Multidisciplinary Optimization Procedure Research Articles

Making multidisciplinary optimization fit for practical usage in car body development

The vehicle structure is a highly complex system as it is subject to different requirements of many engineering disciplines. Multidisciplinary optimization (MDO) is a simulation-based approach for capturing this complexity and achieving the best possible compromise by integrating all relevant CAE-based disciplines. However, to enable operative application of MDO even under consideration of crash, various adjustments to reduce the high numerical resource requirements and to integrate all disciplines in a target way must be carried out. They can be grouped as follows: The use of efficient optimization strategies, the identification of relevant load cases and sensitive variables as well as the reduction of CAE calculation time of costly crash load cases by so-called finite element (FE) submodels. By assembling these components in a clever way, a novel, adaptively controllable MDO process based on metamodels is developed. There are essentially three special features presented within the scope of this paper: First, a module named global sensitivity matrix which helps with targeted planning and implementation of a MDO by structuring the multitude of variables and disciplines. Second, a local, heuristic and thus on all metamodel types computable prediction uncertainty measure that is further used in the definition of the optimization problem. And third, a module called adaptive complexity control which progressively reduces the complexity and dimensionality of the optimization problem. The reduction of resource requirements and the increase in the quality of results are significant, compared to the standard MDO procedure. This statement is confirmed by providing results for a FE full vehicle example in six load cases (five crash load cases and one frequency analysis).

A Novel Optimization Framework to Replicate the Vibro-Acoustics Response of an Aircraft Fuselage

In this work, a novel optimization framework, based on a Multi-Disciplinary Optimization (MDO) procedure, applied to the vibro-acoustic Finite Element Method (FEM) model of an aircraft fuselage mock-up, is proposed. The MDO procedure, based on an Efficient Global Optimization (EGO)-like approach, is implemented to characterize acoustic sources that replicate the sound pressure field generated by the engines on the fuselage. A realistic sound pressure field, evaluated by aeroacoustic simulations, was considered as the reference acoustic load, whereas two equivalent sound fields, displayed by two different arrays of microphones and generated by the same configuration of monopoles, were calculated by the proposed vibro-acoustic FEM-MDO procedure. The proposed FEM-MDO framework enables to set up ground experimental tests on aircraft components, useful to replicate their vibro-acoustic performances as if tested in flight. More in general, such a procedure can also be used as a reference tool to design simplified tests starting from more complex ones.

Multidisciplinary and multifidelity optimization for twin-web turbine disc with asymmetric temperature distribution

While having been proven its significant advantage in losing weight, twin-web turbine disc (TWD) is known to be the novel stage of development in the area of high-pressure turbine discs. There is a significant axial temperature gradient which should be taken into consideration for the asymmetric web structure to obtain the optimal shape of TWD. An expensive three-dimensional fluid-thermal analysis should be introduced and executed to obtain accurate temperature distribution. A kind of multidisciplinary and multifidelity optimization procedure is proposed for the simultaneous combining of two obvious advantages with the low cost of axisymmetric strength analysis and the high fidelity of three-dimensional fluid-thermal analysis and strength analysis. It is executed under the support techniques, including zero circumferential elasticity modulus method at the non-axisymmetric region during axisymmetric strength analysis and inverse distance weighted method with traversing searching radius. A supporting ring with double sides locating mode at the disc hub is designed to avoid two webs being close to each other and provides the inlet for the cooling gas into the inner cavity. The optimization result demonstrates that the proposed method is capable and has an efficient benefit due to the low-cost computing procedure for obtaining the optimal shape of TWD with asymmetric temperature distribution.

Characterization of equivalent acoustic sources to reproduce the acoustic field generated by engines on an aircraft fuselage

This work presents a general procedure to characterize equivalent acoustic sources to reproduce the sound pressure field generated by the engines on an aircraft fuselage. The procedure would allow to set up ground experimental tests on aircraft components, by means of distributed loudspeakers, to obtain their vibro-acoustic performances as if they were tested in flight conditions.A FEM model of an aircraft fuselage mock-up was built up, comprising the structure, the internal acoustic cavities and the external air. The sound pressure field generated by the engines was considered as the reference solution, whereas an equivalent sound field, produced by distributed monopole sources surrounding the structure, was obtained by leveraging on the proposed Multi-Disciplinary Optimization (MDO) procedure.The MDO procedure was based on the mutual interaction between the commercial codes Siemens NX, for the CAE/FEM simulations, and Noesis Optimus, for the optimization framework.

An optimization-based procedure for self-generation of Re-entry Vehicles shape

In the present paper a multidisciplinary optimization procedure for the self-generation of re-entry vehicle shapes has been developed. The procedure relies on a novel parametric model of blended wing-body shapes which is used to create a re-entry configuration around a fixed volume. The flexibility of the model allows us to create lifting body or winged re-entry vehicle from an optimization procedure as monolithic bodies. Multidisciplinary analysis is performed with engineering methods valid in conceptual design. Results of shape optimization for a minimum mass configuration, performed for a Low Earth Orbit Re-entry mission, confirmed the suitability of the procedure by indicating a decrease of vehicle mass configuration that is obtained by reducing the wingspan parameter for a conceptual lifting body configuration.

Study on multidisciplinary design optimization of a 2-degree-of-freedom robot based on sensitivity analysis and structural analysis

The optimization design of a robot was usually conducted by the sequential design, which, however, neglected the interactive impacts of different disciplines. To address this shortage, this article presents a design multidisciplinary optimization procedure for a 2-degree-of-freedom robot. In the proposed design optimization, four disciplines are involved, which are composed of kinematics, dynamics, structure, and control. The coupling relationship among the four disciplines is analyzed based on variable sensitivity analysis. A collaborative optimization is proposed to obtain the optimum values of the system-level optimization. With the method of a genetic algorithm, the individual discipline optimization is executed to obtain the subsystem optimum values. The optimized 2-degree-of-freedom robot is able to synthesize an optimum function value and simultaneously shows a good satisfaction to the requirement of all constraints. The structural analysis results demonstrate that the multidisciplinary design optimization is successfully applied to the multi-degree-of-freedom robot design and provides a beneficial reference for the design of more complicated mechanical system.

Combined preliminary–detailed design of wind turbines

Abstract. This paper is concerned with the holistic optimization of wind turbines. A multi-disciplinary optimization procedure is presented that marries the overall sizing of the machine in terms of rotor diameter and tower height (often termed “preliminary design”) with the detailed sizing of its aerodynamic and structural components. The proposed combined preliminary–detailed approach sizes the overall machine while taking into full account the subtle and complicated couplings that arise due to the mutual effects of aerodynamic and structural choices. Since controls play a central role in dictating performance and loads, control laws are also updated accordingly during optimization. As part of the approach, rotor and tower are sized simultaneously, even in this case capturing the mutual effects of one component over the other due to the tip clearance constraint. The procedure, here driven by detailed models of the cost of energy, results in a complete aero-structural design of the machine, including its associated control laws. The proposed methods are tested on the redesign of two wind turbines, a 2.2 MW onshore machine and a large 10 MW offshore one. In both cases, the optimization leads to significant changes with respect to the initial baseline configurations, with noticeable reductions in the cost of energy. The novel procedures are also exercised on the design of low-induction rotors for both considered wind turbines, showing that they are typically not competitive with conventional high-efficiency rotors.

Aerodynamic and aeroacoustic optimization for design of a forward-curved blades centrifugal fan

This paper presents a multidisciplinary optimization procedure for enhancing the aerodynamic and aeroacoustic performance of a forward-curved blade centrifugal fan for residential ventilation. Flow analysis in a forward-curved blade centrifugal fan was conducted by solving three-dimensional steady and unsteady Reynolds-averaged Navier–Stokes equations using the shear stress transport turbulence model. On the basis of the aerodynamic sources extracted from the unsteady flow, aeroacoustic analysis was implemented in a finite/infinite element method by solving the variational formulation of Lighthill’s analogy. Experiments were performed to obtain aerodynamic and aeroacoustic measurements for validation of numerical results. The single- and multi-objective optimizations were performed sequentially. The single-objective optimization was carried out to improve the efficiency of the fan using a radial basis neural network surrogate model with four design variables defining the scroll cut-off angle, scroll diffuser expansion angle, diameter ratio of the impeller, and blade exit angle. Multi-objective optimization based on the single-objective optimization result was carried out to simultaneously improve the efficiency and reduce the sound pressure through a hybrid multi-objective evolutionary algorithm coupled with a response surface approximation surrogate model with two design variables defining the scroll cut-off radius and distance. These objective functions were accessed numerically through three-dimensional aerodynamic and aeroacoustic analyses at the design points sampled by Latin hypercube sampling in the design space. Arbitrary selected optimum designs in the Pareto-optimal solutions yielded significant increases in efficiency and decreases in the sound pressure level compared to the reference design.

Thermo-structural optimization of integrated thermal protection panels with one-layer and two-layer corrugated cores based on simulated annealing algorithm

Toexplore weight saving potential capability, a multidisciplinary optimization procedure based on simulated annealing algorithm was proposed to unveil the minimum weight design for integrated thermal protection system subjected to in-service thermal and mechanical loads. The panel configurations with one-layer and two-layer corrugated cores are considered for comparison. Heat transfer and structural field analysis for each panel configuration were performed to obtain the temperature, buckling, stress and deflection responses for structural components of interest, which were then considered as critical constraints of the optimization problem. Sensitivity analysis was performed to disclose the effect of individual design variables on the thermo-structural extreme responses, and the designed thermal protection system performance and weight for the two configurations were discussed. The results demonstrated that the two-layer structure provides superior structural efficiency and performance to resist thermal buckling deformation in comparison with the one-layer panel. Its area-specific weight is reduced by more than 14---29 % with respect to the one-layer panel design, and 30---50 % weight efficient can be implemented at higher thermal buckling constraint levels, while keeping considerable temperature, stress and deflection margins.

Reliability modeling and optimization of die-casting existing epistemic uncertainty

Die-casting is a typical multidisciplinary system, in which there are many disciplines involved such as hydrodynamics, heat transfer and elastic-plastic mechanics and their coupled relations are intricate. Moreover, there are inherently epistemic uncertainties in die-casting. This paper aims at reliability modeling and optimization of die-casting. Firstly, finite element analysis is applied to simulate the process of die-casting, and the quadratic response surface is used to represent the multidisciplinary optimization model of die-casting, in which the evidence theory is used to represent the epistemic uncertainty. Then, a reliability-based multidisciplinary optimization (RBMDO) procedure for die-casting is proposed. The results show the RBMDO procedure possesses high computational efficiency in optimizing multidisciplinary system with epistemic uncertainty.

Optimization of Hybrid Sounding Rockets for Hypersonic Testing

The use of ground-launched hybrid rockets to bring subscale models to flight conditions within the hypersonic flight corridor is investigated. The analysis is based on a multidisciplinary optimization procedure that couples the direct optimizations of the parameters that rule the engine geometry and operation and the indirect optimization of the trajectory. The final Mach number is maximized for given initial conditions and assigned payload and final altitude. Different rocket configurations are considered; in particular, the performance of single-stage and two-stage rockets are determined for different payload fractions. Results show that hybrid motors are suitable to accomplish this kind of mission, and that single-stage rockets are preferable. Only when the payload fraction is very small and large final velocity are sought, two-stage rockets may offer better performance.

A Krylov–Arnoldi reduced order modelling framework for efficient, fully coupled, structural–acoustic optimization

In this work, a reduced order multidisciplinary optimization procedure is developed to enable efficient, low frequency, undamped and damped, fully coupled, structural---acoustic optimization of interior cavities backed by flexible structural systems. This new method does not require the solution of traditional eigen value based problems to reduce computational time during optimization, but are instead based on computation of Arnoldi vectors belonging to the induced Krylov Subspaces. The key idea of constructing such a reduced order model is to remove the uncontrollable, unobservable and weakly controllable, observable parts without affecting the noise transfer function of the coupled system. In a unified approach, the validity of the optimization framework is demonstrated on a constrained composite plate/prism cavity coupled system. For the fully coupled, vibro---acoustic, unconstrained optimization problem, the design variables take the form of stacking sequences of a composite structure enclosing the acoustic cavity. The goal of the optimization is to reduce sound pressure levels at the driver's ear location. It is shown that by incorporating the reduced order modelling procedure within the optimization framework, a significant reduction in computational time can be obtained, without any loss of accuracy--when compared to the direct method. The method could prove as a valuable tool to analyze and optimize complex coupled structural---acoustic systems, where, in addition to fast analysis, a fine frequency resolution is often required.

Multidisciplinary Design Optimization Procedure for Improved Design of a Cooled Gas Turbine Blade

A multidisciplinary optimization procedure for gas turbine blade design has been developed and demonstrated on a generic 3-D blade. The blade is cooled both internally and externally (film cooling). Aerodynamic and heat transfer design criteria are integrated along with various constraints on the blade geometry. The blade is divided into numerous spanwise sections and each section is represented by a Bezier-Bernstein polynomial. A comprehensive solver for 3-D Navier-Stokes equations is used for the viscous flow calculations. The finite element method is used to obtain the blade interior temperatures. The average blade temperature and maximum blade temperature at each spanwise section are minimized, with aerodynamic and geometric constraints on the blade geometry. The constrained multiobjective optimization problem is solved using the Kreisselmeier-Steinhauser function approach. The results for a generic turbine blade design problem show significant improvements after optimization.

Optimal Wing Planform Design for Aeroelastic Control

An integrated aeroservoelastic design synthesis for flutter suppression and gust load reduction using multiple control surfaces is presented. For this multidisciplinary optimization procedure, structural design variables, control system, and aerodynamic design variables, such as wing planform, ply orientation of the composite layer, and control surface size and location, are considered simultaneously. The analysis for a composite wing with control surfaces is conducted by the finite element method. Unsteady aerodynamic forces calculated by the doublet lattice method are approximated as transfer functions of the Laplace variable by Roger's method. The output feedback control scheme is applied to design the active control system. Using a swept wing model, the performance of the control system is investigated. The geometry of wing planform and control surface size and location are determined by using the genetic algorithm. Design objectives are to minimize the control performance index and the root mean square of the gust responses for various airspeeds. Numerical results showed substantial improvements in performance index value as well as the root-mean-square values of the gust responses compared with the baseline wing model.

Multidisciplinary optimization for gas turbine airfoil design

A multidisciplinary optimization procedure for gas turbine airfoil design has been developed and demonstrated on a generic blade. Aerodynamic and heat transfer design objectives are integrated along with various constraints on the airfoil geometry. Heat transfer optimization and external aerodynamic shape optimization has been performed on a generic blade. Shape optimization is performed using geometric parameters associated with film cooling and blade external shape. The blade is cooled both internally and externally (film cooling). Thin layer Navier-Stokes equations are used for the external flow field evaluations and finite element analysis is used to determine the blade interior temperatures. Total pressure loss, exit kinetic energy loss, average blade temperature and maximum blade temperature are minimized, with constraints on the blade geometry. The constrained multiobjective optimization problem is solved using the Kreisselmeier-Steinhauser (K-S) function approach. The results for the generic blade demonstrate the effectiveness of the optimization procedure.

Shape optimization of turbine blades with the integration ofaerodynamics and heat transfer

A multidisciplinary optimization procedure, with the integration of aerodynamic and heat transfer criteria, has been developed for the design of gas turbine blades. Two different optimization formulations have been used. In the first formulation, the maximum temperature in the blade section is chosen as the objective function to be minimized. An upper bound constraint is imposed on the blade average temperature and a lower bound constraint is imposed on the blade tangential force coefficient. In the second formulation, the blade average and maximum temperatures are chosen as objective functions. In both formulations, bounds are imposed on the velocity gradients at several points along the surface of the airfoil to eliminate leading edge velocity spikes which deteriorate aerodynamic performance. Shape optimization is performed using the blade external and coolant path geometric parameters as design variables. Aerodynamic analysis is performed using a panel code. Heat transfer analysis is performed using the finite element method. A gradient based procedure in conjunction with an approximate analysis technique is used for optimization. The results obtained using both optimization techniques are compared with a reference geometry. Both techniques yield significant improvements with the multiobjective formulation resulting in slightly superior design.

A multidisciplinary optimization using semi-analytical sensitivity analysis procedure and multilevel decomposition

This paper addresses the development of a multidisciplinary optimization procedure using an efficient semi-analytical sensitivity analysis technique and multilevel decomposition for the design of aerospace vehicles. A semi-analytical sensitivity analysis procedure is developed for aerodynamic design sensitivities. Accuracy and efficiency of the sensitivity analysis procedure is established through comparison of the results with those obtained using a finite difference technique. The optimization problem, with the integration of aerodynamics and structures, is decomposed into two levels. Optimization is performed for improved aerodynamic performance at the first level and improved structural performance at the second level. Aerodynamic analysis is performed by solving the three-dimensional parabolized Navier Stokes equations. A nonlinear programming technique and an approximate analysis procedure are used for optimization. The procedure developed is applied to design the wing of a high speed aircraft. Results obtained show significant improvements in the wing aerodynamic and structural performance when compared to a reference or baseline wing configuration. The use of the semi-analytical sensitivity technique provides significant computational savings.

DESIGN OF HIGH SPEED PROPROTORS USING MULTIOBJECTIVE OPTIMIZATION TECHNIQUES

A multidisciplinary optimization procedure is developed for the design of high speed proprotors. The objectives are to simultaneously maximize the propulsive efficiency in high speed cruise and the rotor figure of merit in hover. Since the problem involves multiple design objectives, multiobjective function formulation techniques are used. Two different multiobjective function procedures, the Kreisselmeier-Steinhauser function approach and the Minimum Sum β approach, are used. A detailed two-celled isotropic box beam is used to model the load carrying member within the rotor blade. Constraints are imposed on rotor blade aeroelastic stability in cruise, the first natural frequency in hover and total blade weight. Both aerodynamic and structural design variables are used. The results obtained using both objective function formulations are compared lo the reference rotor and show significant aerodynamic performance improvements without sacrificing dynamic and aeroelastic stability characteristics. The procedure developed provides significant design trends and trade-off information associated with the two conflicting design objectives.

OPTIMUM DESIGN OF HIGH SPEED PROP-ROTORS USING A MULTIDISCIPLINARY APPROACH

The design of advanced high speed prop-rotor aircraft is addressed using a formal multidisciplinary optimization procedure. The optimization problem is formulated with aerodynamic performance, dynamics, aeroelastic stability and structural design requirements. Both high speed cruise and hover flight conditions are addressed. The analysis is performed at a cruise speed of 400 knots. The efficiency in cruise is maximized without deteriorating hover performance. Constraints are imposed on fundamental frequency, blade weight, thrust in hover, total power required and aeroelastic stability in cruise. A wide selection of structural and aerodynamic design variables are used. The optimization is performed using a nonlinear programming procedure and an approximate analysis technique. The procedure yields significant improvements in the overall rotor performance.

ASTROS - A multidisciplinary automated structural design tool

ASTROS (Automated Structural Optimization System) is a finite-element-based multidisciplinary structural optimization procedure developed under Air Force sponsorship to perform automated preliminary structural design. The design task is the determination of the structural sizes that provide an optimal structure while satisfying numerous constraints from many disciplines. In addition to its automated design features, ASTROS provides a general transient and frequency response capability, as well as a special feature to perform a transient analysis of a vehicle subjected to a nuclear blast. The motivation for the development of a single multidisciplinary design tool is that such a tool can provide improved structural designs in less time than is currently needed. The role of such a tool is even more apparent as modern materials come into widespread use. Balancing conflicting requirements for the structure's strength and stiffness while exploiting the benefits of material anisotropy is perhaps an impossible task without assistance from an automated design tool. Finally, the use of a single tool can bring the design task into better focus among design team members, thereby improving their insight into the overall task.