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

Software failure time forecasting method based on kernel partial least squares regression algorithm Download PDF

Info

Publication number
CN103093094A
CN103093094A CN2013100130053A CN201310013005A CN103093094A CN 103093094 A CN103093094 A CN 103093094A CN 2013100130053 A CN2013100130053 A CN 2013100130053A CN 201310013005 A CN201310013005 A CN 201310013005A CN 103093094 A CN103093094 A CN 103093094A
Authority
CN
China
Prior art keywords
kernel
software failure
regression algorithm
software
failure time
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN2013100130053A
Other languages
Chinese (zh)
Inventor
蒋云良
楼俊钢
江建慧
申情
范婧
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Huzhou University
Original Assignee
Huzhou University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Huzhou University filed Critical Huzhou University
Priority to CN2013100130053A priority Critical patent/CN103093094A/en
Publication of CN103093094A publication Critical patent/CN103093094A/en
Pending legal-status Critical Current

Links

Images

Landscapes

  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

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 forecasting methods based on the Kernel partial least squares regression algorithm
[technical field]
The present invention relates in software reliability test and evaluation process next time or software failure time data Forecasting Methodology in the following long period.
[background technology]
Software reliability refers under rated condition, at the appointed time, and the probability that software did not lose efficacy.The stochastic process reliability model is that software reliability growth model area research is maximum, a most widely used class, but the statistics composition of achieved reliability problem can not only be described with classical statistical distribution functions, and the random process model hypothesis that need to make many priori to attribute and the software failure process of software fault, this causes, and each model shows great precision of prediction difference in different projects, and namely the applicability of model is relatively poor.
Specially for prediction and the classification problem of small sample data, obtain extraordinary result in a lot of similar reliability predictions fields based on the kernel function theory and method, be fit to this challenge of software reliability prediction.By means of computer technology, this class model has adaptive ability and learning functionality, performance is preferably all arranged on model applicability and evaluation prediction ability, the superperformance that shows in the finite sample situation based on the software reliability model of kernel function theory, can solve to a great extent the problems such as study excessively of neural network, become a breach of outbalance in present Research of reliability model.
[summary of the invention]
Technical matters to be solved by this invention is to provide a kind of software failure time forecasting methods based on the Kernel partial least squares regression algorithm, realizes the adaptive prediction of software reliability, effectively improves the adaptive faculty of software faults prediction model.For this reason, the present invention by the following technical solutions, it comprises following steps:
(1), at first observe and record order software failure data collection, and all inputoutput data normalization;
(2), by abstraction and hypothesis, software failure time prediction problem is converted into a function regression problem;
(3), select to be used for the kernel function of prediction and the initialization value of given parameters;
(4), select to be used for the fail data number of study;
(5), adopt the Kernel partial least squares regression algorithm to learn to optimize for different failure dates sets
(6), select at last the parameter after optimization that the new out-of-service time is predicted.
Further, step (2) is described is converted into a function regression problem to software failure time prediction problem, adopts following methods:
Suppose that the software failure time that has occured is t 1, t 2, L, t n, make t l=f (t l-m, t L-m+1, L, t l-1), t lObey fixing but unknown conditional distribution function F (t lt l-m, t L-m+1, L, t l-1), at t 1, t 2, L, t kUnder known conditions to t k+1Predict and become: known k-m observation (T 1, t m+1), (T 2, t m+2), L, (T k-m, t k) and k-m+1 input T K-m+1Situation under, estimate k-m+1 output valve Wherein, T iExpression m dimensional vector [t i, t i+1, L, t m+i].
The kernel function of using in step (3) is gaussian kernel function,
Figure BDA00002732376800022
Its initial parameter value g=1.
Fail data number in step (4) is the integer between 5-8.
Step (5) adopts the Kernel partial least squares regression algorithm to learn to optimize for different failure dates sets, comprises following process:
Step 1, the input data are k dimensional vector X={x 1, x 2, L, x l, be output as vectorial y s, s=1,2, L, m
Step 2 builds kernel matrix: K ij=k (x i, x j) i, j=1,2, L, l, wherein
&kappa; ( x , y ) = e - g < x - y , x - y > 2
Step 3 makes K 1=K,
Figure BDA00002732376800024
Figure BDA00002732376800025
The first row, u j=u j/ || u j||
Step 4, double counting
Figure BDA00002732376800026
u j=u j/ || u j||, until convergence
Step 5 is calculated τ j=K ju j,
Figure BDA00002732376800027
Figure BDA00002732376800028
K j+1＝(I-τ jτ′ j/||τ j|| 2)K j(I-τ jτ′ j/||τ j|| 2)
Step 6 is calculated B=[β 1, L, β k] T=[τ 1, L, τ k], obtain factor alpha=B (T ' KB) -1T ' Y
The present invention takes into full account the small sample characteristic of software failure data, the kernel function theory as a kind of Main Means and method, the dynamic law that presents in conjunction with the software failure process, the software reliability prediction problem is converted into a regression estimation problem, and uses the Kernel partial least squares regression algorithm and solve this problem.
The present invention utilizes the covariance information between the input and output variable to extract the potential feature of data, can overcome observational variable more than the multicollinearity that exists between the situation of observation sample number and variable, model " over-fitting " situation that the modeling method such as neural network produces therefore can not occur.In new Forecasting Methodology, along with software failure constantly occurs, model parameter will constantly adjust to adapt to the dynamic change of failure procedure automatically, thereby realize the adaptive prediction of software reliability, effectively improve the adaptive faculty of software faults prediction model.
[description of drawings]
Fig. 1 is the process flow diagram of software failure time forecasting methods of the present invention.
[embodiment]
1) data normalization
When using regression estimation algorithm to learn to predict, at first need all inputoutput datas are normalized to interval [0.1,0.9], specifically transform formula and be:
Figure BDA00002732376800031
Wherein, y is the value after normalization, and x is actual value, x maxThe maximal value of data centralization, x minMinimum value, Δ=x max-x min, after prediction finishes, adopt following mapping that data-mapping is got back to actual value: x = y - 0.9 0.8 &times; &Delta; + x max .
2) problem transforms
In the prediction model of software reliability based on the kernel function theory, software failure time data and the relation that occurs between m out-of-service time data before it are carried out modeling, the Single-step Prediction problem can be converted into: observe (T for known k-m 1, t m+1), (T 2, t m+2), L, (T k-m, t k) and k-m+1 input T K-m+1Situation under, estimate k-m+1 output valve
Figure BDA00002732376800033
T wherein iExpression m dimensional vector [t i, t i+1, L, t m+i], same,
Figure BDA00002732376800041
As input, can predict
Figure BDA00002732376800042
In like manner can predict and obtain
Figure BDA00002732376800043
Figure BDA00002732376800044
3) kernel function of selecting, the initialization value of parameter
Figure BDA00002732376800045
4) value of definite kernel function parameter
Kernel functional parameter is selected problem, and its essence is exactly an optimization problem, adopts the grid search method to carry out kernel functional parameter and selects, such as when predicting with SVM, adopt gaussian kernel function, need to determine that two parameters be penalty factor and kernel functional parameter g, based on gridding method with C ∈ [C 1, C 2], change step is C s, and g ∈ [g 1, g 2], change step is g t, train for every pair of parameter (C, g), choose the best a pair of parameter of effect as model parameter.
5) Kernel partial least squares regression algorithm
The kernel function regression problem is found the solution and can be described as: given a group vector With corresponding desired value As input, want to find out x iWith t iBetween corresponding relation, make running into a new vector x *The time, can dope its corresponding desired value t *, t iIt is any real number.The corresponding relation of supposing x and t meets following function:
t = y ( x ; w ) = &Sigma; i = 1 M w i k ( x , x i ) + w 0
Wherein, k (x, x i) be kernel function, the purpose of kernel function regression estimation algorithm is to find suitable w iAlgorithm is as follows:
Step 1, the input data are k dimensional vector X={x 1, x 2, L, x l, be output as vectorial y s, s=1,2, L, m
Step 2 builds kernel matrix: K ij=k (x i, x j) i, j=1,2, L, l, wherein
&kappa; ( x , y ) = e - g < x - y , x - y > 2
Step 3 makes K 1=K,
Figure BDA00002732376800052
Figure BDA00002732376800053
The first row, u j=u j/ || u j||
Step 4, double counting
Figure BDA00002732376800054
u j=u j/ || u j||, until convergence
Step 5 is calculated τ j=K ju j,
Figure BDA00002732376800055
Figure BDA00002732376800056
K j+1＝(I-τ jτ′ j/||τ j|| 2)K j(I-τ jτ′ j/||τ j|| 2)
In order to provide rational comparison and analysis to the model of setting up, adopt 10 models that propose from the true fail data set pair of dissimilar software to carry out experimental analysis, as shown in table 1.These data sets have been described the failure procedure of each software systems, and each data point comprises the set of two kinds of observation statistics: accumulative total execution time and accumulative total Failure count.In experiment, training set comprises from the rear complete thrashing process of test beginning, in order to allow kernel function learn fully, in experimentation, get all data sets first three/one as learning data, after back 2/3rds data are predicted and True Data compare.
Listed the AE value of each model on ten data sets in table, wherein model 1-6 represents respectively SRGM With Logistic TEF, SRGM With Rayleigh TEF, Delayed S-Shaped Model With Logistic TEF, Delayed S-Shaped Model With Rayleigh TEF, G-O model, Yamada Delayed S-Shaped; Model 7 represents the method that the present invention adopts, and the kernel function that a, b, c, d representative are adopted is respectively Gaussian Function, Linear Function, Polynomial Function, Symmetric Triangle Function.
Show the AE value of each model prediction on 1:10 data set
Figure BDA00002732376800057
Figure BDA00002732376800061
Conclusion: on the different pieces of information collection, when adopting different kernel functions and adopting different regression estimation methods, the model prediction performance is all variant, adopts estimated performance and the applicability that can effectively improve model based on the prediction model of software reliability of Kernel partial least squares regression algorithm.
Above-described embodiment is to explanation of the present invention, is not limitation of the invention, any scheme after simple transformation of the present invention is all belonged to protection scope of the present invention.

Claims (4)

1. based on the software failure time forecasting methods of Kernel partial least squares regression algorithm, it is characterized in that, it comprises following steps:
(1), at first observe and record order software failure data collection, and all inputoutput data normalization;
(2), by abstraction and hypothesis, software failure time prediction problem is converted into a function regression problem;
(3), select to be used for the kernel function of prediction and the initialization value of given parameters;
(4), select to be used for the fail data number of study;
(5), adopt the Kernel partial least squares regression algorithm to learn to optimize for different failure dates sets
(6), select at last the parameter after optimization that the new out-of-service time is predicted.
2. the software failure time forecasting methods based on the Kernel partial least squares regression algorithm as claimed in claim 1, is characterized in that, step (2) is described is converted into a function regression problem to software failure time prediction problem, adopts following methods:
Suppose that the software failure time that has occured is t 1, t 2, L, t n, make t l=f (t l-m, t L-m+1, L, t l-1), t lObey fixing but unknown conditional distribution function F (t l| t l-m, t L-m+1, L, t l-1), at t 1, t 2, L, t kUnder known conditions to t k+1Predict and become: known k-m observation (T 1, t m+1), (T 2, t m+2), L, (T k-m, t k) and k-m+1 input T K-m+1Situation under, estimate k-m+1 output valve
Figure FDA00002732376700011
Wherein, T iExpression m dimensional vector [t i, t i+1, L, t m+i].
3. the software failure time forecasting methods based on the core principle component regression algorithm as claimed in claim 1, is characterized in that, the kernel function of using in step (3) is gaussian kernel function,
Figure FDA00002732376700012
Its initial parameter value g=1.Fail data number in step (4) is the integer between 5-8.
4. the software failure time forecasting methods based on the Kernel partial least squares regression algorithm as claimed in claim 1, is characterized in that, step (5) adopts the Kernel partial least squares regression algorithm to learn to optimize for different failure dates sets, comprises following process:
Step 1, the input data are k dimensional vector X={x 1, x 2, L, x l, be output as vectorial y s, s=1,2, L, m
Step 2 builds kernel matrix: K ij=k (x i, x j) i, j=1,2, L, l, wherein
Figure FDA00002732376700021
Step 3 makes K 1=K,
Figure FDA00002732376700022
Figure FDA00002732376700023
The first row, u j=u j/ || u j||
Step 4, double counting
Figure FDA00002732376700024
u j=u j/ || u j||, until convergence
Step 5 is calculated τ j=K ju j,
Figure FDA00002732376700025
Figure FDA00002732376700026
K j+1＝(I-τ jτ′ j/||τ j|| 2)K j(I-τ jτ′ j/||τ j|| 2)
Step 6 is calculated B=[β 1, L, β k] T=[τ 1, L, τ k], obtain factor alpha=B (T ' KB) -1T ' Y.
CN2013100130053A 2013-01-14 2013-01-14 Software failure time forecasting method based on kernel partial least squares regression algorithm Pending CN103093094A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN2013100130053A CN103093094A (en) 2013-01-14 2013-01-14 Software failure time forecasting method based on kernel partial least squares regression algorithm

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN2013100130053A CN103093094A (en) 2013-01-14 2013-01-14 Software failure time forecasting method based on kernel partial least squares regression algorithm

Publications (1)

Publication Number Publication Date
CN103093094A true CN103093094A (en) 2013-05-08

Family

ID=48205653

Family Applications (1)

Application Number Title Priority Date Filing Date
CN2013100130053A Pending CN103093094A (en) 2013-01-14 2013-01-14 Software failure time forecasting method based on kernel partial least squares regression algorithm

Country Status (1)

Country Link
CN (1) CN103093094A (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105260304A (en) * 2015-10-19 2016-01-20 湖州师范学院 /Software reliability prediction method based on QBGSA RVR (Quantum-inspired Binary Gravitational Search Algorithm-Relevance Vector Machine)
CN107947984A (en) * 2017-11-24 2018-04-20 浙江网新电气技术有限公司 A kind of failure predication processing method and its system towards railway transport of passengers service
CN108267951A (en) * 2016-12-30 2018-07-10 南京理工大学 A kind of maximum power point-tracing control method based on core offset minimum binary

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
楼俊钢 等: "《软件可靠性预测的核函数方法》", 《计算机科学》 *
蒋红卫 等: "《核偏最小二乘回归及其在医学中的应用》", 《中国卫生统计》 *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105260304A (en) * 2015-10-19 2016-01-20 湖州师范学院 /Software reliability prediction method based on QBGSA RVR (Quantum-inspired Binary Gravitational Search Algorithm-Relevance Vector Machine)
CN105260304B (en) * 2015-10-19 2018-03-23 湖州师范学院 A kind of software reliability prediction method based on QBGSA RVR
CN108267951A (en) * 2016-12-30 2018-07-10 南京理工大学 A kind of maximum power point-tracing control method based on core offset minimum binary
CN107947984A (en) * 2017-11-24 2018-04-20 浙江网新电气技术有限公司 A kind of failure predication processing method and its system towards railway transport of passengers service
CN107947984B (en) * 2017-11-24 2021-08-03 浙江网新电气技术有限公司 Fault prediction processing method and system for railway passenger service

Similar Documents

Publication Publication Date Title
US10929529B2 (en) Cyber physical attack detection
Wang et al. A compound framework for wind speed forecasting based on comprehensive feature selection, quantile regression incorporated into convolutional simplified long short-term memory network and residual error correction
Hosseini-Moghari et al. Monthly and seasonal drought forecasting using statistical neural networks
Liu et al. A two-stage method of quantitative flood risk analysis for reservoir real-time operation using ensemble-based hydrologic forecasts
CN112598248B (en) Load prediction method, load prediction device, computer equipment and storage medium
CN103886218A (en) Lake and reservoir algal bloom predicating method based on multielement nonstationary time series analysis and neural network and support vector machine compensation
CN103093095A (en) Software failure time forecasting method based on kernel principle component regression algorithm
Liu et al. Sparse-gev: Sparse latent space model for multivariate extreme value time serie modeling
Nagahamulla et al. An ensemble of artificial neural networks in rainfall forecasting
Krishna An integrated approach for weather forecasting based on data mining and forecasting analysis
CN104699979B (en) Urban lake storehouse algal bloom Study on prediction technology of chaotic series based on complex network
CN107480344A (en) A kind of series stress-strength system reliability self-adaptive estimation method
CN103093094A (en) Software failure time forecasting method based on kernel partial least squares regression algorithm
Robati et al. Inflation rate modeling: adaptive neuro-fuzzy inference system approach and particle swarm optimization algorithm (ANFIS-PSO)
Wang et al. An improved weighted naive bayesian classification algorithm based on multivariable linear regression model
Kajornrit et al. Estimation of missing precipitation records using modular artificial neural networks
de Castro et al. The generation of synthetic inflows via bootstrap to increase the energy efficiency of long-term hydrothermal dispatches
CN106772354A (en) Method for tracking target and device based on parallel fuzzy gaussian sum particle filter
CN103106139B (en) Based on the software failure time forecasting methods that relevance vector regression is estimated
Yan et al. A stochastic tropical cyclone model for the northwestern Pacific Ocean with improved track and intensity representations
Yusop et al. Disaggregation of daily rainfall data using Bartlett Lewis Rectangular Pulse model: a case study in central Peninsular Malaysia
Wang et al. Comparative study among three different artificial neural networks to infectious diarrhea forecasting
Deb et al. A correlation based imputation method for incomplete traffic accident data
Shi et al. Remaining useful life prediction based on modified relevance vector regression algorithm
Mares et al. Stochastic modeling of the connection between sea level pressure and discharge in the Danube lower basin by means of Hidden Markov Model

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
C02 Deemed withdrawal of patent application after publication (patent law 2001)
WD01 Invention patent application deemed withdrawn after publication

Application publication date: 20130508