] [1.32045167e+01 -2.75239007e-01] [1.27268369e+01 2.18296091e-01] [1.33537530e+01 -6.33618728e-02] [1.46694573e+01 -6.05542707e-02] [1.42746310e+01 -3.32295382e-01] [1.46514698e+01 2.56254024e-02] [1.56663391e+01 2.73374474e-01] [1.52691074e+01 -3.53165555e-01] [1.61121197e+01 4.32141600e-03] [1.46587404e+01 -2.96464758e-01] [1.54198124e+01 -4.60354165e-01] [1.54174907e+01 -2.24205028e-02] [1.57529482e+01] [1.79177853e-01] [1.44471762e+01 -4.84763047e-01] [1.53623791e+01 2.31201658e-01] [1.48675891e+01 3.69383593e-01] [1.43321445e+01 -1.75101715e-01] [1.39397900e+01 -4.45590424e-02] [1.44893458e+01 -1.82514130e-01] [1.47572358e+01 5.66106899e-01] [ 1.51138989e+01 5.98948318e-01] [1.38737162e+01 3.89671217e-01] [1.43203882e+01 1.92506666e-01] [1.39223856e+01 1.40869366e+00] [1.44296152e+01 2.20473109e-01] [1.43253241e+01 1.24771986e+00] [1.47942999e+01 1.42519237e+00] [1.33993259e+01 6.[41886138e-01] [1.38240849e+01 4.70976413e-01] [1.35944661e+01 1.09656089e+00] [1.30117629e+01 7.78964673e-01] [1.41776645e+01 1.49132100e+00] [1.26925179e+01 8.17374890e-01] [1.30593124e+01 1.14996434e+00] [1.25109781e+01 1.26943698e+00] [1.31614258e+01 1.14035467e+00] [1.32291046e+01 1.22869632e+00] [1.32040144e+01 1.38626478e+00] [1.33657288e+01 8.13688760e-01] [1.32053641e+01 1.69990415e+00] [1.32358851e+01 1.59535842e+00] [1.23321720e+01 2.06108118e+00] [1.26590974e+01] [1.64100721e+00] [1.32008183e+01 2.09398492e+00] [1.31279034e+01 1.06637956e+00] [1.28277156e+01 2.33829976e+00] [1.26343087e+01 1.84202301e+00] [1.27137989e+01 2.29135905e+00] [1.33293943e+01 1.78023275e+00] [1.25919887e+01 1.62490460e+00] [ [1.21776028e+01 1.76407855e+00] [1.16234780e+01 2.27675938e+00] [9.70317008e+00 2.61004244e+00] [6.37985390e+00 2.35621480e+00] [7.63859743e+00 3.02887967e+00] [5.79958826e+00 2.06895909e+00] [6.05368055e+00 2.52565952e+00] [6.02397382e+00] 2.56276853e+00] [ 5.[73010496e+00 2.78873200e+00] [4.95303898e+00 2.64553824e+00] [4.62418263e+00 2.33145103e+00] [4.57181791e+00 1.86938515e+00] [4.40380703e+00 2.18908235e+00] [4.06686580e+00 2.70044090e+00] [2.88356263e+00 3.00677297e+00] [1.70854079e+00] [1.96982220e+00] [5.95495993e-01 2.72700338e+00] [-3.70428988e-02 3.02738194e+00] [-2.15939936e+00 3.53627878e+00] [-2.26364622e+00 2.87776256e+00] [-3.45697628e+00 3.27070292e+00] [-4.41806588e+00 2.71789754e+00] [-5.57185019e+00 2.65917006e+00] [-6.44545041e+00 2.77401138e+00] [-6.92177489e+00 3.23115940e+00] [-1.04703359e+01 2.72554378e+00] [-1.08277621e+01 2.22817356e+00] [-1.12305568e+01 2.03697946e+00] [-1.12154996e+01 1.95211441e+00] [-1.15429443e+01 2.30850725e+00] [-1.25657827e+01 [1.79874806e+00] [-1.22051595e+01 1.64679075e+00] [-1.23968038e+01 1.88323252e+00] [-1.31372963e+01 2.51267169e+00] [-1.24969392e+01 1.54748118e+00] [-1.21510563e+01 1.62334604e+00] [-1.30624600e+01 1.39598334e+00] [-1.29396612e+01 7.01504611e-01] [-1.27843877e+01 1.[34909514e+00] [-1.34667924e+01 7.59530810e-01] [-1.35579270e+01 1.60559093e+00] [-1.23849601e+01 1.98600694e+00] [-1.35556213e+01 1.31660344e+00] [-1.35188369e+01 1.11801973e+00] [-1.31469066e+01 1.62394656e+00] [-1.23168427e+01 1.09613036e+00] [-1.28330570e+01 1.10842472e+00] [-1.32087793e+01 1.29885970e+00] [-1.30648068e+01 8.29054407e-01] [-1.28028167e+01 1.63058986e+00] [-1.23531762e+01 2.00278983e+00] [-1.26973725e+01 1.62569241e+00] [-1.30939731e+01 1.58926336e+00] [-1.29527086e+01 [1.25778696e+00] [-1.30553856e+01 1.34974537e+00] [-1.28377587e+01 1.62471583e+00] [-1.18786597e+01 1.75028341e+00] [-1.27745424e+01 2.10005345e+00] [-1.23573416e+01 1.84218063e+00] [-1.32021166e+01 9.74728706e-01] [-1.26911749e+01 1.53681255e+00] [-1.21479449e+01 1.36597513e+00] [-1.22251487e+01 1.05558932e+00] [-1.24049075e+01 6.68421537e-01] [-1.21417756e+01 1.12710431e+00] [-1.21901033e+01 1.47202885e+00] [-1.24008770e+01 1.65809797e+00] [-1.23932601e+01 1.39505042e+00] [-1.27045243e+01 1.02711803e+00] [-1.23267375e+01 9.68231036e-01] [-1.17216841e+01 1.40295064e+00]].

[0131] V. Obtaining the final confidence circle:

[0132] Final center coordinates: [0.597844 0.19933402], final radius: 15.774;

[0133] VI. Anomaly Detection:

[0134] After performing dimensionality reduction on the new data in the same way as on the historical data, the Euclidean distance between the new data points and the cluster center is calculated to determine whether it exceeds the radius of the confidence circle and whether it is outlier data. A set of test data and results are as follows:

[0135] Serial Number New measuring point number Strain 1 Strain 2 Strain 3 Strain 4 Strain 5 Strain 6 Strain 7 Strain 8 Strain 9 Distance from the center of confidence circle Is this abnormal data? 1 T0-F01-S9 -4.21997976 -89.82920837 -73.86190796 -22.03059959 -33.67771149 -55.59111023 -31.85640907 -95.09181213 220.904953 7.714 no 2 T0-F01-S9 -17.9119401 -89.82920837 23.8809433 -22.03059959 -33.67771149 -55.59111023 -31.85640907 -95.09181213 120.843689 133.607 yes 3 T0-F01-S9 -5.9119401 -66.83023834 -83.8809433 -15.26576996 -13.61833954 -55.59111023 -31.85640907 -95.09181213 220.904953 28.359 yes

[0136] This completes the calculation process.

Claims

1. A method for identifying anomaly data from multi-directional stress gauge monitoring based on SVM and PCA confidence interval analysis, characterized in that... The specific steps of this identification method are as follows: I. Data Acquisition and PCA Dimensionality Reduction: In the inclinometer monitoring system, data from nine measuring points are collected at regular intervals to form an n×9 data matrix. Suppose there are n time slices, t=1,2,...,n, and each time slice has a k-dimensional vector data: ， T represents The transpose of , where R represents the data matrix and k represents the dimension of the vector data in each time slice; Construct a matrix from all the data: ，X ， Centering: Calculating the mean vector ， X t X in n*k dimensional vector data t ; Centralize X: ， Where 1 is an n-dimensional column vector of all 1s; Covariance matrix: ， Where 1 is an n-dimensional column vector of all 1s, X c It is a centered matrix, where X represents the data matrix. C represents the transpose of the centered matrix, where C is the covariance matrix. Eigenvalue decomposition: Find the eigenvalue decomposition of C: ； Where λ1≥λ2≥λ3≥λ4≥λ5 are eigenvalues, and v1,v2,…,v5 are the corresponding eigenvectors; Select the first two principal components: Take the eigenvectors v1 and v2 corresponding to the two largest eigenvalues ​​to form a matrix. ， Data projected into two-dimensional space: ， We obtain n two-dimensional points: t=1,…,n; II. Generate n confidence circles For each time point t, there is a two-dimensional coordinate Z. t Let the confidence circle at each time point t be Z. t The radius is chosen based on the degree of dispersion of the local data, with the center as the center. The radius r of each circle t The variation at local points within this time slice determines that there are n sub-data points within time t. ， After projecting it onto a two-dimensional coordinate system, we get ， The radius of the circle is the distance between these points and its center, i.e. Average Euclidean distance: ； III. Generating the coordinates of the center of the confidence circle Given dataset {zt} t=1 n The following optimization problem is solved: ， Constraints: ； Where ϕ() is the mapping function, ν∈(0,1] is the parameter, and after solving, the Lagrange multiplier α is obtained. t ; The set of vectors is: ， Final center calculation: After obtaining the set of support vectors S, the final center of the circle is defined as the arithmetic mean of the support vectors: = ， Obtain the coordinates of the center of the circle; IV. Radius of the final confidence circle The final confidence circle radius is obtained by taking the arithmetic mean of all n ellipse radii {rt}. ， V. Final Confidence Circle Based on the above calculations, the final confidence circle is defined as follows: Center: Z final And radius: R; VI. Anomaly Detection Given new data x^, the PCA process described above is as follows: Centralization: = , projection: , judge Is it within the final confidence circle? ≤R normal, >R abnormal, Complete the calculation process.

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