Identification of block-oriented nonlinear systems using orthonormal bases

In this paper, new noniterative algorithms for the identification of (multivariable) block-oriented nonlinear models consisting of the interconnection of linear time invariant systems and static nonlinearities are presented. The proposed algorithms are numerically robust, since they are based only on least squares estimation and singular value decomposition. Two different block-oriented nonlinear models are considered in this paper, viz., the Hammerstein model, and the Wiener model. For the Hammerstein model, the proposed algorithm provides consistent estimates even in the presence of colored output noise, under weak assumptions on the persistency of excitation of the inputs. For the Wiener model, consistency of the estimates can only be guaranteed in the noise free case. Key in the derivation of the results is the use of basis functions for the representation of the linear and nonlinear parts of the models. The performance of the proposed identification algorithms is illustrated through simulation examples of two benchmark problems drawn from the process control literature, viz., a binary distillation column and a pH neutralization process.     

A unifying construction of orthonormal bases for systemidentification

This paper develops a general and very simple construction for complete orthonormal bases for system identification. This construction provides a unifying formulation of many previously studied orthonormal bases since the common FIR and recently popular Laguerre and two-parameter Kautz model structures are restrictive special cases of the construction presented here. However, in contrast to these special cases, the basis vectors in the unifying construction of this paper can have arbitrary placement of pole position according to the prior information the user wishes to inject. Results characterizing the completeness of the bases and the accuracy properties of models estimated using the bases are provided     

A new approach to linear regression with multivariate splines

A new methodology for creating highly accurate, static nonlinear maps from scattered, multivariate data is presented. This new methodology uses the B-form polynomials of multivariate simplex splines in a new linear regression scheme. This allows the use of standard parameter estimation techniques for estimating the B-coefficients of the multivariate simplex splines. We present a generalized least squares estimator for the B-coefficients, and show how the estimated B-coefficient variances lead to a new model quality assessment measure in the form of the B-coefficient variance surface. The new modeling methodology is demonstrated on a nonlinear scattered bivariate dataset.     

A constructive approach for nonlinear system identification usingmultilayer perceptrons

This paper combines a conventional method of multivariable system identification with a dynamic multi-layer perceptron (MLP) to achieve a constructive method of nonlinear system identification. The class of nonlinear systems is assumed to operate nominally around an equilibrium point in the neighborhood of which a linearized model exists to represent the system, although normal operation is not limited to the linear region. The result is an accurate discrete-time nonlinear model, extended from a MIMO linear model, which captures the nonlinear behavior of the system.     

Exponential splines and minimal-support bases for curve representation

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B-spline with a compact-support distribution. As a direct consequence of this factorization theorem, we show that the minimal-support basis functions of that subspace are linear combinations of derivatives of exponential B-splines. These minimal-support basis functions form a natural multiscale hierarchy, which we utilize to design fast multiresolution algorithms and subdivision schemes for the representation of closed geometric curves. This makes them attractive from a computational point of view. Finally, we illustrate our scheme by constructing minimal-support bases that reproduce ellipses and higher-order harmonic curves.     

A new SQP approach for nonlinear complementarity problems

Sequential quadratic programming (SQP) methods have been extensively studied to handle nonlinear programming problems. In this paper, a new SQP approach is employed to tackle nonlinear complementarity problems (NCPs). At each iterate, NCP conditions are divided into two parts. The inequalities and equations in NCP conditions, which are violated in the current iterate, are treated as the objective function, and the others act as constraints, which avoids finding a feasible initial point and feasible iterate points. NCP conditions are consequently transformed into a feasible nonlinear programming subproblem at each step. New SQP techniques are therefore successful in handling NCPs.     

A new process knowledge representation approach using parameter flow chart

Knowledge in various stages of the product development process has become increasingly important for manufacturing companies to improve their performance, especially for those One-of-a-Kind Production (OKP) companies producing highly customized products. Process knowledge is a very special type of knowledge that controls how products are best manufactured. This knowledge can help OKP companies produce high value-added products with better quality at shorter times and at a competitive cost. Process knowledge is normally hard to capture and manage and is even more difficult to represent. This paper proposes a Parameter Flow Chart (PFC) based new knowledge representation method which efficiently combines parameter information, flow chart technology, and visualization technology. The goal of this research is to provide a user-friendly and effective way of representing process knowledge for OKP companies so they can develop and accumulate their own process knowledge repository. The basic definition and principle of the approach will be introduced first and the software system model then proposed. Two related key issues, the modeling of various chart units used in the PFC approach and dealing with expressions containing various parameters, are discussed in detail. The prototype version of the system has been developed and demonstrated with case studies, which has proven the feasibility of the proposed approach.     

A new kernel-based approach for linear system identification

This paper describes a new kernel-based approach for linear system identification of stable systems. We model the impulse response as the realization of a Gaussian process whose statistics, differently from previously adopted priors, include information not only on smoothness but also on BIBO-stability. The associated autocovariance defines what we call a stable spline kernel. The corresponding minimum variance estimate belongs to a reproducing kernel Hilbert space which is spectrally characterized. Compared to parametric identification techniques, the impulse response of the system is searched for within an infinite-dimensional space, dense in the space of continuous functions. Overparametrization is avoided by tuning few hyperparameters via marginal likelihood maximization. The proposed approach may prove particularly useful in the context of robust identification in order to obtain reduced order models by exploiting a two-step procedure that projects the nonparametric estimate onto the space of nominal models. The continuous-time derivation immediately extends to the discrete-time case. On several continuous- and discrete-time benchmarks taken from the literature the proposed approach compares very favorably with the existing parametric and nonparametric techniques.     

Practical nonlinear system identification using a modified volterra series approach

A functional approach has been developed to represent continuous separable, nonlinear systems of a general type based on a modified Volterra series. The importance of this is that the effects of bias or mean signal level within the nonlinear system can be separated from dynamic effects. This has particular significance in the development of identification procedures based on cross-correlation functions, as these functions can now be estimated practically without any influence from the bias level. Practical identification of the gain characteristics for an electrohydraulic servo is described using three-level pseudorandom input signals which are cross-correlated with the sampled system response in a minicomputer to provide an automated procedure. Good accuracy is achieved even in the presence of severe noise.     

A nonlinear least-squares approach for identification of the induction motor parameters

A nonlinear least-squares method is presented for the identification of the induction motor parameters. A major difficulty with the induction motor is that the rotor state variables are not available measurements so that the system identification model cannot be made linear in the parameters without overparametrizing the model. Previous work in the literature has avoided this issue by making simplifying assumptions such as a "slowly varying speed." Here, no such simplifying assumptions are made. The problem is formulated as a nonlinear least-squares identification problem and uses elimination theory (resultants) to compute the parameter vector that minimizes the residual error. The only requirement is that the system must be sufficiently excited. The method is suitable for online operation to continuously update the parameter values. Experimental results are presented.     

A new class of wavelet networks for nonlinear system identification

A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions.     

Addressing remitting behavior using an ordinal classification approach

The remittance market represents a great business opportunity for financial institutions given the increasing volume of these capital flows throughout the world. However, the corresponding business strategy could be costly and time consuming because immigrants do not respond to general media campaigns. In this paper, the remitting behavior of immigrants have been addressed by a classification approach that predicts the remittance levels sent by immigrants according to their individual characteristics, thereby identifying the most profitable customers within this group. To do so, five nominal and two ordinal classifiers were applied to an immigrant sample and their resulting performances were compared. The ordinal classifiers achieved the best results; the Support Vector Machine with Ordered Partitions (SVMOP) yielded the best model, providing information needed to draw remitting profiles that are useful for financial institutions. The Support Vector Machine with Explicit Constraints (SVOREX), however, achieved the second best results, and these results are presented graphically to study misclassified patterns in a natural and simple way. Thus, financial institutions can use this ordinal SVM-based approach as a tool to generate valuable information to develop their remittance business strategy.     

Gaussian process approach for modelling of nonlinear systems

Parametric modelling principals such as neural networks, fuzzy models and multiple model techniques have been proposed for modelling of nonlinear systems. Research effort has focused on issues such as the selection of the structure, constructive learning techniques, computational issues, the curse of dimensionality, off-equilibrium behaviour, etc. To reduce these problems, the use of non-parametrical modelling approaches have been proposed. This paper introduces the Gaussian process (GP) prior approach for the modelling of nonlinear dynamic systems. The relationship between the GP model and the radial basis function neural network is explained. Issues such as selection of the dimension of the input space and the computation load are also discussed. The GP modelling technique is demonstrated on an example of the nonlinear hydraulic positioning system.     

更有效的非线性系统辨识新方法

介绍了一种基于量子粒子群算法构造径向基函数神经网络进行非线性系统辨识的新方法.在确定径向基函数网络的 隐层结点数后,将相应网络的参数,包括隐层基函数中心、扩展常数以及输出权值和偏移编码成学>-j算法中的粒子个体,在全 局空间中搜索具有最优适应值的参数向量.实例仿真通过和标准粒子群算法进行比较,表明了该方法的有效性和优越性.     

A methodology for control-relevant nonlinear system identification using restricted complexity models

A broadly-applicable, control-relevant system identification methodology for nonlinear restricted complexity models (RCMs) is presented. Control design based on RCMs often leads to controllers which are easy to interpret and implement in real-time. A control-relevant identification method is developed to minimize the degradation in closed-loop performance as a result of RCM approximation error. A two-stage identification procedure is presented. First, a nonlinear ARX model is estimated from plant data using an orthogonal least squares algorithm; a Volterra series model is then generated from the nonlinear ARX model. In the second stage, a RCM with the desired structure is estimated from the Volterra series model through a model reduction algorithm that takes into account closed-loop performance requirements. The effectiveness of the proposed method is illustrated using two chemical reactor examples.     

B-spline neural network design using improved differential evolution for identification of an experimental nonlinear process

B-Spline Neural Network (BSNN), a type of basis function neural network, is trained by gradient-based methods which may fall into local minima during the learning procedure. To overcome the limitations encountered by gradient-based optimization methods, we propose differential evolution (DE) – an evolutionary computation methodology – which can provide a stochastic search to adjust the control points of a BSNN. In this paper, we propose six DE approaches using chaotic sequences based on logistic mapping to train a BSNN. Chaos describes the complex behavior of a nonlinear deterministic system. The application of chaotic sequences instead of random sequences in DE is a powerful strategy to diversify the DE population and improve the DE's performance in preventing premature convergence to local minima. The numerical results presented here indicate that chaotic DE was effective for building a good BSNN model for the nonlinear identification of an experimental nonlinear yo–yo motion control system.     

A systematic approach for performance assessment using process mining

Software performance engineering is a mature field that offers methods to assess system performance. Process mining is a promising research field applied to gain insight on system processes. The interplay of these two fields opens promising applications in the industry. In this work, we report our experience applying a methodology, based on process mining techniques, for the performance assessment of a commercial data-intensive software application. The methodology has successfully assessed the scalability of future versions of this system. Moreover, it has identified bottlenecks components and replication needs for fulfilling business rules. The system, an integrated port operations management system, has been developed by Prodevelop, a medium-sized software enterprise with high expertise in geospatial technologies. The performance assessment has been carried out by a team composed by practitioners and researchers. Finally, the paper offers a deep discussion on the lessons learned during the experience, that will be useful for practitioners to adopt the methodology and for researcher to find new routes.     

A new approach to nonlinear optimal feedback law

For a fixed-time free endpoint optimal control problem it is shown that the optimal feedback control satisfies a system of ordinary differential equations. They are obtained using an elimination procedure of the adjoint vector which appears linearly in a set of differential equations. These equations, involving Lie brackets of vector fields, are derived from the Maximum Principle. An application of this approach to robotics is given.