Operating regime based dynamic engine modelling

In this paper the nonlinear model identification of combustion engines using operating regime model structures is discussed. The split of the engine process into several local operating regimes, characterised by the dominant influence of load and speed, allows one to overcome the highly nonlinear dynamic complexity of the engine. Additionally, local limits in terms of engine protection and combustion stability can be considered much easier. Such a model, with physical a priori information embedded in the model structure, provides excellent generalisation capability and a real-time application of the model is easily possible.     

Active fault detection and control: Unified formulation and optimal design

A new unified formulation of the active fault detection and control problem for discrete-time stochastic systems and its optimal solution are proposed. The problem formulation stems from the optimal stochastic control problem and includes important special cases: an active detector and controller, an active detector and input signal generator, and an active detector with a given input signal generator. The optimal solution is derived using the so-called closed loop information processing strategy. This strategy respects the influence of the current decision and/or input on the future behavior of the observed system, allows penalizing future wrong decisions, and improves the quality of fault detection. The proposed formulation and obtained solution also provide better understanding of the active fault detection and its relation to the optimal stochastic control. The results are illustrated in numerical examples.     

Getting the most out of it: Optimal experiments for parameter estimation of microalgae growth models

Mathematical models are expected to play a pivotal role for driving microalgal production towards a profitable process of renewable energy generation. To render models of microalgae growth useful tools for prediction and process optimization, reliable parameters need to be provided. This reliability implies a careful design of experiments that can be exploited for parameter estimation. In this paper, we provide guidelines for the design of experiments with high informative content based on optimal experiment techniques to attain an accurate parameter estimation. We study a real experimental device devoted to evaluate the effect of temperature and light on microalgae growth. On the basis of a mathematical model of the experimental system, the optimal experiment design problem was formulated and solved with both static (constant light and temperature) and dynamic (time varying light and temperature) approaches. Simulation results indicated that the optimal experiment design allows for a more accurate parameter estimation than that provided by the existing experimental protocol. For its efficacy in terms of the maximum likelihood properties and its practical aspects of implementation, the dynamic approach is recommended over the static approach.     

Approximate robust dynamic programming and robustly stable MPC

We present a technique for approximate robust dynamic programming that is suitable for linearly constrained polytopic systems with piecewise affine cost functions. The approximation method uses polyhedral representations of the cost-to-go function and feasible set, and can considerably reduce the computational burden compared to recently proposed methods for exact robust dynamic programming [Bemporad, A., Borrelli, F., & Morari, M. (2003). Min-max control of constrained uncertain discrete-time linear systems. IEEE Transactions on Automatic Control, 48(9), 1600-1606; Diehl, M., & Björnberg, J. (2004). Robust dynamic programming for min-max model predictive control of constrained uncertain systems. IEEE Transactions on Automatic Control, 49(12), 2253-2257]. We show how to apply the method to robust MPC, and give conditions that guarantee closed-loop stability. We finish by applying the method to a state constrained tutorial example, a parking car with uncertain mass.     

Robust optimal experiment design for system identification

This paper develops the idea of min-max robust experiment design for dynamic system identification. The idea of min-max experiment design has been explored in the statistics literature. However, the technique is virtually unknown by the engineering community and, accordingly, there has been little prior work on examining its properties when applied to dynamic system identification. This paper initiates an exploration of these ideas. The paper considers linear systems with energy (or power) bounded inputs. We assume that the parameters lie in a given compact set and optimise the worst case over this set. We also provide a detailed analysis of the solution for an illustrative one parameter example and propose a convex optimisation algorithm that can be applied more generally to a discretised approximation to the design problem. We also examine the role played by different design criteria and present a simulation example illustrating the merits of the proposed approach.     

Open-loop and closed-loop robust optimal control of batch processes using distributional and worst-case analysis

The recognition that optimal control trajectories for batch processes can be highly sensitive to model uncertainties has motivated the development of methods for explicitly addressing robustness during batch processes. This study explores the incorporation of robust performance analysis into open-loop and closed-loop optimal control design. Several types of robust performance objectives are investigated that incorporate worst-case or distributional robustness metrics for improving the robustness of batch control laws, where the distributional approach computes the distribution of the performance index caused by parameter uncertainty. The techniques are demonstrated on a batch crystallization process. A comprehensive comparison of the robust performance of the open-loop and closed-loop system is provided.     

A computational method for solving optimal control and parameter estimation of linear systems using Haar wavelets

In this article, a computational method based on Haar wavelet in time-domain for solving the problem of optimal control of the linear time invariant systems for any finite time interval is proposed. Haar wavelet integral operational matrix and the properties of Kronecker product are utilized to find the approximated optimal trajectory and optimal control law of the linear systems with respect to a quadratic cost function by solving only the linear algebraic equations. It is shown that parameter estimation of linear system can be done easily using the idea proposed. On the basis of Haar function properties, the results of the article, which include the time information, are illustrated in two examples.     

Optimal non-homogeneous composites for dynamic loading

An algorithm is proposed to optimize the performance of a two-phase composite under dynamic loading. The goal is to determine a series of different layouts of the two base materials in a three-dimensional region such that the time-averaged stress energy is minimized. Four cases with different boundary conditions and ratios of mass density are considered and solved numerically. The resulting optimal designs are compared to the static case to illustrate the effect of the dynamic loading. Furthermore, a qualitative comparison is done to indicate the difference between the optimization of eigenfrequencies and the present formulation.     

An efficient framework for optimal robust stochastic system design using stochastic simulation

The knowledge about a planned system in engineering design applications is never complete. Often, a probabilistic quantification of the uncertainty arising from this missing information is warranted in order to efficiently incorporate our partial knowledge about the system and its environment into their respective models. This leads to a robust stochastic design framework where probabilistic models of excitation uncertainties and system modeling uncertainties can be introduced; the design objective is then typically related to the expected value of a system performance measure, such as reliability or expected life-cycle cost. For complex system models, this expected value can rarely be evaluated analytically and so it is often calculated using stochastic simulation techniques, which involve an estimation error and significant computational cost. An efficient framework, consisting of two stages, is presented here for the optimization in such robust stochastic design problems. The first stage implements a novel approach, called stochastic subset optimization (SSO), for iteratively identifying a subset of the original design space that has high plausibility of containing the optimal design variables. The second stage adopts some other stochastic optimization algorithm to pinpoint the optimal design variables within that subset. The focus is primarily on the theory and implementation issues for SSO but also on topics related to the combination of the two different stages for overall enhanced efficiency. An illustrative example is presented that shows the efficiency of the proposed methodology; it considers the optimization of the reliability of a base-isolated structure considering future near-fault ground motions.     

Identification of a rice drying model with an improved sequential optimal design of experiments

Getting relevant parameter estimation of a non-linear model is often a hard task from both an experimental and numerical point of view. The objective of optimally designed experiments procedure is to diminish the experimental effort needed such that the identification is within acceptable confidence ranges. After each experiment, the next experiment is optimally designed, taking into account all past experimental results. It allows quality information to be extracted from the experimental data with less experimental time and resource consumption.In this paper, we present an original approach and implementation of the classical A-, D- and E-optimality on the estimation of 5 unknown (transfer related) coefficients in a compartmental model used to describe the convective drying of rice. The originality of our method is that it uses reparameterization of both parameter and protocol vectors which permits to avoid using a global optimization algorithm. The presented method is implemented in Matlab as a Toolbox and fully tested on a pilot plant. The case study (drying of rice) is typical in the field of process engineering: the dynamic model is strongly non-linear in its parameters and cannot be analytically solved. In addition, the specific technical constrains (inertias, limits, etc.) on the pilot are explicitly taken into account for improved experimental feasibility.In this drying application, three experiments with non-constant drying conditions are shown to be quite as effective as a two-factor three-level grid of nine experiments at constant conditions, with only one third of the experimental effort.     

An approach to the selection of optimal sensor locations in distributed parameter systems

This paper presents an approach to the selection of optimal sensor locations in distributed parameter systems, which distinguishes the purposes of state estimation from the purposes of parameter estimation. In the first case, the optimality criterion is based on a measure of independence between the sensor responses, while in the second case, it is based on a measure of independence between the parameter sensitivity functions. The procedure, which is general and can be applied to models with any degree of complexity, is illustrated with the optimal placement of temperature sensors in a catalytic fixed-bed reactor. Some numerical results for the on-line estimation of temperature and concentration profiles as well as for the estimation of unknown model parameters are discussed.     

Analytical robustness assessment for robust design

Robust design ensures product performances to be insensitive to various uncertainties and therefore results in high quality and productivity. Robustness assessment, which evaluates the variability of performances, is an important and indispensable component of robust design. An accurate and efficient robustness assessment is essential for obtaining a real robust solution. The aim of this paper is to investigate features of model-based methods for robustness assessment in terms of accuracy, efficiency, and reliability. Recommendations on the use of those methods are provided based on the comparison study through example problems.     

Optimization of a thin film deposition process using a dynamic model extracted from molecular simulations

This study presents and demonstrates an algorithm for computing a dynamic model for a thin film deposition process. The proposed algorithm is used on high dimensional Kinetic Monte Carlo (KMC) simulations and consists of applying principal component analysis (PCA) for reducing the state dimension, a self organizing map (SOM) for grouping similar surface configurations and simple cell mapping (SCM) for identifying the transitions between different surface configuration groups. The error associated with this model reduction approach is characterized by running more than 1000 test simulations with highly dynamic and random input profiles. The global error, which is the normalized Euclidean distance between the simulated and predicted states, is found to be less than 1% on average relative to the test simulation results. This indicates that our reduced order dynamic model, which was developed using a rather small simulation set, was able to accurately predict the evolution of the film microstructure for much larger simulation sets and a wide range of process conditions. Minimization of the deposition time to reach a desired film structure has also been achieved using this model. Hence, our study showed that the proposed algorithm is useful for extracting dynamic models from high dimensional and noisy molecular simulation data.     

Robust maximum-likelihood estimation of multivariable dynamic systems

This paper examines the problem of estimating linear time-invariant state-space system models. In particular, it addresses the parametrization and numerical robustness concerns that arise in the multivariable case. These difficulties are well recognised in the literature, resulting (for example) in extensive study of subspace-based techniques, as well as recent interest in ‘data driven’ local co-ordinate approaches to gradient search solutions. The paper here proposes a different strategy that employs the expectation-maximisation (EM) technique. The consequence is an algorithm that is iterative, with associated likelihood values that are locally convergent to stationary points of the (Gaussian) likelihood function. Furthermore, theoretical and empirical evidence presented here establishes additional attractive properties such as numerical robustness, avoidance of difficult parametrization choices, the ability to naturally and easily estimate non-zero initial conditions, and moderate computational cost. Moreover, since the methods here are maximum-likelihood based, they have associated known and asymptotically optimal statistical properties.     

Towards IoT-enabled dynamic service optimal selection in multiple manufacturing clouds

With the Internet of Things, it is now possible to sense the real-time status of manufacturing objects and processes. For complex Service Selection (SS) in Cloud Manufacturing, real-time information can be utilized to deal with uncertainties emerging during task execution. Moreover, in the face of diversified demands, multiple manufacturing clouds (MCs) can provide a much wider range of choices of services with their real-time status. However, most researchers have neglected the superiority of multiple MCs and failed to make a study of how to utilize the abundant and diverse resources of multiple MCs, let alone the multi-MCs service mode under dynamic environment. Therefore, we first propose a new dynamic SS paradigm that can leverage the abundant services from multiple MCs, real-time sensing ability of the Internet of Things (IoT) and big data analytics technology for knowledge and insights. In this way, providing optimal manufacturing services (with high QoS) for customers can be guaranteed under dynamic environments. In addition, considering that a relatively long time might be spent to complete a complex manufacturing task after SS, a quantified approach, based on the Analytic Hierarchy Process and big data, is proposed to evaluate whether the intended cloud manufacturing services should be reserved to make sure that eligible services are ready to use without compromising cost or time. In this paper, the problem of IoT-enabled dynamic SS across multiple MCs is formulated in detail to enable an event-driven adaptive scheduling when the model is faced with three kinds of uncertainties (of the service market, service execution and the user side respectively). Experiments with different settings are also performed, which show the advantages of our proposed paradigm and optimization model.     

A formula for the optimal cost in the general discrete-time LEQG problem

This paper is aimed at deriving an explicit formula for the optimal cost for discrete-time linear exponential-of-quadratic Gaussian (LEQG) control problems. We make direct calculations for the general case with cross terms in the cost and noise covariance matrices using an information-state approach.     

序贯实验设计方法在变换反应动力学方程模型参数估值研究中的应用

根据序贯实验设计原理,提出用于 B_(110-2)催化剂的动力学模型参数估值程序,并提出B_(110-2)催化剂的中温变换反应本征动力学方程。     

On asymptotic behaviors of a sensitivity penalization based robust state estimator

Asymptotic properties are investigated in this paper for the robust state estimator derived by Zhou (2008) [11]. A new formula is derived for the update of the pseudo-covariance matrix of estimation errors. In the case where plant nominal parameters are time invariant, it is shown that, in order to guarantee that this pseudo-covariance matrix converges to a constant positive definite matrix, it is necessary and sufficient that some stabilizability and detectability conditions are satisfied. It is also proved that when these conditions are satisfied, the robust estimator converges to a stable time-invariant system. Moreover, when the system is exponentially stable, this estimate is asymptotically unbiased and its estimation errors are upper bounded.     

Optimal input design for parameter estimation in a single and double tank system through direct control of parametric output sensitivities

In this paper the traditional and well-known problem of optimal input design for parameter estimation is considered. In particular, the focus is on input design for the estimation of the flow exponent present in Bernoulli's law. The theory will be applied to a water tank system with a controlled inflow and free outflow. The problem is formulated as follows: Given the model structure (f, g), which is assumed to be affine in the input, and the specific parameter of interest (θ), find a feedback law that maximizes the sensitivity of the model output to the parameter under different flow conditions in the water tank. The input design problem is solved analytically. The solution to this problem is used to estimate the parameter of interest with a minimal variance. Real-world experimental results are presented and compared with theoretical solutions.     

Identification and application of nonlinear dynamic load models

An alternating least squares approach is developed in this paper to identify the exponential recovery dynamic load model of wide-area power systems. The nonlinear optimization problem is decomposed to two linear least squares problems, and solved in an alternating way. Then, a new algorithm for numerical derivative calculation using discrete Fourier transform is proposed to attenuate the effect of noises in the process of parameter estimation. Based on the estimated dynamic load characteristics, the application on voltage stability is analyzed. Finally, numerical and laboratory examples are conducted to demonstrate the effectiveness of the proposed methods.