Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

Fopid Controller Design for Robust Performance Using Particle Swarm Optimization

Mathematics Subject Classification: 26A33; 93C15, 93C55, 93B36, 93B35, 93B51; 03B42; 70Q05; 49N05

Novel Formulation and Efficient Solution Strategy for Strategic Optimization of an Industrial Chemical Supply Chain Under Demand Uncertainty

This paper is concerned with strategic optimization of a typical industrial chemical supply chain, which involves a material purchase and transportation network, several manufacturing plants with on-site material and product inventories, a product transportation network and several regional markets. In order to address large uncertainties in customer demands at the different regional markets, a novel robust scenario formulation, which has been developed by the authors recently, is tailored and applied for the strategic optimization. Case study results show that the robust scenario formulation works well for this real industrial supply chain system, and it outperforms the deterministic formulation and the classical scenario-based stochastic programming formulation by generating better expected economic performance and solutions that are guaranteed to be feasible for all uncertainty realizations. The robust scenario problem exhibits a decomposable structure that can be taken advantage of by Benders decomposition for efficient solution, so the application of Benders decomposition to the solution of the strategic optimization is also discussed. The case study results show that Benders decomposition can reduce the solution time by almost an order of magnitude when the number of scenarios in the problem is large.

Optimization of wastepaper sludge ash (WSA) in robust cementitious systems

Abstract : Wastepaper sludge ash (WSA) is generated by a cogeneration station by burning wastepaper sludge. It mainly consists of amorphous aluminosilicate phase, anhydrite, gehlenite, calcite, lime, C2S, C3A, quartz, anorthite, traces of mayenite. Because of its free lime content (~10%), WSA suspension has a high pH (13). Previous researchers have found that the WSA composition has poor robustness and the variations lead to some unsoundness for Portland cement (PC) blended WSA concrete. This thesis focused on the use of WSA in different types of concrete mixes to avoid the deleterious effect of the expansion due to the WSA hydration. As a result, WSA were used in making alkali-activated materials (AAMs) as a precursor source and as a potential activator in consideration of its amorphous content and the high alkaline nature. Moreover, the autogenous shrinkage behavior of PC concrete at low w/b ratio was used in order to compensate the expansion effect due to WSA. The concrete properties as well as the volume change were investigated for the modified WSA blended concrete. The reaction mechanism and microstructure of newly formed binder were evaluated by X-ray diffraction (XRD), calorimetry, thermogravimetric analysis (TGA), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX). When WSA was used as precursor, the results showed incompatible reaction between WSA and alkaline solution. The mixtures were not workable and provided very low compressive strength no matter what kinds of chemical activators were used. This was due to the metallic aluminum in WSA, which releases abundant hydrogen gas when WSA reacts with strong alkaline solution. Besides, the results of this thesis showed that WSA can activate the glassy phase contained in slag, glass powder (GP) and class F fly ash (FFA) with an optimum blended ratio of 50:50. The WSA/slag (mass ratio of 50:50) mortar (w/b of 0.47) attained 46 MPa at 28 days without heat curing assistance. A significant fast setting was noticed for the WSA-activated binder due to the C3A phase, free lime and metallic aluminum contained in the WSA. Adding 5% of gypsum can delay the fast setting, but this greatly increased the potential risk of intern sulfate attack. The XRD, TGA and calorimetry analyses demonstrated the formation of ettringite, C-S-H, portlandite, hydrogarnet and calcium carboaluminate in the hydrated binder. The mechanical performance of different binder was closely related to the microstructure of corresponding binder which was proved by the SEM observation. The hydrated WSA/slag and WSA/FFA binder formed a C-A-S-H type of gel with lower Ca/Si ratio (0.47~1.6). A hybrid gel (i.e. C-N-A-S-H) was observed for the WSA/GP binder with a very low Ca/Si ratio (0.26) and Na/Si ratio (0.03). The SEM/EDX analyses displayed the formation of expansive gel (ettringite and thaumasite) in the gypsum added WSA/slag concrete. The gradual emission of hydrogen gas due to the reaction of WSA with alkaline environment significantly increased the porosity and degraded the microstructure of hydrated matrix after the setting. In the last phase of this research WSA-PC blended binder was tailored to form a high autogenous shrinkage concrete in order to compensate the initial expansion. Different binders were proportioned with PC, WSA, silica fume or slag. The microstructure and mechanical properties of concrete can be improved by decreasing w/b ratios and by incorporating silica fume or slag. The 28-day compressive strength of WSA-blended concrete was above 22 MPa and reached 45 MPa when silica fume was added. The PC concrete incorporating silica fume or slag tended to develop higher autogenous shrinkage at low w/b ratios, and thus the ternary binder with the addition of WSA inhibited the long term shrinkage due to the initial expansion property to WSA. In the restrained shrinkage test, the concrete ring incorporating the ternary binder (PC/WSA/slag) revealed negligible potential to cracking up to 96 days as a result of the offset effect by WSA expansion. The WSA blended regular concrete could be produced for potential applications with reduced expansion, good mechanical property and lower permeability.

Probabilistic design optimization of horizontal axis wind turbine rotors

Considerable interest in renewable energy has increased in recent years due to the concerns raised over the environmental impact of conventional energy sources and their price volatility. In particular, wind power has enjoyed a dramatic global growth in installed capacity over the past few decades. Nowadays, the advancement of wind turbine industry represents a challenge for several engineering areas, including materials science, computer science, aerodynamics, analytical design and analysis methods, testing and monitoring, and power electronics. In particular, the technological improvement of wind turbines is currently tied to the use of advanced design methodologies, allowing the designers to develop new and more efficient design concepts. Integrating mathematical optimization techniques into the multidisciplinary design of wind turbines constitutes a promising way to enhance the profitability of these devices. In the literature, wind turbine design optimization is typically performed deterministically. Deterministic optimizations do not consider any degree of randomness affecting the inputs of the system under consideration, and result, therefore, in an unique set of outputs. However, given the stochastic nature of the wind and the uncertainties associated, for instance, with wind turbine operating conditions or geometric tolerances, deterministically optimized designs may be inefficient. Therefore, one of the ways to further improve the design of modern wind turbines is to take into account the aforementioned sources of uncertainty in the optimization process, achieving robust configurations with minimal performance sensitivity to factors causing variability. The research work presented in this thesis deals with the development of a novel integrated multidisciplinary design framework for the robust aeroservoelastic design optimization of multi-megawatt horizontal axis wind turbine (HAWT) rotors, accounting for the stochastic variability related to the input variables. The design system is based on a multidisciplinary analysis module integrating several simulations tools needed to characterize the aeroservoelastic behavior of wind turbines, and determine their economical performance by means of the levelized cost of energy (LCOE). The reported design framework is portable and modular in that any of its analysis modules can be replaced with counterparts of user-selected fidelity. The presented technology is applied to the design of a 5-MW HAWT rotor to be used at sites of wind power density class from 3 to 7, where the mean wind speed at 50 m above the ground ranges from 6.4 to 11.9 m/s. Assuming the mean wind speed to vary stochastically in such range, the rotor design is optimized by minimizing the mean and standard deviation of the LCOE. Airfoil shapes, spanwise distributions of blade chord and twist, internal structural layup and rotor speed are optimized concurrently, subject to an extensive set of structural and aeroelastic constraints. The effectiveness of the multidisciplinary and robust design framework is demonstrated by showing that the probabilistically designed turbine achieves more favorable probabilistic performance than those of the initial baseline turbine and a turbine designed deterministically.

Robust solutions of bi-blend recipe optimization with quadratic constraints

Production companies use raw materials to compose end-products. They often make different products with the same raw materials. In this research, the focus lies on the production of two end-products consisting of (partly) the same raw materials as cheap as possible. Each of the products has its own demand and quality requirements consisting of quadratic constraints. The minimization of the costs, given the quadratic constraints is a global optimization problem, which can be difficult because of possible local optima. Therefore, the multi modal character of the (bi-) blend problem is investigated. Standard optimization packages (solvers) in Matlab and GAMS were tested on their ability to solve the problem. In total 20 test cases were generated and taken from literature to test solvers on their effectiveness and efficiency to solve the problem. The research also gives insight in adjusting the quadratic constraints of the problem in order to make a robust problem formulation of the bi-blend problem.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.

New Approach on Robust Delay-Dependent H∞ Control for Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay

This paper investigates the robust H∞ control for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

Delay distribution based robust H∞ control of networked control systems with uncertainties

Network induced delay in networked control systems (NCS) is inherently non-uniformly distributed and behaves with multifractal nature. However, such network characteristics have not been well considered in NCS analysis and synthesis. Making use of the information of the statistical distribution of NCS network induced delay, a delay distribution based stochastic model is adopted to link Quality-of-Control and network Quality-of-Service for NCS with uncertainties. From this model together with a tighter bounding technology for cross terms, H∞ NCS analysis is carried out with significantly improved stability results. Furthermore, a memoryless H∞ controller is designed to stabilize the NCS and to achieve the prescribed disturbance attenuation level. Numerical examples are given to demonstrate the effectiveness of the proposed method.

The effect of dialect mismatch on likelihood-maximising speech enhancement for noise-robust speech recognition

Traditional speech enhancement methods optimise signal-level criteria such as signal-to-noise ratio, but these approaches are sub-optimal for noise-robust speech recognition. Likelihood-maximising (LIMA) frameworks are an alternative that optimise parameters of enhancement algorithms based on state sequences generated for utterances with known transcriptions. Previous reports of LIMA frameworks have shown significant promise for improving speech recognition accuracies under additive background noise for a range of speech enhancement techniques. In this paper we discuss the drawbacks of the LIMA approach when multiple layers of acoustic mismatch are present – namely background noise and speaker accent. Experimentation using LIMA-based Mel-filterbank noise subtraction on American and Australian English in-car speech databases supports this discussion, demonstrating that inferior speech recognition performance occurs when a second layer of mismatch is seen during evaluation.

The application of phonetic distribution normalisation to likelihood-maximising speech enhancement for robust ASR

Traditional speech enhancement methods optimise signal-level criteria such as signal-to-noise ratio, but such approaches are sub-optimal for noise-robust speech recognition. Likelihood-maximising (LIMA) frameworks on the other hand, optimise the parameters of speech enhancement algorithms based on state sequences generated by a speech recogniser for utterances of known transcriptions. Previous applications of LIMA frameworks have generated a set of global enhancement parameters for all model states without taking in account the distribution of model occurrence, making optimisation susceptible to favouring frequently occurring models, in particular silence. In this paper, we demonstrate the existence of highly disproportionate phonetic distributions on two corpora with distinct speech tasks, and propose to normalise the influence of each phone based on a priori occurrence probabilities. Likelihood analysis and speech recognition experiments verify this approach for improving ASR performance in noisy environments.

Robust multidisciplinary design optimisation using CFD and advanced evolutionary algorithms

Computation Fluid Dynamics (CFD) has become an important tool in optimization and has seen successful in many real world applications. Most important among these is in the optimisation of aerodynamic surfaces which has become Multi-Objective (MO) and Multidisciplinary (MDO) in nature. Most of these have been carried out for a given set of input parameters such as free stream Mach number and angle of attack. One cannot ignore the fact that in aerospace engineering one frequently deals with situations where the design input parameters and flight/flow conditions have some amount of uncertainty attached to them. When the optimisation is carried out for fixed values of design variables and parameters however, one arrives at an optimised solution that results in good performance at design condition but poor drag or lift to drag ratio at slightly off-design conditions. The challenge is still to develop a robust design that accounts for uncertainty in the design in aerospace applications. In this paper this issue is taken up and an attempt is made to prevent the fluctuation of objective performance by using robust design technique or Uncertainty.

Shock control bump design optimization on Natural Laminar Aerofoil

The chapter investigates Shock Control Bumps (SCB) on a Natural Laminar Flow (NLF) aerofoil; RAE 5243 for Active Flow Control (AFC). A SCB approach is used to decelerate supersonic flow on the suction/pressure sides of transonic aerofoil that leads delaying shock occurrence or weakening of shock strength. Such an AFC technique reduces significantly the total drag at transonic speeds. This chapter considers the SCB shape design optimisation at two boundary layer transition positions (0 and 45%) using an Euler software coupled with viscous boundary layer effects and robust Evolutionary Algorithms (EAs). The optimisation method is based on a canonical Evolution Strategy (ES) algorithm and incorporates the concepts of hierarchical topology and parallel asynchronous evaluation of candidate solution. Two test cases are considered with numerical experiments; the first test deals with a transition point occurring at the leading edge and the transition point is fixed at 45% of wing chord in the second test. Numerical results are presented and it is demonstrated that an optimal SCB design can be found to significantly reduce transonic wave drag and improves lift on drag (L/D) value when compared to the baseline aerofoil design.

Optimization problems for controlled mechanical systems : bridging the gap between theory and application

Mechanical control systems have become a part of our everyday life. Systems such as automobiles, robot manipulators, mobile robots, satellites, buildings with active vibration controllers and air conditioning systems, make life easier and safer, as well as help us explore the world we live in and exploit it’s available resources. In this chapter, we examine a specific example of a mechanical control system; the Autonomous Underwater Vehicle (AUV). Our contribution to the advancement of AUV research is in the area of guidance and control. We present innovative techniques to design and implement control strategies that consider the optimization of time and/or energy consumption. Recent advances in robotics, control theory, portable energy sources and automation increase our ability to create more intelligent robots, and allows us to conduct more explorations by use of autonomous vehicles. This facilitates access to higher risk areas, longer time underwater, and more efficient exploration as compared to human occupied vehicles. The use of underwater vehicles is expanding in every area of ocean science. Such vehicles are used by oceanographers, archaeologists, geologists, ocean engineers, and many others. These vehicles are designed to be agile, versatile and robust, and thus, their usage has gone from novelty to necessity for any ocean expedition.