Hierarchical Multilevel Optimization Research Articles

An Improved Three-Vector-Based Model Predictive Current Control Method for Surface-Mounted PMSM Drives

The conventional model predictive control method suffers from large torque ripples and harmonic current. Moreover, the modulation range of output is limited, leading to the deterioration of performance. To address these problems, this article proposes an improved three-vector model predictive current control method for surface-mounted permanent magnet synchronous motor (SPMSM) drives. First, virtual vectors are introduced to increase the number of available voltage vectors, in which the voltage vector control set can be extended. Furthermore, a hierarchical multilevel optimization control algorithm is adopted to obtain the main control set and the extended control set. According to two different control sets, the first and second vectors can be obtained by the cost function, respectively, which can realize modulation range extension. Then, the zero vectors are added to adjust the magnitude of the output voltage vector, and the output vector action time is obtained based on the deadbeat principle. The ripples can be minimized, and the modulation range can be extended with the proposed method. Finally, a comparative analysis of both the simulation and experimental tests is investigated. The comparative investigation verifies the effectiveness and feasibility of the proposed method.

Hierarchical multilevel optimization with multiple-leaders multiple-followers setting and nonseparable objectives

Hierarchical multilevel multi-leader multi-follower problems are non-cooperative decision problems in which multiple decision-makers of equal status in the upper-level and multiple decision-makers of equal status are involved at each of the lower-levels of the hierarchy. Much of solution methods proposed so far on the topic are either model specific which may work only for a particular sub-class of problems or are based on some strong assumptions and only for two level cases. In this paper, we have considered hierarchical multilevel multi-leader multi-follower problems in which the objective functions contain separable and non-separable terms (but the non-separable terms can be written as a factor of two functions, a function which depends on other level decision variables and a function which is common to all objectives across the same level) and shared constraint. We have proposed a solution algorithm to such problems by equivalent reformulation as a hierarchical multilevel problem involving single decision maker at all levels of the hierarchy. Then, we applied a multi-parametric algorithm to solve the resulting single leader single followers problem.

Mixed uncertainty based analytical target cascading: an approach for hierarchical multilevel optimization under probabilistic and interval mixed uncertainties

Analytical target cascading (ATC) has been extended to the probabilistic formulation to deal with the hierarchical multilevel optimization problem under uncertainty. However, only aleatory uncertainties can be handled by the probabilistic theory. Considering both aleatory and epistemic uncertainties exist in engineering design, a mixed uncertainty based analytical target cascading (MUATC) approach is proposed in this paper. The probability distribution and interval are used to represent the aleatory uncertainties and epistemic uncertainties, respectively. To figure out the mixed uncertainty propagation(MUP) problem, the reliability index approach based MUP (RIA-MUP) and performance measurement approach based MUP (PMA-MUP) are proposed firstly. Based on PMA-MUP, the MUATC method is established. MUATC firstly decouples the mixed uncertainty all-in-one (MUAIO) problem into deterministic optimization problem and mixed uncertainty analysis, and then hierarchically decomposes them into subproblems. All-in-one (AIO) mixed uncertainty analysis and hierarchically mixed uncertainty analysis methods are established to calculate the characteristic of the interrelated responses and shared variables. The accuracy and effectiveness of MUATC are demonstrated with three examples.

Sequential probabilistic analytical target cascading method for hierarchical multilevel optimization under uncertainty

Probabilistic Analytical Target Cascading (PATC) is a methodology for hierarchical multilevel optimization under uncertainty. In PATC, the statisticalmoments of the stochastic interrelated responses are matched between neighbouring levels to ensure the consistency of the solution. When the interrelated response is far from normal distribution, high order moments may need to be matched in the PATC formulation, which results in great computational difficulty. To overcome this disadvantage, a sequential PATC (SPATC) approach is proposed in this paper. SPATC firstly decouples the original probabilistic design problem into deterministic optimization problem and probabilistic analysis, and then hierarchically decomposes them into subproblems. The statistical information matching between neighbouring levels in the existing PATC framework is eliminated in SPATC. All in one probabilistic analysis and hierarchical probabilistic analysis are established to calculate the probabilistic characteristic of the interrelated responses and linking variables. Three examples are used to demonstrate the effectiveness and efficiency of the proposed SPATC approach. The results show that the SPATC approach is more efficient and accurate than PATC, especially for the multilevel design problem with non-normal interrelated responses.

Hierarchical multilevel optimization for reliability target allocation in probabilistic design of decomposed systems

AbstractAnalytical target cascading (ATC) is a methodology for translating system‐level design targets to subsystem and component design specifications in hierarchically decomposed optimal system design problems. In previous work we extended the ATC formulation to account for uncertainties, where the bounds of the probabilistic design constraints were chosen arbitrarily and held fixed during the ATC process. In this work, we extend the probabilistic ATC formulation to include reliability targets in the vector of cascaded quantities. In this manner, we quantify the optimality‐reliability tradeoffs for each element of the decomposed system and compute the probabilistic constraint bounds required to satisfy the overall system reliability target. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Analytical Target Cascading in Automotive Vehicle Design

Target cascading in product development is a systematic effort to propagate the desired top-level system design targets to appropriate specifications for subsystems and components in a consistent and efficient manner. If analysis models are available to represent the consequences of the relevant design decisions, analytical target cascading can be formalized as a hierarchical multilevel optimization problem. The article demonstrates this complex modeling and solution process in the chassis design of a sport-utility vehicle. Ride quality and handling targets are cascaded down to systems and subsystems utilizing suspension, tire, and spring analysis models. Potential incompatibilities among targets and constraints throughout the entire system can be uncovered and the trade-offs involved in achieving system targets under different design scenarios can be quantified.

An Affordable Approach for Robust Design of Thick Laminated Composite Structure

A systematic and affordable approach is proposed for the robust design of thick laminated composite structures. Our approach integrates the principles of the Robust Concept Exploration Method (RCEM) for designing complex engineering systems and the hierarchical multi-level optimization procedure for managing the complexity of composite structure optimization. Foundational to the proposed approach is the use of Design of Experiments (DOE) techniques and the Response Surface Methodology (RSM) for improving computational efficiency in using high fidelity design simulations; and the use of the robust design method for improving the quality of a product that is insensitive to potential variations of design parameters. Our approach is illustrated through the design of a laminated composite femoral component for hip joint arthroplasty. The solution yields the robust design of a composite hip implant, which is applicable for a range of bone stiffness, thereby eliminating the need to design specifically for an individual.