Safe model-based design of experiments using Gaussian processes

The construction of kinetic models has become an indispensable step in developing and scale-up of processes in the industry. Model-based design of experiments (MBDoE) has been widely used to improve parameter precision in nonlinear dynamic systems. Such a framework needs to account for both parametric and structural uncertainty, as the physical or safety constraints imposed on the system may well turn out to be violated, leading to unsafe experimental conditions when an optimally designed experiment is performed. In this work, Gaussian processes are utilized in a two-fold manner: 1) to quantify the uncertainty realization of the physical system and calculate the plant-model mismatch, 2) to compute the optimal experimental design while accounting for the parametric uncertainty. TheOur proposed method, Gaussian process-based MBDoE (GP-MBDoE), guarantees the probabilistic satisfaction of the constraints in the context of the model-based design of experiments. GP-MBDoE is assisted with the use of adaptive trust regions to facilitate a satisfactory local approximation. The proposed method can allow the design of optimal experiments starting from limited preliminary knowledge of the parameter set, leading to a safe exploration of the parameter space. This method’s performance is demonstrated through illustrative case studies regarding the parameter identification of kinetic models in flow reactors

A methodology for direct exploitation of available information in the online model-based redesign of experiments

Online model-based design of experiments techniques were proposed to exploit the progressive increase of the information resulting from the running experiment, but they currently exhibit some limitations: the redesign time points are chosen “a-priori” and the first design may be heavily affected by the initial parametric mismatch. In order to face such issues an information driven redesign optimisation (IDRO) strategy is here proposed: a robust approach is adopted and a new design criterion based on the maximisation of a target profile of dynamic information is introduced. The methodology allows determining when to redesign the experiment in an automatic way, thus guaranteeing that an acceptable increase in the information content has been achieved before proceeding with the intermediate estimation of the parameters and the subsequent redesign of the experiment. The effectiveness of the new experiment design technique is demonstrated through two simulated case studies

Model-based design of experiments in the presence of structural model uncertainty: an extended information matrix approach

The identification of a parametric model, once a suitable model structure is proposed, requires the estimation of its non-measurable parameters. Model-based design of experiment (MBDoE) methods have been proposed in the literature for maximising the collection of information whenever there is a limited amount of resources available for conducting the experiments. Conventional MBDoE methods do not take into account the structural uncertainty on the model equations and this may lead to a substantial miscalculation of the information in the experimental design stage. In this work, an extended formulation of the Fisher information matrix is proposed as a metric of information accounting for model misspecification. The properties of the extended Fisher information matrix are presented and discussed with the support of two simulated case studies

A stochastic modelling approach for the characterisation of collision exchange processes

Collision-exchange process is a common physical process where system members interact with each other to exchange materials and these individual interactions cumulatively drive a macroscopic system evolution in time. In this paper, a compartment-based stochastic model is formulated to study the collision-exchange process between members in a system. The discrete Markov analysis on the stochastic model presents the analytical results that show the independence of the system equilibrium on its initial distribution, and the derived differential equations reveal the deterministic time evolution of material amount on system members. As a specific example of a physical system that can be described via this model, a seed coating process is presented where the inter-particle coating variability is expressed by the stochastic model parameters. The promising agreement between simulation predictions and experimental results demonstrates the feasibility of stochastic modelling on the collision-exchange process and facilitates further model identification and applications to industrial processes

A diagnostic procedure for improving the structure of approximated kinetic models

Kinetic models of chemical and biochemical phenomena are frequently built from simplifying assumptions. Whenever a model is falsified by data, its mathematical structure should be modified embracing the available experimental evidence. A framework based on maximum likelihood inference is illustrated in this work for diagnosing model misspecification and improving the structure of approximated models. In the proposed framework, statistical evidence provides a measure to justify a modification of the model structure, namely a reduction of complexity through the removal of irrelevant parameters and/or an increase of complexity through the replacement of relevant parameters with more complex state-dependent expressions. A tailored Lagrange multipliers test is proposed to support the scientist in the improvement of parametric models when an increase in model complexity is required

Traveling Traders' Exchange Problem: Stochastic Modeling Framework and Two-Layer Model Identification Strategy

The Travelling Traders’ Exchange Problem (TTEP) is formalised, aiming at studying the collision-exchange systems found in various research areas. As an example of the TTEP models, a 1-D model is developed and characterised in detail. The computational stochastic simulation of the 1-D TTEP model relies on a stochastic simulation algorithm implemented based on the Monte Carlo method. A model identification framework is proposed where the money distribution in the system obtained from the stochastic model is characterised in terms of (a) standard deviation of the money redistribution; (b) its probability density function. Results indicate that the expressions of the estimated functions for (a) and (b) are tightly related to the system input conditions. The example of curve fitting on the probability density function shows how the variation of money redistribution in the system in time is driven by different values of the parameters describing the interaction mechanism

A Multi-Objective Optimal Experimental Design Framework for Enhancing the Efficiency of Online Model-Identification Platforms

Recent advances in automation and digitization enable the close integration of physical devices with their virtual counterparts, facilitating the real-time modeling and optimization of a multitude of processes in an automatic way. The rich and continuously updated data environment provided by such systems makes it possible for decisions to be made over time to drive the process toward optimal targets. In many manufacturing processes, in order to achieve an overall optimal process, the simultaneous assessment of multiple objective functions related to process performance and cost is necessary. In this work, a multi-objective optimal experimental design framework is proposed to enhance the efficiency of online model-identification platforms. The proposed framework permits flexibility in the choice of trade-off experimental design solutions, which are calculated online—that is, during the execution of experiments. The application of this framework to improve the online identification of kinetic models in flow reactors is illustrated using a case study in which a kinetic model is identified for the esterification of benzoic acid (BA) and ethanol in a microreactor

Modelling and Nonlinear Model Predictive Control of a Twin Screw Feeder

In this work, a dynamic model of a twin screw feeder, for continuous tablet manufacturing, has been developed. In particular, a First Order Plus Dead Time (FOPDT) model has been suggested. The delayed dynamics depends on operating conditions, equipment design and physical properties of the bulk solid. Model parameters are estimated by fitting the model to experimental data. Due to the nonlinear input-output relationships and the time delays involved, a Nonlinear Model Predictive Control (NMPC) is investigated to maintain an accurate mass flow rate, with the ultimate goal to improve product homogeneity in an inherently complex process. The performance of the designed control system is found to be satisfactory in a wide operating range and its potential use in a continuous manufacturing process is worth being investigated in the future