Dynamic Design of Piezoelectric Laminated Sensors and Actuators using Topology Optimization

Sensors and actuators based on piezoelectric plates have shown increasing demand in the field of smart structures, including the development of actuators for cooling and fluid-pumping applications and transducers for novel energy-harvesting devices. This project involves the development of a topology optimization formulation for dynamic design of piezoelectric laminated plates aiming at piezoelectric sensors, actuators and energy-harvesting applications. It distributes piezoelectric material over a metallic plate in order to achieve a desired dynamic behavior with specified resonance frequencies, modes, and enhanced electromechanical coupling factor (EMCC). The finite element employs a piezoelectric plate based on the MITC formulation, which is reliable, efficient and avoids the shear locking problem. The topology optimization formulation is based on the PEMAP-P model combined with the RAMP model, where the design variables are the pseudo-densities that describe the amount of piezoelectric material at each finite element and its polarization sign. The design problem formulated aims at designing simultaneously an eigenshape, i.e., maximizing and minimizing vibration amplitudes at certain points of the structure in a given eigenmode, while tuning the eigenvalue to a desired value and also maximizing its EMCC, so that the energy conversion is maximized for that mode. The optimization problem is solved by using sequential linear programming. Through this formulation, a design with enhancing energy conversion in the low-frequency spectrum is obtained, by minimizing a set of first eigenvalues, enhancing their corresponding eigenshapes while maximizing their EMCCs, which can be considered an approach to the design of energy-harvesting devices. The implementation of the topology optimization algorithm and some results are presented to illustrate the method.

Piezoresistive sensor design using topology optimization

Piezoresistive materials, materials whose resistivity properties change when subjected to mechanical stresses, are widely utilized in many industries as sensors, including pressure sensors, accelerometers, inclinometers, and load cells. Basic piezoresistive sensors consist of piezoresistive devices bonded to a flexible structure, such as a cantilever or a membrane, where the flexible structure transmits pressure, force, or inertial force due to acceleration, thereby causing a stress that changes the resistivity of the piezoresistive devices. By applying a voltage to a piezoresistive device, its resistivity can be measured and correlated with the amplitude of an applied pressure or force. The performance of a piezoresistive sensor is closely related to the design of its flexible structure. In this research, we propose a generic topology optimization formulation for the design of piezoresistive sensors where the primary aim is high response. First, the concept of topology optimization is briefly discussed. Next, design requirements are clarified, and corresponding objective functions and the optimization problem are formulated. An optimization algorithm is constructed based on these formulations. Finally, several design examples of piezoresistive sensors are presented to confirm the usefulness of the proposed method.

Tailoring vibration mode shapes using topology optimization and functionally graded material concepts

Tailoring specified vibration modes is a requirement for designing piezoelectric devices aimed at dynamic-type applications. A technique for designing the shape of specified vibration modes is the topology optimization method (TOM) which finds an optimum material distribution inside a design domain to obtain a structure that vibrates according to specified eigenfrequencies and eigenmodes. Nevertheless, when the TOM is applied to dynamic problems, the well-known grayscale or intermediate material problem arises which can invalidate the post-processing of the optimal result. Thus, a more natural way for solving dynamic problems using TOM is to allow intermediate material values. This idea leads to the functionally graded material (FGM) concept. In fact, FGMs are materials whose properties and microstructure continuously change along a specific direction. Therefore, in this paper, an approach is presented for tailoring user-defined vibration modes, by applying the TOM and FGM concepts to design functionally graded piezoelectric transducers (FGPT) and non-piezoelectric structures (functionally graded structures-FGS) in order to achieve maximum and/or minimum vibration amplitudes at certain points of the structure, by simultaneously finding the topology and material gradation function. The optimization problem is solved by using sequential linear programming. Two-dimensional results are presented to illustrate the method.

Multi-Objective Optimization Design of Tanker Ships via a Genetic Algorithm

The cost of a new ship design heavily depends on the principal dimensions of the ship; however, dimensions minimization often conflicts with the minimum oil outflow (in the event of an accidental spill). This study demonstrates one rational methodology for selecting the optimal dimensions and coefficients of form of tankers via the use of a genetic algorithm. Therein, a multi-objective optimization problem was formulated by using two objective attributes in the evaluation of each design, specifically, total cost and mean oil outflow. In addition, a procedure that can be used to balance the designs in terms of weight and useful space is proposed. A genetic algorithm was implemented to search for optimal design parameters and to identify the nondominated Pareto frontier. At the end of this study, three real ships are used as case studies. [DOI:10.1115/1.4002740]

Real time optimization (RTO) with model predictive control (MPC)

This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load. (C) 2010 Elsevier Ltd. All rights reserved.

The application of adaptive partitioned random search in feature selection problem

Feature selection is one of important and frequently used techniques in data preprocessing. It can improve the efficiency and the effectiveness of data mining by reducing the dimensions of feature space and removing the irrelevant and redundant information. Feature selection can be viewed as a global optimization problem of finding a minimum set of M relevant features that describes the dataset as well as the original N attributes. In this paper, we apply the adaptive partitioned random search strategy into our feature selection algorithm. Under this search strategy, the partition structure and evaluation function is proposed for feature selection problem. This algorithm ensures the global optimal solution in theory and avoids complete randomness in search direction. The good property of our algorithm is shown through the theoretical analysis.

Surgical correction of scoliosis: Numerical analysis and optimization of the procedure

A previously developed model is used to numerically simulate real clinical cases of the surgical correction of scoliosis. This model consists of one-dimensional finite elements with spatial deformation in which (i) the column is represented by its axis; (ii) the vertebrae are assumed to be rigid; and (iii) the deformability of the column is concentrated in springs that connect the successive rigid elements. The metallic rods used for the surgical correction are modeled by beam elements with linear elastic behavior. To obtain the forces at the connections between the metallic rods and the vertebrae geometrically, non-linear finite element analyses are performed. The tightening sequence determines the magnitude of the forces applied to the patient column, and it is desirable to keep those forces as small as possible. In this study, a Genetic Algorithm optimization is applied to this model in order to determine the sequence that minimizes the corrective forces applied during the surgery. This amounts to find the optimal permutation of integers 1, ... , n, n being the number of vertebrae involved. As such, we are faced with a combinatorial optimization problem isomorph to the Traveling Salesman Problem. The fitness evaluation requires one computing intensive Finite Element Analysis per candidate solution and, thus, a parallel implementation of the Genetic Algorithm is developed.

A short-term risk management tool applied to OMEL electricity market using particle swarm optimization

Short-term risk management is highly dependent on long-term contractual decisions previously established; risk aversion factor of the agent and short-term price forecast accuracy. Trying to give answers to that problem, this paper provides a different approach for short-term risk management on electricity markets. Based on long-term contractual decisions and making use of a price range forecast method developed by the authors, the short-term risk management tool presented here has as main concern to find the optimal spot market strategies that a producer should have for a specific day in function of his risk aversion factor, with the objective to maximize the profits and simultaneously to practice the hedge against price market volatility. Due to the complexity of the optimization problem, the authors make use of Particle Swarm Optimization (PSO) to find the optimal solution. Results from realistic data, namely from OMEL electricity market, are presented and discussed in detail.

Multi-criteria design optimization study of solvent extraction in mixer–settler units

Solvent extraction is considered as a multi-criteria optimization problem, since several chemical species with similar extraction kinetic properties are frequently present in the aqueous phase and the selective extraction is not practicable. This optimization, applied to mixer–settler units, considers the best parameters and operating conditions, as well as the best structure or process flow-sheet. Global process optimization is performed for a specific flow-sheet and a comparison of Pareto curves for different flow-sheets is made. The positive weight sum approach linked to the sequential quadratic programming method is used to obtain the Pareto set. In all investigated structures, recovery increases with hold-up, residence time and agitation speed, while the purity has an opposite behaviour. For the same treatment capacity, counter-current arrangements are shown to promote recovery without significant impairment in purity. Recycling the aqueous phase is shown to be irrelevant, but organic recycling with as many stages as economically feasible clearly improves the design criteria and reduces the most efficient organic flow-rate.

Filters method in direct search optimization, new measures to admissibility

Constrained nonlinear optimization problems are usually solved using penalty or barrier methods combined with unconstrained optimization methods. Another alternative used to solve constrained nonlinear optimization problems is the lters method. Filters method, introduced by Fletcher and Ley er in 2002, have been widely used in several areas of constrained nonlinear optimization. These methods treat optimization problem as bi-objective attempts to minimize the objective function and a continuous function that aggregates the constraint violation functions. Audet and Dennis have presented the rst lters method for derivative-free nonlinear programming, based on pattern search methods. Motivated by this work we have de- veloped a new direct search method, based on simplex methods, for general constrained optimization, that combines the features of the simplex method and lters method. This work presents a new variant of these methods which combines the lters method with other direct search methods and are proposed some alternatives to aggregate the constraint violation functions.

Evolutionary trajectory optimization for redundant robots

The trajectory planning of redundant robots is an important area of research and efficient optimization algorithms have been investigated in the last years. This paper presents a new technique that combines the closed-loop pseudoinverse method with genetic algorithms. In this case the trajectory planning is formulated as an optimization problem with constraints.

A physical packing sequence algorithm for the container loading problem with static mechanical equilibrium conditions

The container loading problem (CLP) is a combinatorial optimization problem for the spatial arrangement of cargo inside containers so as to maximize the usage of space. The algorithms for this problem are of limited practical applicability if real-world constraints are not considered, one of the most important of which is deemed to be stability. This paper addresses static stability, as opposed to dynamic stability, looking at the stability of the cargo during container loading. This paper proposes two algorithms. The first is a static stability algorithm based on static mechanical equilibrium conditions that can be used as a stability evaluation function embedded in CLP algorithms (e.g. constructive heuristics, metaheuristics). The second proposed algorithm is a physical packing sequence algorithm that, given a container loading arrangement, generates the actual sequence by which each box is placed inside the container, considering static stability and loading operation efficiency constraints.

Materials selection for a set of multiple parts considering manufacturing costs and weight reduction with structural isoperformance using direct multisearch optimization

Materials selection is a matter of great importance to engineering design and software tools are valuable to inform decisions in the early stages of product development. However, when a set of alternative materials is available for the different parts a product is made of, the question of what optimal material mix to choose for a group of parts is not trivial. The engineer/designer therefore goes about this in a part-by-part procedure. Optimizing each part per se can lead to a global sub-optimal solution from the product point of view. An optimization procedure to deal with products with multiple parts, each with discrete design variables, and able to determine the optimal solution assuming different objectives is therefore needed. To solve this multiobjective optimization problem, a new routine based on Direct MultiSearch (DMS) algorithm is created. Results from the Pareto front can help the designer to align his/hers materials selection for a complete set of materials with product attribute objectives, depending on the relative importance of each objective.

Multiobjective optimization of cold-formed steel columns

The optimal design of cold-formed steel columns is addressed in this paper, with two objectives: maximize the local-global buckling strength and maximize the distortional buckling strength. The design variables of the problem are the angles of orientation of cross-section wall elements the thickness and width of the steel sheet that forms the cross-section are fixed. The elastic local, distortional and global buckling loads are determined using Finite Strip Method (CUFSM) and the strength of cold-formed steel columns (with given length) is calculated using the Direct Strength Method (DSM). The bi-objective optimization problem is solved using the Direct MultiSearch (DMS) method, which does not use any derivatives of the objective functions. Trade-off Pareto optimal fronts are obtained separately for symmetric and anti-symmetric cross-section shapes. The results are analyzed and further discussed, and some interesting conclusions about the individual strengths (local-global and distortional) are found.

Extremum estimators and stochastic optimization methods

Submitted in partial fulfillment for the Requirements for the Degree of PhD in Mathematics, in the Speciality of Statistics in the Faculdade de Ciências e Tecnologia