Gaussian process based model predictive control : a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Engineering, School of Engineering and Advanced Technology, Massey University, New Zealand

The performance of using Model Predictive Control (MPC) techniques is highly dependent on a model that is able to accurately represent the dynamical system. The datadriven modelling techniques are usually used as an alternative approach to obtain such a model when first principle techniques are not applicable. However, it is not easy to assess the quality of learnt models when using the traditional data-driven models, such as Artificial Neural Network (ANN) and Fuzzy Model (FM). This issue is addressed in this thesis by using probabilistic Gaussian Process (GP) models. One key issue of using the GP models is accurately learning the hyperparameters. The Conjugate Gradient (CG) algorithms are conventionally used in the problem of maximizing the Log-Likelihood (LL) function to obtain these hyperparameters. In this thesis, we proposed a hybrid Particle Swarm Optimization (PSO) algorithm to cope with the problem of learning hyperparameters. In addition, we also explored using the Mean Squared Error (MSE) of outputs as the fitness function in the optimization problem. This will provide us a quality indication of intermediate solutions. The GP based MPC approaches for unknown systems have been studied in the past decade. However, most of them are not generally formulated. In addition, the optimization solutions in existing GP based MPC algorithms are not clearly given or are computationally demanding. In this thesis, we first study the use of GP based MPC approaches in the unconstrained problems. Compared to the existing works, the proposed approach is generally formulated and the corresponding optimization problem is eff- ciently solved by using the analytical gradients of GP models w.r.t. outputs and control inputs. The GPMPC1 and GPMPC2 algorithms are subsequently proposed to handle the general constrained problems. In addition, through using the proposed basic and extended GP based local dynamical models, the constrained MPC problem is effectively solved in the GPMPC1 and GPMPC2 algorithms. The proposed algorithms are verified in the trajectory tracking problem of the quadrotor. The issue of closed-loop stability in the proposed GPMPC algorithm is addressed by means of the terminal cost and constraint technique in this thesis. The stability guaranteed GPMPC algorithm is subsequently proposed for the constrained problem. By using the extended GP based local dynamical model, the corresponding MPC problem is effectively solved

Optimizing Photonic Nanostructures via Multi-fidelity Gaussian Processes

We apply numerical methods in combination with finite-difference-time-domain (FDTD) simulations to optimize transmission properties of plasmonic mirror color filters using a multi-objective figure of merit over a five-dimensional parameter space by utilizing novel multi-fidelity Gaussian processes approach. We compare these results with conventional derivative-free global search algorithms, such as (single-fidelity) Gaussian Processes optimization scheme, and Particle Swarm Optimization---a commonly used method in nanophotonics community, which is implemented in Lumerical commercial photonics software. We demonstrate the performance of various numerical optimization approaches on several pre-collected real-world datasets and show that by properly trading off expensive information sources with cheap simulations, one can more effectively optimize the transmission properties with a fixed budget.Comment: NIPS 2018 Workshop on Machine Learning for Molecules and Materials. arXiv admin note: substantial text overlap with arXiv:1811.0075

Assessing hyper parameter optimization and speedup for convolutional neural networks

The increased processing power of graphical processing units (GPUs) and the availability of large image datasets has fostered a renewed interest in extracting semantic information from images. Promising results for complex image categorization problems have been achieved using deep learning, with neural networks comprised of many layers. Convolutional neural networks (CNN) are one such architecture which provides more opportunities for image classification. Advances in CNN enable the development of training models using large labelled image datasets, but the hyper parameters need to be specified, which is challenging and complex due to the large number of parameters. A substantial amount of computational power and processing time is required to determine the optimal hyper parameters to define a model yielding good results. This article provides a survey of the hyper parameter search and optimization methods for CNN architectures

Optimizing Photonic Nanostructures via Multi-fidelity Gaussian Processes

We apply numerical methods in combination with finite-difference-time-domain (FDTD) simulations to optimize transmission properties of plasmonic mirror color filters using a multi-objective figure of merit over a five-dimensional parameter space by utilizing novel multi-fidelity Gaussian processes approach. We compare these results with conventional derivative-free global search algorithms, such as (single-fidelity) Gaussian Processes optimization scheme, and Particle Swarm Optimization---a commonly used method in nanophotonics community, which is implemented in Lumerical commercial photonics software. We demonstrate the performance of various numerical optimization approaches on several pre-collected real-world datasets and show that by properly trading off expensive information sources with cheap simulations, one can more effectively optimize the transmission properties with a fixed budget

Adequate model complexity and data resolution for effective constraint of simulation models by 4D seismic data

4D seismic data bears valuable spatial information about production-related changes in the reservoir. It is a challenging task though to make simulation models honour it. Strict spatial tie of seismic data requires adequate model complexity in order to assimilate details of seismic signature. On the other hand, not all the details in the seismic signal are critical or even relevant to the flow characteristics of the simulation model so that fitting them may compromise the predictive capability of models. So, how complex should be a model to take advantage of information from seismic data and what details should be matched? This work aims to show how choices of parameterisation affect the efficiency of assimilating spatial information from the seismic data. Also, the level of details at which the seismic signal carries useful information for the simulation model is demonstrated in light of the limited detectability of events on the seismic map and modelling errors. The problem of the optimal model complexity is investigated in the context of choosing model parameterisation which allows effective assimilation of spatial information in the seismic map. In this study, a model parameterisation scheme based on deterministic objects derived from seismic interpretation creates bias for model predictions which results in poor fit of historic data. The key to rectifying the bias was found to be increasing the flexibility of parameterisation by either increasing the number of parameters or using a scheme that does not impose prior information incompatible with data such as pilot points in this case. Using the history matching experiments with a combined dataset of production and seismic data, a level of match of the seismic maps is identified which results in an optimal constraint of the simulation models. Better constrained models were identified by quality of their forecasts and closeness of the pressure and saturation state to the truth case. The results indicate that a significant amount of details in the seismic maps is not contributing to the constructive constraint by the seismic data which is caused by two factors. First is that smaller details are a specific response of the system-source of observed data, and as such are not relevant to flow characteristics of the model, and second is that the resolution of the seismic map itself is limited by the seismic bandwidth and noise. The results suggest that the notion of a good match for 4D seismic maps commonly equated to the visually close match is not universally applicable

The role of surrogate models in the development of digital twins of dynamic systems

Digital twin technology has significant promise, relevance and potential of widespread applicability in various industrial sectors such as aerospace, infrastructure and automotive. However, the adoption of this technology has been slower due to the lack of clarity for specific applications. A discrete damped dynamic system is used in this paper to explore the concept of a digital twin. As digital twins are also expected to exploit data and computational methods, there is a compelling case for the use of surrogate models in this context. Motivated by this synergy, we have explored the possibility of using surrogate models within the digital twin technology. In particular, the use of Gaussian process (GP) emulator within the digital twin technology is explored. GP has the inherent capability of addressing noisy and sparse data and hence, makes a compelling case to be used within the digital twin framework. Cases involving stiffness variation and mass variation are considered, individually and jointly, along with different levels of noise and sparsity in data. Our numerical simulation results clearly demonstrate that surrogate models, such as GP emulators, have the potential to be an effective tool for the development of digital twins. Aspects related to data quality and sampling rate are analysed. Key concepts introduced in this paper are summarised and ideas for urgent future research needs are proposed

Automatic object classification for surveillance videos.

PhDThe recent popularity of surveillance video systems, specially located in urban scenarios, demands the development of visual techniques for monitoring purposes. A primary step towards intelligent surveillance video systems consists on automatic object classification, which still remains an open research problem and the keystone for the development of more specific applications. Typically, object representation is based on the inherent visual features. However, psychological studies have demonstrated that human beings can routinely categorise objects according to their behaviour. The existing gap in the understanding between the features automatically extracted by a computer, such as appearance-based features, and the concepts unconsciously perceived by human beings but unattainable for machines, or the behaviour features, is most commonly known as semantic gap. Consequently, this thesis proposes to narrow the semantic gap and bring together machine and human understanding towards object classification. Thus, a Surveillance Media Management is proposed to automatically detect and classify objects by analysing the physical properties inherent in their appearance (machine understanding) and the behaviour patterns which require a higher level of understanding (human understanding). Finally, a probabilistic multimodal fusion algorithm bridges the gap performing an automatic classification considering both machine and human understanding. The performance of the proposed Surveillance Media Management framework has been thoroughly evaluated on outdoor surveillance datasets. The experiments conducted demonstrated that the combination of machine and human understanding substantially enhanced the object classification performance. Finally, the inclusion of human reasoning and understanding provides the essential information to bridge the semantic gap towards smart surveillance video systems

Joint Communication and Positioning based on Channel Estimation

Mobile wireless communication systems have rapidly and globally become an integral part of everyday life and have brought forth the internet of things. With the evolution of mobile wireless communication systems, joint communication and positioning becomes increasingly important and enables a growing range of new applications. Humanity has already grown used to having access to multimedia data everywhere at every time and thereby employing all sorts of location-based services. Global navigation satellite systems can provide highly accurate positioning results whenever a line-of-sight path is available. Unfortunately, harsh physical environments are known to degrade the performance of existing systems. Therefore, ground-based systems can assist the existing position estimation gained by satellite systems. Determining positioning-relevant information from a unified signal structure designed for a ground-based joint communication and positioning system can either complement existing systems or substitute them. Such a system framework promises to enhance the existing systems by enabling a highly accurate and reliable positioning performance and increased coverage. Furthermore, the unified signal structure yields synergetic effects. In this thesis, I propose a channel estimation-based joint communication and positioning system that employs a virtual training matrix. This matrix consists of a relatively small training percentage, plus the detected communication data itself. Via a core semi- blind estimation approach, this iteratively includes the already detected data to accurately determine the positioning-relevant parameter, by mutually exchanging information between the communication part and the positioning part of the receiver. Synergy is created. I propose a generalized system framework, suitable to be used in conjunction with various communication system techniques. The most critical positioning-relevant parameter, the time-of-arrival, is part of a physical multipath parameter vector. Estimating the time-of-arrival, therefore, means solving a global, non-linear, multi-dimensional optimization problem. More precisely, it means solving the so-called inverse problem. I thoroughly assess various problem formulations and variations thereof, including several different measurements and estimation algorithms. A significant challenge, when it comes to solving the inverse problem to determine the positioning-relevant path parameters, is imposed by realistic multipath channels. Most parameter estimation algorithms have proven to perform well in moderate multipath environments. It is mathematically straightforward to optimize this performance in the sense that the number of observations has to exceed the number of parameters to be estimated. The typical parameter estimation problem, on the other hand, is based on channel estimates, and it assumes that so-called snapshot measurements are available. In the case of realistic channel models, however, the number of observations does not necessarily exceed the number of unknowns. In this thesis, I overcome this problem, proposing a method to reduce the problem dimensionality via joint model order selection and parameter estimation. Employing the approximated and estimated parameter covariance matrix inherently constrains the estimation problem’s model order selection to result in optimal parameter estimation performance and hence optimal positioning performance. To compare these results with the optimally achievable solution, I introduce a focused order-related lower bound in this thesis. Additionally, I use soft information as a weighting matrix to enhance the positioning algorithm positioning performance. For demonstrating the feasibility and the interplay of the proposed system components, I utilize a prototype system, based on multi-layer interleave division multiple access. This proposed system framework and the investigated techniques can be employed for multiple existing systems or build the basis for future joint communication and positioning systems. The assessed estimation algorithms are transferrable to all kinds of joint communication and positioning system designs. This thesis demonstrates their capability to, in principle, successfully cope with challenging estimation problems stemming from harsh physical environments