Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences

Frontmatter

Chapter 1. A Bi-Level Optimization Approach to Define Dynamic Tariffs with Variable Prices and Periods in the Electricity Retail Market

Abstract

Dynamic time-differentiated pricing structures are expected to become a common practice in smart grids, bringing benefits for all stakeholders involved: grid operators, retailers and consumers. The optimization of dynamic time-of-use (ToU) tariffs by a retailer considering the consumers’ response can be modeled through bi-level (BL) programming. The retailer first defines the prices for each period and the consumer then reacts by rescheduling the operation of appliances, in face of prices and comfort requirements. In this paper, we present two BL models to define dynamic tariffs, in which the goal is to determine both the price values and the periods in which they hold by considering: (i) variable periods with a maximum number of different prices and (ii) total freedom to define the periods and the corresponding prices. Both models are highly difficult to solve, mainly due to the size of the search space of the upper level (UL) problem, in which the combinations of prices and periods are determined. We describe the development of hybrid approaches considering a population metaheuristic for the UL problem and a mixed-integer linear programming (MILP) solver to address the lower level (LL) problem, in which the optimal appliance scheduling for the pricing structure is computed. The exploration of the UL search space is crucial to obtain good solutions within an acceptable computational effort.

Inês Soares, Maria João Alves, Carlos Henggeler Antunes

Chapter 2. An Evolutionary Algorithm for a Bilevel Biobjective Location-Routing-Allocation Problem

Abstract

In the distribution of goods to final customers, interrelated decisions have to be made, such as the location of the collection points for the goods, the routes served from the central warehouse and the allocation of customers to the collection points. The problem becomes even more complex when several decision makers are involved and multiple objectives should be taken into consideration. This paper addresses a vehicle routing problem in which customers are allowed to select the location in which they want to receive their goods among those made available by the distribution company. The aim of this company is to minimize the total cost of serving the routes as well as to satisfy customers. A bilevel biobjective problem with multiple followers is proposed to model this hierarchical supply chain. The upper level decision maker is the distribution company which decides on the locations made available and the routes which are used to serve these locations. Each customer plays the role of a follower and decides where to collect his/her goods. An evolutionary algorithm involving the solution of several optimization problems is developed for approaching the Pareto front, whose performance is assessed in a computational experiment.

Herminia I. Calvete, Carmen Galé, José A. Iranzo

Chapter 3. Incorporation of Region of Interest in a Decomposition-Based Multi-objective Evolutionary Algorithm

Abstract

Preference-based Multi-Objective Evolutionary Algorithm (MOEA) restrict the search to a given region of the Pareto front preferred by the Decision Maker (DM), called the Region of Interest (ROI). In this paper, a new preference-guided MOEA is proposed. In this method, we define the ROI as a preference cone in the objective space. The preferential direction and the aperture of the cone are parameters that the DM has to provide to define the ROI. Given the preference cone, we employ a weight vector generation method that is based on a steady-state evolutionary algorithm. The main idea of our method is to evolve a population of weight vectors towards the characteristics that are desirable for a set of weight vectors in a decomposition-based MOEA framework. The main advantage is that the DM can define the number of weight vectors and thus can control the population size. Once the ROI is defined and the set of weight vectors are generated within the preference cone, we start a decomposition-based MOEA using the provided set of weights in its initialization. Therefore, this enforces the algorithm to converge to the ROI. The results show the benefit and adequacy of the preference cone MOEA/D for preference-guided many-objective optimization.

Ivan Reinaldo Meneghini, Frederico Gadelha Guimarães, António Gaspar-Cunha, Miri Weiss Cohen

Chapter 4. Solving Multiobjective Engineering Design Problems Through a Scalarized Augmented Lagrangian Algorithm (SCAL)

Abstract

In this paper, a set of multiobjective engineering design problems is solved using a methodology that combines an Augmented Lagrangian technique to deal with the constraints and the Augmented Weighted Tchebycheff method to tackle the multiobjective nature of the problems to find the Pareto frontier. In order to compare and validate the performance of this strategy, the problems were also solved with gamultiobj from MATLAB™. We present the algorithm, as well as some results that seem very promising.

Lino Costa, Isabel Espírito Santo, Pedro Oliveira

Chapter 5. Many-Objective Multidisciplinary Evolutionary Design for Hybrid-Wing-Body-Type Flyback Booster on an Entirely Automated System

Abstract

The study aims to create pragmatic geometries of flyback booster on reusable launch systems with a high degree of freedom efficiently by evolutionary computations and to present its design candidates based on physics. This article performed a second optimal design that we sophisticated the first trial on many-objective multidisciplinary evolutionary design. The result has revealed that the surface discontinuity of the body back evaded in the hypersonic range could be beneficial for improving the lift-drag ratio in the transonic range. We hypothesized that deliberately dug grooves must be adequate to accomplish flyback boosters generally requires aerodynamic performance in the low-speed range.

Taiki Hatta, Masataka Sawahara, Kazuhisa Chiba

Chapter 6. A Neuroevolutionary Approach to Feature Selection Using Multiobjective Evolutionary Algorithms

Abstract

Feature selection plays a central role in predictive analysis where datasets have hundreds or thousands of variables available. It can also reduce the overall training time and the computational costs of the classifiers used. However, feature selection methods can be computationally intensive or dependent of human expertise to analyze data. This study proposes a neuroevolutionary approach which uses multiobjective evolutionary algorithms to optimize neural network parameters in order to find the best network able to identify the most important variables of analyzed data. Classification is done through a Support Vector Machine (SVM) classifier where specific parameters are also optimized. The method is applied to datasets with different number of features and classes.

Renê S. Pinto, M. Fernanda P. Costa, Lino A. Costa, António Gaspar-Cunha

Chapter 7. Multi-objective Optimization in the Build Orientation of a 3D CAD Model

Abstract

Over the years, rapid prototyping technologies have grown and have been implemented in many 3D model production companies. A variety of different additive manufacturing (AM) techniques are used in rapid prototyping. AM refers to a process by which digital 3D design data is used to build up a component in layers by depositing material. Several high-quality parts are being created in various engineering materials, including metal, ceramics, polymers and their combinations in the form of composites, hybrids, or functionally classified materials. The orientation of 3D models is very important since it can have a great influence on the surface quality characteristics, such as process planning, post-processing, processing time and cost. Thus, the identification of the optimal build orientation for a part is one of the main issues in AM. The quality measures to optimize the build orientation problem may include the minimization of the surface roughness, build time, need of supports, maximize of the part stability in building process or part accuracy, among others. In this paper, a multi-objective approach was applied to a computer-aided design model using MATLAB^® multi-objective genetic algorithm, aiming to optimize the support area, the staircase effect and the build time. Preliminary results show the effectiveness of the proposed approach.

Marina A. Matos, Ana Maria A. C. Rocha, Lino A. Costa, Ana I. Pereira

Chapter 8. The Effects of Crowding Distance and Mutation in Multimodal and Multi-objective Optimization Problems

Abstract

In this paper, we study the effects of a modified crowding distance method and a Polynomial mutation operator on multimodal multi-objective optimization algorithms. Our goal is to provide an in-depth analysis on these two modifications which we apply to NSGA-II: The weighted sum crowding distance and the neighborhood-based mutation operator. Furthermore, we examine the performance of the proposed weighted sum crowding distance method under different weight values to find a trend for the behaviour of the proposed algorithm. We compare the different variations of the proposed method with state-of-the-art algorithms and the baseline NSGA-II. The results show that our modifications can improve the functionality of NSGA-II on multimodal multi-objective problems.

Mahrokh Javadi, Heiner Zille, Sanaz Mostaghim

Chapter 9. Combining Manhattan and Crowding Distances in Decision Space for Multimodal Multi-objective Optimization Problems

Abstract

This paper presents a new variant of the Non-dominated Sorting Genetic Algorithm to solve Multimodal Multi-objective optimization problems. We introduce a novel method to augment the diversity of solutions in decision space by combining the Manhattan and crowding distance. In our experiments, we use six test problems with different levels of complexity to examine the performance of our proposed algorithm. The results are compared with NSGA-II and NSGA-II-WSCD algorithms. Using IGDX and IGD performance indicators, we demonstrate the superiority of our proposed method over the rest of competitors to provide a better approximation of the Pareto Set (PS) while not getting much worse results in objective space.

Mahrokh Javadi, Cristian Ramirez-Atencia, Sanaz Mostaghim

Chapter 10. An Unsteady Aerodynamic/Aeroacoustic Optimization Framework Using Continuous Adjoint

Abstract

In this paper, an unsteady aerodynamic/aeroacoustic optimization framework is presented. This is based on the continuous adjoint method to a hybrid acoustic prediction tool, in which the near-field flow solution results from an unsteady CFD simulation while the acoustic propagation to far-field makes use of an acoustic analogy. The CFD simulation is performed using the in-house GPU-enabled URANS equations’ solver for which a continuous adjoint solver is available. The noise prediction tool and its adjoint are developed based on the permeable version of the Ffowcs Williams and Hawkings (FW-H) analogy, solved in the frequency domain. Its implementation is verified w.r.t. the analytical solution of the sound field from a monopole source in uniform flow. Then, the accuracy of the hybrid solver is verified by comparing the sound directivity computed by the FW-H analogy with that of a CFD run, for a 2D pitching airfoil in a subsonic inviscid flow. The accuracy of the sensitivities computed using the unsteady adjoint solver is verified w.r.t. those computed by finite differences. Finally, the programmed software is used to optimize the shape of the pitching airfoil, aiming at min. noise with an equality constraint for the lift.

M. Monfaredi, X. S. Trompoukis, K. T. Tsiakas, K. C. Giannakoglou

Chapter 11. Discrete Adjoint Approaches for CHT Applications in OpenFOAM

Abstract

Conjugate Heat Transfer (CHT) simulations allow the prediction of complex interactions between fluid and solid mediums. Our application is the optimization of heat transfer between heat sinks and a cooling fluid, used to extract the heat from server infrastructure. Adjoint methods allow the optimization of high dimensional parameter settings, using sensitivity information. Compared to classical approaches to sensitivity generation, e.g. finite differences, a significant improvement in run time can be achieved, as the complexity of deriving the sensitivity scales with the output dimension, instead of the input (parameter) dimension. As an initial prove of concept, our discrete adjoint OpenFOAM framework has been extended to facilitate the differentiation of the chtMultiRegionSimpleFoam solver. To combat prohibitive memory loads a traditional and a novel checkpointing approach are used. We will present results of the heat transfer of a copper heat sink immersed in water.

Markus Towara, Johannes Lotz, Uwe Naumann

Chapter 12. Robustness Measures for Multi-objective Robust Design

Abstract

A significant step to engineering design is to take into account uncertainties and to develop optimal designs that are robust with respect to perturbations. Furthermore, when multiple optimization objectives are involved it is important to define suitable descriptions for robustness. We introduce robustness measures for robust design with multiple objectives that are suitable for considering the effect of uncertainties in objective space. A direct formulation and a two-phase formulation based on expected losses in objective space are presented for finding robust optimal solutions. We apply both formulations to the robust design of an airfoil. Fluid mechanical quantities are optimized under the consideration of aleatory uncertainties. The uncertainties are propagated with the help of the non-intrusive polynomial chaos approach. The resulting multi-objective optimization problem is solved with a constraint-based approach, that combines adjoint-based optimization methods and evolutionary methods evaluated on surrogate models.

Lisa Kusch, Nicolas R. Gauger

Chapter 13. Uncertainty Assessment of an Optimized ERCOFTAC Pump

Abstract

Centrifugal pumps, being used nowadays for many applications, must be suited for a wide range of pressure ratios and flow rates. To overcome difficulties arising from the design and performance prediction of this class of turbomachinery, many researchers proposed the coupling of CFD codes and optimization algorithms for a fast and effective design procedure. However, uncertainties are present in most engineering applications such as turbomachines, and their influence on turbomachinery performance should be considered. In this work we apply some advanced optimization techniques to the blade optimization of an ERCOFTAC-like pump, and we assess the robustness of the optimal profiles through an uncertainty propagation study. The main sources of uncertainty are related to the operating conditions, primarily the rotational speed of the pump shaft that affects also the flow rate.

R. De Donno, A. Fracassi, A. Ghidoni, P. M. Congedo

Chapter 14. Gradient-Based Aerodynamic Robust Optimization Using the Adjoint Method and Gaussian Processes

Abstract

The use of robust design in aerodynamic shape optimization is increasing in popularity in order to come up with configurations less sensitive to operational conditions. However, the addition of uncertainties increases the computational cost as both design and stochastic spaces must be explored. The objective of this work is the development of an efficient framework for gradient-based robust design by using an adjoint formulation and a non-intrusive surrogate-based uncertainty quantification method. At each optimization iteration, the statistic of both the quantity of interest and its gradients are efficiently obtained through Gaussian Processes models. The framework is applied to the aerodynamic shape optimization of a 2D airfoil. With the presented approach it is possible to reduce both the mean and standard deviation of the drag compared to the deterministic optimum configuration. The robust solution is obtained at a reduced run time that is independent of the number of design parameters.

Christian Sabater, Stefan Görtz

Chapter 15. A Multi Layer Evidence Network Model for the Design Process of Space Systems Under Epistemic Uncertainty

Abstract

The purpose of this paper is to introduce a new method for the design process of complex systems affected by epistemic uncertainty. In particular, a multi-layer network is proposed to model the whole design process and describe the transition between adjacent phases. Each layer represents a design phase with a particular detail definition, each node a subsystem and each link a sharing of information. The network is used to quantify and propagate uncertainty through the different layers (design phases) where, proceeding from phase A to phase F, the detail of the mathematical model is increased. Thus, it can be considered as a multi-fidelity approach for the design of a complex system affected by epistemic uncertainty. The framework of Dempster-Shafer Theory of Evidence (DST) is used to model epistemic uncertainty. The model is then called Multi-Layer Evidence Network Model (ML-ENM).

Gianluca Filippi, Massimiliano Vasile

Chapter 16. Solving Multi-objective Optimal Design and Maintenance for Systems Based on Calendar Times Using NSGA-II

Abstract

Due to technical progress and business competition, design alternatives and maintenance strategies have to be contemplated to optimize the performance of physical assets when new facilities are projected and built. That combined optimization (Design & Maintenance) is required by all industrial installations to develop their activity in an increasingly competitive environment. The Design and Maintenance combined optimization process is a complex problem which requires research and development. The objectives to optimize are Unavailability (due to production losses) and Maintenance Cost (due to overcharge when it is not optimal). The Design and Maintenance strategy for a technical system are optimized jointly by modifying its Functionability Profile, which is closely related to the system’s availability. The Functionability Profile is generated by applying Monte Carlo Simulation that allows characterizing the process’ randomness until the failure and to modify that Functionability Profile by the optimal Maintenance strategy. An application case is presented, where several configurations of the elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) are used to optimize the multi-objective problem, successfully finding non-dominated solutions with optimum performance for the simultaneous Design and Maintenance strategy combination.

Andrés Cacereño, Blas Galván, David Greiner

Chapter 17. Assessment of Exergy Analysis of CFD Simulations for the Evaluation of Aero-Thermo-Propulsive Performance of Aerial Vehicles

Abstract

The purpose of this paper is to present an exergetic approach which provides a good complement to classical drag computation in order to assess aerodynamical performances. Unlike drag methods and, on a more general level, unlike any force-based analysis, no distinction between drag and thrust is required. Thus the exergy approach can be applied to a great variety of novel configurations for which the propulsion system is highly integrated within the airframe such as configurations with boundary layer ingestion for example. It also provides information about thermal effects which can not be extracted from drag computation. This paper aims at giving an insight into the exergetic approach and analysing its sensibilities to numerical parameters such as CFD computation convergence and mesh refinement, an assessment which is important as a basis for the improvement of the method’s accuracy.

Christelle Wervaecke, Ilias Petropoulos, Didier Bailly

Chapter 18. Surrogate-Based Shape Optimization of Centrifugal Pumps for Automotive Engine Cooling Systems

Abstract

This paper investigates the capability of a surrogate-based optimization technique for the fast and robust design of centrifugal pumps. The centrifugal pump considered in this work is designed for automotive cooling system and consists of an impeller and a volute. A fully three-dimensional geometry parametrization based on Bézier surfaces for the impeller and the volute is presented. The optimization strategy is based only on open-source software (with the exception of the mesh generation process), i.e. Scilab for the geometric parametrization, OpenFOAM for the CFD simulations and DAKOTA for the optimization. To assess the potential and robustness of the proposed methodology, the initial geometry was chosen very far from the optimum design, having an impeller with straight blades. The operating conditions have been provided by the Italian company Industrie Saleri Italo S.p.A. and are typical of a Diesel engine.

R. De Donno, A. Fracassi , G. Noventa, A. Ghidoni, S. Rebay

Chapter 19. Towards an Open-Source Framework for Aero-Structural Design and Optimization Within the SU2 Suite

Abstract

Ongoing efforts to develop a fully open-source framework for the aero-structural design and optimization of wings, including aerodynamic and structural geometric nonlinearities, are presented. The framework is self-contained and relies on the well-established SU2 suite for the computation of the aerodynamic part of the problem. SU2 is a python-wrapped C++ suite for multiphysics problems, able to compute accurate adjoint sensitivities by means of Algorithmic Differentiation techniques. For the structural problem, a C++ library featuring a nonlinear FE beam is employed. The library is fully wrapped in python and coupled to SU2 by means of a python orchestrator and a splining module for force and displacement transferring. The applicability of this approach is demonstrated using a known aeroelastic test case based on the ONERA M6 wing geometry. The structural solver is differentiated by means of Algorithmic Differentiation and structural and coupled adjoint-based sensitivities are evaluated and validated by comparison to Finite Differences for a variety of cases. The final goal of this research is to provide an integrated infrastructure for aeroelastic design and optimization of wings by means of coupled adjoint sensitivities, including challenging cases in which wings are operating in non-linear aerodynamic regimes, e.g., transonic flows, and subject to large displacements.

Rocco Bombardieri, Ruben Sanchez, Rauno Cavallaro, Nicolas R. Gauger

Chapter 20. Neuroevolutionary Multiobjective Optimization of Injection Stretch Blow Molding Process in the Blowing Phase

Abstract

Injection stretch blow molding is a very important thermoplastic processing technique producing hollow containers with mechanical performance. One of the main challenges in optimizing this process consists in finding the best thickness profile for each part in order to achieve the desired mechanical properties with less material use. In a previous study, a new methodology based on a neuroevolutionary multiobjective optimization approach was proposed to enhance the entire process, which considers that the process is optimized by phases, starting by the end. In that initial study only the final phase of the process was addressed, where the best thickness profile for an industrial bottle was found in order to satisfy the required mechanical properties with less material use. In the present study, the focus is the second stage of the optimization methodology, concerning the blowing phase of injection blow molding process. The optimal results obtained in the first phase are used as the optimal thickness profile for the bottle with the goal to find the best preform thickness profile which produces the desired bottle. The same procedures are used and the results show that the methodology was successfully applied to its second phase.

Renê S. Pinto, Hugo M. Silva, Fernando M. Duarte, João P. Nunes, António Gaspar-Cunha

Chapter 21. Simulation of Vacuum Assisted Resin Infusion (VARI) Process for the Production of Composite Material Parts

Abstract

The Vacuum Assisted Resin Infusion (VARI) is manufacturing process used worldwide to produce composite parts having great diversity of dimensions (from small to very large ones) and geometrical complexity. This manufacturing process is particularly versatile, to produce small series of high performance structural parts. In these cases, the simulations of the VARI process is a very useful tool to define the infusion strategy and to plan and predict the resin flow progress in order to reduce the material waste and manufacturing cycle time and obtaining lighter structures, having lower void fraction and higher fibre content and mechanical performance. The numerical simulation of the VARI process implies the modelling of different complex phenomena, such as flow in porous media, mechanical deformation, heat exchange and chemical reaction. Therefore, a finite element software was used to solve a combination of governing equations based on a combination of pre-defined theoretical assumptions, by considering a moving mesh and appropriated boundary conditions. In this work, results obtained from simulations of VARI process were used to define the best strategy to be applied in the production of composite parts with different geometries, sizes and materials and predict the possibility of defects occur. In order to validate the accuracy of simulations, the numerical results were compared with those experimental ones obtained from the production of different composite parts where the best processing strategies were implemented. After analysing and discussing the theoretical and experimental obtained results, changes were applied to the numerical model to improve simulation accuracy.

Joana M. Malheiro, J. P. Nunes

Chapter 22. Towards CAD-Based Shape Optimization of Aircraft Engine Nozzles

Abstract

Shape optimization is a powerful method to design efficient aerodynamic shapes for aircraft and engine configurations at a limited cost. However, performing an optimization on “real-world” problems, including industrial tools and processes, remains challenging. In this paper, an original approach is presented, aiming at integrating expert knowledge and reducing the dimension of the optimization search space. Thanks to this method, it becomes possible to perform gradient-free or gradient-based optimization with an industrial design workflow comprising CAD. When applied to a nozzle shape optimization problem, this approach leads to encouraging performance improvements in both inviscid and viscous cases, for a given level of fuel consumption. Moreover, the reduced number of parameters enables the use of response surfaces and a better understanding of the design space.

Simon Bagy, Bijan Mohammadi, Michaël Mèheut, Mathieu Lallia, Pascal Coat

Chapter 23. A Two-Phase Heuristic Coupled DIRECT Method for Bound Constrained Global Optimization

Abstract

In this paper, we investigate the use of a simple heuristic in the DIRECT method context, aiming to select a set of the hyperrectangles that have the lowest function values in each size group. For solving bound constrained global optimization problems, the proposed heuristic divides the region where the hyperrectangles with the lowest function values in each size group lie into three subregions. From each subregion, different numbers of hyperrectangles are selected depending on the subregion they lie. Subsequently, from those selected hyperrectangles, the potentially optimal ones are identified for further division. Furthermore, the two-phase strategy aims to firstly encourage the global search and secondly enhance the local search. Global and local phases differ on the number of selected hyperrectangles from each subregion. The process is repeated until convergence. Numerical experiments carried out until now show that the proposed two-phase heuristic coupled DIRECT method is effective in converging to the optimal solution.

M. Fernanda P. Costa, Edite M. G. P. Fernandes, Ana Maria A. C. Rocha

Chapter 24. A Multiple Shooting Descent-Based Filter Method for Optimal Control Problems

Abstract

A direct multiple shooting (MS) method is implemented to solve optimal control problems (OCP) in the Mayer form. The use of an MS method gives rise to the so-called ‘continuity conditions’ that must be satisfied together with general algebraic equality and inequality constraints. The resulting finite nonlinear optimization problem is solved by a first-order descent method based on the filter methodology. In the equivalent tri-objective problem, the descent method aims to minimize the objective function, the violation of the ‘continuity conditions’ and the violation of the algebraic constraints simultaneously. The numerical experiments carried out with different types of benchmark OCP are encouraging.

Gisela C. V. Ramadas, Edite M. G. P. Fernandes, Ana Maria A. C. Rocha, M. Fernanda P. Costa

Chapter 25. Irrigation Planning with Fine Meshes

Abstract

In this work, we study a mathematical model for a smart irrigation system, formulated as an optimal control problem and discretized and transcribed into a nonlinear programming problem using a fine mesh. In order to solve the resulting optimization problem, one needs to use Optimization solvers. Hence, we implemented the proposed mathematical model in AMPL and solved it using the IPOPT solver on the NEOS server (https://​neos-server.​org/​neos/​index.​html). We also tested the model creating several scenarios. The numerical results shows that the mathematical model produces qualitatively good responses. Moreover the execution times are made in few seconds.

Sofia O. Lopes, M. Fernanda P. Costa, Rui M. S. Pereira, M. T. Malheiro, Fernando A. C. C. Fontes

Chapter 26. Optimal Path and Path-Following Control in Airborne Wind Energy Systems

Abstract

An Airborne Wind Energy System (AWES) is a concept to convert wind energy into electricity, which comprises a tethered aircraft connected to a ground station. These systems are capable of harvesting high altitude winds, which are more frequent and more consistent. Among AWES, there are Pumping Kite Generators (PKG) that involve a rigid or flexible kite connected to a motor/generator placed on the ground through a light–weight tether. Such PKG produces electrical power in a cyclical two–phased motion with a traction phase and a retraction phase. During the traction phase, the aim is to maximize power production. This goal is achieved by controlling the kite such that it performs an almost crosswind motion, keeping a low elevation angle in order to maximize the tether tension. During the retraction phase, the tether tension force is minimized by steering the kite while the tether is reeled–in. Such strategy assures that the cyclical two–phased motion has a positive electrical balance at the end of the overall cycle. In a first stage, we solve an optimal control problem to compute the optimal plan for the kite trajectory during the traction phase, maximizing power production. Such trajectory is then used to define a time–independent geometrical path, which in turn is used as the reference path for the path–following control procedure that is developed in a second stage, and for which results are also presented.

Manuel C. R. M. Fernandes, Luís Tiago Paiva, Fernando A. C. C. Fontes

Chapter 27. Temperature Time Series Forecasting in the Optimal Challenges in Irrigation (TO CHAIR)

Abstract

Predicting and forecasting weather time series has always been a difficult field of research analysis with a very slow progress rate over the years. The main challenge in this project—The Optimal Challenges in Irrigation (TO CHAIR)—is to study how to manage irrigation problems as an optimal control problem: the daily irrigation problem of minimizing water consumption. For that it is necessary to estimate and forecast weather variables in real time in each monitoring area of irrigation. These time series present strong trends and high-frequency seasonality. How to best model and forecast these patterns has been a long-standing issue in time series analysis. This study presents a comparison of the forecasting performance of TBATS (Trigonometric Seasonal, Box-Cox Transformation, ARMA errors, Trend and Seasonal Components) and regression with correlated errors models. These methods are chosen due to their ability to model trend and seasonal fluctuations present in weather data, particularly in dealing with time series with complex seasonal patterns (multiple seasonal patterns). The forecasting performance is demonstrated through a case study of weather time series: minimum air temperature.

A. Manuela Gonçalves, Cláudia Costa, Marco Costa, Sofia O. Lopes, Rui Pereira