CN108197824B - High dam service safety space alert domain diagnosis method - Google Patents

Abstract

The invention discloses a method for diagnosing a high dam service safety space alert domain, which is characterized by comprising the following steps of: (1) constructing high dam effect according to high dam effect monitoring dataMeasuring the original monitoring data information source matrix X to obtain a standardized data matrix

(3) Selecting proper kernel function and standardizing the data matrix

Mapping from the low-dimensional data space to the high-dimensional data space; (4) obtaining a covariance matrix of a data matrix in a high dimensional data space

Solving a characteristic root and a characteristic vector v of the covariance matrix; (5) for the characteristic root lambda_iSorting in a descending order and adjusting corresponding feature vectors; (6) determining the number of principal components and extracting a feature vector v_i(ii) a (7) Calculating a normalized data matrix

In the feature vector v_iProjection of (2); (8) by means of T²The statistics realizes the construction of a high dam security alert domain; (9) if the observed value falls outside the warning domain, the service state of the dam is changed; and if the observed value falls into the warning area, the service state of the dam is not changed.

Description

High dam service safety space alert domain diagnosis method

Technical Field

The invention relates to a method for diagnosing a high-dam service safety space alert domain, and belongs to the field of high-dam safety monitoring.

Background

At present, the construction of water projects with favorable terrain and medium-low height is basically finished, the construction height and scale of dams are gradually increased, high dams of 300m level are continuously generated, meanwhile, the adverse working conditions of the surrounding environment are more and more, how to construct and ensure the safe operation of the high dams in extremely severe environment becomes extremely difficult, how to ensure that the safe construction and the later operation of the heavy projects are realized under the condition that the heavy projects exceed the requirements of all current standards is an important subject, and the problems that the technical standard is lagged, the monitoring means is old, the referential performance of test technical results is poor, the practical application of new technology cannot be popularized and the like exist, so that the continuous increase of the high dam construction and operation service risks and the shortage of related risk assessment and regulation theories and technologies and extreme regulations thereof seriously affect the high-efficiency construction and long-term service of the high dam projects, is not matched with the enhancement technology application and scientific research innovation in various fields of China at present, and is a key field which needs to be enhanced urgently.

The early warning of the service state transition of the dam is an important means for preventing the dam from being out of service, advanced theories and methods such as mathematics and mechanics are comprehensively applied according to high dam safety actual measurement data, the warning values of dam deformation, seepage, stress and the like under various load combinations are accurately estimated, the high dam safety early warning can be realized, potential hidden dangers in the dam service process can be found in time, and then suitable engineering and non-engineering regulation measures are taken, so that the dam catastrophe risk is effectively reduced.

The consciousness shape determines that people are used to univariate analysis, and the complicated relationship among multiple objectively existing variables is split, so that the single variable is independently used as a basis for evaluating the quality of an object, and the evolution essence of the object is not easy to be fully revealed. The dam safety early warning is realized by a method for simulating the effect warning value of a single measuring point in the prior art, the problem of drawing up the warning values of deformation, seepage, stress and the like of a certain point of the dam is mostly researched, most of the selected monitoring data is monitoring data of the certain point, the correlation among adjacent measuring points or measuring points of the same dam section is less considered, and the evaluation on the service safety state of a dam bank cannot be met; on the other hand, the method for drawing up the warning value of the single measuring point, such as a small probability method, has the limitations of long requirement on the monitoring sequence, difficulty in selecting a probability distribution model, uncertain physical concept of a confidence interval method, large workload, time consumption for calculation and the like of a structural analysis method; furthermore, the single-measuring-point establishment warning value is often artificially split the connection between the measuring points. Therefore, the research of the multi-point combined early warning method is of great significance.

Disclosure of Invention

The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides a method for diagnosing the alert domain of the high-dam service security space, which breaks through the rapid early warning of the transfer of the dam security from points to the space, extracts the internal characteristics among multi-point effect quantities by means of a Kernel Principal Component Analysis (KPCA) method in manifold learning, constructs a model for discriminating the alert domain of the transfer of the high-dam service state to the transfer of the high-dam service state, and realizes the drawing up of the alert domain of the high-dam security space.

The technical scheme is as follows: in order to solve the technical problem, the method for diagnosing the alert domain of the high-dam service safety space, provided by the invention, specifically comprises the following steps:

step (1) according to high dam effect monitoring data, forming an original monitoring data information source matrix X;

the Kernel Principal Component Analysis (KPCA) method is based on Principal Component Analysis (PCA) method. In statistical sense, the PCA method replaces the original numerous variables with a small number of comprehensive variables, so that the small number of comprehensive variables have no correlation between the variables while expressing enough information of the original numerous variables, thereby realizing feature extraction and accurate reduction of the variables.

Assuming that m monitoring effect quantities exist in a dam service system, each effect quantity sequence has n monitoring values { x_ijAnd (i ═ 1,2, …, n ═ 1,2, …, m), constructing an n × m monitoring data matrix X:

in the formula: the matrix X may also be represented as [ X ]_j](j ═ 1,2, …, m) or [ x [ (-)_i]^T(i＝1,2,…,n)；

Assuming effect quantity reduction to obtain comprehensive characteristic variable z₁,z₂,…,z_pAnd (p is less than or equal to m), the comprehensive characteristic variable is formed by linearly combining original effect quantities and is expressed as:

in the formula: the matrix L may also be represented as [ L ]_j](j ═ 1,2, …, m) or [ l_i]^T(i＝1,2,L,m)。

To facilitate analysis of the comprehensive characteristic variable properties, assume { x }_jThe maximum square difference in all linear combinations of (1, 2, …, m) } (j) is z₁I.e. var (z)₁) Most preferablyLarge, then z₁Referred to as the first principal component; (l)₂₁,l₂₂,…,l_2m) Perpendicular to (l)₁₁,l₁₂,…,l_1m) And let var (z)₂) Maximum, then z₂Referred to as the second principal component; by analogy with this, z_pIs the pth principal component. { z₁,z₂,…,z_pThe extraction result of the internal characteristics of the dam service state can be represented. The PCA method has the following characteristics and properties:

the principal components are unrelated to each other. I.e. for any i, j (i ≠ j), the principal component z_iAnd z_jAre not correlated with each other, and have a correlation coefficient of 0, corr (z)_i,z_j)＝0；

② combination coefficient { l_iThe constructed vector is a unit vector which substantially expresses the direction of the corresponding principal component in space;

③ the variance of each principal component is decreased in turn, but the sum of the variances is kept unchanged, namely var (z) exists₁)≥var(z₂)≥…≥var(z_p) And

the sum of variance remains unchanged, and the principal component analysis is essentially a linear combination of the original effect quantities, only the original effect quantities are converted, and in the process, the information contained in the original effect quantities is not changed.

Fourthly, the combination coefficient { l is proved mathematically_ijWhere (i-1, 2, …, p; j-1, 2, …, m) is the original effect quantity { x }_jThe feature vectors corresponding to the first p larger feature roots of the (j ═ 1,2, …, m) covariance matrix, and the principal component z, which is the composite variable_iVar (z) of_i) (i ═ 1,2, …, p) is exactly the first p larger feature roots λ_iIt is possible to obtain:

step (2) carrying out standardization processing on an original monitoring data information source matrix X so as to eliminate dimension and avoid the phenomenon of 'large number and small number' in the calculation process;

the principal component can be estimated from the properties of the principal component. Constructing a matrix X for dam effect quantities_n×mStandardizing each effect quantity to eliminate dimension difference or avoid 'large number eating small number' phenomenon, and standardizing the result

Comprises the following steps:

in the formula: a. the_jThe measured data mean value of the effect quantity is used as the measured data mean value; s_jThe standard deviation of the measured data is the effect quantity.

Seeking matrix L_m×mThe conversion from the original effect quantity to the comprehensive variable is realized:

[z_j]^T＝L[x_j]^T (4)

ith row L of matrix L_iIs a sample covariance matrix C_m×mThe ith feature vector of (1):

namely, the key to PCA is to solve eigenvalues of the covariance matrix:

λ_il_i＝Cl_i(i＝1,2,…,m) (6)

in the formula: lambda [ alpha ]_iIs the characteristic root of the covariance matrix C; l_iIs λ_iThe corresponding feature vector.

And after the number of the principal components is determined, projecting the standardized data matrix on the selected characteristic vector to obtain a comprehensive variable, and finishing the internal characteristic extraction of the service state of the dam.

Selecting a proper kernel function, and standardizing the data matrix

Mapping from the low-dimensional data space to the high-dimensional data space;

a Kernel Principal Component Analysis (KPCA) method projects actual measured dam effect data of an input space to a high-dimensional feature space through nonlinear mapping, and PCA analysis is carried out on the mapped data in the high-dimensional feature space, so that the KPCA method has strong nonlinear processing capability, and the basic principle and the realization idea of the KPCA method are shown in figure 2.

Step (4) obtaining the covariance matrix of the data matrix in the high-dimensional data space

And find its characteristic root lambda_iAnd a feature vector v;

the premise of analyzing by using the KPCA method is to understand the necessity of performing a dimension-increasing analysis from a low dimension to a high dimension, and to map the non-linear or linear indivisible effect data features in the low dimension space to the high dimension space, and then to make the features linear or nearly linear and further separable. The KPCA method has two key points in the implementation process:

the key one is as follows: in order to better process nonlinear data, a nonlinear mapping function is introduced, and the dam effect quantity original data space is mapped to a high-dimensional characteristic space;

the key is as follows: any vector in a space can be linearly represented by all samples in that space.

In m-dimensional space

In n points { x_iThe (i ═ 1,2, …, n) constitutes a dam effect quantity raw data matrix X_n×m. Defining a non-linear mapping function phi (-) to map the points from the low-dimensional input space to the high-dimensional feature space

The corresponding original effect quantity point set can be composed of

Showing that the key point is to realize the KPCA method, and the key point is obtained by carrying out standardization processing according to the formula (3)

Namely, it is

PCA analysis in feature space requires obtaining a matrix

Covariance matrix of

On the basis, solving the covariance matrix

Eigenvalue and eigenvector of (c):

since the non-linear mapping function φ (-) has implicit, φ (x)_i) The eigenvalues λ and eigenvectors v of the above formula cannot be obtained directly by using conventional eigenvalue decomposition or singular value solution.

Combining formula (7) and formula (8) can yield:

as can be seen from equation (9), the feature vector v can be represented by the sample φ (x)_i) Linear combination representation, which is the key to the KPCA method implementation, is then:

in the formula: α ═ a₁,a₂,…,a_n]^TIs a linear coefficient tensor.

Integrating equations (7), (8) and (10), and left-multiplying the matrix

Obtaining:

introducing n x n kernel matrix

Equation (11) can be expressed as:

i.e. to solve the following characteristic root problem:

Kα＝λ^Kα (13)

in the formula: lambda [ alpha ]^K＝nλ。

A solution satisfying the equation (13) is obtained from the eigenvalue decomposition or singular value solution method. To this end, the coefficient tensor matrix α and the eigenvector v are also calculated. Since the feature vector is a unit vector, having v^TThe property of v ═ 1, derived from equation (10):

by substituting formula (13), it is possible to obtain:

determining a feature vector lambda of a kernel matrix K^KAnd the eigen matrix u, the coefficient tensor matrix α is obtained by:

to this end, the covariance matrix

Characteristic root λ of^KN lambda, the eigenvector is formed by

And (4) obtaining.

Step (5) for the characteristic root lambda_iSorting in a descending order and adjusting corresponding feature vectors;

after solving the covariance matrix characteristic root, sorting the characteristic root by lambda₁≥λ₂≥…≥λ_mAnd paying attention to the corresponding relation between the characteristic root and the characteristic vector, wherein the information contained in the kth and the first k principal components accounts for the percentage of the total amount of the information (contribution rate g)_kAnd the cumulative contribution rate G_k) Are calculated by the following formulas, respectively:

step (6) determining the number of the principal components and extracting the feature vector v according to the principal component number determining method_i；

The number of principal components is determined according to the following method:

the method of cumulative contribution rate. The cumulative contribution rate method is the most commonly used method, and is to arrange feature roots in a descending order, calculate the cumulative contribution rate according to the method of equation (17b), and generally consider that when the cumulative contribution rate is higher than 85%, the selected principal component can well reflect the inherent features of the original data.

② average characteristic root method. The method takes the average value of all characteristic roots as a boundary, and takes the characteristic root higher than the average characteristic root as a preferred object. The learners find that the main components screened by the method are accurate when the number of the original variables is less than 30 and high correlation exists.

And lithotripsy. And drawing a characteristic root lithotripsy graph, wherein the inflection point of the curve is regarded as a boundary point of the main component and the secondary component.

And fourthly, a signal noise method. The method considers that the main component is a signal and the secondary component is noise, and separates the signal and the noise by utilizing the characteristic that the ratio of the signal to the noise is greater than the ratio between the signal and the noise:

seeking gamma_kLet it represent the minimum principal component (signal) λ_kWith the largest minor component (noise) lambda_k+1The ratio of (a) to (b).

It is to be noted here that: when the principal components are selected, the feature values need to be sorted in a descending order, and the corresponding relation between feature roots and feature vectors is noticed; when the point set does not satisfy in the feature space

Then, the kernel matrix needs to be corrected according to the following formula:

in the formula:

step (7) calculating a standardized data matrix

In the feature vector v_iThe projection is data after dimensionality reduction, and the extraction work of the main components of the service state of the dam is completed;

it can be seen from the realization principle of the KPCA method that because of the recessiveness of the nonlinear mapping function phi (·), the mapping from the effect quantity original data space to the feature space needs to be carried out in a certain way, and the kernel function K (x) meeting the Mercer condition is introduced_j,x_i) Commonly used kernel functions are polynomial kernel functions:

K(x_j,x_i)＝[(x_j·x_i)+1]^p p＝1,2,…(20)

gaussian radial basis kernel function:

multi-layer perceptron kernel:

K(x_j,x_i)＝tanh[v(x_j·x_i)+c] (22)

in formulae (20) to (22): x is the number of_i、x_jRepresenting the ith and jth actually measured data sequence of the effect quantity as a vector;

(. -) represents the vector inner product; i | · | purple wind²Represents a vector 2 norm; σ, v, c are nuclear parameters.

Step (8) on the basis of obtaining the main components of the service state of the dam by means of T²And the statistic realizes the construction of the dam security alert domain.

Actual measurement data sequence { x) for dam effect quantity_i(i ═ 1,2, …, n), and principal component { z was extracted by KPCA method_iAnd (i is 1,2, …, p), determining a dam service state transition warning domain, and if the dam service state does not change, considering that the dam service state changes independently and identically. Let principal component { z_iIndependently distributed (i ═ 1,2, …, p), subject to N_p(μ, Σ), Z is the future observation from the same distribution, then T²Statistics:

in the formula:

compliance

A distribution, and its p-dimensional ellipsoid for 100(1- α)% confidence domain consists of all z's satisfying the following inequality:

since the matrix S is symmetrical and positive, its characteristic root is set as lambda₁≥λ₂≥…≥λ_pMore than or equal to 0, and the unit orthogonal feature vector corresponding to the feature root is { u_iJ (i ═ 1,2, …, p), noted U ═ U₁,u₂,…,u_p]^TThen U is an orthogonal array, U^TU＝UU^TAs I, so:

equation (24) can be rewritten as:

thus the confidence domain of the observed value 1-alpha is the sample mean

As the center, the half shaft length is respectively:

and constructing an alert domain by using the confidence domain, and if the observed value Z falls outside the alert domain, failing, namely, the service state of the dam is changed.

Has the advantages that: the method for diagnosing the alert domain of the high dam service safety space introduces a Kernel Principal Component Analysis (KPCA) in a manifold learning algorithm, realizes the goal of converting dam service state from single-point early warning to multi-point combined early warning by constructing the alert domain on the basis of realizing reduction and accurate extraction of internal characteristics of a plurality of effect data, provides a practical and feasible method for diagnosing the alert domain of the high dam service safety space, and has good practical application value and popularization significance.

Drawings

FIG. 1 is a flow chart of an implementation of the present invention;

FIG. 2 is a diagram of the basic principle and implementation idea of the KPCA method of the present invention;

FIG. 3 is a diagram of a deformed safety warning domain of a 35# dam section of the invention, FIG. 3a is a deformed multi-measuring-point combined warning domain, and FIG. 3b is a deformed T²Verifying the graph;

FIG. 4 is a seepage safety warning domain diagram of a 35# dam segment of the invention, FIG. 4a is a seepage multi-measuring point combined warning domain, and FIG. 4b is seepage T²And (5) verifying the graph.

Detailed Description

Example (b): as shown in fig. 1 to 4, the diagnosis technique for the high dam service safety space alert domain of the invention takes a certain reservoir dam project as an example, and a typical dam section deformation and seepage safety alert domain is drawn up based on a KPCA method.

(1) Typical dam section deformation safety warning domain drawing and analysis

Based on 35^#The actual measurement data of the typical dam section is shown in table 1, the high dam effect original monitoring data information source matrix is constructed, and the actual measurement value matrix is established

And to

Carrying out standardization processing to obtain a standardized data matrix

Will normalize the data matrix

Mapping from a low-dimensional data space to a high-dimensional data space, in which a covariance matrix of the data matrix is obtained

Comprehensively considering the correlation among the measuring points, and utilizing the KPCA method to kernel principal elements and T of the deformation characteristics of the typical dam section²The statistic calculation result is listed in table 1, the characteristic root and the characteristic vector of the covariance matrix are obtained, specifically referring to the characteristic kernel principal component part in table 1, the principal component extraction work of the high dam service safety space alert domain diagnosis is completed, and T is used²The statistics realizes the construction of a high dam safety alert domain, the typical dam section deformation safety alert domain is shown in an attached figure 3, and the reasonability of the result is analyzed and verified.

Watch 135^#Dam section deformation characteristic kernel principal element and T²Statistics

Note: 35^#The half-axis length of the dam section deformation setting warning domain is 0.2973 and 0.1659 respectively, T²The statistic was 0.0102.

FIG. 3 shows the calculated 35^#The dam section deformation safety warning area can be seen from the following steps: 35^#After the dam section deformation actual measurement data is subjected to kernel principal component analysis, part of measured values fall outside a 'domain', and the deformation T of the measured values is analyzed²The statistic verification chart shows that the deformation behavior of the dam section changes between 2 months and 3 months in 1990, and the comparison of actual measurement process lines shows that the dam crest laser horizontal displacement D35 has larger upstream deformation in the period, and reaches the analysis timeMaximum of the segment (13/3/2009-21/3).

(2) Typical dam section seepage safety alert domain drawing and analysis

Based on 35^#The actual measurement data of the seepage of the dam section is shown in table 2, the information source matrix of the original monitoring data of the high dam effect quantity is constructed, and the actual measurement value matrix is established

And to

Carrying out standardization processing to obtain a standardized data matrix

Will normalize the data matrix

Mapping from a low-dimensional data space to a high-dimensional data space, in which a covariance matrix of the data matrix is obtained

Comprehensively considering the correlation among the measuring points, and utilizing the KPCA method to kernel principal elements and T of seepage characteristics of a typical dam section²The statistic calculation result is listed in Table 2, and the main component extraction work of the diagnosis of the security space alert domain of the high dam service is completed by means of T²The statistics realizes the construction of a high dam safety alert domain, a typical dam section seepage safety alert domain is shown in an attached figure 4, and the reasonability of the result is analyzed and verified.

Watch 235^#Dam section seepage characteristic kernel principal component and T²Statistics

Note: 35^#The half-axis length of the dam section deformation setting warning domain is 0.3388 and 0.2117 respectively, T²The statistic was 0.0176.

FIG. 4 shows 35^#The dam section seepage safety alert domain can be seen from the following steps: 35^#The measured data of dam section seepage has individual measured value which falls outside the 'domain' after nuclear principal component analysis, which shows that the dam section seepage behavior does not have serious change.

Claims (7)

1. A method for diagnosing a high dam service safety space alert domain is characterized by comprising the following steps:

(1) constructing a high dam effect original monitoring data information source matrix X according to the high dam effect monitoring data;

m monitoring effect quantities exist in the dam service system in the step (1), and each effect quantity sequence has n monitoring values { x }_ijAnd (i ═ 1,2, …, n ═ 1,2, …, m), constructing an n × m monitoring data matrix X:

in the formula: the matrix X may also be represented as [ X ]_j](j ═ 1,2, …, m) or [ x [ (-)_i]^T(i＝1,2,…,n)；

(2) Standardizing the original data information source matrix X to obtain a standardized data matrix

In the step (2), assuming effect quantity reduction, a comprehensive characteristic variable { z is obtained₁,z₂,…,z_pAnd (p is less than or equal to m), the comprehensive characteristic variable is formed by linearly combining original effect quantities and is expressed as:

in the formula: matrix L may also be tabulatedIs shown as [ l_j](j ═ 1,2, …, m) or [ l_i]^T(i＝1,2,L,m)；

To facilitate analysis of the comprehensive characteristic variable properties, assume { x }_jThe maximum square difference in all linear combinations of (1, 2, …, m) } (j) is z₁I.e. var (z)₁) Maximum, then z₁Referred to as the first principal component; (l)₂₁,l₂₂,…,l_2m) Perpendicular to (l)₁₁,l₁₂,…,l_1m) And let var (z)₂) Maximum, then z₂Referred to as the second principal component; by analogy with this, z_pIs the pth principal component, { z₁,z₂,…,z_pThe extraction result of the internal characteristics of the service state of the dam can be represented;

the principal component can be calculated according to the properties of the principal component, and a matrix X is formed aiming at the dam effect quantity_n×mStandardizing each effect quantity to eliminate dimension difference or avoid 'large number eating small number' phenomenon, and standardizing the result

Comprises the following steps:

in the formula: a. the_jThe measured data mean value of the effect quantity is used as the measured data mean value; s_jThe standard deviation of actually measured data of the effect quantity;

(3) selecting kernel functions meeting Mercer conditions, and standardizing the data matrix

Mapping from the low-dimensional data space to the high-dimensional data space;

(4) obtaining a covariance matrix of a data matrix in a high dimensional data space

Solving a characteristic root and a characteristic vector v of the covariance matrix;

(5) for the characteristic root lambda_iSorting in a descending order and adjusting corresponding feature vectors;

(6) determining the number of principal components and extracting a feature vector v according to the principal component number determination method_i；

(7) Calculating a normalized data matrix

In the feature vector v_iThe projection is data after dimension reduction, and the main component extraction work of diagnosis of the high dam service safety space alert domain is completed;

(8) on the basis of obtaining the main component of the diagnosis of the security space alert domain of the high dam service, with the help of T²The statistics realizes the construction of a high dam security alert domain;

(9) if the observed value falls outside the warning domain, the service state of the dam is changed; and if the observed value falls into the warning area, the service state of the dam is not changed.

2. The method for diagnosing the alert domain of the safety space in service of the high dam as recited in claim 1, wherein: in the step (3), the normalized data matrix is subjected to kernel function meeting Mercer conditions

From the low-dimensional data space to the high-dimensional data space.

3. The method for diagnosing the alert domain of the safety space in service of the high dam as recited in claim 1, wherein: in the step (4), in the m-dimensional space

In n points { x_iThe (i ═ 1,2, …, n) constitutes a dam effect quantity raw data matrix X_n×mA non-linear mapping function phi (·) is defined to map the points from the low-dimensional input space to the high-dimensional feature space

The corresponding original effect quantity point set can be formed by phi ═ phi (x)_i) Is expressed by 1,2, …, n, and is normalized by the following formula (3) to obtain

Namely, it is

PCA analysis in feature space requires obtaining a matrix

Covariance matrix of

On the basis, solving the covariance matrix

Eigenvalue and eigenvector of (c):

combining formula (7) and formula (8) can yield:

as can be seen from equation (9), the feature vector v can be represented by the sample φ (x)_i) Linear combinations represent, then:

in the formula: alpha ═ alpha₁,α₂,…,α_n]^TIs a linear coefficient tensor;

integrating equations (7), (8) and (10), and left-multiplying the matrix

Obtaining:

introducing n x n kernel matrix

Equation (11) can be expressed as:

i.e. to solve the following characteristic root problem:

Kα＝λ^Kα (13)

in the formula: lambda [ alpha ]^K＝nλ；

Obtaining a solution satisfying the formula (13) according to an eigenvalue decomposition or singular value solution method, and calculating a coefficient tensor matrix alpha and an eigenvector v, wherein the eigenvector is a unit vector and has v^TThe property of v ═ 1, derived from equation (10):

by substituting formula (13), it is possible to obtain:

determining a feature vector lambda of a kernel matrix K^KAnd the eigen matrix u, the coefficient tensor matrix α is obtained by:

to this end, the covariance matrix

Characteristic root λ of^KN lambda, the eigenvector is formed by

And (4) obtaining.

4. The method for diagnosing the alert domain of the safety space in service of the high dam as recited in claim 1, wherein: in the step (5), the characteristic root lambda is processed_iSorting in descending order and adjusting corresponding feature vectors.

5. The method for diagnosing the alert domain of the safety space in service of the high dam as recited in claim 1, wherein: in the step (6), the number of the principal components is determined and the feature vector v is extracted according to the principal component number determination method_i。

6. The method for diagnosing the alert domain of the safety space in service of the high dam as recited in claim 1, wherein: calculating the normalized data matrix X in the step (7) in the eigenvector v_iIn the upper partAnd (5) shadow, namely the projection is the data after dimension reduction.

7. The method for diagnosing the alert domain of the safety space in service of the high dam as recited in claim 1, wherein: the measured data sequence { x) of the dam effect quantity in the step (8)_i(i ═ 1,2, …, n), and principal component { z was extracted by KPCA method_i1 (i-1, 2, …, p), let principal component { z }_iIndependently distributed (i ═ 1,2, …, p), subject to N_p(mu, ∑), Z is a future observation from the same distribution, then T²Statistics:

in the formula:

compliance

A distribution, and its p-dimensional ellipsoid for 100(1- α)% confidence domain consists of all z's satisfying the following inequality:

since the matrix S is symmetrical and positive, its characteristic root is set as lambda₁≥λ₂≥…≥λ_pMore than or equal to 0, and the unit orthogonal feature vector corresponding to the feature root is { u_iJ (i ═ 1,2, …, p), noted U ═ U₁,u₂,…,u_p]^TThen U is an orthogonal array, U^TU＝UU^TAs I, so:

equation (24) can be rewritten as:

thus the confidence domain of the observed value 1-alpha is the sample mean

As the center, the half shaft length is respectively:

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