CN105740212A - Sensor exception detection method based on regularized vector autoregression model - Google Patents

Abstract

The invention relates to a sensor exception detection method based on a regularized vector autoregression model. The sensor exception detection method comprises the following steps: (1) establishing a multielement linear regression model, and determining a target function; collecting data by a sensor; establishing a nearest neighbor graph of data points, wherein the graph consists of n vertexes, each vertex corresponds to one data point, and the weight matrix of edges is defined by considering a relationship between fixed points; constructing a bound term in order to keep similarity among original data points while the obstacles of high dimension and overfitting can be overcome; and utilizing the target function to train a model parameter to obtain an optimal parameter coefficient, and utilizing the model obtained by training to carry out exception detection. The sensor exception detection method can better predict original data.

Description

A kind of sensor abnormality detection method based on regularization Vector Autoression Models

Technical field

The invention belongs to sensor abnormality detection technique field, particularly relate to sensor abnormality detection technique.

Background technology

Abnormality detection refers to detection and finds not meet in observation sample data the data pattern of normally desired behavior, and it is one of problem very active in data mining research, in occupation of leading status, is widely used.The application of abnormality detection technology can effectively prevent the invasion of network; ensure industrial safety; the fault etc. of monitoring equipment; therefore the research of abnormality detection is rich in theory significance and actual application value; and had been subjected to concern widely, become a very active and popular research subject.Abnormality detection is the task of a great particularity, this is mainly in truthful data great majority and only meets the data pattern of expectation (normal class) behavior, and rare or unknown violation meets the data pattern of expectation (exception class) behavior, this two class observes the extreme disequilibrium (exception class sample number is much smaller than normal class sample) of sample allows abnormality detection become more difficult.

Vector Autoression Models (VAR) is a kind of multivariate statistical method, is used to the linear dependence catching between multivariate time series, has promoted single argument autoregression (AR) model, be widely used.VAR model is based on the statistical property of data and sets up model, with current variablees all in model, some lagged variables of all variablees is returned, it is possible to estimate the dynamic relationship between joint endogenous variables, and need not anything first constraints.VAR model is a popular multivariate time series analytical model, but maximum the haveing the drawback that of this model can meet with overparameterization, because the quantity of parameter becomes square number to increase along with the seasonal effect in time series increase comprised.When seasonal effect in time series number is relative to seasonal effect in time series length, standard estimation technique is inaccurate.This destruction identifies the ability of important relationship in data, thus can not make predictive ability accurately.In order to solve the excessive parameter problem in VAR model, the model (SVAR) of sparse estimation is suggested.Utilizing regularization penalty term to retrain VAR model can so that some parameter estimation be zero, and the method is sparse in this sense, and then can overcome the obstacle of higher-dimension and overfitting.Similar with the method basic thought, utilize figure regular terms VAR to carry out retraining the advantage being possible not only to keep the sparse constraint of SVAR, simultaneously can also in conjunction with the information between sensing data.Compared with SVAR method, utilize figure canonical constraint VAR to enable to model more sparse, and may apply to large-scale data concentration.

Sensing data is set up model based on the statistical property of data by VAR, it is prone to estimate, it is possible to matching initial data well, there is considerable flexibility and practicality, the generation process particularly describing little variables collection data is most suitable, and therefore this model is widely used.But, in many practical applications, such as sensing data, data volume is relatively more, and the predictive ability of the method will decline.In order to overcome the problem of higher-dimension and overfitting, adopt regularization penalty term that VAR is retrained to solve coefficient more sparse.Simultaneously taking account of relation implicit between data, this bound term can ensure that interior spatial structure original between data, whereby it can be detected that the relation between multivariate.Therefore, the sensor abnormality detection technique based on regularization Vector Autoression Models just has even more important researching value.

Summary of the invention

The present invention devises a kind of sensor abnormality detection technique method based on regularization Vector Autoression Models.Comparing with original Vector Autoression Models, the method has advantage, and the method take into account the similarity relationships between data, be ensure that by increase bound term and solves the openness of coefficient, also maintains the interior geometry between initial data simultaneously.

A kind of sensor abnormality detection method based on regularization Vector Autoression Models, comprises the following steps:

(1) set up multiple linear regression model, and determine object function；

(2) sensor acquisition data are utilized；

(3) arest neighbors figure, the figure that set up data point are made up of n summit, one data point of each of which vertex correspondence, it is considered to the relation between fixed point and fixed point, and the weight matrix W on definition limit is as follows:

Wherein N_p(x_i) represent data point x_iThe data acquisition system of p nearest neighbor point composition, definition L=D-W, D are diagonal matrix, and its diagonal element is current line or column vector sum, namelyClaiming L is figure Laplacian Matrix；

(4) similarity for the obstacle of higher-dimension and overfitting can be overcome to be maintained with between original data point, structure constraint item:

(5) utilize object function training pattern parameter to draw the parameter coefficient of optimum, utilize the model of training gained to carry out abnormality detection.

Beneficial effects of the present invention is as follows:

First, when processing sensing data, so that model is more sparse, compared with VAR, solution procedure can reduce and select less parametric variable by increasing the constraint of figure canonical.

Second, set up regularization VAR model so that most of coefficient of model becomes 0, reduces the complexity solved, adopt figure canonical bound term, it is possible to find the inherent mutual relation between data, predict initial data better simultaneously.

Accompanying drawing explanation

Fig. 1 institute extracting method block diagram

Detailed description of the invention

Consider the geometry between data, when constructing regularization constraint item, use for reference the thought assumed based on stream: if two data points have close geometric distribution at higher dimensional space, then after dimensionality reduction, in gained space, the two data point also should be close, and stream is assumed to occupy an important position in Data Dimensionality Reduction Algorithm.The arest neighbors figure of data point can be utilized to approach when data stream is unknown, such that it is able to consider that the arest neighbors figure of data point constructs corresponding bound term.If a figure is made up of n summit, one data point of each of which vertex correspondence, consider the relation between fixed point and fixed point simultaneously, the weight matrix W on definition limit is as follows:

Wherein N_p(x_i) represent x_iThe data acquisition system of p nearest neighbor point composition.Definition L=D-W, D are diagonal matrix, and its diagonal element is current line or column vector sum, namelyClaiming L is figure Laplacian Matrix.

In order to overcome the similarity that the obstacle of higher-dimension and overfitting is maintained with between original data point, it is possible to structure constraint item:

The present invention is described in detail below.

The general type of Vector Autoression Models is

x_t=x_t-1β₁+…+x_t-pβ_p+ε_t, t=p+1 ..., n (3)

For each t > 1, with X=[x_t-1,…,x_t-p]^TRepresent x_tP forward direction sample data, then Vector Autoression Models can be re-expressed as multiple linear regression model:

Y=XB+ ε (4)

Wherein Y=[x₂,…,x_n]^T, B=[β₂,…,β_n]^TIt is the unknown regression coefficient vector of p dimension, ε=[ε₂,…,ε_n]^TIt is error vector, and ε～N (0, σ²I), σ²Unknown.

In order to overcome the defect of higher-dimension and overfitting, SVAR model utilizes ElasticNet bound term to be diluted restriction, is actually and utilizes LASSO to return (l₁Norm) and ridge regression ((l₂Norm) VAR object function is increased bound term so that and expressions below reaches minimum B:

l₁Norm item is exactly LASSO penalty term, and it is able to ensure that coefficient matrix B is sparse, even if its most elements is 0 value.l₂Norm is ridge regression penalty term, and it is able to ensure that the slickness of coefficient matrix.

Consistent with the general idea of SVAR model, we also take the thought increasing bound term that archetype is limited, the difference is that we not only consider that the obstacle that can overcome higher-dimension and overfitting also keeps the similarity between original data point simultaneously.Such object function is just

Owing to above formula comprises l₁Norm constraint item, when B has comprise 0 value time, above formula is non-differentiable, and the Optimization without restriction of standard can not directly be brought application and solve, and the method for coordinate gradient can be utilized to solve about this problem.

First, keep its dependent variable constant, individually more new variables β_n.In order to pass through to minimize each β_nSolve expression formula (6), then reconstructed error can be expressed again:

Laplce bound term Tr (B^TLB) can also again be write as:

So (6) formula just can be expressed as again:

When updating β_iTime, keep its dependent variable { β_j}_j≠iFixing, then just can be optimized by expressions below and solve β_i:

Wherein, h_i=2 λ₂(Σ_j≠iL_iiβ_i),It is β_iJth correlation coefficient.

Solving to be optimized by characteristic symbol searching algorithm and solve for (1.10), thus can obtain optimizedFor each variable β_nAll take above-mentioned optimisation strategy to carry out one by one solving optimal solution, then can obtain the optimized coefficients matrix needed

As follows in actual treatment step:

1. initialize: prepare data set, and initialize B.

2. couple each β_iCarry out formula iteration

3. utilize characteristic symbol searching algorithm optimizing expression (10)

4. draw the result B of optimum^*。

Claims (1)

1., based on a sensor abnormality detection method for regularization Vector Autoression Models, comprise the following steps:

(1) set up multiple linear regression model, and determine object function；

(2) sensor acquisition data are utilized；

(3) arest neighbors figure, the figure that set up data point are made up of n summit, one data point of each of which vertex correspondence, it is considered to the relation between fixed point and fixed point, and the weight matrix W on definition limit is as follows:

$w_{ij}=\left\{\begin{array}{cc}1,& \begin{array}{cccc}if& x_i\∈N_p\left(x_j\right)& or& x_j\∈N_p\left(x_i\right)\end{array}\\ 0,& otherwise\end{array}\right.$

Wherein N_p(x_i) represent data point x_iThe data acquisition system of p nearest neighbor point composition, definition L=D-W, D are diagonal matrix, and its diagonal element is current line or column vector sum, namelyClaiming L is figure Laplacian Matrix；

(4) similarity for the obstacle of higher-dimension and overfitting can be overcome to be maintained with between original data point, structure constraint item:

$R=\frac{1}{2}\underset{i,j=1}{\overset{N}{\Σ}}\left|\right|x_i-x_j|{|}_2^2{W}_{ij}=\underset{j=1}{\overset{N}{\Σ}}{x}_i^T{x}_i{D}_{ij}-\underset{i,j=1}{\overset{N}{\Σ}}{x}_i^T{x}_j{W}_{ij}$

(5) utilize object function training pattern parameter to draw the parameter coefficient of optimum, utilize the model of training gained to carry out abnormality detection.