A unified approach for the identification of SISO/MIMO Wiener and Hammerstein systems

Hammerstein and Wiener models are nonlinear representations of systems composed by the coupling of a static nonlinearity N and a linear system L in the form N-L and L-N respectively. These models can represent real processes which made them popular in the last decades. The problem of identifying the static nonlinearity and linear system is not a trivial task, and has attracted a lot of research interest. It has been studied in the available literature either for Hammerstein or Wiener systems, and either in a discrete-time or continuous-time setting. The objective of this paper is to present a uni ed framework for the identification of these systems that is valid for SISO and MIMO systems, discrete and continuous-time setting, and with the only a priori knowledge that the system is either Wiener or Hammerstein.Preprin

A comparison of nonlinear control performance assessment techniques for nonlinear processes

Assessing the quality of industrial control loops is an important auditing task for the control engineer. However, there are complications when considering the ubiquitous nonlinearities present in many industrial control loops. If one simply ignores these nonlinearities, there is the danger of over-estimating the performance of the control loop in rejecting disturbances and thereby possibly overlooking loops that need attention. To address this problem, several techniques have been recently developed to extend the control performance assessment (CPA) of single input/single output linear systems to nonlinear systems. This article surveys these nonlinear CPA techniques and compares their performances using three case studies. These results can be used to guide control engineers to select the most suitable CPA techniques for their particular applications

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)

Use of system identification techniques for improving airframe finite element models using test data

A method for using system identification techniques to improve airframe finite element models using test data was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in the total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all of the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory

Adaptive Input Reconstruction with Application to Model Refinement, State Estimation, and Adaptive Control.

Input reconstruction is the process of using the output of a system to estimate its input. In some cases, input reconstruction can be accomplished by determining the output of the inverse of a model of the system whose input is the output of the original system. Inversion, however, requires an exact and fully known analytical model, and is limited by instabilities arising from nonminimum-phase zeros. The main contribution of this work is a novel technique for input reconstruction that does not require model inversion. This technique is based on a retrospective cost, which requires a limited number of Markov parameters. Retrospective cost input reconstruction (RCIR) does not require knowledge of nonminimum-phase zero locations or an analytical model of the system. RCIR provides a technique that can be used for model refinement, state estimation, and adaptive control. In the model refinement application, data are used to refine or improve a model of a system. It is assumed that the difference between the model output and the data is due to an unmodeled subsystem whose interconnection with the modeled system is inaccessible, that is, the interconnection signals cannot be measured and thus standard system identification techniques cannot be used. Using input reconstruction, these inaccessible signals can be estimated, and the inaccessible subsystem can be fitted. We demonstrate input reconstruction in a model refinement framework by identifying unknown physics in a space weather model and by estimating an unknown film growth in a lithium ion battery. The same technique can be used to obtain estimates of states that cannot be directly measured. Adaptive control can be formulated as a model-refinement problem, where the unknown subsystem is the idealized controller that minimizes a measured performance variable. Minimal modeling input reconstruction for adaptive control is useful for applications where modeling information may be difficult to obtain. We demonstrate adaptive control of a seeker-guided missile with unknown aerodynamics.Ph.D.Aerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91520/1/amdamato_1.pd

Identification of nonlinear processes based on Wiener-Hammerstein models and heuristic optimization.

[ES] En muchos campos de la ingeniería los modelos matemáticos son utilizados para describir el comportamiento de los sistemas, procesos o fenómenos. Hoy en día, existen varias técnicas o métodos que pueden ser usadas para obtener estos modelos. Debido a su versatilidad y simplicidad, a menudo se prefieren los métodos de identificación de sistemas. Por lo general, estos métodos requieren la definición de una estructura y la estimación computacional de los parámetros que la componen utilizando un conjunto de procedimientos y mediciones de las señales de entrada y salida del sistema. En el contexto de la identificación de sistemas no lineales, un desafío importante es la selección de la estructura. En el caso de que el sistema a identificar presente una no linealidad de tipo estático, los modelos orientados a bloques, pueden ser útiles para definir adecuadamente una estructura. Sin embargo, el diseñador puede enfrentarse a cierto grado de incertidumbre al seleccionar el modelo orientado a bloques adecuado en concordancia con el sistema real. Además de este inconveniente, se debe tener en cuenta que la estimación de algunos modelos orientados a bloques no es sencilla, como es el caso de los modelos de Wiener-Hammerstein que consisten en un bloque NL en medio de dos subsistemas LTI. La presencia de dos subsistemas LTI en los modelos de Wiener-Hammerstein es lo que principalmente dificulta su estimación. Generalmente, el procedimiento de identificación comienza con la estimación de la dinámica lineal, y el principal desafío es dividir esta dinámica entre los dos bloques LTI. Por lo general, esto implica una alta interacción del usuario para desarrollar varios procedimientos, y el modelo final estimado depende principalmente de estas etapas previas. El objetivo de esta tesis es contribuir a la identificación de los modelos de Wiener-Hammerstein. Esta contribución se basa en la presentación de dos nuevos algoritmos para atender aspectos específicos que no han sido abordados en la identificación de este tipo de modelos. El primer algoritmo, denominado WH-EA, permite estimar todos los parámetros de un modelo de Wiener-Hammerstein con un solo procedimiento a partir de un modelo dinámico lineal. Con WH-EA, una buena estimación no depende de procedimientos intermedios ya que el algoritmo evolutivo simultáneamente busca la mejor distribución de la dinámica, ajusta con precisión la ubicación de los polos y los ceros y captura la no linealidad estática. Otra ventaja importante de este algoritmo es que bajo consideraciones específicas y utilizando una señal de excitación adecuada, es posible crear un enfoque unificado que permite también la identificación de los modelos de Wiener y Hammerstein, que son casos particulares del modelo de Wiener-Hammerstein cuando uno de sus bloques LTI carece de dinámica. Lo interesante de este enfoque unificado es que con un mismo algoritmo es posible identificar los modelos de Wiener, Hammerstein y Wiener-Hammerstein sin que el usuario especifique de antemano el tipo de estructura a identificar. El segundo algoritmo llamado WH-MOEA, permite abordar el problema de identificación como un Problema de Optimización Multiobjetivo (MOOP). Sobre la base de este algoritmo se presenta un nuevo enfoque para la identificación de los modelos de Wiener-Hammerstein considerando un compromiso entre la precisión alcanzada y la complejidad del modelo. Con este enfoque es posible comparar varios modelos con diferentes prestaciones incluyendo como un objetivo de identificación el número de parámetros que puede tener el modelo estimado. El aporte de este enfoque se sustenta en el hecho de que en muchos problemas de ingeniería los requisitos de diseño y las preferencias del usuario no siempre apuntan a la precisión del modelo como un único objetivo, sino que muchas veces la complejidad es también un factor predominante en la toma de decisiones.[CA] En molts camps de l'enginyeria els models matemàtics són utilitzats per a descriure el comportament dels sistemes, processos o fenòmens. Hui dia, existeixen diverses tècniques o mètodes que poden ser usades per a obtindre aquests models. A causa de la seua versatilitat i simplicitat, sovint es prefereixen els mètodes d'identificació de sistemes. En general, aquests mètodes requereixen la definició d'una estructura i l'estimació computacional dels paràmetres que la componen utilitzant un conjunt de procediments i mesuraments dels senyals d'entrada i eixida del sistema. En el context de la identificació de sistemes no lineals, un desafiament important és la selecció de l'estructura. En el cas que el sistema a identificar presente una no linealitat de tipus estàtic, els models orientats a blocs, poden ser útils per a definir adequadament una estructura. No obstant això, el dissenyador pot enfrontar-se a cert grau d'incertesa en seleccionar el model orientat a blocs adequat en concordança amb el sistema real. A més d'aquest inconvenient, s'ha de tindre en compte que l'estimació d'alguns models orientats a blocs no és senzilla, com és el cas dels models de Wiener-Hammerstein que consisteixen en un bloc NL enmig de dos subsistemes LTI. La presència de dos subsistemes LTI en els models de Wiener-Hammerstein és el que principalment dificulta la seua estimació. Generalment, el procediment d'identificació comença amb l'estimació de la dinàmica lineal, i el principal desafiament és dividir aquesta dinàmica entre els dos blocs LTI. En general, això implica una alta interacció de l'usuari per a desenvolupar diversos procediments, i el model final estimat depén principalment d'aquestes etapes prèvies. L'objectiu d'aquesta tesi és contribuir a la identificació dels models de Wiener-Hammerstein. Aquesta contribució es basa en la presentació de dos nous algorismes per a atendre aspectes específics que no han sigut adreçats en la identificació d'aquesta mena de models. El primer algorisme, denominat WH-EA (Algorisme Evolutiu per a la identificació de sistemes de Wiener-Hammerstein), permet estimar tots els paràmetres d'un model de Wiener-Hammerstein amb un sol procediment a partir d'un model dinàmic lineal. Amb WH-EA, una bona estimació no depén de procediments intermedis ja que l'algorisme evolutiu simultàniament busca la millor distribució de la dinàmica, afina la ubicació dels pols i els zeros i captura la no linealitat estàtica. Un altre avantatge important d'aquest algorisme és que sota consideracions específiques i utilitzant un senyal d'excitació adequada, és possible crear un enfocament unificat que permet també la identificació dels models de Wiener i Hammerstein, que són casos particulars del model de Wiener-Hammerstein quan un dels seus blocs LTI manca de dinàmica. L'interessant d'aquest enfocament unificat és que amb un mateix algorisme és possible identificar els models de Wiener, Hammerstein i Wiener-Hammerstein sense que l'usuari especifique per endavant el tipus d'estructura a identificar. El segon algorisme anomenat WH-MOEA (Algorisme evolutiu multi-objectiu per a la identificació de models de Wiener-Hammerstein), permet abordar el problema d'identificació com un Problema d'Optimització Multiobjectiu (MOOP). Sobre la base d'aquest algorisme es presenta un nou enfocament per a la identificació dels models de Wiener-Hammerstein considerant un compromís entre la precisió aconseguida i la complexitat del model. Amb aquest enfocament és possible comparar diversos models amb diferents prestacions incloent com un objectiu d'identificació el nombre de paràmetres que pot tindre el model estimat. L'aportació d'aquest enfocament se sustenta en el fet que en molts problemes d'enginyeria els requisits de disseny i les preferències de l'usuari no sempre apunten a la precisió del model com un únic objectiu, sinó que moltes vegades la complexitat és també un factor predominant en la presa de decisions.[EN] In several engineering fields, mathematical models are used to describe the behaviour of systems, processes or phenomena. Nowadays, there are several techniques or methods for obtaining mathematical models. Because of their versatility and simplicity, system identification methods are often preferred. Generally, systems identification methods require defining a structure and estimating computationally the parameters that make it up, using a set of procedures y measurements of the system's input and output signals. In the context of nonlinear system identification, a significant challenge is the structure selection. In the case that the system to be identified presents a static type of nonlinearity, block-oriented models can be useful to define a suitable structure. However, the designer may face a certain degree of uncertainty when selecting the block-oriented model in accordance with the real system. In addition to this inconvenience, the estimation of some block-oriented models is not an easy task, as is the case with the Wiener-Hammerstein models consisting of a NL block in the middle of two LTI subsystems. The presence of two LTI subsystems in the Wiener-Hammerstein models is what mainly makes their estimation difficult. Generally, the identification procedure begins with the estimation of the linear dynamics, and the main challenge is to split this dynamic between the two LTI block. Usually, this implies a high user interaction to develop several procedures, and the final model estimated mostly depends on these previous stages. The aim of this thesis is to contribute to the identification of the Wiener-Hammerstein models. This contribution is based on the presentation of two new algorithms to address specific aspects that have not been addressed in the identification of this type of model. The first algorithm, called WH-EA (An Evolutionary Algorithm for Wiener-Hammerstein System Identification), allows estimating all the parameters of a Wiener-Hammerstein model with a single procedure from a linear dynamic model. With WH-EA, a good estimate does not depend on intermediate procedures since the evolutionary algorithm looks for the best dynamic division, while the locations of the poles and zeros are fine-tuned, and nonlinearity is captured simultaneously. Another significant advantage of this algorithm is that under specific considerations and using a suitable excitation signal; it is possible to create a unified approach that also allows the identification of Wiener and Hammerstein models which are particular cases of the Wiener-Hammerstein model when one of its LTI blocks lacks dynamics. What is interesting about this unified approach is that with the same algorithm, it is possible to identify Wiener, Hammerstein, and Wiener-Hammerstein models without the user specifying in advance the type of structure to be identified. The second algorithm called WH-MOEA (Multi-objective Evolutionary Algorithm for Wiener-Hammerstein identification), allows to address the identification problem as a Multi-Objective Optimisation Problem (MOOP). Based on this algorithm, a new approach for the identification of Wiener-Hammerstein models is presented considering a compromise between the accuracy achieved and the model complexity. With this approach, it is possible to compare several models with different performances, including as an identification target the number of parameters that the estimated model may have. The contribution of this approach is based on the fact that in many engineering problems the design requirements and user's preferences do not always point to the accuracy of the model as a single objective, but many times the complexity is also a predominant factor in decision-making.Zambrano Abad, JC. (2021). Identification of nonlinear processes based on Wiener-Hammerstein models and heuristic optimization [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/171739TESI

Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials

System identification (SI) is the discipline of inferring mathematical models from unknown dynamic systems using the input/output observations of such systems with or without prior knowledge of some of the system parameters. Many valid algorithms are available in the literature, including Volterra series expansion, Hammerstein–Wiener models, nonlinear auto-regressive moving average model with exogenous inputs (NARMAX) and its derivatives (NARX, NARMA). Different nonlinear estimators can be used for those algorithms, such as polynomials, neural networks or wavelet networks. This paper uses a different approach, named particle-Bernstein polynomials, as an estimator for SI. Moreover, unlike the mentioned algorithms, this approach does not operate in the time domain but rather in the spectral components of the signals through the use of the discrete Karhunen–Loève transform (DKLT). Some experiments are performed to validate this approach using a publicly available dataset based on ground vibration tests recorded from a real F-16 aircraft. The experiments show better results when compared with some of the traditional algorithms, especially for large, heterogeneous datasets such as the one used. In particular, the absolute error obtained with the prosed method is 63% smaller with respect to NARX and from 42% to 62% smaller with respect to various artificial neural network-based approaches