A recursive parametric estimation algorithm of multivariable nonlinear systems described by Hammerstein mathematical models

The objective of this paper is to construct reliable belief rule-based (BRB) models for the identification of uncertain nonlinear systems. The BRB methodology is developed from the evidential reasoning (ER) approach and traditional IF–THEN rule based system. It can be used to model complicated nonlinear causal relationships between antecedent attributes and consequents under different types of uncertainty. In a BRB model, various types of information and knowledge with uncertainties can be represented using belief structures, and a belief rule is designed with belief degrees embedded in its possible consequents. In this paper, we first introduce the BRB methodology for modelling uncertain nonlinear systems. Then we present a comparative analysis of three BRB identification models through combining the BRB methodology with nonlinear optimisation techniques. The novel BRB identification models using l8-norm and minimising mean uncertainties in belief rules (MUBR) show remarkable capabilities of capturing the lower and upper bounds of the interval outputs of uncertain nonlinear systems simultaneously. Trade-off analysis between identification accuracy and interval credibility are briefly discussed. Finally, a numerical study of a simplified car dynamics is conducted to demonstrate the capability and effectiveness of the BRB identification models for the modelling and identification of uncertain nonlinear systems.

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Identification of uncertain nonlinear systems: constructing belief rule-based models

Gradient based iterative parameter identification for Wiener nonlinear systems

This paper presents the development of a flexible, multi-axis, intensity modulated-based fiber-optic force sensor for concurrently measuring normal and shear forces. The proposed sensor was prototyped to measure the three force components by monitoring the variation of the light intensity induced by a deformation as a result of the applied force. One end of the sensor incorporates three orthogonal reflective planes. The other end brings three pairs of fibers; one fiber connected to an LED, and the other to a light-to-voltage (LTV) converter in each pair. Upon the application of the force, the distance between the planes and the fiber tips changes, thus, the LTV voltage changes, enabling the simultaneous measurement of forces along three normal axes utilizing only one set of force measurement unit. The fabricated sensor was tested in both static and dynamic loading conditions as the experimental results have confirmed that the prototype has the capability to accurately measure the normal and shear forces in real time ranging from 0 to 1000 N and 0 to 140 N along the z, x, and y axes, respectively. The feasible applications of the sensor are ground reaction force measurements and robot–human collision detection. Sensor performance was evaluated for the cross-talk effects, which were found to be less than 5%. A nonlinear Hammerstein–Winer model is proposed to characterize the linear and nonlinear behavior of the sensor. The optimized results have shown a reduction of over 40% in the root mean-square errors in comparison with the linear estimation models.

A Compliant 3-Axis Fiber-Optic Force Sensor for Biomechanical Measurement

This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalised orthonormal basis functions. The paper is separated in two parts. In this first part, the mathematical foundations of these models as well as their advantages and limitations are discussed within the context of linear and robust system identification. The second part approaches the issues related with non-linear models. The discussions comprise a broad bibliographical survey of the subjects involving linear models within the orthonormal basis functions framework. Theoretical and practical issues regarding the identification of these models are presented and illustrated by means of a case study involving a polymerisation process.

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S. I. Biagiola

Papers

Wiener and Hammerstein uncertain models identification