Analysing time series structure with hidden Markov models

This paper consides the problem of extracting the relationships between two time series in a non-linear non-stationary environment with Hidden Markov Models (HMMs). We describe an algorithm which is capable of identifying associations between variables. The method is applied both to synthetic data and real data. We show that HMMs are capable of modelling the oil drilling process and that they outperform existing methods.

Delay estimation for multivariate time series

Most traditional methods for extracting the relationships between two time series are based on cross-correlation. In a non-linear non-stationary environment, these techniques are not sufficient. We show in this paper how to use hidden Markov models (HMMs) to identify the lag (or delay) between different variables for such data. We first present a method using maximum likelihood estimation and propose a simple algorithm which is capable of identifying associations between variables. We also adopt an information-theoretic approach and develop a novel procedure for training HMMs to maximise the mutual information between delayed time series. Both methods are successfully applied to real data. We model the oil drilling process with HMMs and estimate a crucial parameter, namely the lag for return.

Modelling financial time series with switching state space models

The deficiencies of stationary models applied to financial time series are well documented. A special form of non-stationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for financial markets. We use a dynamic switching (modelled by a hidden Markov model) combined with a linear dynamical system in a hybrid switching state space model (SSSM) and discuss the practical details of training such models with a variational EM algorithm due to [Ghahramani and Hilton,1998]. The performance of the SSSM is evaluated on several financial data sets and it is shown to improve on a number of existing benchmark methods.

A hybrid genetic algorithm for the multi-depot vehicle routing problem

The distribution of finished products from depots to customers is a practical and challenging problem in logistics management. Better routing and scheduling decisions can result in higher level of customer satisfaction because more customers can be served in a shorter time. The distribution problem is generally formulated as the vehicle routing problem (VRP). Nevertheless, there is a rigid assumption that there is only one depot. In cases, for instance, where a logistics company has more than one depot, the VRP is not suitable. To resolve this limitation, this paper focuses on the VRP with multiple depots, or multi-depot VRP (MDVRP). The MDVRP is NP-hard, which means that an efficient algorithm for solving the problem to optimality is unavailable. To deal with the problem efficiently, two hybrid genetic algorithms (HGAs) are developed in this paper. The major difference between the HGAs is that the initial solutions are generated randomly in HGA1. The Clarke and Wright saving method and the nearest neighbor heuristic are incorporated into HGA2 for the initialization procedure. A computational study is carried out to compare the algorithms with different problem sizes. It is proved that the performance of HGA2 is superior to that of HGA1 in terms of the total delivery time.

Component scheduling for chip shooter machines: a hybrid genetic algorithm approach

A chip shooter machine for electronic component assembly has a movable feeder carrier, a movable X–Y table carrying a printed circuit board (PCB), and a rotary turret with multiple assembly heads. This paper presents a hybrid genetic algorithm (HGA) to optimize the sequence of component placements and the arrangement of component types to feeders simultaneously for a chip shooter machine, that is, the component scheduling problem. The objective of the problem is to minimize the total assembly time. The GA developed in the paper hybridizes different search heuristics including the nearest-neighbor heuristic, the 2-opt heuristic, and an iterated swap procedure, which is a new improved heuristic. Compared with the results obtained by other researchers, the performance of the HGA is superior in terms of the assembly time. Scope and purpose When assembling the surface mount components on a PCB, it is necessary to obtain the optimal sequence of component placements and the best arrangement of component types to feeders simultaneously in order to minimize the total assembly time. Since it is very difficult to obtain the optimality, a GA hybridized with several search heuristics is developed. The type of machines being studied is the chip shooter machine. This paper compares the algorithm with a simple GA. It shows that the performance of the algorithm is superior to that of the simple GA in terms of the total assembly time.

A genetic algorithm approach to optimising component placement and retrieval sequence for chip shooter machines

A chip shooter machine in printed circuit board (PCB) assembly has three movable mechanisms: an X-Y table carrying a PCB, a feeder carrier with several feeders holding components and a rotary turret with multiple assembly heads to pick up and place components. In order to get the minimal placement or assembly time for a PCB on the machine, all the components on the board should be placed in a perfect sequence, and the components should be set up on a right feeder, or feeders since two feeders can hold the same type of components, and additionally, the assembly head should retrieve or pick up a component from a right feeder. The entire problem is very complicated, and this paper presents a genetic algorithm approach to tackle it.

A hybrid genetic algorithm for component sequencing and feeder arrangement

This paper presents a hybrid genetic algorithm to optimize the sequence of component placements on a printed circuit board and the arrangement of component types to feeders simultaneously for a pick-and-place machine with multiple stationary feeders, a fixed board table and a movable placement head. The objective of the problem is to minimize the total travelling distance, or the travelling time, of the placement head. The genetic algorithm developed in the paper hybrisizes different search heuristics including the nearest neighbor heuristic, the 2-opt heuristic, and an iterated swap procedure, which is a new improving heuristic. Compared with the results obtained by other researchers, the performance of the hybrid genetic algorithm is superior to others in terms of the distance travelled by the placement head.

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Time complexity and convergence analysis of domain theoretic Picard method

We present an implementation of the domain-theoretic Picard method for solving initial value problems (IVPs) introduced by Edalat and Pattinson [1]. Compared to Edalat and Pattinson's implementation, our algorithm uses a more efficient arithmetic based on an arbitrary precision floating-point library. Despite the additional overestimations due to floating-point rounding, we obtain a similar bound on the convergence rate of the produced approximations. Moreover, our convergence analysis is detailed enough to allow a static optimisation in the growth of the precision used in successive Picard iterations. Such optimisation greatly improves the efficiency of the solving process. Although a similar optimisation could be performed dynamically without our analysis, a static one gives us a significant advantage: we are able to predict the time it will take the solver to obtain an approximation of a certain (arbitrarily high) quality.

Quantifying simulator discrepancy in discrete-time dynamical simulators

When making predictions with complex simulators it can be important to quantify the various sources of uncertainty. Errors in the structural specification of the simulator, for example due to missing processes or incorrect mathematical specification, can be a major source of uncertainty, but are often ignored. We introduce a methodology for inferring the discrepancy between the simulator and the system in discrete-time dynamical simulators. We assume a structural form for the discrepancy function, and show how to infer the maximum-likelihood parameter estimates using a particle filter embedded within a Monte Carlo expectation maximization (MCEM) algorithm. We illustrate the method on a conceptual rainfall-runoff simulator (logSPM) used to model the Abercrombie catchment in Australia. We assess the simulator and discrepancy model on the basis of their predictive performance using proper scoring rules. This article has supplementary material online. © 2011 International Biometric Society.

Estimating parameters in stochastic systems:a variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein–Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.

Real-time process plant fault diagnosis

Operators can become confused while diagnosing faults in process plant while in operation. This may prevent remedial actions being taken before hazardous consequences can occur. The work in this thesis proposes a method to aid plant operators in systematically finding the causes of any fault in the process plant. A computer aided fault diagnosis package has been developed for use on the widely available IBM PC compatible microcomputer. The program displays a coloured diagram of a fault tree on the VDU of the microcomputer, so that the operator can see the link between the fault and its causes. The consequences of the fault and the causes of the fault are also shown to provide a warning of what may happen if the fault is not remedied. The cause and effect data needed by the package are obtained from a hazard and operability (HAZOP) study on the process plant. The result of the HAZOP study is recorded as cause and symptom equations which are translated into a data structure and stored in the computer as a file for the package to access. Probability values are assigned to the events that constitute the basic causes of any deviation. From these probability values, the a priori probabilities of occurrence of other events are evaluated. A top-down recursive algorithm, called TDRA, for evaluating the probability of every event in a fault tree has been developed. From the a priori probabilities, the conditional probabilities of the causes of the fault are then evaluated using Bayes' conditional probability theorem. The posteriori probability values could then be used by the operators to check in an orderly manner the cause of the fault. The package has been tested using the results of a HAZOP study on a pilot distillation plant. The results from the test show how easy it is to trace the chain of events that leads to the primary cause of a fault. This method could be applied in a real process environment.

A constructive learning algorithm based on back-propagation

There are been a resurgence of interest in the neural networks field in recent years, provoked in part by the discovery of the properties of multi-layer networks. This interest has in turn raised questions about the possibility of making neural network behaviour more adaptive by automating some of the processes involved. Prior to these particular questions, the process of determining the parameters and network architecture required to solve a given problem had been a time consuming activity. A number of researchers have attempted to address these issues by automating these processes, concentrating in particular on the dynamic selection of an appropriate network architecture.The work presented here specifically explores the area of automatic architecture selection; it focuses upon the design and implementation of a dynamic algorithm based on the Back-Propagation learning algorithm. The algorithm constructs a single hidden layer as the learning process proceeds using individual pattern error as the basis of unit insertion. This algorithm is applied to several problems of differing type and complexity and is found to produce near minimal architectures that are shown to have a high level of generalisation ability.

An advanced real-time predictive maintenance framework for large scale machine systems

This thesis introduces and develops a novel real-time predictive maintenance system to estimate the machine system parameters using the motion current signature. Recently, motion current signature analysis has been addressed as an alternative to the use of sensors for monitoring internal faults of a motor. A maintenance system based upon the analysis of motion current signature avoids the need for the implementation and maintenance of expensive motion sensing technology. By developing nonlinear dynamical analysis for motion current signature, the research described in this thesis implements a novel real-time predictive maintenance system for current and future manufacturing machine systems. A crucial concept underpinning this project is that the motion current signature contains infor­mation relating to the machine system parameters and that this information can be extracted using nonlinear mapping techniques, such as neural networks. Towards this end, a proof of con­cept procedure is performed, which substantiates this concept. A simulation model, TuneLearn, is developed to simulate the large amount of training data required by the neural network ap­proach. Statistical validation and verification of the model is performed to ascertain confidence in the simulated motion current signature. Validation experiment concludes that, although, the simulation model generates a good macro-dynamical mapping of the motion current signature, it fails to accurately map the micro-dynamical structure due to the lack of knowledge regarding performance of higher order and nonlinear factors, such as backlash and compliance. Failure of the simulation model to determine the micro-dynamical structure suggests the pres­ence of nonlinearity in the motion current signature. This motivated us to perform surrogate data testing for nonlinearity in the motion current signature. Results confirm the presence of nonlinearity in the motion current signature, thereby, motivating the use of nonlinear tech­niques for further analysis. Outcomes of the experiment show that nonlinear noise reduction combined with the linear reverse algorithm offers precise machine system parameter estimation using the motion current signature for the implementation of the real-time predictive maintenance system. Finally, a linear reverse algorithm, BJEST, is developed and applied to the motion current signature to estimate the machine system parameters.

The application of parallel processing methods to vibrational analysis

The trend in modal extraction algorithms is to use all the available frequency response functions data to obtain a global estimate of the natural frequencies, damping ratio and mode shapes. Improvements in transducer and signal processing technology allow the simultaneous measurement of many hundreds of channels of response data. The quantity of data available and the complexity of the extraction algorithms make considerable demands on the available computer power and require a powerful computer or dedicated workstation to perform satisfactorily. An alternative to waiting for faster sequential processors is to implement the algorithm in parallel, for example on a network of Transputers. Parallel architectures are a cost effective means of increasing computational power, and a larger number of response channels would simply require more processors. This thesis considers how two typical modal extraction algorithms, the Rational Fraction Polynomial method and the Ibrahim Time Domain method, may be implemented on a network of transputers. The Rational Fraction Polynomial Method is a well known and robust frequency domain 'curve fitting' algorithm. The Ibrahim Time Domain method is an efficient algorithm that 'curve fits' in the time domain. This thesis reviews the algorithms, considers the problems involved in a parallel implementation, and shows how they were implemented on a real Transputer network.