A modified orthogonal forward regression least-squares algorithm for system modelling from noisy regressors

In this paper, a modified Orthogonal Forward Regression (OFR) least-squares algorithm is presented for system identification and modelling from noisey regressors. Under the asumption that the energy and signal-to-noise ratio (SNR) of the signals are known or can be estimated , it is shown that unbiased estimates of the Error Reducation Ratios (ERRs) and the parameters can be obtained in each forward regression step. Examples are provided to illustrate the proposed approach

Multiscale identification of spatio-temporal dynamical systems using a wavelet multiresolution analysis

In this paper, a new algorithm for the multiscale identification of spatio-temporal dynamical systems is derived. It is shown that the input and output observations can be represented in a multiscale manner based on a wavelet multiresolution analysis. The system dynamics at some specific scale of interest can then be identified using an orthogonal forward leastsquares algorithm. This model can then be converted between different scales to produce predictions of the system outputs at different scales. The method can be applied to both multiscale and conventional spatio-temporal dynamical systems. For multiscale systems, the method can generate a parsimonious and effective model at a coarser scale while considering the effects from finer scales. Additionally, the proposed method can be used to improve the performance of the identification when measurements are noisy. Numerical examples are provided to demonstrate the application of the proposed new approach

Identification of binary cellular automata from spatiotemporal binary patterns using a fourier representation

The identification of binary cellular automata from spatio-temporal binary patterns is investigated in this paper. Instead of using the usual Boolean or multilinear polynomial representation, the Fourier transform representation of Boolean functions is employed in terms of a Fourier basis. In this way, the orthogonal forward regression least-squares algorithm can be applied directly to detect the significant terms and to estimate the associated parameters. Compared with conventional methods, the new approach is much more robust to noise. Examples are provided to illustrate the effectiveness of the proposed approach

An adaptive orthogonal search algorithm for model subset selection and non-linear system identification

A new adaptive orthogonal search (AOS) algorithm is proposed for model subset selection and non-linear system identification. Model structure detection is a key step in any system identification problem. This consists of selecting significant model terms from a redundant dictionary of candidate model terms, and determining the model complexity (model length or model size). The final objective is to produce a parsimonious model that can well capture the inherent dynamics of the underlying system. In the new AOS algorithm, a modified generalized cross-validation criterion, called the adjustable prediction error sum of squares (APRESS), is introduced and incorporated into a forward orthogonal search procedure. The main advantage of the new AOS algorithm is that the mechanism is simple and the implementation is direct and easy, and more importantly it can produce efficient model subsets for most non-linear identification problems

Aerodynamic parameter identification for an unmanned aerial vehicle

A dissertation submitted to the Faculty of Engineering and the Built Environment, School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, May 2016The present work describes the practical implementation of systems identification techniques to the development of a linear aerodynamic model for a small low-cost UAV equipped with a basic navigational and inertial measurement systems. The assessment of the applicability of the techniques were based on determining whether adequate aerodynamic models could be developed to aid in the reduction of wind tunnel testing when characterising new UAVs. The identification process consisted of postulating a model structure, flight test manoeuvre design, data reconstruction, aerodynamic parameter estimation, and model validation. The estimators that were used for the post-flight identification were the output error maximum likelihood method and an iterated extended Kalman filter with a global smoother. SIDPAC and FVSysID systems identification toolboxes were utilised and modified where appropriate. The instrumentation system on board the UAV consisted of three-axis accelerometers and gyroscopes, a three-axis vector magnetometer and GPS tracking while data was logged at 25 Hz. The angle of attack and angle of sideslip were not measured directly and were estimated using tailored data reconstruction methods. Adequate time domain lateral model correlation with flight data was achieved for the cruise flight condition. Adequacy was assessed against Theil’s inequality coefficients and Theil’s covariance. It was found that the simplified estimation algorithms based on the linearized equations of motion yielded the most promising model matches. Due to the high correlation between the pitch damping derivatives, the longitudinal analysis did not yield valid model parameter estimates. Even though the accuracy of the resulting models was below initial expectations, the detailed data compatibility analysis provided valuable insight into estimator limitations, instrumentation requirements and test procedures for systems identification on low-cost UAVs.MT201

Dynamic non-linear system modelling using wavelet-based soft computing techniques

The enormous number of complex systems results in the necessity of high-level and cost-efficient modelling structures for the operators and system designers. Model-based approaches offer a very challenging way to integrate a priori knowledge into the procedure. Soft computing based models in particular, can successfully be applied in cases of highly nonlinear problems. A further reason for dealing with so called soft computational model based techniques is that in real-world cases, many times only partial, uncertain and/or inaccurate data is available. Wavelet-Based soft computing techniques are considered, as one of the latest trends in system identification/modelling. This thesis provides a comprehensive synopsis of the main wavelet-based approaches to model the non-linear dynamical systems in real world problems in conjunction with possible twists and novelties aiming for more accurate and less complex modelling structure. Initially, an on-line structure and parameter design has been considered in an adaptive Neuro- Fuzzy (NF) scheme. The problem of redundant membership functions and consequently fuzzy rules is circumvented by applying an adaptive structure. The growth of a special type of Fungus (Monascus ruber van Tieghem) is examined against several other approaches for further justification of the proposed methodology. By extending the line of research, two Morlet Wavelet Neural Network (WNN) structures have been introduced. Increasing the accuracy and decreasing the computational cost are both the primary targets of proposed novelties. Modifying the synoptic weights by replacing them with Linear Combination Weights (LCW) and also imposing a Hybrid Learning Algorithm (HLA) comprising of Gradient Descent (GD) and Recursive Least Square (RLS), are the tools utilised for the above challenges. These two models differ from the point of view of structure while they share the same HLA scheme. The second approach contains an additional Multiplication layer, plus its hidden layer contains several sub-WNNs for each input dimension. The practical superiority of these extensions is demonstrated by simulation and experimental results on real non-linear dynamic system; Listeria Monocytogenes survival curves in Ultra-High Temperature (UHT) whole milk, and consolidated with comprehensive comparison with other suggested schemes. At the next stage, the extended clustering-based fuzzy version of the proposed WNN schemes, is presented as the ultimate structure in this thesis. The proposed Fuzzy Wavelet Neural network (FWNN) benefitted from Gaussian Mixture Models (GMMs) clustering feature, updated by a modified Expectation-Maximization (EM) algorithm. One of the main aims of this thesis is to illustrate how the GMM-EM scheme could be used not only for detecting useful knowledge from the data by building accurate regression, but also for the identification of complex systems. The structure of FWNN is based on the basis of fuzzy rules including wavelet functions in the consequent parts of rules. In order to improve the function approximation accuracy and general capability of the FWNN system, an efficient hybrid learning approach is used to adjust the parameters of dilation, translation, weights, and membership. Extended Kalman Filter (EKF) is employed for wavelet parameters adjustment together with Weighted Least Square (WLS) which is dedicated for the Linear Combination Weights fine-tuning. The results of a real-world application of Short Time Load Forecasting (STLF) further re-enforced the plausibility of the above technique