Fault Detection for Systems with Multiple Unknown Modes and Similar Units

This dissertation considers fault detection for large-scale practical systems with many nearly identical units operating in a shared environment. A special class of hybrid system model is introduced to describe such multi-unit systems, and a general approach for estimation and change detection is proposed. A novel fault detection algorithm is developed based on estimating a common Gaussian-mixture distribution for unit parameters whereby observations are mapped into a common parameter-space and clusters are then identified corresponding to different modes of operation via the Expectation- Maximization algorithm. The estimated common distribution incorporates and generalizes information from all units and is utilized for fault detection in each individual unit. The proposed algorithm takes into account unit mode switching, parameter drift, and can handle sudden, incipient, and preexisting faults. It can be applied to fault detection in various industrial, chemical, or manufacturing processes, sensor networks, and others. Several illustrative examples are presented, and a discussion on the pros and cons of the proposed methodology is provided. The proposed algorithm is applied specifically to fault detection in Heating Ventilation and Air Conditioning (HVAC) systems. Reliable and timely fault detection is a significant (and still open) practical problem in the HVAC industry { commercial buildings waste an estimated 15% to 30% ($20.8B -$41.61B annually) of their energy due to degraded, improperly controlled, or poorly maintained equipment. Results are presented from an extensive performance study based on both Monte Carlo simulations as well as real data collected from three operational large HVAC systems. The results demonstrate the capabilities of the new methodology in a more realistic setting and provide insights that can facilitate the design and implementation of practical fault detection for systems of similar type in other industrial applications

Sequential Modelling and Inference of High-frequency Limit Order Book with State-space Models and Monte Carlo Algorithms

The high-frequency limit order book (LOB) market has recently attracted increasing research attention from both the industry and the academia as a result of expanding algorithmic trading. However, the massive data throughput and the inherent complexity of high-frequency market dynamics also present challenges to some classic statistical modelling approaches. By adopting powerful state-space models from the field of signal processing as well as a number of Bayesian inference algorithms such as particle filtering, Markov chain Monte Carlo and variational inference algorithms, this thesis presents my extensive research into the high-frequency limit order book covering a wide scope of topics. Chapter 2 presents a novel construction of the non-homogeneous Poisson process to allow online intensity inference of limit order transactions arriving at a central exchange as point data. Chapter 3 extends a baseline jump diffusion model for market fair-price process to include three additional model features taken from real-world market intuitions. In Chapter 4, another price model is developed to account for both long-term and short-term diffusion behaviours of the price process. This is achieved by incorporating multiple jump-diffusion processes each exhibiting a unique characteristic. Chapter 5 observes the multi-regime nature of price diffusion processes as well as the non-Markovian switching behaviour between regimes. As such, a novel model is proposed which combines the continuous-time state-space model, the hidden semi-Markov switching model and the non-parametric Dirichlet process model. Additionally, building upon the general structure of the particle Markov chain Monte Carlo algorithm, I further propose an algorithm which achieves sequential state inference, regime identification and regime parameters learning requiring minimal prior assumptions. Chapter 6 focuses on the development of efficient parameter-learning algorithms for state-space models and presents three algorithms each demonstrating promising results in comparison to some well-established methods. The models and algorithms proposed in this thesis not only are practical tools for analysing high-frequency LOB markets, but can also be applied in various areas and disciplines beyond finance

Multi-Scan Implementation of the Trajectory Poisson Multi-Bernoulli Mixture Filter

The Poisson multi-Bernoulli mixture (PMBM) and the multi-Bernoulli mixture (MBM) are two multitarget distributions for which closed-form filtering recursions exist. The PMBM has a Poisson birth process, whereas the MBM has a multi-Bernoulli birth process. This paper considers a recently developed formulation of the multitarget tracking problem using a random finite set of trajectories, through which the track continuity is explicitly established. A multiscan trajectory PMBM filter and a multiscan trajectory MBM filter, with the ability to correct past data association decisions to improve current decisions, are presented. In addition, a multiscan trajectory MBM01 filter, in which the existence probabilities of all Bernoulli components are either 0 or 1, is presented. This paper proposes an efficient implementation that performs track-oriented N-scan pruning to limit computational complexity, and uses dual decomposition to solve the involved multiframe assignment problem. The performance of the presented multitarget trackers, applied with an efficient fixed-lag smoothing method, is evaluated in a simulation study

Model-based trajectory reconstruction with IMM smoothing and segmentation

This paper presents a new approach for off-line trajectory reconstruction in air traffic control domain. The proposed algorithm, called model-based reconstruction, performs an accurate IMM smoothing process whose parameters are modified along time according to the flight modes segmented from trajectory measurements. Its competitive performance is demonstrated through comparison with previous reconstruction methods used in ATC and with classical IMM smoothing, using simulated data.This work was supported in part by Projects EUROCONTROL TRES, MEyC TEC2012-37832-C02-01, MEyC TEC2011-28626-C02-01/02 and CAM CONTEXTS (S2009/TIC-1485).Publicad