CN103093094A - Software failure time forecasting method based on kernel partial least squares regression algorithm - Google Patents

Abstract

The invention discloses a software failure time forecasting method based on a kernel partial least squares regression algorithm. Through the application of a kernel function technology, the problem of software reliability forecast is converted to the problem of recession estimation, and the kernel partial least squares regression algorithm is used for resolving the problem of the software reliability forecast. Through fully consideration of a small sample property of the software reliability forecast, the situations that the size of observational variables is bigger than that of observational samples and multicollinearity exists among the variables can be overcome by using the kernel function technology, and so that a model 'overfitting' situation arises in modeling approaches such as a neural network does not occur. By means of the software failure time forecasting method based on the kernel partial least squares regression algorithm, model parameters are automatically and continuously adjusted to fit the dynamic change in a failure process, therefore adaptive forecasting of the software reliability is achieved, and the adaptive capability of a software failure forecasting model is improved effectively.

Description

Software Failure Time Prediction Method Based on Kernel Partial Least Squares Regression Algorithm

【Technical field】

The invention relates to a software reliability test and a method for predicting software failure time data in the next or a long time in the future.

【Background technique】

Software reliability refers to the probability that software will not fail within a specified time under specified conditions. The stochastic process reliability model is the most researched and widely used category in the field of software reliability growth models, but the statistical components of actual reliability problems cannot be described only by classical statistical distribution functions, and the stochastic process model needs to analyze software faults. Many a priori assumptions are made for the attributes and software failure process, which leads to great differences in the prediction accuracy of each model in different projects, that is, the applicability of the model is poor.

The method based on kernel function theory is specially aimed at the prediction and classification of small sample data, and has obtained very good results in many similar fields of reliability prediction, which is suitable for complex problems such as software reliability prediction. With the help of computer technology, this type of model has adaptive ability and learning function, and has good performance in model applicability and evaluation and prediction ability. The software reliability model based on kernel function theory shows good performance in the case of limited samples. Features, to a large extent, can solve the problems of neural network over-learning, and become an important breakthrough in the research of software reliability model.

【Content of invention】

The technical problem to be solved by the present invention is to provide a software failure time prediction method based on kernel partial least squares regression algorithm, realize self-adaptive prediction of software reliability, and effectively improve the adaptability of software failure prediction model. For this reason, the present invention adopts following technical scheme, and it comprises the steps:

(1), first observe and record the sequential software failure data set, and normalize all input and output data;

(2) Through reasonable abstraction and assumptions, the software failure time prediction problem is transformed into a function regression problem;

(3), select the kernel function used for prediction, and give the initialization value of the parameter;

(4) Select the number of failure data for learning;

(5) Using kernel partial least squares regression algorithm to optimize learning for different failure data sets

(6). Finally, the optimized parameters are selected to predict the new failure time.

Further, the software failure time prediction problem described in step (2) is transformed into a function regression problem, and the following method is adopted:

Assuming that the software failure time that has occurred is t ₁ , t ₂ , L, t _n , let t _l = f(t _lm ,t _l-m+1 , L,t _l-1 ), then t _l follows a fixed but unknown The conditional distribution function F(t _l t _lm ,t _l-m+1 ，L,t _l-1 ), when t ₁ ,t ₂ ,L,t _k are known, the prediction of t _k+1 becomes : Known km observations (T ₁ ,t _m+1 ),(T ₂ ,t _m+2 ),L,(T _km ,t _k ) and the k-m+1th input T _k-m+1 In the case of , estimate the k-m+1th output value Wherein, T _i represents an m-dimensional vector [t _i ,t _i+1 , L,t _m+i ].

其参数初始值g＝1。The kernel function used in step (3) is a Gaussian kernel function,

Its parameter initial value g=1.

The number of failure data in step (4) is an integer between 5-8.

Step (5) Use the kernel partial least squares regression algorithm to optimize learning for different failure data sets, including the following process:

Step 1, the input data is a k-dimensional vector X={x ₁ ,x ₂ ,L,x _l }, and the output is a vector y ^s , s=1,2,L,m

Step 2, construct the kernel function matrix: K _ij =k( _xi ,x _j )i,j=1,2,L,l, where

$\mathrm{<span\; class="notranslate">\; \&kappa;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ></span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

的第一行，u_j＝u_j/||u_j||Step 3, let K ₁ =K,

The first line of , u _j ＝u _j /||u _j ||

u_j＝u_j/||u_j||，直到收敛Step 4, recalculate

u _j ＝u _j /||u _j ||, until convergence

Step 5, calculate τ _j =K _j u _j ,

K _j+1 ＝(I-τ _j τ′ _j /||τ _j || ² )K _j (I-τ _j τ′ _j /||τ _j || ² )

Step 6, calculate B=[β ₁ ,L,β _k ]T=[τ ₁ ,L,τ _k ], get the coefficient α=B(T′KB) ^-1 T′Y

The present invention fully considers the small sample characteristics of software failure data, uses the kernel function theory as a main means and method, combines the dynamic law presented by the software failure process, transforms the software reliability prediction problem into a regression estimation problem, and applies Kernel partial least squares regression algorithm to solve this problem.

The present invention utilizes the covariance information between the input and output variables to extract the latent features of the data, which can overcome the situation that the observed variables are more than the number of observed samples and the multicollinearity between the variables, so there will be no modeling methods such as neural networks Resulting model "overfitting" cases. In the new prediction method, as software failures continue to occur, model parameters will be automatically adjusted to adapt to the dynamic changes in the failure process, thereby realizing adaptive prediction of software reliability and effectively improving the adaptability of software failure prediction models.

【Description of drawings】

FIG. 1 is a flow chart of the software failure time prediction method of the present invention.

【Detailed ways】

1) Data normalization

其中，y是归一化后的值，x是实际值，x_max是数据集中的最大值，x_min是最小值，Δ＝x_max-x_min，预测结束后，采用以下映射把数据映射回到实际值： $x=\frac{y-0.9}{0.8}\&times;\mathrm{\&Delta;}+x_{\max }.$ When using the regression estimation algorithm for learning prediction, it is first necessary to normalize all input and output data to the interval [0.1,0.9]. The specific conversion formula is:

Among them, y is the normalized value, x is the actual value, x _max is the maximum value in the data set, x _min is the minimum value, Δ=x _max -x _min , after the prediction is over, use the following mapping to map the data back to to the actual value: $x=\frac{\mathrm{the\; y}-0.9}{0.8}\&times;\mathrm{\&Delta;}+x_{\max }.$

2) Problem Transformation

其中T_i表示m维向量[t_i,t_i+1,L,t_m+i]，同样的，把

作为输入，则可以预测

同理可以预测得到

In the software reliability prediction model based on kernel function theory, the relationship between software failure time data and the failure time data of m times before it is modeled, and the single-step prediction problem can be transformed into: known km In the case of observing (T ₁ ,t _m+1 ),(T ₂ ,t _m+2 ),L,(T _km ,t _k ) and the k-m+1th input T _k-m+1 , estimate k-m+1th output value

Where T _i represents the m-dimensional vector [t _i ,t _i+1 ,L,t _m+i ], similarly, put

As input, you can predict

Similarly, it can be predicted that

3) The selected kernel function, the initialization value of the parameter

4) Determine the value of the kernel function parameter

The kernel function parameter selection problem is essentially an optimization problem. The grid search method is used to select the kernel function parameter. For example, when using SVM prediction, the Gaussian kernel function is used. Two parameters need to be determined, namely the penalty factor C and the kernel function parameter g , based on the grid method, C∈[C ₁ ,C ₂ ], the change step is C _s , and g∈[g ₁ ,g ₂ ], the change step is g _t , for each pair of parameters (C,g) For training, select a pair of parameters with the best effect as model parameters.

5) Kernel partial least squares regression algorithm

The solution to the kernel function regression problem can be described as: given a group of vectors with the corresponding target value As an input, we want to find out the corresponding relationship between x _i and t _i , so that when we encounter a new vector x _* , we can predict its corresponding target value t _* , and t _i is any real number. Assume that the corresponding relationship between x and t conforms to the following function:

$\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}$

Among them, k(x, x _i ) is the kernel function, and the purpose of the kernel function regression estimation algorithm is to find the appropriate w _i . The algorithm is as follows:

Step 1, the input data is a k-dimensional vector X={x ₁ ,x ₂ ,L,x _l }, and the output is a vector y ^s , s=1,2,L,m

Step 2, construct the kernel function matrix: K _ij =k( _xi ,x _j )i,j=1,2,L,l, where

$\mathrm{<span\; class="notranslate">\; \&kappa;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ></span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

的第一行,u_j＝u_j/||u_j||Step 3, let K ₁ =K,

The first line of , u _j ＝u _j /||u _j ||

u_j＝u_j/||u_j||，直到收敛Step 4, recalculate

u _j ＝u _j /||u _j ||, until convergence

Step 5, calculate τ _j =K _j u _j ,

K _j+1 ＝(I-τ _j τ′ _j /||τ _j || ² )K _j (I-τ _j τ′ _j /||τ _j || ² )

In order to provide a reasonable comparison and analysis of the established models, 10 real failure datasets from different types of software were used to carry out experimental analysis on the proposed model, as shown in Table 1. These data sets describe the failure process of each software system, and each data point contains two sets of observation statistics: cumulative execution time and cumulative failure times. In the experiment, the training set includes the complete system failure process from the beginning of the test. In order to allow the kernel function to fully learn, during the experiment, the first third of all data sets are taken as learning data, and the latter third is used as learning data. The second data is predicted and compared with the real data.

The table lists the AE values of each model on ten datasets, among which models 1-6 represent SRGMWith Logistic TEF, SRGM With Rayleigh TEF, Delayed S-Shaped Model WithLogistic TEF, Delayed S-Shaped Model With Rayleigh TEF, G-O model, Yamada Delayed S-Shaped; model 7 represents the method adopted in the present invention, a, b, c, d represent the kernel functions used are Gaussian Function, Linear Function, Polynomial Function, Symmetric Triangle Function respectively.

Table 1: AE values predicted by each model on 10 datasets

Conclusion: On different data sets, when using different kernel functions and different regression estimation methods, the prediction performance of the model is different. Using the software reliability prediction model based on the kernel partial least squares regression algorithm can effectively improve the prediction of the model. performance and applicability.

The above-mentioned embodiment is an illustration of the present invention, not a limitation of the present invention, and any solution after a simple transformation of the present invention belongs to the protection scope of the present invention.

Claims (4)

1. The software failure time prediction method based on nuclear partial least squares regression algorithm is characterized in that it comprises the following steps: (1), first observe and record the sequential software failure data set, and normalize all input and output data; (2) Through reasonable abstraction and assumptions, the software failure time prediction problem is transformed into a functional regression problem; (3), select the kernel function used for prediction, and give the initialization value of the parameter; (4) Select the number of failure data for learning; (5) Using kernel partial least squares regression algorithm to optimize learning for different failure data sets (6). Finally, the optimized parameters are selected to predict the new failure time. the 2. The method for predicting software failure time based on kernel partial least squares regression algorithm as claimed in claim 1, characterized in that, the software failure time prediction problem described in step (2) is converted into a function regression problem, using the following method: Assuming that the software failure time that has occurred is t ₁ , t ₂ , L, t _n , let t _l = f(t _lm ,t _l-m+1 , L,t _l-1 ), then t _l follows a fixed but unknown The conditional distribution function F(t _l |t _lm ,t _l-m+1 ,L,t _l-1 ), under the condition that t ₁ ,t ₂ ,L,t _k are known, predicts the change of t _k+1 For: known km observations (T ₁ ,t _m+1 ),(T ₂ ,t _m+2 ),L,(T _km ,t _k ) and the k-m+1th input T _k-m+ In the case of ₁ , estimate the k-m+1th output value

Wherein, T _i represents an m-dimensional vector [t _i ,t _i+1 , L,t _m+i ]. 3. The software failure time prediction method based on kernel principal component regression algorithm as claimed in claim 1, wherein the kernel function used in step (3) is a Gaussian kernel function,

Its parameter initial value g=1. The number of failure data in step (4) is an integer between 5-8. 4. The software failure time prediction method based on nuclear partial least squares regression algorithm as claimed in claim 1, characterized in that, step (5) adopts nuclear partial least squares regression algorithm to carry out learning optimization for different failure data sets, including The following process: Step 1, the input data is a k-dimensional vector X={x ₁ ,x ₂ ,L,x _l }, and the output is a vector y ^s , s=1,2,L,m Step 2, construct the kernel function matrix: K _ij =k( _xi ,x _j )i,j=1,2,L,l, where

Step 3, let K ₁ =K,

The first line of , u _j ＝u _j /||u _j || Step 4, recalculate

u _j ＝u _j /||u _j ||, until convergence Step 5, calculate τ _j =K _j u _j ,

K _j+1 ＝(I-τ _j τ′ _j /||τ _j || ² )K _j (I-τ _j τ′ _j /||τ _j || ² ) Step 6, calculate B=[β ₁ ,L,β _k ]T=[τ ₁ ,L,τ _k ], and obtain the coefficient α=B(T′KB) ⁻¹ T′Y.

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