Reliability of complex chemical engineering processes

This paper presents a stochastic performance modelling approach that can be used to optimise design and operational reliability of complex chemical engineering processes. The framework can be applied to processes comprising multiple units, including the cases where closed form process performance functions are unavailable or difficult to derive from first principles, which is often the case in practice. An interface that facilitates automated two-way communication between Matlab^® and process simulation environment is used to generate large process responses. The resulting constrained optimisation problem is solved using both Monte Carlo Simulation (MCS) and First Order Reliability Method (FORM); providing a wide range of stochastic process performance measures. Adding such capabilities to traditional deterministic process simulators provides a more informed basis for selecting optimum design factors; giving a simple way of enhancing overall process reliability and cost-efficiency. Two case study systems are considered to highlight the applicability and benefits of the approach.     

Evolving an Accurate Decision Tree-Based Model for Predicting Carbon Dioxide Solubility in Polymers

Solubility is one of the most indispensable physicochemical properties determining the compatibility of components of a blending system. Research has been focused on the solubility of carbon dioxide in polymers as a significant application of green chemistry. To replace costly and time-consuming experiments, a novel solubility prediction model based on a decision tree, called the stochastic gradient boosting algorithm, was proposed to predict CO₂ solubility in 13 different polymers, based on 515 published experimental data lines. The results indicate that the proposed ensemble model is an effective method for predicting the CO₂ solubility in various polymers, with highly satisfactory performance and high efficiency. It produces more accurate outputs than other methods such as machine learning schemes and an equation of state approach.     

Control theory for stochastic distributed parameter systems,an engineering perspective

The main purpose of this paper is to survey some recent progresses on control theory for stochastic distributed parameter systems, i.e., systems governed by stochastic differential equations in infinite dimensions, typically by stochastic partial differential equations. We will explain the new phenomenon and difficulties in the study of controllability and optimal control problems for one dimensional stochastic parabolic equations and stochastic hyperbolic equations. In particular, we shall see that both the formulation of corresponding stochastic control problems and the tools to solve them may differ considerably from their deterministic/finite-dimensional counterparts. More importantly, one has to develop new tools, say, the stochastic transposition method introduced in our previous works, to solve some problems in this field.     

Optimal resilient power grid operation during the course of a progressing wildfire

We study a two-stage stochastic and nonlinear optimization model for operating a power grid exposed to a natural disaster. Although this approach can be generalized to any natural hazard of continuous (and not instantaneous) nature, our focus is on wildfires. We assume that an approaching wildfire impacts the power grid by reducing the transmission capacity of its overhead lines. At the time when proactive decisions have to be taken, the severity of the wildfire is not known. This introduces uncertainty. In this paper, we extend previous work by more realistically capturing this uncertainty and by strengthening the mathematical programming formulation through standard reformulation techniques. With these reformulation techniques, the resulting two-stage, convex mixed-integer quadratically constrained programming formulation can be efficiently solved using commercial quadratic programming solvers as demonstrated on a case study on a modified version of the IEEE 123-bus test system with 100 scenarios. We also quantify the uncertainties through a second case study using the following three standard metrics of two-stage stochastic optimization: the expected value of perfect information, the expected result of using the expected value solution and the value of the stochastic solution.     

Convergence analysis of the alternating RGLS algorithm for the identification of the reduced complexity Volterra model

In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS).     

The PAR(p) Interconfigurations model used by the Brazilian Electric Sector

This study discusses the characteristics of the Periodic Autoregressive model, PAR(p), which is used to generate synthetic series of inflow energies that serve as entries for computer platforms that implement the planning and expansion of the operations of the BES – the Brazilian Electric Sector (SEB – Sistema Elétrico Brasileiro). The methodology for the design of a generating plant is presented in addition to the fundamentals of the “PAR(p) Interconfigurations” Model, which is referred to as the Inflow Energy Generation Model (IEGM) in this study. The major contribution of this study is to provide the first scientific discussion of the representation of multiple configurations using the PAR(p) model. For this purpose, several topics related to the time series are discussed, such as the definition of the model order, the matter of stationarity and the need to address possible outliers. Finally, a case study is presented, wherein the results of the estimation and generation of the described model’s scenarios are demonstrated.     

Robust nonlinear feedback–feedforward control of a coupled kinetic Monte Carlo–finite difference simulation

Robust nonlinear feedforward–feedback controllers are designed for a multiscale system that dynamically couples kinetic Monte Carlo (KMC) and finite difference (FD) simulation codes. The coupled codes simulate the copper electrodeposition process for manufacturing on-chip copper interconnects in electronic devices. The control objective is to regulate the current density subject to the condition that the steady-state fluctuation of the overpotential remains bounded within ±0.01 V. The controller designs incorporate a low-order stochastic model that captures the input–output behavior of the coupled KMC–FD code. The controllers achieve the objectives and the closed-loop responses implemented on the low-order model and the coupled KMC–FD code match well within stochastic variations. The nonlinear feedforward control reduces the rise time of the controller response while the feedback control ensures robustness in the presence of model uncertainty.     

A stochastic model for localized disturbances and its applications

A stochastic model for local disturbances, particularly for a temporal harmonic with random modulations in amplitude and/or phase, is proposed in this paper. Results for the second moment responses of a linear single-degree-of-freedom system to this type of stochastic loading demonstrate a significant change in response characteristics due to a small uncertainty. A local phenomenon may last much longer and resonance may be smeared to a broad range. Integrated with wavelet transform, the proposed approach may be used to model a random process with non-stationary frequency content. Especially, it can be effectively used for Monte Carlo simulation to generate large size of samples that have similar characteristics in time and frequency domains as a pre-selected mother sample has. The technique has a great potential for the case where uncertainty study is warranted but the available samples are limited.     

Continuous time stochastic adaptive control: non-explosion, ε-consistency and stability

For completely observed continuous time constant parameter stochastic linear systems, an indirect adaptive control law is presented which, subject principally to a weak location hypothesis concerning the true parameter, and a persistent excitation hypothesis, generates ε-consistent recursive least squares parameter estimates and ensures the system is mean square sample path stable. The adaptive control algorith mentails (i) recursively calculating the least squares estimate of the system parameter, and (ii) recursively generating the LQR feedback gain matrix lying in a set of matrix gains γ known to contain a stabilizing gain. The a.s. non-explosion of the system is a direct consequence of this construction.     

Design of minimax robust LQG controllers under parameter and noise uncertainties

The problem of design of minimax robust LQG controllers for linear systems with parameter and noise uncertainties is considered in this paper. Necessary and sufficient conditions for converting this problem to a two-person, zero-sum continuous game problem are presented. A simple procedure for design of a suboptimal minimax robust LQG controller, i.e., the LQG controller for least-favourable model, is proposed. Necessary and sufficient conditions for the existence of a saddle point are established. Under these conditions, the controller obtained is exactly the minimax LQG controller. When there does not exist a saddle point, the worst-case error between the controller obtained and the minimax robust LQG controllers under described uncertainties is bounded.