Design Centering of Compact Microwave Components Using Response Features and Trust Regions

Fabrication tolerances, as well as uncertainties of other kinds, e.g., concerning material parameters or operating conditions, are detrimental to the performance of microwave circuits. Mitigating their impact requires accounting for possible parameter deviations already at the design stage. This involves optimization of appropriately defined statistical figures of merit such as yield. Although important, robust (or tolerance-aware) design is an intricate endeavor because manufacturing inaccuracies are normally described using probability distributions, and their quantification has to be based on statistical analysis. The major bottleneck here is high computational cost: for reliability reasons, miniaturized microwave components are evaluated using full-wave electromagnetic (EM) models, whereas conventionally utilized analysis methods (e.g., Monte Carlo simulation) are associated with massive circuit evaluations. A practical approach that allows for circumventing the aforementioned obstacles offers surrogate modeling techniques, which have been a dominant trend over the recent years. Notwithstanding, a construction of accurate metamodels may require considerable computational investments, especially for higher-dimensional cases. This paper brings in a novel design-centering approach, which assembles forward surrogates founded at the level of response features and trust-region framework for direct optimization of the system yield. Formulating the problem with the use of characteristic points of the system response alleviates the issues related to response nonlinearities. At the same time, as the surrogate is a linear regression model, a rapid yield estimation is possible through numerical integration of the input probability distributions. As a result, expenditures related to design centering equal merely few dozens of EM analyses. The introduced technique is demonstrated using three microstrip couplers. It is compared to recently reported techniques, and its reliability is corroborated using EM-based Monte Carlo analysis.

Optimization Design of Extrusion Roller of RP1814 Roller Press Based on ANSYS Workbench

Firstly, the force of an extrusion roller under actual working condition was analyzed while the contact stress between the roller shaft and the roller sleeve and the extrusion force between the roller sleeve and the material were calculated. Secondly, static analysis of the extrusion roller was carried out using ANSYS software, and conclusively, the stress concentration appears at the roller sleeve’s inner ring step. Furthermore, an optimization scheme of the setting transition arc at the step of the contact surface between roller shaft and roller sleeve was proposed, and a simulation test was carried out., Finally, the maximum equivalent stress of the extrusion roller was set at the minimum value of the objective function; the extrusion roller was further optimized by using the direct optimization module in ANSYS Workbench. The results from optimization show that the maximum equivalent stress is reduced by 29% and the maximum deformation is decreased by 28%. It can be seen that the optimization scheme meets the strength and deformation requirements of the extrusion roller design. The optimization scheme can effectively improve the bearing capacity of the extrusion roller and reduce its production cost. This can provide a reference for the design of the roller press.

Space mapping-based optimization with the macroscopic limit of interacting particle systems

We propose a space mapping-based optimization algorithm for microscopic interacting particle dynamics which are infeasible for direct optimization. This is of relevance for example in applications with bounded domains for which the microscopic optimization is difficult. The space mapping algorithm exploits the relationship of the microscopic description of the interacting particle system and a corresponding macroscopic description as partial differential equation in the “many particle limit”. We validate the approach with the help of a toy problem that allows for direct optimization. Then we study the performance of the algorithm in two applications. A pedestrian flow is considered and the transportation of goods on a conveyor belt is optimized. The numerical results underline the feasibility of the proposed algorithm.

Optimization of Return Channels of High Flow Centrifugal Compressor Stages by CFD-Methods

Calculations performed with modern computer fluid dynamics (CFD) programs aid in optimizing the flow path of a centrifugal compressor. The characteristics of the stator elements of the flow path, calculated by CFD methods, are considered to be quite accurate. Optimization of three-stage reverse-directing devices with a large flow rate (0.15) and different theoretical head coefficients (0.45; 0.60; 0.70) has been carried out. For optimizing return channels a parameterized model was created. Optimization was performed with MOGA (Multi-Objective Genetic Algorithm) optimization method in the Direct Optimization program of the ANSYS software package. The optimization goal was to achieve the minimum loss factor at the design point. In the optimization process, the following parameters were varied: the number of and the inlet angle of the vanes, the height of the vanes at the inlet, external and internal radii of curvature of the U-bend. For the return channel with a minimum loss coefficient, the dependences of this parameter on the flow coefficient were calculated. Comparison with the characteristics of the initial variant showed that the optimized return channels are more efficient over the entire flow range. Optimization allowed reducing the loss factor by 20%.

Magnetic FEA Direct Optimization of High-Power Density, Halbach Array Permanent Magnet Electric Motors

Hybrid electric aero-propulsion requires high power-density electric motors. The use of a constrained optimization method with the finite element analysis (FEA) is the best way to design these motors and to find the best solutions which maximize the power density. This makes it possible to take into account all the details of the geometry as well as the non-linear characteristics of magnetic materials, the conductive material and the current control strategy. Simulations were performed with a time stepping magnetodynamic solver while taking account the rotor movement and the stator winding was connected by an external electrical circuit. This study describes the magnetic FEA direct optimization approach for the design of Halbach array permanent magnet synchronous motors (PMSMs) and its advantages. An acceptable compromise between precision and computation time to estimate the electromagnetic torque, iron losses and eddy current losses was found. The finite element simulation was paired with analytical models to compute stress on the retaining sleeve, aerodynamic losses, and copper losses. This type of design procedure can be used to find the best machine configurations and establish design rules based on the specifications and materials selected. As an example, optimization results of PM motors minimizing total losses for a 150-kW application are presented for given speeds in the 2000 rpm to 50,000 rpm range. We compare different numbers of poles and power density between 5 kW/kg and 30 kW/kg. The choice of the number of poles is discussed in the function of the motor nominal speed and targeted power density as well as the compromise between iron losses and copper losses. In addition, the interest of having the current-control strategy as an optimization variable to generate a small amount of flux weakening is clearly shown.

Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation

Recent force-fatigue mathematical models in biomechanics [7] allow to predict the muscular force response to functional electrical stimulation (FES) and leads to the optimal control problem of maximizing the force. The stimulations are Dirac pulses and the control parameters are the pulses amplitudes and times of application, the number of pulses is physically limited and the model leads to a sampled data control problem. The aim of this article is to present and compare two methods. The first method is a direct optimization scheme where a further refined numerical discretization is applied on the dynamics. The second method is an indirect scheme: first-order Pontryagin type necessary conditions are derived and used to compute the optimal sampling times.