| Dr. Renaud conducts his research in the Design Automation Laboratory at Fitzpatrick Hall of Engineering. Current Research
Biomechanics and Biomaterials in Orthopaedics Website Faculty Profile - Biomechanics and Biomaterials in Orthopaedics Website Trust Region Meta-Model Management for the Optimal Design of a High Speed Supercavitating VehicleThe performance of a high speed supercavitating vehicle (HSSV) results from the complex interactions among the many different physical phenomena and hardware components. Traditionally underwater vehicle designers have created systems exhibiting desired behaviors based on past experience, experimentation, intuition, and graphical tools and statistics to manipulate design variables. Computational analysis tools were used primarily for feedback and verification in the design process. The designers of the high speed supercavitating vehicle are tasked with incorporating advanced concepts subject to previously unattainable performance requirements at an affordable cost and acceptable risk. Increasingly the use of meta-models in place of expensive computer simulations are being used to drive multidisciplinary design processes based on nonlinear optimization techniques. The use of meta-model strategies is designed to reduce the number of detailed, costly computer simulations required during optimization while maintaining the pertinent features of the design problem. The concern addressed in this study is how to manage the interaction between the optimization and the fidelity of the HSSV meta-models to ensure that the process converges to a solution of the original design problem. Initial studies will focus on obtaining a feasible design of the HSSV using a trust region meta-model management strategy to drive a sequential meta-model optimization process. The sequence of meta-model optimizations will make use of an exterior penalty function approach, based on the augmented Lagrangian that has been demonstrated to be provably convergent by Dr. Renaud and his students. The exterior penalty approach can simultaneously drive the feasibility of the HSSV while at the same time seeking performance improvements in the stability and control of the vehicle. A new adaptive meta-modeling technique that constructs cumulative meta-models of the high speed supercavitating vehicle’s (HSSV) performance by actively modifying the experimental sample points will be developed. The methodology will make use of a new adaptive experimental design (AED) approach for meta-modeling that has been pioneered by Dr. Renaud and his students. The novel AED meta-modeling technique reduces from order n-squared to order n the amount of data needed to construct meta-models. This is particularly important for the conceptual design optimization of systems that involve very large simulation codes such as the high speed supercavitating vehicle. The cumulative meta-models will be constructed over the design spaces visited during sequential meta-model optimizations, providing a global reference for designers. In addition as part of this research Dr. Renaud and students will make use of a new interior point approach being developed for trust region managed sequential meta-model optimization. The interior point approach insures that feasibility is maintained throughout the optimization process. This facilitates the delivery of a consistent and feasible design when subject to reduced design cycle time constraints. In order to deal with infeasible starting points which will be the case for the HSSV, probability one homotopy methods will be used to relax constraints and push designs toward feasibility. The two student supported in this effort will have an opportunity to work with state of the art physics based models of the HSSV developed by Penn State’s Applied Research Laboratory. The students will develop advance skills in meta-model construction and optimization. Aerodynamic Shape Optimization for Morphing Aircraft UAVs Interest in the design and development of small unmanned aerial vehicles (UAVs) has increased dramatically in the last two and a half decades. These vehicles can perform a large variety of missions related to surveillance and detection including video and IR surveillance, communication relay links, and the detection of biological, chemical, or nuclear materials.
Future classes of small UAVs are envisioned that will be designed for missions requiring both endurance and maneuverability components (i.e., multiple mission profiles). Such missions could include; long endurance/range flight performance for surveillance combined with profiles that call for, survivability, attack, targeting, detection (e.g., precision video and IR imaging), communication, chemical and biological weapons sensing and the placement of unattended sensors. This requires that the UAV be capable of dramatically altering its aerodynamic performance characteristics.
The adaptive airframe UAV concept being proposed is a unique morphing biplane referred to as the Buckle-Wing Biplane. The wing consists of two highly elastic beam-like lifting surfaces joined at the outboard wing tips in either a pinned or clamped configuration. The Buckle-Wing Biplane UAV is capable of morphing between a bi-plane configuration designed for maneuverability to a single fixed wing configuration designed for long range/high endurance. As part of this technology development effort the design of the Buckle-Wing’s aerodynamic shapes will be critical to the functioning of this adaptive UAV airframe. The airfoils must be capable of functioning both as independent lifting surfaces and as a fused single wing. The aerodynamic shape of the two independent airfoils and the fused single airfoil must be determined to provide maximum efficiency under a variety of takeoff, cruise, maneuver, loiter and landing conditions. Aerodynamic design begins by considering wing sections as two dimensional airfoils and then proceeds to include sweep and wing body interactions and finally aeroelastic (aerodynamic and structural interaction) effects. In this investigation we will use NASA’s CFL3D computational fluid dynamic software to predict the aerodynamic performance of the three different wing geometries. These CFD simulations will be coupled to a large scale numerical optimizer in order to numerically determine the best shape for the specified flight envelopes. Response surface approximations will be used reduce the computational cost associated with linking a numerical optimizer to the high fidelity CFL3D models.
The optimization problem will be posed as a multi-objective optimization problem. The optimizer will simultaneously seek to maximize the range and/or endurance of the vehicle flying in the fused single wing configuration, while optimizing the maneuverability characteristics of the vehicle with two independent airfoils deployed. Maneuverability characteristics include for example maximum acceleration, and instantaneous and sustained turn rates where low wing loading is required. Maximum acceleration requires a wing loading that is proportional to the minimum-drag lift coefficient (CL_min-drag). Therefore an airfoil with a large "drag bucket" is preferable. A high instantaneous turn rate requires an airfoil section shape that gives a high maximum lift coefficient (CL_max). The maximum sustained turn rate has an optimum W/S, which varies with load factor. Implicit Uncertainty Estimation in Multilevel Optimization This research focuses on the development of a collaborative optimization framework for the robust design of complex engineering systems such as automobiles, aircraft or consumer products. The collaborative optimization framework will account for and manage the uncertainties in the performance predictions generated by the computer simulation tools used for the design of these systems. Each computer simulation model is an abstraction of reality and has some uncertainty associated with its performance predictions. This uncertainty must be accounted for in the simulation based design process. An implicit method for estimating system performance uncertainties within a bilevel optimization algorithm that employs decomposition techniques to facilitate distributed computation will be developed. The methodology will account for both the uncertainty associated with design inputs and the uncertainty of performance predictions from each of the simulation tools. A mathematical proof of convergence will be developed to validate the bilevel optimization algorithm being developed in this investigation. The framework will be implemented in a distributed computing environment providing for parallel computation and concurrent design. Industry partners will test the framework and measure the computational improvements using a suite of benchmark test problems. It is anticipated that the use of the collaborative optimization framework developed in this research will lead to reduced product development times at reduced cost and risk. The collaborative optimization framework will facilitate the concurrent design of complex engineering systems in a parallel-computing environment. The benefits of parallel computation lead to reductions in product development times. The ability to manage uncertainty and risk in this parallel design environment will insure robust performance of the resulting system. The development of the non-deterministic collaborative optimization framework will demonstrate that designers can effectively manage both the uncertainty and risk associated with the simulation based design of new products in a parallel computing environment.. Topology Optimization in Biomechanics Degenerated lumbar spines are often treated by replacing one or more intervertebral discs by bone grafts and inserting an implant such as an internal spinal fixator in order to achieve painless spinal stability. A new surgical technique for interbody fusion is currently in development. The procedure makes use of an interbody fusion implant that is inserted between the vertebral bodies to be fused. The interbody fusion implant is used to provide support structure during fusion. The implant is packed with bone graft material to facilitate the fusion of the two vertebral bodies. Our goal in this work is to obtain the optimal topology (i.e., shape) of the interbody fusion implant. The implant must be capable of supporting the mechanical loads of the lumbar spine while solid fusion of the vertebral bodies occurs. The implant restrains the bone graft material and maintains proper intervertebral spacing during fusion. Finite element analysis and topology optimization software will be used to drive the topology design. The topology optimization process will seek to satisfy stress contraints for five different loading conditions of the implant. Loading conditions include flexion, extension, left lateral bending, right lateral bending and a combination of flexion and lateral bending. A fixed compressive load is applied in all cases. Additional constraints include limits on deformations for the implant and minimal wall thickness constraints. These constraints insure that the implant design will facilitate fusion without graft crumbling and displacement. The objective of minimizing the volume of the implant subject to the constraints will inherently maximize the available bone graft area/volume for lumbar spine fusion. Selected Recent Publications Perez,
V.M., Renaud, J.E., Watson, L.W., "Adaptive Experimental Design
for Construction of Response Surface Approximations", AIAA Journal.
(accepted for publication).
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