Emulating dynamic non-linear simulators using Gaussian processes

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models of the climate or the functioning of the human brain. The models we are interested in are highly non-linear and exhibit tipping points, bifurcations and chaotic behaviour. However, each simulation run could be too time-consuming to perform analyses that require many runs, including quantifying the variation in model output with respect to changes in the inputs. Therefore, Gaussian process emulators are used to approximate the output of the code. To do this, the flow map of the system under study is emulated over a short time period. Then, it is used in an iterative way to predict the whole time series. A number of ways are proposed to take into account the uncertainty of inputs to the emulators, after fixed initial conditions, and the correlation between them through the time series. The methodology is illustrated with two examples: the highly non-linear dynamical systems described by the Lorenz and Van der Pol equations. In both cases, the predictive performance is relatively high and the measure of uncertainty provided by the method reflects the extent of predictability in each system

Globally supported surrogate model based on support vector regression for nonlinear structural engineering applications

This work presents a global surrogate modelling of mechanical systems with elasto-plastic material behaviour based on support vector regression (SVR). In general, the main challenge in surrogate modelling is to construct an approximation model with the ability to capture the non-smooth behaviour of the system under interest. This paper investigates the ability of the SVR to deal with discontinuous and high non-smooth outputs. Two different kernel functions, namely the Gaussian and Matèrn 5/2 kernel functions, are examined and compared through one-dimensional, purely phenomenological elasto-plastic case. Thereafter, an essential part of this paper is addressed towards the application of the SVR for the two-dimensional elasto-plastic case preceded by a finite element method. In this study, the SVR computational cost is reduced by using anisotropic training grid where the number of points are only increased in the direction of the most important input parameters. Finally, the SVR accuracy is improved by smoothing the response surface based on the linear regression. The SVR is constructed using an in-house MATLAB code, while Abaqus is used as a finite element solver

Adaptive Gaussian process emulators for efficient reliability analysis

This paper presents an approximation method for performing efficient reliability analysis with complex computer models. The computational cost of industrial-scale models can cause problems when performing sampling-based reliability analysis. This is due to the fact that the failure modes of the system typically occupy a small region of the performance space and thus require relatively large sample sizes to accurately estimate their characteristics. The sequential sampling method proposed in this article, combines Gaussian process-based optimisation and subset simulation. Gaussian process emulators construct a statistical approximation to the output of the original code, which is both affordable to use and has its own measure of predictive uncertainty. Subset simulation is used as an integral part of the algorithm to efficiently populate those regions of the surrogate which are likely to lead to the performance function exceeding a predefined critical threshold. The emulator itself is used to inform decisions about efficiently using the original code to augment its predictions. The iterative nature of the method ensures that an arbitrarily accurate approximation of the failure region is developed at a reasonable computational cost. The presented method is applied to an industrial model of a biodiesel filter

Maximin Designs for Event-Related fMRI with Uncertain Error Correlation

abstract: One of the premier technologies for studying human brain functions is the event-related functional magnetic resonance imaging (fMRI). The main design issue for such experiments is to find the optimal sequence for mental stimuli. This optimal design sequence allows for collecting informative data to make precise statistical inferences about the inner workings of the brain. Unfortunately, this is not an easy task, especially when the error correlation of the response is unknown at the design stage. In the literature, the maximin approach was proposed to tackle this problem. However, this is an expensive and time-consuming method, especially when the correlated noise follows high-order autoregressive models. The main focus of this dissertation is to develop an efficient approach to reduce the amount of the computational resources needed to obtain A-optimal designs for event-related fMRI experiments. One proposed idea is to combine the Kriging approximation method, which is widely used in spatial statistics and computer experiments with a knowledge-based genetic algorithm. Through case studies, a demonstration is made to show that the new search method achieves similar design efficiencies as those attained by the traditional method, but the new method gives a significant reduction in computing time. Another useful strategy is also proposed to find such designs by considering only the boundary points of the parameter space of the correlation parameters. The usefulness of this strategy is also demonstrated via case studies. The first part of this dissertation focuses on finding optimal event-related designs for fMRI with simple trials when each stimulus consists of only one component (e.g., a picture). The study is then extended to the case of compound trials when stimuli of multiple components (e.g., a cue followed by a picture) are considered.Dissertation/ThesisDoctoral Dissertation Statistics 201

Advanced Bayesian framework for uncertainty estimation of sediment transport models

2018 Summer.Includes bibliographical references.Numerical sediment transport models are widely used to forecast the potential changes in rivers that might result from natural and/or human influences. Unfortunately, predictions from those models always possess uncertainty, so that engineers interpret the model results very conservatively, which can lead to expensive over-design of projects. The Bayesian inference paradigm provides a formal way to evaluate the uncertainty in model forecasts originating from uncertain model elements. However, existing Bayesian methods have rarely been used for sediment transport models because they often have large computational times. In addition, past research has not sufficiently addressed ways to treat the uncertainty associated with diverse sediment transport variables. To resolve those limitations, this study establishes a formal and efficient Bayesian framework to assess uncertainty in the predictions from sediment transport models. Throughout this dissertation, new methodologies are developed to represent each of three main uncertainty sources including poorly specified model parameter values, measurement errors contained in the model input data, and imperfect sediment transport equations used in the model structure. The new methods characterize how those uncertain elements affect the model predictions. First, a new algorithm is developed to estimate the parameter uncertainty and its contribution to prediction uncertainty using fewer model simulations. Second, the uncertainties of various input data are described using simple error equations and evaluated within the parameter estimation framework. Lastly, an existing method that can assess the uncertainty related to the selection and application of a transport equation is modified to enable consideration of multiple model output variables. The new methodologies are tested with a one-dimensional sediment transport model that simulates flume experiments and a natural river. Overall, the results show that the new approaches can reduce the computational time about 16% to 55% and produce more accurate estimates (e.g., prediction ranges can cover about 6% to 46% more of the available observations) compared to existing Bayesian methods. Thus, this research enhances the applicability of Bayesian inference for sediment transport modeling. In addition, this study provides several avenues to improve the reliability of the uncertainty estimates, which can help guide interpretation of model results and strategies to reduce prediction uncertainty

Automation and analysis of high-dimensionality experiments in biocatalytic reaction screening

Biological catalysts are increasingly used in industry in high-throughput screening for drug discovery or for the biocatalytic synthesis of active pharmaceutical intermediates (APIs). Their activity is dependent on high-dimensionality physiochemical processes which are affected by numerous potentially interacting factors such as temperature, pH, substrates, solvents, salinity, and so on. To generate accurate models that map the performance of such systems, it is critical to developing effective experimental and analytical frameworks. However, investigating numerous factors of interest can become unfeasible for conventional manual experimentation which can be time-consuming and prone to human error. In this thesis, an effective framework for the execution and analysis of highdimensionality experiments that implement a Design of Experiments (DoE) methodology was created. DoE applies a statistical framework to the simultaneous investigation of multiple factors of interest. To convert the DoE design into a physically executable experiment, the Synthace Life Sciences R&D cloud platform was used where experimental conditions were translated into liquid handling instructions and executed on multiple automated devices. The framework was exemplified by quantifying the activity of an industrially relevant biocatalyst, the CV2025 ωtransaminase enzyme from Chromobacterium violaceum, for the conversion of Smethylbenzylamine (MBA) and pyruvate into acetophenone and sodium alanine. The automation and analysis of high-dimensionality experiments for screening of the CV2025 TAm biocatalytic reaction were carried out in three sequential stages. In the first stage, the basic process of Synthace-driven automated DoE execution was demonstrated by executing traditional DoE studies. This comprised of a screening study that investigated the impact of nine factors of interest, after which an optimisation study was conducted by taking forward five factors of interest using two automated devices to optimise assay conditions further. In total, 480 experimental conditions were executed and analysed to generate mathematical models that identified an optimum. Robust assay conditions were identified which increased enzyme activity >3-fold over the starting conditions. In the second stage, nonbiological considerations that impact absorbance-based assay performance were systematically investigated. These considerations were critical to ensuring reliable and precise data generation from future high-dimensionality experiments and include confirming spectrophotometer settings, selecting microplate type and reaction volume, testing device precision, and managing evaporation as a function of time. The final stage of the work involved development of a framework for the implementation of a modern type of DoE design called a space-filling design (SFD). SFDs sample factors of interest at numerous settings and can provide a fine-grained characterisation of high-dimensional systems in a single experimental run. However, they are rarely used in biological research due to a large number of experiments required and their demanding, highly variable pipetting requirements. The established framework enabled the execution and analysis of an automated end-toend SFD where 3,456 experimental conditions were prepared to investigate a 12- dimensional space characterising CV2025 TAm activity. Factors of interest included temperature, pH, buffering agent types, enzyme stability, co-factor, substrate, salt, and solvent concentrations. MATLAB scripts were developed to calculate important biocatalysis metrics of product yield and initial rate which were then used to build mathematical models that were physically validated to confirm successful model prediction. The implementation of the framework provided greater insight into numerous factors influencing CV2025 TAm activity in more dimensions than what was previously reported in the literature and to our knowledge is the first large-scale study that employs a SFD for assay characterisation. The developed framework is generic in nature and represents a powerful tool for rapid one-step characterisation of high-dimensionality systems. Industrial implementation of the framework could help reduce the time and costs involved in the development of high throughput screens and biocatalytic reaction optimisation

Observer-based engine air charge characterisation: rapid, observer-assisted engine air charge characterisation using a dynamic dual-ramp testing method

Characterisation of modern complex powertrains is a time consuming and expensive process. Little effort has been made to improve the efficiency of testing methodologies used to obtain data for this purpose. Steady-state engine testing is still regarded as the golden standard, where approximately 90% of testing time is wasted waiting for the engine to stabilize. Rapid dynamic engine testing, as a replacement for the conventional steady-state method, has the potential to significantly reduce the time required for characterisation. However, even by using state of the art measurement equipment, dynamic engine testing introduces the problem that certain variables are not directly measurable due to the excitation of the system dynamics. Consequently, it is necessary to develop methods that allow the observation of not directly measurable quantities during transient engine testing. Engine testing for the characterisation of the engine air-path is specifically affected by this problem since the air mass flow entering the cylinder is not directly measurable by any sensor during transient operation. This dissertation presents a comprehensive methodology for engine air charge characterisation using dynamic test data. An observer is developed, which allows observation of the actual air mass flow into the engine during transient operation. The observer is integrated into a dual-ramp testing procedure, which allows the elimination of unaccounted dynamic effects by averaging over the resulting hysteresis. A simulation study on a 1-D gas dynamic engine model investigates the accuracy of the developed methodology. The simulation results show a trade-off between time saving and accuracy. Experimental test result confirm a time saving of 95% compared to conventional steady-state testing and at least 65% compared to quasi steady-state testing while maintaining the accuracy and repeatability of conventional steady-state testing