Distinguishability Analysis for Multiple Mass Models of Servo Systems with Commissioning Sensors

Physically motivated models of electromechanical motion systems enable model-based control theory and facilitate system interpretation. Unfortunately, the effort of modelling restricts the usage of model-based methods in many applications. Some approaches to automatically generate models from measurements choose the best model based on minimizing the residual. These model selection attempts are limited due to ambiguities in reconstructing the internal structure from the input-output behaviour because usually motion systems have only one actuator and one sensor. Often, it is unknown if the resulting model is unique or if other models with different structure would fit equally well. The set of candidate models should be designed to contain only distinguishable models but ambiguities are often unknown to the experimenter. In this paper distinguishability is investigated systematically for a class of multiple mass models representing servo positioning systems. In the analysis a new criterion for indistinguishability is used. The benefit of additional, structural sensors on distinguishability of models is demonstrated which suggests to mount them temporarily for the commissioning phase in order to facilitate the model selection. It turns out that the best results can be achieved if synergies among sensor signals are utilized. © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Inference of complex biological networks: distinguishability issues and optimization-based solutions

<p>Abstract</p> <p>Background</p> <p>The inference of biological networks from high-throughput data has received huge attention during the last decade and can be considered an important problem class in systems biology. However, it has been recognized that reliable network inference remains an unsolved problem. Most authors have identified lack of data and deficiencies in the inference algorithms as the main reasons for this situation.</p> <p>Results</p> <p>We claim that another major difficulty for solving these inference problems is the frequent lack of uniqueness of many of these networks, especially when prior assumptions have not been taken properly into account. Our contributions aid the distinguishability analysis of chemical reaction network (CRN) models with mass action dynamics. The novel methods are based on linear programming (LP), therefore they allow the efficient analysis of CRNs containing several hundred complexes and reactions. Using these new tools and also previously published ones to obtain the network structure of biological systems from the literature, we find that, often, a unique topology cannot be determined, even if the structure of the corresponding mathematical model is assumed to be known and all dynamical variables are measurable. In other words, certain mechanisms may remain undetected (or they are falsely detected) while the inferred model is fully consistent with the measured data. It is also shown that sparsity enforcing approaches for determining 'true' reaction structures are generally not enough without additional prior information.</p> <p>Conclusions</p> <p>The inference of biological networks can be an extremely challenging problem even in the utopian case of perfect experimental information. Unfortunately, the practical situation is often more complex than that, since the measurements are typically incomplete, noisy and sometimes dynamically not rich enough, introducing further obstacles to the structure/parameter estimation process. In this paper, we show how the structural uniqueness and identifiability of the models can be guaranteed by carefully adding extra constraints, and that these important properties can be checked through appropriate computation methods.</p

Mathematical modelling of epidemic systems influenced by maternal antibodies and public health intervention

The general subject area of research considered in this thesis is population level epidemic modelling of infectious diseases, with specific application to the problems of model indeterminacy and systems that include processes associated with maternally acquired immunity. The work presents the derivation and analysis of a lumped systems model framework to study the influence of maternal antibodies on the population dynamics of infection among neonate and young infant age classes. The proposed models are defined by sets of ordinary and partial differential equations that describe the variation of distinct states in the natural history of infection with respect to time and/or age. The model framework is extended to explore the potential population level outcomes and consequences of mass maternal immunisation: an emerging targeted vaccine strategy that utilises the active transfer of neutralising antibodies during pregnancy in order to supplement neonatal immunity during the first few months of life. A qualitative analysis of these models has highlighted the importance of interaction with early childhood targeted vaccination campaigns, the potential to invoke transient epidemic behaviour and the prospective advantages of seasonal administration. The work considers the implications of structural identifiability, indistinguishability and formal sensitivity analyses on a number of fundamental model structures within the proposed framework. These methods are used to establish whether a postulated model structure, or the individual parameters within a known structure, are uniquely determinable from a given set of empirical observations. The main epidemiological measures available for the validation of epidemic models are inherently based on records of clinical disease or age serological surveys, which are not explicitly representative of infection and provide a very limited observation of the full system state. The analyses suggest that these issues give rise to problems of indeterminacy even in the most simple models, such that certain system characteristics cannot be uniquely estimated from available data

Structural identifiability and indistinguishability analyses of glucose-insulin models

In this thesis, the structural identifiability analyses of established and novel glucose-insulin models was performed, to determine whether the models are globally structurally identifiable with the observations available. Structural identifiability analysis is an essential step in the modelling process and a key prerequisite to experimental design and parameter estimation. Analyses were performed assuming observations of both glucose and insulin concentrations on two versions of the well-cited Minimal Model (MM), the Original Minimal Model (OMM) and Extended Minimal Model (EMM) for the modelling of the responses to an Intravenous Glucose Tolerance Test (IVGTT); a Euglycemic Hyperinsulinemic Clamp model and two novel modified versions of the MM, a Closed-Loop Minimal Model (CLMM) and a Double-Pole in Closed-Loop Minimal Model (DPCLMM), when the models describe a complete course of glucose-insulin dynamics during an IVGTT. The CLMM proved to be unidentifiable so a reparameterisation procedure was performed on this model, yielding a globally structurally identifiable reparameterised model. Parameter estimation using these models was also performed for sets of IVGTT and glucose clamp data. The results of the parameter estimation demonstrated that global structural identifiability does not as always guarantee numerical identifiability, or vice versa. A structural indistinguishability analysis was also performed to compare the MM and the CLMM, given the same observations, where it was shown that both models are distinguishable over both pre- and post- insulin switching phases. This is the first time that all such analyses have been performed on these specific model structures. The generic and numerical results obtained demonstrate issues that may arise in practice when attempting to calculate insulin sensitivity when using such models.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Mathematical modelling of epidemic systems influenced by maternal antibodies and public health intervention

The general subject area of research considered in this thesis is population level epidemic modelling of infectious diseases, with specific application to the problems of model indeterminacy and systems that include processes associated with maternally acquired immunity. The work presents the derivation and analysis of a lumped systems model framework to study the influence of maternal antibodies on the population dynamics of infection among neonate and young infant age classes. The proposed models are defined by sets of ordinary and partial differential equations that describe the variation of distinct states in the natural history of infection with respect to time and/or age. The model framework is extended to explore the potential population level outcomes and consequences of mass maternal immunisation: an emerging targeted vaccine strategy that utilises the active transfer of neutralising antibodies during pregnancy in order to supplement neonatal immunity during the first few months of life. A qualitative analysis of these models has highlighted the importance of interaction with early childhood targeted vaccination campaigns, the potential to invoke transient epidemic behaviour and the prospective advantages of seasonal administration. The work considers the implications of structural identifiability, indistinguishability and formal sensitivity analyses on a number of fundamental model structures within the proposed framework. These methods are used to establish whether a postulated model structure, or the individual parameters within a known structure, are uniquely determinable from a given set of empirical observations. The main epidemiological measures available for the validation of epidemic models are inherently based on records of clinical disease or age serological surveys, which are not explicitly representative of infection and provide a very limited observation of the full system state. The analyses suggest that these issues give rise to problems of indeterminacy even in the most simple models, such that certain system characteristics cannot be uniquely estimated from available data.EThOS - Electronic Theses Online ServiceUniversity of Warwick. Dept. of EngineeringEngineering and Physical Sciences Research Council (EPSRC)GBUnited Kingdo

Observability and observer design for switched linear systems

Hybrid vehicles, HVAC systems in new/old buildings, power networks, and the like require safe, robust control that includes switching the mode of operation to meet environmental and performance objectives. Such switched systems consist of a set of continuous-time dynamical behaviors whose sequence of operational modes is driven by an underlying decision process. This thesis investigates feasibility conditions and a methodology for state and mode reconstruction given input-output measurements (not including mode sequence). An application herein considers insulation failures in permanent magnet synchronous machines (PMSMs) used in heavy hybrid vehicles. Leveraging the feasibility literature for switched linear time-invariant systems, this thesis introduces two additional feasibility results: 1) detecting switches from safe modes into failure modes and 2) state and mode estimation for switched linear time-varying systems. This thesis also addresses the robust observability problem of computing the smallest structured perturbations to system matrices that causes observer infeasibility (with respect to the Frobenius norm). This robustness framework is sufficiently general to solve related robustness problems including controllability, stabilizability, and detectability. Having established feasibility, real-time observer reconstruction of the state and mode sequence becomes possible. We propose the embedded moving horizon observer (EMHO), which re-poses the reconstruction as an optimization using an embedded state model which relaxes the range of the mode sequence estimates into a continuous space. Optimal state and mode estimates minimize an L2-norm between the measured output and estimated output of the associated embedded state model. Necessary conditions for observer convergence are developed. The EMHO is adapted to solve the surface PMSM fault detection problem

A systems biology analysis of feedback control in pheromone signalling of fission yeast

Cell signalling comprises the systems used by cells to detect changes in their environment and to transduce the information into appropriate adjustments enforced by regulatory proteins. Due to its central role in all life processes, the study of cell signalling is a major focus of current biomedical research. The fission yeast Schizosaccharomyces pombe (S. pombe) is a single-celled organism used as a model to simplify the study of eukaryotic cell signalling, as it shares many features of interest with human cells. In this thesis a systems biology approach was used to investigate the roles of feedback regulation to control the dynamics of pheromone signalling in S. pombe. To this end, a quantitative dynamical model was built describing the pheromone-induced activation of the master transcription factor Ste11, as well as the coupled positive and negative feedback loops that arise from Ste11 activity. To constrain the model, a collection of data sets were generated by performing absolute quantification measurements of pheromone-dependent changes in the concentration of the model species. Structural identifiability analyses were used to select the measured species, while confidence intervals of the estimated parameters were determined through profile likelihood estimation. Analysis of the resulting model revealed a role for the pheromone signalling feedback loops to aid in the discrimination of different pheromone input doses. Through their combined action, feedback control defines the concentration and time thresholds in Ste11 activity that must be satisfied for the cell to commit to a sexual development fate

Modeling diversity by strange attractors with application to temporal pattern recognition

This thesis belongs to the general discipline of establishing black-box models from real-word data, more precisely, from measured time-series. This is an old subject and a large amount of papers and books has been written about it. The main difficulty is to express the diversity of data that has essentially the same origin without creating confusion with data that has a different origin. Normally, the diversity of time-series is modeled by a stochastic process, such as filtered white noise. Often, it is reasonable to assume that the time series is generated by a deterministic dynamical system rather than a stochastic process. In this case, the diversity of the data is expressed by the variability of the parameters of the dynamical system. The parameter variability itself is then, once again, modeled by a stochastic process. In both cases the diversity is generated by some form of exogenous noise. In this thesis a further step has been taken. A single chaotic dynamical system is used to model the data and their diversity. Indeed, a chaotic system produces a whole family of trajectories that are different but nonetheless very similar. It is believed that chaotic dynamics not only are a convenient means to represent diversity but that in many cases the origin of diversity stems actually from chaotic dynamic. Since the approach of this thesis explores completely new grounds the most suitable kind of data is considered, namely approximately periodic signals. In nature such time-series are rather common, in particular the physiological signal of living beings, such as the electrocardiograms (ECG), parts of speech signals, electroencephalograms (EEG), etc. Since there are strong arguments in favor of the chaotic nature of these signals, they appear to be the best candidates for modeling diversity by chaos. It should be stressed however, that the modeling approach pursued in this thesis is thought to be quite general and not limited to signals produced by chaotic dynamics in nature. The intended application of the modeling effort in this thesis is temporal signal classification. The reason for this is twofold. Firstly, classification is one of the basic building block of any cognitive system. Secondly, the recently studied phenomenon of synchronization of chaotic systems suggests a way to test a signal against its chaotic model. The essential content of this work can now be formulated as follows. Thesis: The diversity of approximately periodic signals found in nature can be modeled by means of chaotic dynamics. This kind of modeling technique, together with selective properties of the synchronization of chaotic systems, can be exploited for pattern recognition purposes. This Thesis is advocated by means of the following five points. Models of randomness (Chapter 2) It is argued that the randomness observed in nature is not necessarily the result of exogenous noise, but it could be endogenally generated by deterministic chaotic dynamics. The diversity of real signals is compared with signals produced by the most common chaotic systems. Qualitative resonance (Chapter 3) The behavior of chaotic systems forced by periodic or approximately periodic input signals is studied theoretically and by numerical simulation. It is observed that the chaotic system "locks" approximately to an input signal that is related to its internal chaotic dynamic. In contrast to this, its chaotic behavior is reinforced when the input signal has nothing to do with its internal dynamics. This new phenomenon is called "qualitative resonance". Modeling and recognizing (Chapter 4) In this chapter qualitative resonance is used for pattern recognition. The core of the method is a chaotic dynamical system that is able to reproduce the class of time-series that is to be recognized. This model is excited in a suitable way by an input signal such that qualitative resonance is realized. This means that if the input signal belongs to the modeled class of time-series, the system approximately "locks" into it. If not, the trajectory of the system and the input signal remain unrelated. Automated design of the recognizer (Chapters 5 and 6) For the kind of signals considered in this thesis a systematic design method of the recognizer is presented. The model used is a system of Lur'e type, i.e. a model where the linear dynamic and nonlinear static part are separated. The identification of the model parameters from the given data proceed iteratively, adapting in turn the linear and the nonlinear part. Thus, the difficult nonlinear dynamical system identification task is decomposed into the easier problems of linear dynamical and nonlinear static system identification. The way to apply the approximately periodic input signal in order to realize qualitative resonance is chosen with the help of periodic control theory. Validation (Chapter 7) The pattern recognition method has been validated on the following examples — A synthetic example — Laboratory measurement from Colpitts oscillator — ECG — EEG — Vowels of a speech signals In the first four cases a binary classification and in the last example a classification with five classes was performed. To the best of the knowledge of the author the recognition method is original. Chaotic systems have been already used to produce pseudo-noise and to model signal diversity. Also, parameter identification of chaotic systems has been already carried out. However, the direct establishment of the model from the given data and its subsequent use for classification based on the phenomenon of qualitative resonance is entirely new