Optimal experiment design for regression polynomial models identification

In this paper the problem of optimal experimental design for parameter identification of static non-linear blocks is addressed. Non-linearities are assumed to be polynomial and represented according to the Vandermonde base. The optimality problem is formulated in a set membership context and the cost functions to be minimized are the worst case parameter uncertainties. Closed form optimal input sequences are derived when the input u is allowed to vary on a given interval [ u a, u b ]. Since optimal input sequences are, in general, not invariant to base changes, results and criteria for representing polymomials with different bases, still preserving the optimal set of input levels derived from the Vandermonde parameterization, are introduced as well. Finally numerical results are reported showing the effectiveness of using optimal input sequences especially when identifying some block described dynamic models that include in their structure static non-linearities (such as Hammerstein and LPV models). In such cases the improvement achieved in the confidence of the estimates can add up to a factor of several hundreds with respect to the case of random generated inputs.     

Term and variable selection for non-linear system identification

The purpose of variable selection is to pre-select a subset consisting of the significant variables or to eliminate the redundant variables from all the candidate variables of a system under study prior to model term detection. It is required that the selected significant variables alone should sufficiently represent the system. Generally, not all the model terms, which are produced by combining different variables, make an equal contribution to the system output and terms, which make little contribution, can be omitted. A parsimonious representation, which contains only the significant terms, can often be obtained without the loss of representational accuracy by eliminating the redundant terms. Based on these observations, a new variable and term selection algorithm is proposed in this paper. The term detection algorithm can be applied to the general class of non-linear modelling problems which can be expressed as a linear-in-the-parameters form. The variable selection procedure is based on locally linear and cross-bilinear models, which are used together with the forward orthogonal least squares (OLS) and error reduction ratio (ERR) approach to determine the significant terms and to pre-select the important variables for both time series and input–output systems. Several numerical examples are provided to illustrate the applicability and effectiveness of the new approach.     

A nonparametric polynomial identification algorithm for theHammerstein system

Almost all existing Hammerstein system nonparametric identification algorithms can recover the unknown system nonlinear element up to an additive constant, and one functional value of the nonlinearity is usually assumed to be known to make the constant solvable. To overcome this defect, in this paper, a new nonparametric polynomial identification algorithm for the Hammerstein system is proposed which extends the idea in the author's previous work (1993, 1994) on the Hammerstein system identification to a more general and practical case, where no functional value of the system nonlinearity is known a priori. Convergence and convergence rates in both uniform and global senses are established, and simulation studies demonstrate the effectiveness and advantage of the new algorithm     

函数优化的遗传算法策略优选

为了提高函数优化的准确性和效率,提出一种基于表达式构造的函数聚类和策略优选的方法.使用英国Sheffield大学开发的Matlab遗传算法工具箱(GATBX)设计不同的算法策略,对随机选取的3种常见的函数构造因子按不同比例组合得到的不同模式进行了策略试算,以收敛率、平均截止代数及截止代数分布熵作为由主到次的性能评价指标来优选策略,并归纳出规则.最后利用4个具有试验模式的数值函数验证了规则的有效性.     

Nonparametric algorithm for input signals identification in static distributed-parameter systems

In this correspondence, a nonparametric algorithm for identification of input signals in linear, static distributed-parameter systems is proposed and investigated. Integral mean-square convergence of the algorithm is proved for an infinite number of point measurements of the system state. The algorithm is a generalized version of the one recently proposed by Rutkowski [10] for nonparametric function fitting, and in a common area, the presented results are complementary.     

敏捷制造中制造资源选择问题的遗传算法

对敏捷制造系统重构中的制造资源选择问题进行了分析,建立了数学模型,提出了一种适合求解该问题的遗传算法。该算法与解决同类问题的已有算法相比,编码方案和遗传算子均比较简单。实验结果表明,遗传算法在解的质量、稳定性和收敛速度方面具有优良性能。     

Genetic algorithm for non-linear mixed integer programming problems and its applications

In this paper we propose a method for solving non-linear mixed integer programming (NMIP) problems using genetic algorithm (GAs) to get an optimal or near optimal solution. The penalty function method was used to evaluate those infeasible chromosomes generated from genetic reproduction. Also, we apply the method for solving several optimization problems of system reliability which belong to non-linear integer programming (NIP) or (NMIP) problems, using the proposed method. Numerical experiments and comparisons with previous works are illustrated to demonstrate the efficiency of the proposed method.     

A regression tree algorithm for the identification of convergence clubs

The concept of convergence clubs is analyzed and compared with classical methods for the study of economic β-convergence, which often consider the entire data set as one sample. A technique for the identification of convergence clubs is proposed. The algorithm is based on a modified version of the usual regression trees procedure. The objective function of the method is represented by the difference among the parameters of the model under investigation. Different strategies are adopted in the definition of the model used in the objective function of the algorithm. The first is the classical non-spatial β-convergence model. The others are modified β-convergence models which take into account the dependence showed by spatially distributed data. The proposed procedure identifies situation of local stationarity in the economic growth of the different regions: a group of regions is divided into two sub-groups if the parameter estimates are significantly different among them. The algorithm is applied to 191 European regions for the period 1980-2002. Given the adaptability of the algorithm, its implementation provides a flexible tool for the use of any regression model in the analysis of non-stationary spatial data.     

Supervised feature selection algorithm via discriminative ridge regression

This paper studies a new feature selection method for data classification that efficiently combines the discriminative capability of features with the ridge regression model. It first sets up the global structure of training data with the linear discriminant analysis that assists in identifying the discriminative features. And then, the ridge regression model is employed to assess the feature representation and the discrimination information, so as to obtain the representative coefficient matrix. The importance of features can be calculated with this representative coefficient matrix. Finally, the new subset of selected features is applied to a linear Support Vector Machine for data classification. To validate the efficiency, sets of experiments are conducted with twenty benchmark datasets. The experimental results show that the proposed approach performs much better than the state-of-the-art feature selection algorithms in terms of the evaluating indicator of classification. And the proposed feature selection algorithm possesses a competitive performance compared with existing feature selection algorithms with regard to the computational cost.     

Stability analysis of a discrete-time adaptive control algorithm having a polynomial input

Stability and convergence are shown for adaptive control of a cascade connection of a finite-odd order polynomial followed by a linear system. The main point is the establishment of the linear boundedness condition of the key technical lemma [7].     

An identification algorithm for polynomial NARX models based on simulation error minimization

Classical prediction error approaches for the identification of non-linear polynomial NARX/NARMAX models often yield unsatisfactory results for long-range prediction or simulation purposes, mainly due to incorrect or redundant model structure selection. The paper discusses some limitations of the standard approach and suggests two modifications: namely, a new index, based on the simulation error, is employed as the regressor selection criterion and a pruning mechanism is introduced in the model selection algorithm. The resulting algorithm is shown to be effective in the identification of compact and robust models, generally yielding model structures closer to the correct ones. Computational issues are also discussed. Finally, the identification algorithm is tested on a long-range prediction benchmark application.     

An extended orthogonal forward regression algorithm for system identification using entropy

In this paper, a fast identification algorithm for non-linear dynamic stochastic system identification is presented. The algorithm extends the classical orthogonal forward regression (OFR) algorithm so that instead of using the error reduction ratio (ERR) for term selection, a new optimality criterion, Shannon's entropy power reduction ratio (EPRR), is introduced to deal with both Gaussian and non-Gaussian signals. It is shown that the new algorithm is both fast and reliable and examples are provided to illustrate the effectiveness of the new approach.     

An extended DEIM algorithm for subset selection and class identification

Machine Learning - The discrete empirical interpolation method (DEIM) has been shown to be a viable index-selection technique for identifying representative subsets in data. Having gained some...     

Genetic drift in genetic algorithm selection schemes

A method for calculating genetic drift in terms of changing population fitness variance is presented. The method allows for an easy comparison of different selection schemes and exact analytical results are derived for traditional generational selection, steady-state selection with varying generation gap, a simple model of Eshelman's CHC algorithm (1991), and (μ+λ) evolution strategies. The effects of changing genetic drift on the convergence of a GA are demonstrated empirically     

Genetic algorithm for effective open port selection for a web filter

As cyber security is a major challenge in the widespread deployment of the latest technologies, the importance of selecting the open ports for a given web filter cannot be overemphasized. A network administrator would want to select a combination of ports that would be most beneficial to the users and these ports would be treated as least vulnerable. However, this is not a trivial task and can be very time-consuming, O(n!), if brute force or other naïve approaches are used to select a given number of ports from 65,536 ports available. As genetic algorithms (GAs) are commonly used to obtain near-optimal solution for complex and time-consuming tasks, this paper proposes a GA for the selection of open ports for a web filter. The gene value for each port is based on the malicious issues associated with the port and the importance of the port to the client using the web filter. The proposed algorithm is implemented in Java, and the simulation results show that GA is very accurate in identifying open ports for a given web filter.     

Genetic algorithm for robot selection and work station assignment problem

In this paper, we introduce Genetic Algorithm (GA) for optimal Robot Selection and Work station Assignment (RS/WA) problem for a CIM system. In particular, the RS/WA problem can be considered as a generalized two-dimensional multi-type bin packing problem that has been shown to be NP-hard. A multichromosome GA combined with heuristic bin packing algorithm is implemented for solving the problem and the effeciency of proposed method is shown by numerical example. Our approach may be applicable to other this kind of bin packing problems.     

Genetic algorithms for outlier detection and variable selection in linear regression models

This article addresses some problems in outlier detection and variable selection in linear regression models. First, in outlier detection there are problems known as smearing and masking. Smearing means that one outlier makes another, non-outlier observation appear as an outlier, and masking that one outlier prevents another one from being detected. Detecting outliers one by one may therefore give misleading results. In this article a genetic algorithm is presented which considers different possible groupings of the data into outlier and non-outlier observations. In this way all outliers are detected at the same time. Second, it is known that outlier detection and variable selection can influence each other, and that different results may be obtained, depending on the order in which these two tasks are performed. It may therefore be useful to consider these tasks simultaneously, and a genetic algorithm for a simultaneous outlier detection and variable selection is suggested. Two real data sets are used to illustrate the algorithms, which are shown to work well. In addition, the scalability of the algorithms is considered with an experiment using generated data.I would like to thank Dr Tero Aittokallio and an anonymous referee for useful comments.     

A diagnostic method for simultaneous feature selection and outlier identification in linear regression

A diagnostic method along the lines of forward search is proposed to simultaneously study the effect of individual observations and features on the inferences made in linear regression. The method operates by appending dummy variables to the data matrix and performing backward selection on the augmented matrix. It outputs sequences of feature-outlier combinations which can be evaluated by plots similar to those of forward search and includes the capacity to incorporate prior knowledge, in order to mitigate issues such as collinearity. It also allows for alternative ways to understand the selection of the final model. The method is evaluated on five data sets and yields promising results.