Multidisciplinary Design Optimization of Turbine Disks Based on ANSYS Workbench Platforms

Uncertainties in multidisciplinary design optimization (MDO) have a significant influence on the whole design process of the engineering system. If uncertainty in the engineering system is not considered, optimization results may be unreliable. On the basis of the existing methods for uncertainty analysis, a new method for MDO under uncertainty, i.e. First-Order Second-Moment based collaborative optimization (FOSM-CO), is proposed, and its particular computational process is described in detail. The FOSM-CO is an optimization approach that utilizes reliability index to evaluate the probability that the random variables are in the safe region and instead of the original constraints with the probability. The computation results of the example indicate that FOSM-CO is an effective reliability design method for MDO under uncertainty.

Multidisciplinary Design Optimization (MDO) has been used to investigate the use of anew concept for a transonic transport, the strut-braced wing. The incorporation of a strutinto more traditional transonic transport concepts required the application of computationaldesign techniques that had been developed at Virginia Tech over the previous decade.Formalized MDO methods were required to reveal the benefits of the tightly coupledinteraction between the wing structural weight and the aerodynamic performance. Toperform this study, a suite of approximate analysis tools was assembled into a complete,conceptual-level MDO code. A typical mission of the Boeing 777-200IGW was chosen as thedesign mission profile. Several single-strut configurations were optimized for minimumtakeoff gross weight, with the best single-strut configuration showing a nearly20% reductionin takeoff gross weight, a 29% reduction in fuel weight, a 28% increase in the lift-to-dragratio, and a 41% increase in seat-miles per gallon relative to a comparable cantileverconfiguration. The use of aeroelastic tailoring in the design illustrated ways to obtain furtherbenefits. The paper synthesizes the results of the five-year effort, and concludes with adiscussion of the effects various constraints have on the design, and lessons learned oncomputational design during the project.

It is necessary to employ the Multidisciplinary Design Optimization (MDO) method in the design process of automatic weapon, because the process in itself is related to many disciplines and their couplings. The knowledge structure of MDO is analyzed, which includes mathematic modeling, system decomposition, optimization framework, approximation model, sensitivity analysis, optimization method, software integration, and etc.. The idea of using MDO in the design process of individual soldier automatic weapon is also explored. Based on the software package of iSIGHT, the primary multidisciplinary integration is carried out. Current research work will be helpful for further research on integrating MDO into the design of automatic weapon.

A ZJ-type high pressure lubrication pump is analyzed by multidisciplinary design optimization (MDO) method, where data are sampled via optimal Latin hypercube experiments, and the response surface models (RSMs) for the plunger piston and cylinder body of the pump are built.Lightweight design of the piston mechanism is conducted by using the improved collaborative optimization with a relaxation factor combined with sequential quadratic programming (SQP) algorithm.The results show that the approximate model accelerates the opimization speed greatly, the mass of optimized plunger mechanism is reduced by 8.03%, and MDO can effectivelly deal with the coupling factors between the different components to reduce mass while the stress constraints and fatigue life are met.

In studying multidisciplinary design optimization method for non-hierarchic system, Multidisciplinary Object Compatibility Design Optimization method based on simulated annealing algorithm is presented. In order to coordinate the independent optimization of subsystems, the compatibility constraint in system level and compatibility objective in subsystem work together. As optimization process continued, the coupling relationship between system level and different subsystems is gradually improved by state accepting function which is embedded in compatibility constraint. In this way, abnormal program termination and premature convergence will be avoided and ideal global optimal solution will be achieved effectually. Then the method is used in the optimization design of TR-B triple-redundancy transmission system. The multidisciplinary object compatibility design optimization model is established and the comprehensive optimal solution is obtained which meets the matching relationship of gear teeth, strength requirement and dynamic requirement, etc

In this paper, we develop an easy-to-implement approximate method to take uncertainties into account during a multidisciplinary optimization. Multidisciplinary robust design usually involves setting up a full uncertainty propagation within the system, requiring major modifications in every discipline and on the shared variables. Uncertainty propagation is an expensive process, but robust solutions can be obtained more easily when the disciplines affected by uncertainties have a significant effect on the objectives of the problem. A heuristic method based on local uncertainty processing (LOUP) is presented here, allowing approximate solving of specific robust optimization problems with minor changes in the initial multidisciplinary system. Uncertainty is processed within the disciplines that it impacts directly, without propagation to the other disciplines. A criterion to verify a posteriori the applicability of the method to a given multidisciplinary system is provided. The LOUP method is applied to an aircraft preliminary design industrial test case, in which it allowed to obtain robust designs whose performance is more stable than the one of deterministic solutions, relatively to uncertain parameter variations.

The area of Multiparametric Optimization (MPO) solves problems that contain unknown problem data represented by parameters. The solutions map parameter values to optimal design and objective function values. In this paper, for the first time, MPO techniques are applied to improve and advance Multidisciplinary Design Optimization (MDO) to solve engineering problems with parameters. A multiparametric subgradient algorithm is proposed and applied to two MDO methods: Analytical Target Cascading (ATC) and Network Target Coordination (NTC). Numerical results on test problems show the proposed parametric ATC and NTC methods effectively solve parametric MDO problems and provide useful insights to designers. In addition, a novel Two-Stage ATC method is proposed to solve nonparametric MDO problems. In this new approach elements of the subproblems are treated as parameters and optimal design functions are constructed for each one. When the ATC loop is engaged, steps involving the lengthy optimization of subproblems are replaced with simple function evaluations.

On-orbit applications, such as active debris removal, satellite refueling, maintenance and satellite health diagnosis require the ability for low-cost spacecraft to closely inspect other orbital objects in a non-cooperative manner. During this kind of mission, the relative navigation process becomes of critical importance for guaranteeing safe and collision-free proximity operations and maneuvers. The selection of relative navigation sensors appears being a critical task as it might drive the design choices in other subsystems (e.g., Attitude and orbit control system (AOCS), payload, power supply). This paper aims at studying the application of a Multidisciplinary Design Optimization (MDO) method to the design of AOCS and Navigation subsystems under small satellite constraints. The porposed MDO process is based on the optimization of navigation performance and mass reduction while respecting volume and power constraints for orbital close rendezvous. The navigation chain, including sensor simulation and navigation filter is simulated and integrated into the design cost function. The proposed MDO process based on a Genetic Algorithm (GA) and on an Extended Kalman Filter (EKF) aims at simplifying satellite design by determining a set of optimal admissible sensor combinations despite contradictory objectives on navigation and payload accuracy, mass reduction, power consumption and volume. Possible key advantages of the inclusion of the relative navigation subsystem within MDO process are the reduction of the design process time, the automation and optimization of the navigation architecture while respecting volume and power constraints of small satellites. A demonstration of the effectiveness of the proposed MDO method is provided on the benchmark of AVANTI mission.

In order to design a vehicle body with high strength and high stiffness, a multi-disciplinary design process should include careful consideration of multi-disciplinary design constraints to properly account for vehicle static stiffness (bending/torsional), durability, Noise/Vibration/Harshness (NVH), crash worthiness, light weight vehicle structure during the early stage of vehicle design process. With this approach, fast development of new vehicle body structures can be achieved with minimal number of iterations to match the conflicting design goals from each discipline. In the current research, a multi-disciplinary design optimization (MDO) based on a meta model is developed and refined to apply for the design of body structure. In an effort to apply the MDO for vehicle body structure, 4 phase procedures were established in the current research. In Phase I, a base model is created. In Phase II, an effect analysis is carried out. In Phase III, a meta model is created. Finally in Phase IV, using the optimization algorithm, the meta model created in Phase III is eventually refined through the process of optimization. In this research, static stiffness (bending / torsional), dynamic stiffness (1st torsion mode) were used for constrained conditions and the mass minimization was the object function for optimization.

<p>Multidisciplinary design optimization (MDO) refers to the process of designing systems characterized by the interaction of multiple interconnected disciplines. High-fidelity MDO usually requires large computational resources due to the computational cost of achieving multidisciplinary consistent solutions by coupling high-fidelity physics-based solvers. Gradient-based minimization algorithms are generally applied to find local minima, due to their efficiency in solving problems with a large number of design variables. This represents a limitation to performing global MDO and integrating black-box type analysis tools, usually not providing gradient information. The latter issues generally inhibit a wide use of MDO in complex industrial applications.</p><p>An architecture named multi-criterion adaptive sampling MDO (MCAS-MDO) is presented in the current research for complex simulation-based applications. This research aims at building a global derivative-free optimization tool able to employ high-fidelity/expensive black-box solvers for the analysis of the disciplines. MCAS-MDO is a surrogate-based architecture featuring a variable level of coupling among the disciplines and is driven by a multi-criterion adaptive sampling (MCAS) assessing coupling and sampling uncertainties. MCAS uses the dynamic radial basis function surrogate model to identify the optimal solution and explore the design space through parallel infill of new solutions.</p><p>The MCAS-MDO is tested versus a global derivative-free multidisciplinary feasible (MDF) approach, which solves fully-coupled multidisciplinary analyses, for two analytical test problems. Evaluation metrics include number of function evaluations required to achieve the optimal solution and sample distribution. The MCAS-MDO outperforms the MDF showing a faster convergence by clustering refined function evaluations in the optimum region.</p><p>The architecture is applied to a steady fluid-structure interaction (FSI) problem, namely the design of a tapered three-dimensional carbon fiber-reinforced plastic hydrofoil for minimum drag. The objective is the design of shape and composite material layout subject to hydrodynamic, structural, and geometrical constraints. Experimental data are available for the original configuration of the hydrofoil and allow validating the FSI analysis, which is performed coupling computational fluid dynamics, solving the Reynolds averaged Navier-Stokes equations, and finite elements, solving the structural equation of elastic motion. Hydrofoil forces, tip displacement, and tip twist are evaluated for several materials providing qualitative agreement with the experiments and confirming the need for the two-way versus one-way coupling approach in case of significantly compliant structures.</p><p>The free-form deformation method is applied to generate shape modifications of the hydrofoil geometry. To reduce the global computational expense of the optimization, a design space assessment and dimensionality reduction based on the Karhunen–Loève expansion (KLE) is performed off-line, i.e. without the need for high-fidelity simulations. It provides with a selection of design variables for the problem at hand through basis rotation and re-parametrization. By using the KLE, an efficient design space is identified for the current problem and the number of design variables is reduced by 92%.</p><p>A sensitivity analysis is performed prior to the optimization to assess the variability associated with the shape design variables and the composite material design variable, i.e. the fiber orientation. These simulations are used to initialize the surrogate model for the optimization, which is carried out for two models: one in aluminum and one in composite material. The optimized designs are assessed by comparison with the original models through evaluation of the flow field, pressure distribution on the body, and deformation under the hydrodynamic load. The drag of the aluminum and composite material hydrofoils is reduced by 4 and 11%, respectively, increasing the hydrodynamic efficiency by 4 and 7%. The optimized designs are obtained by evaluating approximately 100 designs. The quality of the results indicates that global derivative-free MDO of complex engineering applications using expensive black-box solvers can be achieved at a feasible computational cost by minimizing the design space dimensionality and performing an intelligent sampling to train the surrogate-based optimization.</p>

Multidisciplinary design optimization (MDO) is expected to play a major role in the competitive transportation industries of tomorrow, i.e., in the design of aircraft and spacecraft, of high speed trains, boats, and automobiles. All of these vehicles require maximum performance at minimum weight to keep fuel consumption low and conserve resources. Here, MDO can deliver mathematically based design tools to create systems with optimum performance subject to the constraints of disciplines such as structures, aerodynamics, controls, etc. Although some applications of MDO are beginning to surface, the key to a widespread use of this technology lies in the improvement of its efficiency. This aspect is investigated here for the MDO subset of structural optimization, i.e., for the weight minimization of a given structure under size, strength, and displacement constraints. Specifically, finite element based multilevel optimization of structures (here, statically indeterminate trusses and beams for proof of concept) is performed. In the system level optimization, the design variables are the coefficients of assumed displacement functions, and the load unbalance resulting from the solution of the stiffness equations is minimized. Constraints are placed on the deflection amplitudes and the weight of the structure. In the subsystems level optimizations, the weight of each element is minimized under the action of stress constraints, with the cross sectional dimensions as design variables. This approach is expected to prove very efficient, especially for complex structures, since the design task is broken down into a large number of small and efficiently handled subtasks, each with only a small number of variables. This partitioning will also allow for the use of parallel computing, first, by sending the system and subsystems level computations to two different processors, ultimately, by performing all subsystems level optimizations in a massively parallel manner on separate processors. It is expected that the subsystems level optimizations can be further improved through the use of controlled growth, a method which reduces an optimization to a more efficient analysis with only a slight degradation in accuracy. The efficiency of all proposed techniques is being evaluated relative to the performance of the standard single level optimization approach where the complete structure is weight minimized under the action of all given constraints by one processor and to the performance of simultaneous analysis and design which combines analysis and optimization into a single step. It is expected that the present approach can be expanded to include additional structural constraints (buckling, free and forced vibration, etc.) or other disciplines (passive and active controls, aerodynamics, etc.) for true MDO.

Effect of Variable Selection on Multidisciplinary Design Optimization: a Flight Vehicle Example

Collaborative optimization (CO), a decomposition-based multidisciplinary design optimization (MDO) method, is generally used in aeronautical systems. However, the subsystems optimizations of CO method are nested into system optimization of it in the execution process, numerous subsystem analyses are required to achieve consistency for entire system. For this problem, a nonnested collaborative optimization (NNCO) method is developed, in which system and subsystem optimizations are solved sequentially and repeatedly, and system consistancy is coordinated by a loop process together with the update of penalty parameters. Through test results of common analytical problems, which are generally used in the experiments of CO method, it's shown that the NNCO method requires two third fewer calls of the subsystem analysis than the CO method at least. Further more, CO and NNCO method are used to solve a satellite MDO problem, 0.05 and 8.05 hours are consumed for these two methods respectively. The efficiency of NNCO method in practical engineering design problem is proved.

Design of haptic devices requires trade-off between many conflicting requirements, such as high stiffness, large workspace, small inertia, low actuator force/torque, and a small size of the device. With the traditional design and optimization process, it is difficult to effectively fulfill the system requirements by separately treating the different discipline domains. To solve this problem and to avoid sub-optimization, this work proposes a design methodology, based on Multidisciplinary Design Optimization (MDO) methods and tools, for design optimization of six degree-of-freedom (DOF) haptic devices for medical applications, e.g. simulators for surgeon and dentist training or for remote surgery. The proposed model-based and simulation-driven methodology aims to enable different disciplines and subsystems to be included in the haptic device optimization process by using a robust model architecture that integrates discipline-specific models in an optimization framework and thus enables automation of design activities in the concept and detail design phase. Because of the multi-criteria character of the performance requirements, multi-objective optimization is included as part of the proposed methodology. Because of the high-level requirements on haptic devices for medical applications in combination with a complex structure, models such as CAD (Computer Aided Design), CAE (Computer Aided Engineering), and kinematic models are considered to be integrated in the optimization process and presenting a systems view to the design engineers. An integration tool for MDO is used as framework to manage, integrate, and execute the optimization process. A case study of a 6-DOF haptic device based on a TAU structure is used to illustrate the proposed methodology. With this specific case, a Multi-objective Genetic Algorithm (MOGA) with an initial population based on a pseudo random SOBOL sequence and Monte Carlo samplings is used for the optimization.

The design of space systems is a complex and multidisciplinary process with multiple conflicting objectives, large number of design variables, and constraints that limits application of the existing multidisciplinary design optimization architectures to this class of design problems. This paper presents an enhanced multidisciplinary design optimization architecture to concurrent holistic design optimization of a satellite system. The proposed multidisciplinary design optimization architecture extends concepts of multidiscipline feasible and bi-level integrated system synthesis into a unified architecture using metamodels. The proposed architecture was evaluated and compared with the existing multidisciplinary design optimization architectures that include all-at-once, bi-level integrated system synthesis, and multidisciplinary design optimization using a remote sensing small satellite in low earth orbit. The satellite design optimization problem deals with the minimization of the total mass of the satellite, involving disciplines of mission analysis, payload, structures, attitude determination and control, communication, command and data handling, power and thermal. The computational performance and accuracy of the proposed architecture were compared with multidisciplinary design optimization benchmark problems. Then the proposed architecture is successfully applied to the satellite system design problem. The results obtained show that metamodel-based bi-level integrated system synthesis-multidisciplinary design optimization architecture presented in this paper provides an effective way of solving large-scale design problems.