Emission Modelling and Model-Based Optimisation of the Engine Control

Modern Diesel engines require a model based optimisation of the engine control to fully exploit the additional degrees of freedom of modern engines. For identification of combustion engines, different experimental model structures are presented and compared to each other. The local adaptive model approach LOPOMOT is derived from the the local linear model approach LOLIMOT and an adaptive polynomial approach. Further regarded model structures are the in automotive industry well known look-up tables and the individual approximators kernel models. The model structures are generally presented and are rated with regard to applications in an electronic control unit. For the identification of the combustion engine, the combustion outputs NOx, soot and the engine torque are regarded. Experimental models are presented for measurements from the engine test bed. Stationary and dynamic effects are modelled separately, to avoid the influence of measurement dynamics. Thus, stationary measurements can be applied to identify the combustion models. The connection of these stationary combustion models to a dynamic air path model enables a dynamic overall simulation of the Diesel engine. The stationary and the dynamic model qualities are demonstrated using measurements from the engine test bed. The models are then applied for a stationary and a dynamic optimisation of control functions for the engine control unit. At first a local optimisation is presented for the stationary optimisation, which shows the Pareto front of the emissions NOx and soot. The subsequent global optimisation minimises the fuel consumption over a test cycle and formulates the emission limits as constraints. Initial values for the global optimisation are taken from the results of the local optimisation. Finally, a robust global optimisation is presented, which regards model uncertainties and variations due to series tolerances. For the dynamic optimisation, the trajectories of the air path actuators are optimised for a typical acceleration event. Because of the high computationally effort, such an optimisation can not be performed during engine operation, but it enables conclusions about suitable control structures. Thereafter, a smoke limitation based on the soot model is presented. This model based smoke limitation requires no additional calibration effort, but the model parameters are difficult to interpret. Therefore, a simplification to an open loop control structure with look-up tables is shown, which enables a manual fine tuning of the maps. This dissertation contributes to the model based optimisation of engine control functions and presents new modelling and optimisation approaches. Furthermore, new model structures are compared to the in automotive industry well known look-up tables and assets and drawbacks are discussed

Utilising Reverse Hydrology to quantify and improve the spatio-temporal information content of catchment rainfall estimates for flood modelling

Reverse Hydrology is a term describing methods for estimating rainfall from streamflow. The method presented here is based on combining inversion of a causal rainfall-runoff model with regularisation. This novel method, termed RegDer, combines a continuous-time transfer function model with regularised derivative estimates and is compared with an alternative method for direct inversion of a discrete-time transfer function using sub-hourly data from two catchments with contrasting rainfall and catchment storage characteristics. It has been demonstrated to recover the prominent features of the observed rainfall enabling it to generate a streamflow hydrograph indistinguishable from the observed catchment outflow. The loss of temporal resolution of the resultant rainfall series is the price paid for the numerical stability of the RegDer method, however this does not affect its ability to capture the dynamics required for streamflow generation. The inferred rainfall series was initially interpreted as an estimate of catchment rainfall but was later more precisely described as the rainfall necessary for generating streamflow – Discharge Generating Rainfall (DGR). The spatial aspect of the method was investigated using data from a densely gauged catchment. Frequency domain aspects of RegDer dual interpretation as a composite spectral decomposition method are analysed and discussed in the context of catchment data. Potential applications and developments of the approach include in-filling and extending rainfall records, reducing uncertainty in both gauged and ungauged catchments by improving rainfall estimates, assessing and refining rain gauge networks and re-evaluating areal rainfall estimation

Nonlinear Dynamic System Identification and Model Predictive Control Using Genetic Programming

During the last century, a lot of developments have been made in research of complex nonlinear process control. As a powerful control methodology, model predictive control (MPC) has been extensively applied to chemical industrial applications. Core to MPC is a predictive model of the dynamics of the system being controlled. Most practical systems exhibit complex nonlinear dynamics, which imposes big challenges in system modelling. Being able to automatically evolve both model structure and numeric parameters, Genetic Programming (GP) shows great potential in identifying nonlinear dynamic systems. This thesis is devoted to GP based system identification and model-based control of nonlinear systems. To improve the generalization ability of GP models, a series of experiments that use semantic-based local search within a multiobjective GP framework are reported. The influence of various ways of selecting target subtrees for local search as well as different methods for performing that search were investigated; a comparison with the Random Desired Operator (RDO) of Pawlak et al. was made by statistical hypothesis testing. Compared with the corresponding baseline GP algorithms, models produced by a standard steady state or generational GP followed by a carefully-designed single-objective GP implementing semantic-based local search are statistically more accurate and with smaller (or equal) tree size, compared with the RDO-based GP algorithms. Considering the practical application, how to correctly and efficiently apply an evolved GP model to other larger systems is a critical research concern. Currently, the replication of GP models is normally done by repeating other’s work given the necessary algorithm parameters. However, due to the empirical and stochastic nature of GP, it is difficult to completely reproduce research findings. An XML-based standard file format, named Genetic Programming Markup Language (GPML), is proposed for the interchange of GP trees. A formal definition of this standard and details of implementation are described. GPML provides convenience and modularity for further applications based on GP models. The large-scale adoption of MPC in buildings is not economically viable due to the time and cost involved in designing and adjusting predictive models by expert control engineers. A GP-based control framework is proposed for automatically evolving dynamic nonlinear models for the MPC of buildings. An open-loop system identification was conducted using the data generated by a building simulator, and the obtained GP model was then employed to construct the predictive model for the MPC. The experimental result shows GP is able to produce models that allow the MPC of building to achieve the desired temperature band in a single zone space

Implementation of gaussian process models for non-linear system identification

This thesis is concerned with investigating the use of Gaussian Process (GP) models for the identification of nonlinear dynamic systems. The Gaussian Process model is a non-parametric approach to system identification where the model of the underlying system is to be identified through the application of Bayesian analysis to empirical data. The GP modelling approach has been proposed as an alternative to more conventional methods of system identification due to a number of attractive features. In particular, the Bayesian probabilistic framework employed by the GP model has been shown to have potential in tackling the problems found in the optimisation of complex nonlinear models such as those based on multiple model or neural network structures. Furthermore, due to this probabilistic framework, the predictions made by the GP model are probability distributions composed of mean and variance components. This is in contrast to more conventional methods where a predictive point estimate is typically the output of the model. This additional variance component of the model output has been shown to be of potential use in model-predictive or adaptive control implementations. A further property that is of potential interest to those working on system identification problems is that the GP model has been shown to be particularly effective in identifying models from sparse datasets. Therefore, the GP model has been proposed for the identification of models in off-equilibrium regions of operating space, where more established methods might struggle due to a lack of data. The majority of the existing research into modelling with GPs has concentrated on detailing the mathematical methodology and theoretical possibilities of the approach. Furthermore, much of this research has focused on the application of the method toward statistics and machine learning problems. This thesis investigates the use of the GP model for identifying nonlinear dynamic systems from an engineering perspective. In particular, it is the implementation aspects of the GP model that are the main focus of this work. Due to its non-parametric nature, the GP model may also be considered a ‘black-box’ method as the identification process relies almost exclusively on empirical data, and not on prior knowledge of the system. As a result, the methods used to collect and process this data are of great importance, and the experimental design and data pre-processing aspects of the system identification procedure are investigated in detail. Therefore, in the research presented here the inclusion of prior system knowledge into the overall modelling procedure is shown to be an invaluable asset in improving the overall performance of the GP model. In previous research, the computational implementation of the GP modelling approach has been shown to become problematic for applications where the size of training dataset is large (i.e. one thousand or more points). This is due to the requirement in the GP modelling approach for repeated inversion of a covariance matrix whose size is dictated by the number of points included in the training dataset. Therefore, in order to maintain the computational viability of the approach, a number of different strategies have been proposed to lessen the computational burden. Many of these methods seek to make the covariance matrix sparse through the selection of a subset of existing training data. However, instead of operating on an existing training dataset, in this thesis an alternative approach is proposed where the training dataset is specifically designed to be as small as possible whilst still containing as much information. In order to achieve this goal of improving the ‘efficiency’ of the training dataset, the basis of the experimental design involves adopting a more deterministic approach to exciting the system, rather than the more common random excitation approach used for the identification of black-box models. This strategy is made possible through the active use of prior knowledge of the system. The implementation of the GP modelling approach has been demonstrated on a range of simulated and real-world examples. The simulated examples investigated include both static and dynamic systems. The GP model is then applied to two laboratory-scale nonlinear systems: a Coupled Tanks system where the volume of liquid in the second tank must be predicted, and a Heat Transfer system where the temperature of the airflow along a tube must be predicted. Further extensions to the GP model are also investigated including the propagation of uncertainty from one prediction to the next, the application of sparse matrix methods, and also the use of derivative observations. A feature of the application of GP modelling approach to nonlinear system identification problems is the reliance on the squared exponential covariance function. In this thesis the benefits and limitations of this particular covariance function are made clear, and the use of alternative covariance functions and ‘mixed-model’ implementations is also discussed

Efficient Multidimensional Regularization for Volterra Series Estimation

This paper presents an efficient nonparametric time domain nonlinear system identification method. It is shown how truncated Volterra series models can be efficiently estimated without the need of long, transient-free measurements. The method is a novel extension of the regularization methods that have been developed for impulse response estimates of linear time invariant systems. To avoid the excessive memory needs in case of long measurements or large number of estimated parameters, a practical gradient-based estimation method is also provided, leading to the same numerical results as the proposed Volterra estimation method. Moreover, the transient effects in the simulated output are removed by a special regularization method based on the novel ideas of transient removal for Linear Time-Varying (LTV) systems. Combining the proposed methodologies, the nonparametric Volterra models of the cascaded water tanks benchmark are presented in this paper. The results for different scenarios varying from a simple Finite Impulse Response (FIR) model to a 3rd degree Volterra series with and without transient removal are compared and studied. It is clear that the obtained models capture the system dynamics when tested on a validation dataset, and their performance is comparable with the white-box (physical) models

Variation-aware behavioural modelling using support vector machines and affine arithmetic

AGIAS Generalised Interval Arithmetic Simulator (AGIAS) is a specialised simulator which uses affine arithmetic to model parameter variations. It uses a specialised root-finding algorithm to simulate analogue circuits with parameter variations in one single simulation run. This is a significant speed-up compared to the multiple runs needed by industrialised solutions such as Monte-Carlo (MC) or Worst-Case Analysis (WCA). Currently, AGIAS can simulate analogue circuits only under very specific conditions. In many cases, circuits can only be simulated for certain operating points. If the circuits is to be evaluated in other operating points, the solver becomes numerically unstable and simulation fails. In these cases, interval widths approach infinity. Behavioural modelling of analogue circuits was introduced by researchers working around limitations of simulators. Most early approaches require expert knowledge and insight into the circuit which is modelled. In recent years, Machine Learning techniques for automatic generation of behavioural models have made their way into the field. This thesis combines Machine Learning techniques with affine arithmetic to include the effects of parameter variations into models. Support Vector Machines (SVMs) train two sets of parameters: one slope parameter and one offset parameter. These parameters are replaced by affine forms. Using these two parameters allows affine SVMs to model effects of parameter variations with varying widths. Training requires additional information about maximum and minimum values in addition to the nominal values in the data set. Based on these changes, affine ε Support Vector Machine (ε̂SVR) and ν Support Vector Machine (ν̂SVR) algorithms for regression are presented. To train the affine parameters directly and profit from the Sequential Minimal Optimisation algorithm (SMO)’s selectivity, the SMO is extended to handle the new, larger optimisation problems. The new affine SVMs are tested on analogue circuits that have been chosen based on whether they could be simulated with AGIAS and how strongly non-linear their characteristic function is

A Behavioral Approach to Robust Machine Learning

Machine learning is revolutionizing almost all fields of science and technology and has been proposed as a pathway to solving many previously intractable problems such as autonomous driving and other complex robotics tasks. While the field has demonstrated impressive results on certain problems, many of these results have not translated to applications in physical systems, partly due to the cost of system fail- ure and partly due to the difficulty of ensuring reliable and robust model behavior. Deep neural networks, for instance, have simultaneously demonstrated both incredible performance in game playing and image processing, and remarkable fragility. This combination of high average performance and a catastrophically bad worst case performance presents a serious danger as deep neural networks are currently being used in safety critical tasks such as assisted driving. In this thesis, we propose a new approach to training models that have built in robustness guarantees. Our approach to ensuring stability and robustness of the models trained is distinct from prior methods; where prior methods learn a model and then attempt to verify robustness/stability, we directly optimize over sets of models where the necessary properties are known to hold. Specifically, we apply methods from robust and nonlinear control to the analysis and synthesis of recurrent neural networks, equilibrium neural networks, and recurrent equilibrium neural networks. The techniques developed allow us to enforce properties such as incremental stability, incremental passivity, and incremental l2 gain bounds / Lipschitz bounds. A central consideration in the development of our model sets is the difficulty of fitting models. All models can be placed in the image of a convex set, or even R^N , allowing useful properties to be easily imposed during the training procedure via simple interior point methods, penalty methods, or unconstrained optimization. In the final chapter, we study the problem of learning networks of interacting models with guarantees that the resulting networked system is stable and/or monotone, i.e., the order relations between states are preserved. While our approach to learning in this chapter is similar to the previous chapters, the model set that we propose has a separable structure that allows for the scalable and distributed identification of large-scale systems via the alternating directions method of multipliers (ADMM)