Concurrent Optimization Method Research Articles

Interval Type-2 Fuzzy PID Controller Using Disassembled Gradational Optimization.

This paper presents an interval type-2 fuzzy proportional-integral-derivative (IT2F-PID) controller that is designed using a new disassembled gradational optimization (D-GO) method. A PID controller is first optimized using the D-GO method and then connected to a type-1 fuzzy logic system (T1-FLS). The parameters of the T1-FLS are optimized, and the T1-FLS is blurred into the interval type-2 fuzzy logic system (IT2-FLS). Finally, the IT2F-PID controller is formed. The proposed method is compared with the concurrent and general optimization methods. The simulation results show that the D-GO method reduces the optimization time by over 90% compared with the general method, and decreases the integral-of-time-absolute-error (ITAE) by 30%. Beyond that, compared with the concurrent optimization method, the D-GO method reduces time by over 25%, and the ITAE value by about 95%. In the normal case, model uncertainty, target uncertainty, and external disturbance, the control ability of the IT2F-PID controller designed using the D-GO method is verified via simulations using a nonlinear forced closed-loop system. The results show that the overshoot is reduced by 80% and the fluctuation is reduced by 67% compared with a traditional PID controller and an IT2F-PID controller built using the general method.

Concurrent optimization method of principal stress orientation interpolated continuous fiber angle (PSO-CFAO) and structural topology

Continuous fiber-reinforced polymers (CFRPs) have been widely applied in aerospace and other fields due to their excellent mechanical properties, which highly depends on the material distribution and fiber orientations. The designability of CFRP structures and fiber distributions provides an opportunity for achieving better physical properties through optimization. However, local optima and the dependence of initial fiber angle variables make the concurrent optimization of fiber orientation and topology a challenging problem. In this paper, the principal stress orientation interpolated continuous fiber angle optimization (PSO-CFAO) method combined with the independent continuous mapping (ICM) method is proposed to realize the design of CFRP structures with a clear macroscopic topology and microscopic fiber distribution. A sigmoid function is applied to interpolate the fiber angle variables by the principal stress orientation. The fiber angle variables are modified and a continuous fiber design is obtained during the iteration process, which reduces the possibility of a local optimum. Several examples are provided to prove the effectiveness and stability of the proposed method, and the expected results are acquired for different initial fiber angles, material parameters and mesh densities. The proposed method provides guidance for the design of CFRP structures and the planning of fiber laying paths.

A sequential mixed-integer programming method for concurrent optimization of core topology and face sheet thickness of a sandwich beam

A method is proposed that allows for the concurrent optimization of core topology and face sheet thickness of a sandwich beam under compliance constraints. The problem is solved using a novel mixed-linear extension of the Topology Optimization of Binary Structure (TOBS) topology optimization method aiming to minimize the total mass of the beam. The method has been demonstrated on a clamped beam example and the results have been compared to results from topology optimization of the core with a range of a priori fixed face sheet thicknesses. It is shown that the new method, starting from a fully populated core, finds a minimum mass that is lower than but in the neighbourhood of the best results from the topology optimization with fixed face sheet thicknesses. By varying the compliance constraint it is shown that the core topology approaches an ideal corrugated geometry as the compliance constraint is relaxed. The trends observed in the results are compared to analytical models for an idealized core.

Concurrent optimization method of shape and topology for natural vibration problem of shell structures

In this paper, a concurrent optimization method of shape and topology for natural vibration design of shell structures is presented. The fundamental vibration eigenvalue is maximized under volume constraints for shape and topology optimization. The free-form optimization method for shells and the solid isotropic material with penalization (SIMP) method are respectively employed and combined effectively for shape and topology design, in which shape and fictitious homogenized-density variations are used as design variables and simultaneously determined. In other words, the optimal topology is determined in the variable design surface optimized by shape optimization. The optimal design problem is formulated as a distributed-parameter optimization problem, and the sensitivity functions with respect to shape and density variations are theoretically derived. Both the optimal shape and density variations are determined with the unified H1 gradient method, where the sensitivity functions are respectively applied as the Robin condition to the design surface in order to determine the optimal shape and topology. We also show an improved method for the spurious (or localized) mode problem of shell structures, which often occurs in the lower density region in topology optimization for vibration design. With the proposed method, shell structure for light weight and improved low-order vibration characteristics can be obtained without any design parameterization, free of numerical instabilities such as checkerboard pattern and zigzag-shape problems.

Phase-field based robust topology and orientation optimization under fiber orientation uncertainty

Recently, there has been an increased usage of fiber-reinforced composites in aerospace and automobile due to their celebrated mechanical properties. Thus, a massive research effort has hitherto been done to develop a method for concurrent optimization of structural topology and fiber orientation. Topology-optimized continuous fiber-reinforced structures tend to show complex morphologies with spatially varying fiber orientation. Due to this nature, it is nearly possible to manufacture the results only through additive manufacturing technology However, a gap must exist between prescribed optimized fiber orientation and fiber orientation of manufactured composites under a limited degree of precision of the manufacturing process. Robust anisotropic topology optimization under such uncertainty, therefore, needs to be developed. This presentation aims to present a novel robust topology optimization methodology for fiber-reinforced materials under fiber orientation uncertainty. Our method is built upon Phase-Field based topology optimization which is suitable for this type of optimization method. The effectiveness of our method is validated through the stiffness maximization problem and the fundamental eigenfrequency maximization problem.

Multidisciplinary design optimization in design for additive manufacturing

ABSTRACT Design for additive manufacturing (AM) involves decision making in various design domains, including product design, material selection, and process planning. In practice, engineers typically adopt a sequential design process to optimize these design domains in consecutive order. However, coupling factors, e.g. shared variables, related constraints, and conflicting objectives, are not sufficiently considered within the sequential design process, resulting in an inefficient workflow and suboptimal design solutions. To address the above issues, this paper proposes a multidisciplinary design optimization framework to simultaneously optimize different domains, which enables rapid exploration and complete exploitation of the AM design space under complex constraints. More specifically, the proposed framework is based on the concurrent optimization method, which coordinates the optimization of different design domains by allowing an automated exchange of design information. Also, the framework utilizes the surrogate modeling approach to approximate high-fidelity simulations for facilitating the iterative process. The effectiveness of the proposed framework is validated with two examples, a plate with a hole design and a hook design, which involve multiple design objectives from both process and structure domains, i.e. the print time, print area, strain energy, and maximum von Mises stress.

Concurrent Optimization of Mountain Railway Alignment and Station Locations With a Three-Dimensional Distance Transform Algorithm Incorporating a Perceptual Search Strategy

The design of railway alignment and station locations involves two intertwined problems, which makes it a complex and time-consuming task. Especially in mountainous regions, the large 3-dimensional (3D) search spaces, complex terrain conditions, coupling constraints and infinite numbers of potential alternatives of this problem pose many challenges. However, most current optimization methods emphasize either alignment optimization or station locations optimization independently. Only a few methods consider coordinated optimization of alignment and stations, but optimize them sequentially. This paper proposes a concurrent optimization method based on a 3-dimensional distance transform algorithm (3D-DT) to solve this problem. It includes the following components: (1) To optimize the location of stations within specified spacing intervals, a novel perceptual search strategy is proposed and incorporated into the basic 3D-DT optimization process. (2) A combined-alignment-station 3D search neighboring mask is developed and employed to search for both the alignment and stations. In order to implement the perceptual process, two additional kinds of 3D reverse perceptual neighboring masks are also developed and employed in the algorithm. (3) Multiple coupling constraints between alignment and stations are also formulated and addressed during the search process. In this study, the effectiveness of the method is verified through a real-world case study in a complex mountainous region. The optimization results show that the proposed method can find high-quality alternatives satisfying multiple coupling constraints.

Concurrent optimization of the internal flow channel, inlets, and outlets in forced convection heat sinks

With the increasing dissipated power levels of electronic equipment, heat sink design problems are significant aspects of some industrial design fields. Topology optimization theory has attracted much research interest in thermal-fluid problems to design high-performance heat sinks. These researches focus on optimizing the internal flow channel of heat sinks under predefined inlet and outlet schemes. However, inlet/outlet schemes also exhibit great influence on the performance of optimized heat sinks. This paper intends to demonstrate a concurrent optimization method of the internal flow channel, inlets, and outlets in forced convection heat sinks. The porosity field and moving morphable components (MMCs) are adopted to describe structural topologies of the internal channel design domain and the inlet/outlet design domains, respectively. The internal porosity field and the shape/position parameters of MMCs are applied as design variables. A conventional inlet/outlet component is presented and the corresponding topology description transformation function is constructed to convert the inlet/outlet topology into corresponding porosity fields. Further, the thermal-fluid coupling problems are solved through porosity-interpolated fluid flow and heat transfer governing equations. To ensure accurate inlet flow and temperature conditions during the topology iteration, continuous design-dependent inlet governing equations are established under inlet pressure, velocity, and flow flux boundary conditions. Design variables are concurrently optimized based on the sensitivity information. The proposed method is shown in detail by taking design problems of water-cooled heat sinks as examples. Various numerical examples are presented to validate the applicability and efficiency of this method.

Concurrent density distribution and build orientation optimization of additively manufactured functionally graded lattice structures

Functionally graded conformal lattice structures (FGCLSs) are a particular type of lattice structure in which lattice unit cells are populated following structural boundaries and the density of the lattice unit cells is optimally distributed. Additionally, additively manufactured parts are reported to have anisotropic mechanical properties that highly depend on the part build orientations. This is extremely important in designing FGCLS parts where orientations of lattice unit cells are not uniform, making the build orientation selection more challenging. In this study, a concurrent density distribution and build orientation optimization framework of additively manufactured FGCLSs for structure-performance maximization was developed. The proposed approach was validated via case studies on lightweight part design for compliance minimization, with three design examples having geometric complexity levels varying from low to high. The results showed that the proposed concurrent optimization method was more effective at enhancing structural performance than optimizing only the density distribution of the structure. In addition, the build orientation configurations determined by the proposed method provided better structural performance compared to those determined using other slicing software. Moreover, compared to the pseudo-worst build orientation configuration, the configuration obtained from the proposed approach could enhance structural performance by up to 47.56%.

Concurrent optimization of macrostructures and material microstructures and orientations for maximizing natural frequency

In this paper, an efficient concurrent optimization method of macrostructures, and material microstructures and orientations is proposed for maximizing natural frequency. It is assumed that the macrostructure is composed of uniform material with the same microstructure but with various orientation. The bi-directional evolutionary structural optimization (BESO) method is applied to optimize the macrostructure and its material microstructure under a given weight constraint. Meanwhile, the optimality condition with respect to local material orientation is derived and embedded in the two-scale design of macrostructures and material microstructures. Numerical examples are presented to demonstrate the capability and effectiveness of the proposed optimization algorithm. The results show that the current design of macrostructures, material microstructures, and local material orientation greatly improves structural dynamic performance.

Concurrent optimization of additive manufacturing fabricated lattice structures for natural frequencies

Lattice structures exhibit enormous potential for multi-functional implementations for their high stiffness/ strength-to-weight ratio. While Additive Manufacturing (AM) techniques present great opportunities in the application of lattice structures, its process limitations impose challenges in design for AM. This paper develops a concurrent design method of AM fabricated lattice structures and its printing part orientation in natural frequency optimization problems. Specifically, void units are introduced into the design domain for better frequency objectives. Density filtering and projection approaches are designed to consider the Minimum Feature Size and the self-supporting constraints. Further, a concurrent optimization model is constructed to optimize the unit density layout and the part orientation. The proposed method was validated with a fundamental frequency optimization problem. Numerically, the proposed concurrent optimization method achieves high-quality solutions with low computational costs. Experimentally, the structure designed by the proposed method exhibits a higher fundamental frequency than that designed by the comparison method.

Concurrent optimization of mountain railway alignment and station locations using a distance transform algorithm

Abstract Railway location design is a complex and time-consuming task in which the intricate interactions among railway alignment and station locations must be considered. However, most optimization methods emphasize either alignment optimization or station locations optimization while ignoring the coupling constraints for railway alignment and station locations. In addition, these methods are mainly applied to plain areas with relatively simple topographies and often fail to find feasible alternatives in complex mountainous areas. This paper proposes a concurrent optimization method for railway alignment and station locations. Coupling constraints for railway alignment and station locations are formulated and addressed, and station locations are generated while searching the railway alignment. The method can be applied for more general terrains, including complex mountainous areas. The effectiveness of the method is verified through a real-world case study in a complex mountainous area. The results show that the proposed method can concurrently find the optimal railway alignment and station locations for specific objectives and multiple constraints and provide various promising alternatives.

Concurrent topological design of composite structures and materials containing multiple phases of distinct Poisson’s ratios

ABSTRACTMost studies on composites assume that the constituent phases have different values of stiffness. Little attention has been paid to the effect of constituent phases having distinct Poisson’s ratios. This research focuses on a concurrent optimization method for simultaneously designing composite structures and materials with distinct Poisson’s ratios. The proposed method aims to minimize the mean compliance of the macrostructure with a given mass of base materials. In contrast to the traditional interpolation of the stiffness matrix through numerical results, an interpolation scheme of the Young’s modulus and Poisson’s ratio using different parameters is adopted. The numerical results demonstrate that the Poisson effect plays a key role in reducing the mean compliance of the final design. An important contribution of the present study is that the proposed concurrent optimization method can automatically distribute base materials with distinct Poisson’s ratios between the macrostructural and microstructural levels under a single constraint of the total mass.

Concurrent material and structural optimization of hollow plate with truss-like material

In this paper, optimum stress distribution for hollow plates composed of linear cellular materials (LCMs), a kind of truss-like material, is investigated. To reduce the computational cost, we model the material as micropolar continua representation. Two classes of design variables, relative density, and cell-size distribution of truss-like materials are to be determined by optimization under given total material volume constraint. And the concurrent designs of material and structure are obtained for three different optimization formulations. For the first formulation, we aim at the minimization of the maximum stress that appears at the initial uniform design; for the second formulation, we minimize the highest stress within the specified point set. As the yield strength of truss-like material is dependent on the relative material density, we minimize the ratio of stress over the corresponding yield strength along the hole boundary in our third formulation, which maximizes the strength reserve and seems more rational. The numerical results for the three objectives validate the concurrent optimization method proposed in this paper. And the influence of ply angle (angle between the principle direction of material and the axes of the system’s coordinates) on the optimum result is discussed. The dependence of optimum design on finite element meshes is also investigated. An approximate discrete model is established to verify the method proposed in this paper, and the stress concentration near a hole is reduced significantly.