A Control Systems Perspective to Condition Monitoring and Fault Diagnosis

Modern industrial processors, engineering systems and structures, have grown significantly in complexity and in scale during the recent years. Therefore, there is an increase in the demand for automatic processors, to avoid faults and severe break downs, through predictive maintenance. In this context, the research into nonlinear systems analysis has attained much interest in recent years as linear models cannot be used to represent some of these systems. In the field of control systems, the analysis of such systems is conducted in the frequency domain using methods of Frequency Response Analysis. Generalised Frequency Response Functions (GFRFs) and the Nonlinear Output Frequency Response Functions (NOFRFs) are Frequency Response Analysis techniques used for the analysis of nonlinear dynamical behaviour in the frequency domain. The problem of Condition Monitoring and Fault Diagnosis has been investigated in the perspective of modelling, signal processing and multivariate statistical analysis, data-driven methods such as neural networks have gained significant popularity. This is because possible faulty conditions related to complex systems are often difficult to interpret. In such a background, recently, a new data-driven approach based on a systems perspective has been proposed. This approach uses a controls systems analysis method of System Identification and Frequency Response Analysis and has been shown before as a potential technique. However, this approach has certain practical concerns regarding real-world applications. Motivated by these concerns in this thesis, the following contributions are put forward: 1. The method of evaluating NOFRFs, using input-output data of a nonlinear system may experience numerical errors. This is a major concern, hence the development of a method to overcome these numerical issues effectively. 2. Frequency Response Analysis cannot be used in its current state for nonlinear systems that exhibit severe nonlinear behaviour. Although theoretically, it has been argued that this is possible, even though, it has been impossible in a practical point of view. Therefore, the possibility and the manner in which Frequency Response Analysis can be conducted for these types of systems is presented. 3. Development of a System Identification methodology to overcome the issues of inadequately exciting inputs and appropriately capturing system dynamics under general circumstances of Condition Monitoring and Fault Diagnosis. In addition to the above, the novel implementation of a control systems analysis approach is implemented in characterising corrosion, crack depth and crack length on metal samples. The approach is applied to the data collected, using a newly proposed non-invasive Structural Health Monitoring method called RFID (Radio Frequency IDentification) wireless eddy current probing. The control systems analysis approach along with the RFID wireless eddy current probing method shows the clear potential of being a new technology in non-invasive Structural Health Monitoring systems

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Statistical Vibro-Acoustic Modelling of Nonlinear Systems with Applications in Vehicles

Designing quiet cars has become an important issue in the automotive industry, where passive and active noise control techniques can be employed to improve the acoustic comfort without compromising the vehicle performance. At the design stage of a noise control system, the estimation of the structure-borne sound pressure levels in the car cabin is a challenging problem, as uncertainties in a physical structural-acoustic system have an impact on the vehicle dynamics at high frequencies. Additionally, the response of the system can be affected by nonlinearities in the vibrations transmission path. Therefore, this research has been focused in developing computationally efficient vibro-acoustic models to predict the statistical structural-acoustic response of a system to random inputs, as well as analysing the degree of dependency of the response to nonlinear behaviour in the interface between the excitation and the structure. Key aspects of the impact that a nonlinear transmission path might have in the response of a statistical structural-acoustic system, were investigated from an equivalent damper model of the structural vibrating subsystem, under the assumption of weak acoustic coupling and the infinite plate theory. Numerical data in the time domain were generated from the simplified nonlinear system excited by random inputs with known power spectral density. The effects of nonlinearities were observed and quantified in the power spectral density of the response, as well as in the reduction of coherence between the input and output. Additionally, the Wiener theory in the frequency domain has been explored to estimate the degree of contribution of a nonlinearity of second order to the total response of the system. Finally, an extended hybrid Finite Element-Statistical Energy Analysis (FE-SEA) model was proposed to analyse the response of a deterministic-statistic structural-acoustic system, where the nonlinear transmission path is considered as a deterministic structure. The equations of an existing FE-SEA approach, based on the diffuse field reciprocity, have been generalised to include prescribed displacements as inputs, in addition to external forces. The nonlinear analysis with the FE-SEA approach has been carried out by adopting the concept of equivalent linearisation of the deterministic dynamic stiffness matrix, and the capability of the approach has been validated against experimental data from a physical nonlinear structural-acoustic setup

Parameter inference for stochastic biological models

PhD ThesisParameter inference is the field concerned with estimating reliable model parameters from data. In recent years there has been a trend in the biology community toward single cell technologies such as fluorescent flow cytometry, transcriptomics and mass cytometry: providing a rich array of stochastic time series and temporal distribution data for analysis. Deterministically, there are a wide range of parameter inference and global optimisation techniques available. However, these do not always scale well to non-deterministic (i.e., stochastic) settings — whereby the temporal evolution of the system can be described by a chemical master equation for which the solution is nearly always intractable, and the dynamic behaviour of a system is hard to predict. For systems biology, the inference of stochastic parameters remains a bottleneck for accurate model simulation. This thesis is concerned with the parameter inference problem for stochastic chemical reaction networks. Stochastic chemical reaction networks are most frequently modelled as a continuous time discretestate Markov chain using Gillespie’s stochastic simulation algorithm. Firstly, I present a new parameter inference algorithm, SPICE, that combines Gillespie’s algorithm with the cross-entropy method. The cross-entropy method is a novel approach for global optimisation inspired from the field of rare-event probability estimation. I then present recent advances in utilising the generalised method of moments for inference, and seek to provide these approaches with a direct stochastic simulation based correction. Subsequently, I present a novel use of a recent multi-level tau-leaping approach for simulating population moments efficiently, and use this to provide a simulation based correction to the generalised method of moments. I also propose a new method for moment closures based on the use of Padé approximants. The presented algorithms are evaluated on a number of challenging case studies, including bistable systems — e.g., the Schlögl System and the Genetic Toggle Switch — and real experimental data. Experimental results are presented using each of the given algorithms. We also consider ‘realistic’ data — i.e., datasets missing model species, multiple datasets originating from experiment repetitions, and datasets containing arbitrary units (e.g., fluorescence values). The developed approaches are found to be viable alternatives to existing state-ofthe-art methods, and in certain cases are able to outperform other methods in terms of either speed, or accuracyNewcastle/Liverpool/Durham BBSRC Doctoral Training Partnership for financial suppor

Multi-layer functional approximation of non-linear unsteady aerodynamic response

Non-linear unsteady aerodynamic effects present major modelling difficulties in the analysis of aeroelastic response and in the subsequent design of appropriate controllers. As the direct use of the basic fluid mechanic equations is still not practical for aeroelastic applications, approximate models of the non-linear unsteady aerodynamic response are required. A rigorous mathematical framework, that can account for the complex non-linearities and time-history effects of the unsteady aerodynamic response, is provided by the use of functional representations. A recent development, based on functional approximation theory, has provided a new functional form; namely, multi-layer functionals. Moreover, the multi-layer functional representation for time-invariant, infinite memory systems is shown to be realisable in terms of temporal neural networks. In this work, a multi-layer functional representation of non-linear motion-induced unsteady aerodynamic response is presented. A discrete-time, finite memory temporal neural network, in the form of a finite impulse response (FIR) neural network, is used as a practical realisation of a multi-layer functional. This model form permits the identification of parametric input-output models of the non-linear motion-induced unsteady aerodynamic response. Identification of an appropriate FIR neural network model is facilitated by means of a supervised training process using multiple sets of motion-induced unsteady aerodynamic response. The training process is based on a conventional genetic algorithm to optimise the FIR neural network architecture, and is combined with a simplification of the simulated annealing algorithm to update weight and bias values

Bayesian multi-modal model comparison: a case study on the generators of the spike and the wave in generalized spike–wave complexes

We present a novel approach to assess the networks involved in the generation of spontaneous pathological brain activity based on multi-modal imaging data. We propose to use probabilistic fMRI-constrained EEG source reconstruction as a complement to EEG-correlated fMRI analysis to disambiguate between networks that co-occur at the fMRI time resolution. The method is based on Bayesian model comparison, where the different models correspond to different combinations of fMRI-activated (or deactivated) cortical clusters. By computing the model evidence (or marginal likelihood) of each and every candidate source space partition, we can infer the most probable set of fMRI regions that has generated a given EEG scalp data window. We illustrate the method using EEG-correlated fMRI data acquired in a patient with ictal generalized spike–wave (GSW) discharges, to examine whether different networks are involved in the generation of the spike and the wave components, respectively. To this effect, we compared a family of 128 EEG source models, based on the combinations of seven regions haemodynamically involved (deactivated) during a prolonged ictal GSW discharge, namely: bilateral precuneus, bilateral medial frontal gyrus, bilateral middle temporal gyrus, and right cuneus. Bayesian model comparison has revealed the most likely model associated with the spike component to consist of a prefrontal region and bilateral temporal–parietal regions and the most likely model associated with the wave component to comprise the same temporal–parietal regions only. The result supports the hypothesis of different neurophysiological mechanisms underlying the generation of the spike versus wave components of GSW discharges