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

Extended State Dependent Parameter modelling with a Data-Based Mechanistic approach to nonlinear model structure identification

Abstract A unified approach to Multiple and single State Dependent Parameter modelling, termed Extended State Dependent Parameters (ESDP) modelling, of nonlinear dynamic systems described by time-varying dynamic models applied to ARX or transfer-function model structures. Crucially, the approach proposes an effective model structure identification method using a novel Information Criterion (IC) taking into account model complexity in terms of the number of states involved. In ESDP, model structure involves not only the model orders, but also selection of the states driving the parameters, which effectively prevents the use of most current IC. This leads to a powerful methodology for investigating nonlinear systems building on the Data-Based Mechanistic (DBM) philosophy of Young and expanding the applications of the existing DBM methods. The methodologies presented are tested and demonstrated on both simulated data and on high frequency hydrological observations, showing how structure identification leads to discovery of dynamic relationships between system variables

Bayesian Time Series Learning with Gaussian Processes

The analysis of time series data is important in fields as disparate as the social sciences, biology, engineering or econometrics. In this dissertation, we present a number of algorithms designed to learn Bayesian nonparametric models of time series. The goal of these kinds of models is twofold. First, they aim at making predictions which quantify the uncertainty due to limitations in the quantity and the quality of the data. Second, they are flexible enough to model highly complex data whilst preventing overfitting when the data does not warrant complex models. We begin with a unifying literature review on time series models based on Gaussian processes. Then, we centre our attention on the Gaussian Process State-Space Model (GP-SSM): a Bayesian nonparametric generalisation of discrete-time nonlinear state-space models. We present a novel formulation of the GP-SSM that offers new insights into its properties. We then proceed to exploit those insights by developing new learning algorithms for the GP-SSM based on particle Markov chain Monte Carlo and variational inference. Finally, we present a filtered nonlinear auto-regressive model with a simple, robust and fast learning algorithm that makes it well suited to its application by non-experts on large datasets. Its main advantage is that it avoids the computationally expensive (and potentially difficult to tune) smoothing step that is a key part of learning nonlinear state-space models.EPSR

Dynamical probabilistic graphical models applied to physiological condition monitoring

Intensive Care Units (ICUs) host patients in critical condition who are being monitored by sensors which measure their vital signs. These vital signs carry information about a patient’s physiology and can have a very rich structure at fine resolution levels. The task of analysing these biosignals for the purposes of monitoring a patient’s physiology is referred to as physiological condition monitoring. Physiological condition monitoring of patients in ICUs is of critical importance as their health is subject to a number of events of interest. For the purposes of this thesis, the overall task of physiological condition monitoring is decomposed into the sub-tasks of modelling a patient’s physiology a) under the effect of physiological or artifactual events and b) under the effect of drug administration. The first sub-task is concerned with modelling artifact (such as the taking of blood samples, suction events etc.), and physiological episodes (such as bradycardia), while the second sub-task is focussed on modelling the effect of drug administration on a patient’s physiology. The first contribution of this thesis is the formulation, development and validation of the Discriminative Switching Linear Dynamical System (DSLDS) for the first sub-task. The DSLDS is a discriminative model which identifies the state-of-health of a patient given their observed vital signs using a discriminative probabilistic classifier, and then infers their underlying physiological values conditioned on this status. It is demonstrated on two real-world datasets that the DSLDS is able to outperform an alternative, generative approach in most cases of interest, and that an a-mixture of the two models achieves higher performance than either of the two models separately. The second contribution of this thesis is the formulation, development and validation of the Input-Output Non-Linear Dynamical System (IO-NLDS) for the second sub-task. The IO-NLDS is a non-linear dynamical system for modelling the effect of drug infusions on the vital signs of patients. More specifically, in this thesis the focus is on modelling the effect of the widely used anaesthetic drug Propofol on a patient’s monitored depth of anaesthesia and haemodynamics. A comparison of the IO-NLDS with a model derived from the Pharmacokinetics/Pharmacodynamics (PK/PD) literature on a real-world dataset shows that significant improvements in predictive performance can be provided without requiring the incorporation of expert physiological knowledge

Developing models for the data-based mechanistic approach to systems analysis:Increasing objectivity and reducing assumptions

Stochastic State-Space Time-Varying Random Walk models have been developed, allowing the existing Stochastic State Space models to operate directly on irregularly sampled time-series. These TVRW models have been successfully applied to two different classes of models benefiting each class in different ways. The first class of models - State Dependent Parameter (SDP) models and used to investigate the dominant dynamic modes of nonlinear dynamic systems and the non-linearities in these models affected by arbitrary State Variables. In SDP locally linearised models it is assumed that the parameters that describe system’s behaviour changes are dependent upon some aspect of the system (it’s ‘state’). Each parameter can be dependent on one or more states. To estimate the parameters that are changing at a rate related to that of it’s states, the estimation procedure is conducted in the state-space along the potentially multivariate trajectory of the states which drive the parameters. The introduction of the newly developed TVRW models significantly improves parameter estimation, particularly in data rich neighbourhoods of the state-space when the parameter is dependent on more than one state, and the ends of the data-series when the parameter is dependent on one state with few data points. The second class of models are known as Dynamic Harmonic Regression (DHR) models and are used to identify the dominant cycles and trends of time-series. DHR models the assumption is that a signal (such as a time-series) can be broken down into four (unobserved) components occupying different parts of the spectrum: trend, seasonal cycle, other cycles, and a high frequency irregular component. DHR is confined to uniformly sampled time-series. The introduction of the TVRW models allows DHR to operate on irregularly sampled time-series, with the added benefit of forecasting origin no longer being confined to starting at the end of the time-series but can now begin at any point in the future. Additionally, the forecasting sampling rate is no longer limited to the sampling rate of the time-series. Importantly, both classes of model were designed to follow the Data-Based Mechanistic (DBM) approach to modelling environmental systems, where the model structure and parameters are to be determined by the data (Data-Based) and then the subsequent models are to be validated based on their physical interpretation (Mechanistic). The aim is to remove the researcher’s preconceptions from model development in order to eliminate any bias, and then use the researcher’s knowledge to validate the models presented to them. Both classes of model lacked model structure identification procedures and so model structure was determined by the researcher, against the DBM approach. Two different model structure identification procedures, one for SDP and the other for DHR, were developed to bring both classes of models back within the DBM framework. These developments have been presented and tested here on both simulated data and real environmental data, demonstrating their importance, benefits and role in environmental modelling and exploratory data analysis

Reduced order modelling through system identification using stochastic filtering

This thesis presents a novel approach to model order reduction, through system identification and using stochastic filtering. Order reduction is a particularly relevant application in the automotive context, as the generation of simplified simulation models for the whole vehicle and its subsystems is an increasingly important aspect of vehicle design. First, grey-box parameter identification of vehicle handling dynamics is explored, including identification of a combined-slip tyre model. This introductory study serves as an intermediate step to review three alternative stochastic filters: identifying forms of the unscented Kalman filter, extended Kalman filter and particle filter are here compared for effectiveness, complexity and computational efficiency. Despite being initially merely considered as a stepping stone towards black-box identification, this phase of the PhD generated its own and independent outcomes and might be viewed as a spin-off of the main research topic. All three filters appear suited to system identification and could operate in on-line model predictive controllers or estimators, with varying levels of practicability at different sampling rates. Work on black-box system identification then starts through a non-linear Kalman filter, extended to identify all the parameters of a canonical linear state-space structure. In spite of all model parameters being unknown at the start, the filter is able to evolve parameter estimates to achieve 100$\%$ accuracy in noise-free test cases, and is also proven to be robust to noise in the measurements. The canonical form ensures that a minimal number of parameters need to be identified and produces additional information in terms of eigenvalues and dominant modes. After extensive testing in the linear domain, state-space is extended into a non-linear framework, with each parameter becoming a non-linear function of system inputs or states. Parameter variation is first constrained by cubic spline polynomials, to provide continuity and maintain relatively small extended state-parameter vectors. This early approach is later simplified, with each element of state-space generated through unconstrained, generic non-linear functions and defined through a number of equally spaced, fixed nodes. Conditioning and convergence are maintained through the definition of additional system outputs, based on specific functions of the non-linear node ordinates. Unlike other methods published in the literature, this new approach does not focus on a specific non-linear structure, but consists in the prescription of a generic and yet simple non-linear state-space model structure, that allows various non-linearities to be identified and approximated solely based on inputs and outputs. The method is illustrated in practice through simple non-linear examples and test cases, which include the identification of a full vehicle model, a highly non-linear brake model and CFD data. These applications show that it is possible to easily expand the order of the system and the complexity of the non-linearities, to achieve higher accuracy while ensuring good parameter conditioning. The approach is completely black-box and requires no physical understanding of the process for successful identification, making it an ideally suited mechanism for order reduction of high order simulation models. In addition to high order simulation data, the developed approach can be used as a tool for conventional system identification and applied to experimental test data as well.</div