Multidirectional stressometer monitoring abnormal data identification method based on SVM and PCA confidence interval analysis

Abstract

The invention discloses a multidirectional stressometer monitoring abnormal data identification method based on SVM and PCA confidence interval analysis, and relates to the field of multidirectional stressometer monitoring data analysis. The method comprises the specific steps of data and PCA dimension reduction, generation of n confidence circles, generation of circle center coordinates of the confidence circles, final confidence circle radius, final confidence circle and anomaly detection. According to the invention, the SVM is used for analyzing the circle center coordinates of the confidence circle obtained after PCA dimensionality reduction analysis of monitoring data in multiple time periods, so that support vectors are selected and averaged to serve as a final circle center. The method can focus on a key point for determining a data distribution boundary to a great extent, improves the sensitivity to abnormal values and boundary points, and reduces the solving influence of the abnormal points on the optimal circle center under the condition that the number of the abnormal points in the whole data is large or the data distribution is multi-modal. The finally obtained circle center and the radius obtained through average calculation form a global confidence circle, and anomaly detection is achieved.

Description

Technical Field

[0001] The present invention relates to the field of multi-directional stress gauge monitoring data analysis, and in particular to a multi-directional stress gauge monitoring abnormal data identification method based on SVM and PCA confidence interval analysis, which accurately identifies new abnormal data by learning the distribution of historical data. Background Art

[0002] Multi-directional strain gauges are widely used in hydropower dam safety monitoring, providing important mechanical monitoring data. As the volume of monitoring data increases, noise and anomalies in the data 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 boundary. Using support vector machines (SVMs), particularly single-class SVMs, can help determine the data's decision boundary and thus select representative support vectors. These support vectors possess higher discriminative power when forming the final confidence circle center, enabling better performance 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 multi-directional stress gauge monitoring anomaly data identification method based on SVM and PCA confidence interval analysis, which can accurately identify new anomaly data by learning the distribution of historical data.

[0004] The present invention provides a method for identifying abnormal data from multi-directional stress gauge monitoring based on SVM and PCA confidence interval analysis, characterized in that the specific steps of the identification method are as follows:

[0005] 1. 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 stands for The transpose of R represents the data matrix, that is, the data set, and k represents the dimension of each time slice vector data.

[0009] Make all the data into a matrix:

[0010] , X

[0011] Centering: Calculating the mean vector

[0012]

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

[0014] Centralize X:

[0015]

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

[0017] Covariance matrix:

[0018]

[0019] Where 1 is an n-dimensional all-1 column vector, X c is the centralized matrix, X represents the data matrix, represents the transpose of the centralized matrix, and C is the covariance matrix

[0020] Eigen decomposition: perform eigen decomposition on C:

[0021]

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

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

[0024]

[0025] Data projection to two-dimensional space:

[0026]

[0027] Get 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 , and the confidence circle of each time point t is centered at Z t , and the radius is determined by the dispersion degree of the local data;

[0031] The radius r t of each circle is determined by the variation of the local points within the time slice. There are n sub-data points within time t,

[0032]

[0033] After projecting it into the two-dimensional coordinate system, we get

[0034] ,

[0035] Then the radius of the circle is the distance of these points relative to its center, that is The average Euclidean distance of:

[0036] ;

[0037] 3. Generate the coordinates of the center of the confidence circle

[0038] Given a dataset {zt} t=1 n , by solving the following optimization problem:

[0039]

[0040] Constraints:

[0041]

[0042] in is the mapping function, ν∈(0,1] is the parameter, and after solving, we get the Lagrange multiplier α t ;

[0043] The vector set is:

[0044]

[0045] Final circle center calculation:

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

[0047] =

[0048] Get the coordinates of the circle center;

[0049] 4. Final confidence circle radius

[0050] Calculate the arithmetic mean of all n ellipse radii {rt} to obtain the final confidence circle radius:

[0051]

[0052] 5. Final Confidence Circle

[0053] Through the above calculations, the final confidence circle is defined as:

[0054] Center of circle: z final and radius: R;

[0055] 6. Anomaly Detection

[0056] Given new data x^, after the above PCA process:

[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] The present invention relates to the field of multi-dimensional stress gauge monitoring data analysis. Using SVM (Support Vector Machine) to analyze the confidence circle center coordinates obtained after PCA dimensionality reduction analysis of monitoring data from multiple time periods, support vectors are selected and averaged to form the final center. This method can largely focus on the key points that determine the boundaries of the data distribution, improve sensitivity to outliers and boundary points, and reduce the impact of a high number of outliers on the optimal center solution when the data is highly distributed or the data distribution is multimodal. The resulting center, together with the radius obtained through averaging, forms a global confidence circle, enabling anomaly detection. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0066] Figure 3 This is a screenshot of the test data 3 results. DETAILED DESCRIPTION

[0067] Example 1: A method for identifying abnormal data from multi-directional strain gauge monitoring based on SVM and PCA confidence interval analysis, characterized in that the specific steps of the identification method are as follows:

[0068] 1. Data and PCA Dimensionality Reduction

[0069] 1. Data acquisition:

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

[0071]

[0072] 1. PCA dimensionality reduction processing:

[0073] Suppose there are n time slices, t=1,2,...,n, and each time slice has an n-dimensional vector data:

[0074]

[0075] Make all the data into a matrix:

[0076] , X

[0077] Centering: Calculating the mean vector

[0078]

[0079] Centralize X:

[0080]

[0081] Where 1 is an n-dimensional all-one column vector;

[0082] Covariance matrix:

[0083]

[0084] Eigendecomposition: Find the eigendecomposition of C:

[0085]

[0086] Among them, λ1≥λ2≥λ3≥λ4≥λ5 are eigenvalues, and v1,v2,…,v5 are corresponding eigenvectors;

[0087] Select the first two principal components:

[0088] Take the first two eigenvalues ​​corresponding to the eigenvectors v1 and v2 to form the matrix

[0089]

[0090] Project the data into two-dimensional space:

[0091]

[0092] Get n two-dimensional points:

[0093] t=1,…,n

[0094] The data obtained after standardization are as follows:

[0095] [[-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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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 -1.0880e+00 -1.0300e-01 -1.1500e-01 -1.4170e+00 5.9900e-013.9700e-01 -6.4000e-01 -4.7850e+00] [2.8500e-01 -8.4900e-01 -1.1500e+001.6000e-01 -2.2160e+00 1.5900e-01 3.4700e-01 -3.7900e-01 -3.4900e+00][6.4900e-01 -8.0000e-01 -1.5210e+00 1.9300e-01 -1.1290e+00 -1.4900e-014.3000e-02 -6.7800e-01 -2.2050e+00] [7.5000e-01 -1.7930e+00 -1.8180e+002.3300e-01 -1.1690e+00 5.5300e-01 3.4700e-01 -3.5200e-01 -1.4840e+00][6.9900e-01 -1.8530e+00 -2.5230e+00 1.7800e-01 -1.7970e+00 2.3900e-013.5700e-01 -3.4700e-01 -8.4400e-01] [1.7410e+00 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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]].

[0096] The data after PCA dimensionality reduction is as follows:

[0097] [[-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.[9.6360e+00 2.0350e+00] [9.6370e+00 1.1060e+00] [9.2110e+00 2.1140e+00] [8.9890e+00 2.4810e+00] [8.4450e+00 1.5150e+00] [8.4130e+00 1.3340e+00] [7.7620e+00 2.1730e+00] [7.6970e+00 2.2880e+00] [7.7520e+00 2.3350e+00] [6.3800e+00 2.3560e+00] [7.6390e+00 3.0290e+00] [6.1020e+00 2.0200e+00] [6.3120e+00 1.9170e+00] [5.8000e+00 2.0690e+00] [6.0540e+00 2.5260e+00] [5.5480e+00 1.9300e+00] [6.0240e+00 2.5630e+00] [5.7300e+00 2.7890e+00] [4.9530e+00 2.6460e+00] [4.6240e+00 2.3310e+00] [4.5720e+00 1.8690e+00] [4.4040e+00 2.1890e+00] [4.0670e+00 2.7000e+00] [2.8840e+00 3.0070e+00] [1.7090e+00 1.9700e+00] [5.9500e-01 2.7270e+00] [-3.7000e-02 3.0270e+00] [-2.1590e+00 3.5360e+00] [-2.2640e+00 2.8780e+00] [-3.4570e+00 3.2710e+00] [-4.4180e+00 2.7180e+00] [-5.5720e+00 2.6590e+00] [-6.4450e+00 2.7740e+00] [-6.9220e+00 3.2310e+00] [-7.6390e+00 2.0410e+00] [-7.6740e+00 2.3880e+00] [-8.0240e+00 2.5390e+00] [-8.9960e+00 2.7460e+00] [-8.8860e+00 2.1830e+00] [-9.5680e+00 2.1700e+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]];.

[0098] 1. Train the SVM model for the center coordinates {zt} of n confidence circles;

[0099] For each time point t, there is a two-dimensional coordinate Z t , let the confidence circle of each time point t be Z t The selection method of radius is determined by the degree of discreteness of local data;

[0100] The radius r of each circle t Determined by the variation of the local point in the time slice, there are n sub-data points in time t ,

[0101] After projecting it into two dimensions, we get

[0102] ,

[0103] Then the radius of the circle is the distance of these points relative to its center, that is The average Euclidean distance of:

[0104] ;

[0105] 3. Generate the coordinates of the center of the confidence circle

[0106] Given a dataset {zt} t=1 n , by solving the following optimization problem:

[0107]

[0108] Constraints:

[0109]

[0110] Where ϕ( ) is the mapping function, ν∈(0,1] is the parameter, and after solving, we get the Lagrange multiplier α t ;

[0111] The vector set is:

[0112]

[0113] Final circle center calculation:

[0114] After obtaining the support vector set S, the final center of the circle is defined as the arithmetic mean of the support vectors:

[0115] =

[0116] Get the coordinates of the circle center;

[0117] Get the support vector set S and generate 182 support vectors:

[0118] [[-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]].

[0119] V. Get the final confidence circle:

[0120] Final center coordinates: [0.597844 0.19933402], final radius: 15.774;

[0121] VI. Anomaly detection:

[0122] After the new data is reduced dimensionally consistent with historical data, the Euclidean distance between the new data point and the center of the cluster is calculated to determine whether it exceeds the radius of the confidence circle to determine whether it is abnormal data. Take a set of test data and the results are as follows:

[0123] Serial number New measurement 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 the confidence circle Is it 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

[0124] At this point, the calculation process is complete.

Claims

1. A method for identifying abnormal 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:

1. Data and PCA Dimensionality Reduction Suppose there are n time slices, t=1,2,...,n, and each time slice has a k-dimensional vector data: ， T stands for The transpose of , R represents the data matrix (data set), and k represents the dimension of each time slice vector data; Make all the data into a matrix: ，X ， Centering: Calculating the mean vector ， X t X in n*k dimensional vector data t ; Centralize X: ， Where 1 is an n-dimensional all-one column vector; Covariance matrix: ， Where 1 is an n-dimensional all-one column vector, X c is the centralized matrix, X represents the data matrix, represents the transpose of the centered matrix, and C is the covariance matrix; Eigendecomposition: Find the eigendecomposition of C: ； Among them, λ1≥λ2≥λ3≥λ4≥λ5 are eigenvalues, and v1,v2,…,v5 are corresponding eigenvectors; Select the first two principal components: Take the first two eigenvalues ​​corresponding to the eigenvectors v1 and v2 to form the matrix ， Project the data into two-dimensional space: ， Get n two-dimensional points: t=1,…,n; 2. Generate n confidence circles For each time point t, there is a two-dimensional coordinate Z t , let the confidence circle of each time point t be Z t The selection method of radius is determined by the degree of discreteness of local data; The radius r of each circle t Determined by the variation of the local point in the time slice, there are n sub-data points in time t ， After projecting it into the two-dimensional coordinate system, we get ， Then the radius of the circle is the distance of these points relative to its center, that is The average Euclidean distance of: ； 3. Generate the coordinates of the center of the confidence circle Given a dataset {zt} t=1 n , by solving the following optimization problem: ， Constraints: ； Where ϕ( ) is the mapping function, ν∈(0,1] is the parameter, and after solving, we get the Lagrange multiplier α t ; The vector set is: ， Final circle center calculation: After obtaining the support vector set S, the final center of the circle is defined as the arithmetic mean of the support vectors: = ， Get the coordinates of the circle center; 4. Final confidence circle radius Calculate the arithmetic mean of all n ellipse radii {rt} to obtain the final confidence circle radius: ， 5. Final Confidence Circle Through the above calculations, the final confidence circle is defined as: Center of circle: z final and radius: R; 6. Anomaly Detection Given new data x^, after the above PCA process: Centralization: = , projection: , Determine whether z^ is within the final confidence circle: ≤R normal, >R abnormal, Complete the calculation process.

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