Identification of nonlinear interconnected systems

This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.In this work we address the problem of identifying a discrete-time nonlinear system composed of a linear dynamical system connected to a static nonlinear component. We use linear fractional representation to provide a united framework for the identification of two classes of such systems. The first class consists of discrete-time systems consists of a linear time invariant system connected to a continuous nonlinear static component. The identification problem of estimating the unknown parameters of the linear system and simultaneously fitting a math order spline to the nonlinear data is addressed. A simple and tractable algorithm based on the separable least squares method is proposed for estimating the parameters of the linear and the nonlinear components. We also provide a sufficient condition on data for consistency of the identification algorithm. Numerical examples illustrate the performance of the algorithm. Further, we examine a second class of systems that may involve a nonlinear static element of a more complex structure. The nonlinearity may not be continuous and is approximated by piecewise a±ne maps defined on different convex polyhedra, which are defined by linear combinations of lagged inputs and outputs. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine system identification techniques are employed for the estimation of the nonlinear component. Numerical examples show that the proposed procedure is able to successfully profit from the knowledge of the interconnection structure, in comparison with a direct black box identification of the piecewise a±ne system.Funding was obtained as a Marie Curie Early Stage Researcher Training fellowship, under the NET-ACE project (MEST-CT-2004-6724)

Advances in model identification using the block-oriented exact solution technique in a predictive modeling framework

Obtaining an accurate model has always been a challenging objective in implementation of Model Predictive Control, especially for nonlinear processes. Part of this work here proposed a model building methodology for a complex block-oriented process, namely a Hammerstein-Wiener system in order to meet such a demand. It is a general system of the more simple structures which are known as Hammerstein and Wiener. This methodology uses sequential step test training data determined from an optimal experimental design and simultaneously estimates all the model coefficients under nonlinear least squares objective function. It is evaluated using four process examples and is compared with a recently proposed method in three of them. Even with less frequent sampling, the proposed method is demonstrated to have advantages in simplicity, the ability to model non-invertible systems, the ability to model multiple input and non-minimum phase processes, and accuracy.;This class of modeling method is also being applied to model normal operation plant data. The common problem seen in this type of dataset including high multi-collinearities of the inputs and low signal to noise ratios for the outputs inhibit modelers to acquire cause and effect relationship. The second part of the work here is to introduced this modeling approach that is capable of developing accurate cause and effect models. It is a special application of the Wiener block-oriented system and the unique and powerful attributes of this approach over existing techniques are demonstrated in a mathematically simulated processes and real processes

Safe Experimentation Dynamics Algorithm for Identification of Cupping Suction Based on the Nonlinear Hammerstein Model

The use of cupping therapy for various health benefits has increased in popularity recently. Potential advantages of cupping therapy include pain reduction, increased circulation, relaxation, and skin health. The increased blood flow makes it easier to supply nutrients and oxygen to the tissues, promoting healing. Nevertheless, the effectiveness of this technique greatly depends on the negative pressure's ability to create the desired suction effect on the skin. This research paper suggests a method to detect the cupping suction model by employing the Hammerstein model and utilizing the Safe Experimentation Dynamics (SED) algorithm. The problem is that the cupping suction system experiences pressure leaks and is difficult to control. Although, stabilizing the suction pressure and developing an effective controller requires an accurate model. The research contribution lies in utilizing the SED algorithm to tune the parameters of the Hammerstein model specifically for the cupping suction system and figure out the real system with a continuous-time transfer function. The experimental data collected for cupping therapy exhibited nonlinearity attributed to the complex dynamics of the system, presenting challenges in developing a Hammerstein model. This work used a nonlinear model to study the cupping suction system. Input and output data were collected from the differential pressure sensor for 20 minutes, sampling every 0.1 seconds. The single-agent method SED has limited exploration capabilities for finding optimum value but excels in exploitation. To address this limitation, incorporating initial values leads to improved performance and a better match with the real experimental observations. Experimentation was conducted to find the best model parameters for the desired suction pressure. The therapy can be administered with greater precision and efficacy by accurately identifying the suction pressure. Overall, this research represents a promising development in cupping therapy. In particular, it has been demonstrated that the proposed nonlinear Hammerstein models improve accuracy by 84.34% through the tuning SED algorithm

Fuzzy System Identification Based Upon a Novel Approach to Nonlinear Optimization

Fuzzy systems are often used to model the behavior of nonlinear dynamical systems in process control industries because the model is linguistic in nature, uses a natural-language rule set, and because they can be included in control laws that meet the design goals. However, because the rigorous study of fuzzy logic is relatively recent, there is a shortage of well-defined and understood mechanisms for the design of a fuzzy system. One of the greatest challenges in fuzzy modeling is to determine a suitable structure, parameters, and rules that minimize an appropriately chosen error between the fuzzy system, a mathematical model, and the target system. Numerous methods for establishing a suitable fuzzy system have been proposed, however, none are able to demonstrate the existence of a structure, parameters, or rule base that will minimize the error between the fuzzy and the target system. The piecewise linear approximator (PLA) is a mathematical construct that can be used to approximate an input-output data set with a series of connected line segments. The number of segments in the PLA is generally selected by the designer to meet a given error criteria. Increasing the number of segments will generally improve the approximation. If the location of the breakpoints between segments is known, it is a straightforward process to select the PLA parameters to minimize the error. However, if the location of the breakpoints is not known, a mechanism is required to determine their locations. While algorithms exist that will determine the location of the breakpoints, they do not minimize the error between data and the model. This work will develop theory that shows that an optimal solution to this nonlinear optimization problem exists and demonstrates how it can be applied to fuzzy modeling. This work also demonstrates that a fuzzy system restricted to a particular class of input membership functions, output membership functions, conjunction operator, and defuzzification technique is equivalent to a piecewise linear approximator (PLA). Furthermore, this work develops a new nonlinear optimization technique that minimizes the error between a PLA and an arbitrary one-dimensional set of input-output data and solves the optimal breakpoint problem. This nonlinear optimization technique minimizes the approximation error of several classes of nonlinear functions leading up to the generalized PLA. While direct application of this technique is computationally intensive, several paths are available for investigation that may ease this limitation. An algorithm is developed based on this optimization theory that is significantly more computationally tractable. Several potential applications of this work are discussed including the ability to model the nonlinear portions of Hammerstein and Wiener systems