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NASA NTRS2004

A Most Probable Point-Based Method for Reliability Analysis, Sensitivity Analysis and Design Optimization

A major step in a most probable point (MPP)-based method for reliability analysis is to determine the MPP. This is usually accomplished by using an optimization search algorithm. The minimum distance associated with the MPP provides a measurement of safety probability, which can be obtained by approximate probability integration methods such as FORM or SORM. The reliability sensitivity equations are derived first in this paper, based on the derivatives of the optimal solution. Examples are provided later to demonstrate the use of these derivatives for better reliability analysis and reliability-based design optimization (RBDO).

Hou, Gene J.-W↗

NASA NTRS2004

A Most Probable Point-Based Method for Reliability Analysis, Sensitivity Analysis and Design Optimization

A major step in a most probable point (MPP)-based method for reliability analysis is to determine the MPP. This is usually accomplished by using an optimization search algorithm. The optimal solutions associated with the MPP provide measurements related to safety probability. This study focuses on two commonly used approximate probability integration methods; i.e., the Reliability Index Approach (RIA) and the Performance Measurement Approach (PMA). Their reliability sensitivity equations are first derived in this paper, based on the derivatives of their respective optimal solutions. Examples are then provided to demonstrate the use of these derivatives for better reliability analysis and Reliability-Based Design Optimization (RBDO).

Hou, Gene J.-W.↗

NASA NTRS2011

Multidisciplinary Modeling Software for Analysis, Design, and Optimization of HRRLS Vehicles

The concept for Highly Reliable Reusable Launch Systems (HRRLS) under the NASA Hypersonics project is a two-stage-to-orbit, horizontal-take-off / horizontal-landing, (HTHL) architecture with an air-breathing first stage. The first stage vehicle is a slender body with an air-breathing propulsion system that is highly integrated with the airframe. The light weight slender body will deflect significantly during flight. This global deflection affects the flow over the vehicle and into the engine and thus the loads and moments on the vehicle. High-fidelity multi-disciplinary analyses that accounts for these fluid-structures-thermal interactions are required to accurately predict the vehicle loads and resultant response. These predictions of vehicle response to multi physics loads, calculated with fluid-structural-thermal interaction, are required in order to optimize the vehicle design over its full operating range. This contract with ResearchSouth addresses one of the primary objectives of the Vehicle Technology Integration (VTI) discipline: the development of high-fidelity multi-disciplinary analysis and optimization methods and tools for HRRLS vehicles. The primary goal of this effort is the development of an integrated software system that can be used for full-vehicle optimization. This goal was accomplished by: 1) integrating the master code, FEMAP, into the multidiscipline software network to direct the coupling to assure accurate fluid-structure-thermal interaction solutions; 2) loosely-coupling the Euler flow solver FEFLO to the available and proven aeroelasticity and large deformation (FEAP) code; 3) providing a coupled Euler-boundary layer capability for rapid viscous flow simulation; 4) developing and implementing improved Euler/RANS algorithms into the FEFLO CFD code to provide accurate shock capturing, skin friction, and heat-transfer predictions for HRRLS vehicles in hypersonic flow, 5) performing a Reynolds-averaged Navier-Stokes computation on an HRRLS configuration; 6) integrating the RANS solver with the FEAP code for coupled fluid-structure-thermal capability; and 7) integrating the existing NASA SRGULL propulsion flow path prediction software with the FEFLO software for quasi-3D propulsion flow path predictions, 8) improving and integrating into the network, an existing adjoint-based design optimization code.

Spradley, Lawrence W.↗

NASA NTRS2012

Metroplex Optimization Model Expansion and Analysis: The Airline Fleet, Route, and Schedule Optimization Model (AFRS-OM)

This report describes the Airline Fleet, Route, and Schedule Optimization Model (AFRS-OM) that is designed to provide insights into airline decision-making with regards to markets served, schedule of flights on these markets, the type of aircraft assigned to each scheduled flight, load factors, airfares, and airline profits. The main inputs to the model are hedged fuel prices, airport capacity limits, and candidate markets. Embedded in the model are aircraft performance and associated cost factors, and willingness-to-pay (i.e. demand vs. airfare curves). Case studies demonstrate the application of the model for analysis of the effects of increased capacity and changes in operating costs (e.g. fuel prices). Although there are differences between airports (due to differences in the magnitude of travel demand and sensitivity to airfare), the system is more sensitive to changes in fuel prices than capacity. Further, the benefits of modernization in the form of increased capacity could be undermined by increases in hedged fuel prices

Sherry, Lance↗

NASA NTRS1992

On options for interdisciplinary analysis and design optimization

The interdisciplinary optimization of engineering systems is discussed from the standpoint of the computational alternatives available to the designer. The analysis of such systems typically requires the solution of coupled systems of nonlinear algebraic equations. The solution procedure is necessarily iterative in nature. It is shown that the system can be solved by fixed point iteration, by Newton's method, or by a combination of the two. However, the need for sensitivity analysis may affect the choice of analysis solution method. Similarly, the optimization of the system can be formulated in several ways that are discussed in the paper. It is shown that the effect of the topology of the interaction between disciplines is a key factor in the choice of analysis, sensitivity and optimization methods. Several examples are presented to illustrate the discussion.

Haftka, R. T.↗

NASA NTRS1999

Development of Response Surface Models for Rapid Analysis and Multidisciplinary Optimization of Launch Vehicle Design Concepts

Multidisciplinary design optimization (MDO) is an important step in the design and evaluation of launch vehicles, since it has a significant impact on performance and lifecycle cost. The objective in MDO is to search the design space to determine the values of design parameters that optimize the performance characteristics subject to system constraints. Vehicle Analysis Branch (VAB) at NASA Langley Research Center has computerized analysis tools in many of the disciplines required for the design and analysis of launch vehicles. Vehicle performance characteristics can be determined by the use of these computerized analysis tools. The next step is to optimize the system performance characteristics subject to multidisciplinary constraints. However, most of the complex sizing and performance evaluation codes used for launch vehicle design are stand-alone tools, operated by disciplinary experts. They are, in general, difficult to integrate and use directly for MDO.

Unal, Resit↗

NASA NTRS2013

Robust Maneuvering Envelope Estimation Based on Reachability Analysis in an Optimal Control Formulation

This paper discusses an algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. Starting with an optimal control formulation, the optimization problem can be rewritten as a Hamilton- Jacobi-Bellman equation. This equation can be solved by level set methods. This approach has been applied on an aircraft example involving structural airframe damage. Monte Carlo validation tests have confirmed that this approach is successful in estimating the safe maneuvering envelope for damaged aircraft.

optimal control↗

NASA NTRS1992

Application of a neural network to simulate analysis in an optimization process

A new experimental software package called NETS/PROSSS aimed at reducing the computing time required to solve a complex design problem is described. The software combines a neural network for simulating the analysis program with an optimization program. The neural network is applied to approximate results of a finite element analysis program to quickly obtain a near-optimal solution. Results of the NETS/PROSSS optimization process can also be used as an initial design in a normal optimization process and make it possible to converge to an optimum solution with significantly fewer iterations.

Rogers, James L.↗

NASA NTRS1990

Parallel structural optimization with different parallel analysis interfaces

The real benefit of structural optimization techniques is in the application of these techniques to large structures such as full vehicles or full aircraft. For these structures, however, the sequential computer's time and memory requirements prohibit the solutions. With the rapid development of parallel computers, parallel processing of large scale structural optimization problems is achievable. In this paper we discuss the parallel processing of structural optimization problems with parallel structural analysis. Two different types of interface between the optimization and analysis routines are developed and tested.

El-Sayed, Mohamed E. M.↗

NASA NTRS1991

Aerodynamic shape optimization using sensitivity analysis on third-order Euler equations

Two major advancements of an aerodynamic optimization method with two design variables are described. The first is represnted by an improved flow prediction method that uses the third-order accurate discretization of the Euler equations. This method makes it possible to predict the flowfield of a perturbed shape which generates shocks and other large gradients without intermediate CFD analysis. The second advancement is the use of every surface grid point as a design variable in the aerodynamic shape optimization problem. The improved algorithm is demonstrated by optimizing the ramp shape of a scramjet-afterbody configuration for maximum axial thrust. It is concluded that the improved flow-field prediction method eliminates most of the flow analysis and a priori guessing of all possible shapes from which the optimum is to be selected.

Baysal, Oktay↗

NASA NTRS1984

Aerospace engineering design by systematic decomposition and multilevel optimization

A method for systematic analysis and optimization of large engineering systems, by decomposition of a large task into a set of smaller subtasks that is solved concurrently is described. The subtasks may be arranged in hierarchical levels. Analyses are carried out in each subtask using inputs received from other subtasks, and are followed by optimizations carried out from the bottom up. Each optimization at the lower levels is augmented by analysis of its sensitivity to the inputs received from other subtasks to account for the couplings among the subtasks in a formal manner. The analysis and optimization operations alternate iteratively until they converge to a system design whose performance is maximized with all constraints satisfied. The method, which is still under development, is tentatively validated by test cases in structural applications and an aircraft configuration optimization.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1990

Optimal trajectories for an aerospace plane. Part 1: Formulation, results, and analysis

The optimization of the trajectories of an aerospace plane is discussed. This is a hypervelocity vehicle capable of achieving orbital speed, while taking off horizontally. The vehicle is propelled by four types of engines: turbojet engines for flight at subsonic speeds/low supersonic speeds; ramjet engines for flight at moderate supersonic speeds/low hypersonic speeds; scramjet engines for flight at hypersonic speeds; and rocket engines for flight at near-orbital speeds. A single-stage-to-orbit (SSTO) configuration is considered, and the transition from low supersonic speeds to orbital speeds is studied under the following assumptions: the turbojet portion of the trajectory has been completed; the aerospace plane is controlled via the angle of attack and the power setting; the aerodynamic model is the generic hypersonic aerodynamics model example (GHAME). Concerning the engine model, three options are considered: (EM1), a ramjet/scramjet combination in which the scramjet specific impulse tends to a nearly-constant value at large Mach numbers; (EM2), a ramjet/scramjet combination in which the scramjet specific impulse decreases monotonically at large Mach numbers; and (EM3), a ramjet/scramjet/rocket combination in which, owing to stagnation temperature limitations, the scramjet operates only at M approx. less than 15; at higher Mach numbers, the scramjet is shut off and the aerospace plane is driven only by the rocket engines. Under the above assumptions, four optimization problems are solved using the sequential gradient-restoration algorithm for optimal control problems: (P1) minimization of the weight of fuel consumed; (P2) minimization of the peak dynamic pressure; (P3) minimization of the peak heating rate; and (P4) minimization of the peak tangential acceleration.

Miele, Angelo↗

NASA NTRS2008

Risk Analysis for Resource Planning Optimization

This paper describes a systems engineering approach to resource planning by integrating mathematical modeling and constrained optimization, empirical simulation, and theoretical analysis techniques to generate an optimal task plan in the presence of uncertainties.

optimization↗

NASA NTRS1998

Unstructured Finite Volume Computational Thermo-Fluid Dynamic Method for Multi-Disciplinary Analysis and Design Optimization

This paper describes a finite volume computational thermo-fluid dynamics method to solve for Navier-Stokes equations in conjunction with energy equation and thermodynamic equation of state in an unstructured coordinate system. The system of equations have been solved by a simultaneous Newton-Raphson method and compared with several benchmark solutions. Excellent agreements have been obtained in each case and the method has been found to be significantly faster than conventional Computational Fluid Dynamic(CFD) methods and therefore has the potential for implementation in Multi-Disciplinary analysis and design optimization in fluid and thermal systems. The paper also describes an algorithm of design optimization based on Newton-Raphson method which has been recently tested in a turbomachinery application.

Majumdar, Alok↗

NASA NTRS2003

Using Plate Finite Elements for Modeling Fillets in Design, Optimization, and Dynamic Analysis

A methodology has been developed that allows the use of plate elements instead of numerically inefficient solid elements for modeling structures with 90 degree fillets. The technique uses plate bridges with pseudo Young's modulus (Eb) and thickness (tb) values placed between the tangent points of the fillets. These parameters are obtained by solving two nonlinear simultaneous equations in terms of the independent variables rlt and twallt. These equations are generated by equating the rotation at the tangent point of a bridge system with that of a fillet, where both rotations are derived using beam theory. Accurate surface fits of the solutions are also presented to provide the user with closed-form equations for the parameters. The methodology was verified on the subcomponent level and with a representative filleted structure, where the technique yielded a plate model exhibiting a level of accuracy better than or equal to a high-fidelity solid model and with a 90-percent reduction in the number of DOFs. The application of this method for parametric design studies, optimization, and dynamic analysis should prove extremely beneficial for the finite element practitioner. Although the method does not attempt to produce accurate stresses in the filleted region, it can also be used to obtain stresses elsewhere in the structure for preliminary analysis. A future avenue of study is to extend the theory developed here to other fillet geometries, including fillet angles other than 90 and multifaceted intersections.

Brown, A. M.↗

NASA NTRS1977

Display analysis with the optimal control model of the human operator

Application of the optimal control model of the human operator to problems in display analysis is discussed. Those aspects of the model pertaining to the operator-display interface and to operator information processing are reviewed and discussed. The techniques are then applied to the analysis of advanced display/control systems for a Terminal Configured Vehicle. Model results are compared with those obtained in a large, fixed-base simulation.

Baron, S.↗

NASA NTRS2024

Harnessing Collaborative Learning Automata to Guide Multi-objective Optimization based Inverse Analysis for Structural Damage Identification

Structural damage identification based on physical models is often transformed into an optimization problem that minimizes the difference between measurement information of structure being monitored and the model prediction in the parametric space. However, the objective function in this context often exhibits multimodality, involving high-dimensional variables due to the reliance on finite element models for damage identification. These features pose challenges to optimization algorithms, where entrapment in local solutions can lead to false positives and false negatives in damage identification. In this research, we propose a reinforcement learning based multi-swarm optimizer to tackle such challenges in pursuit of a small yet diverse solution set that can capture the true damage scenario as one of the solutions. The proposed method leverages the flexibility of the particle swarm optimizer and incorporates novel strategies of metaheuristics to realize targeted improvement. To enable the particle swarm to adaptively select the appropriate search strategy based on the current environment, we adopt the learning automata technique, which sidesteps the need for reward strategy selection that is usually ad hoc at each step of the search. The integration harnesses the automatic learning and self-adaptation capabilities of learning automata, enabling the particles to navigate based on environmental signals. This leads to accumulated probabilities tied to advantageous movements, fostering an adaptive exploration of particles in the search space. The proposed approach is first validated through implementing into benchmark test cases with comparisons. It is then applied to structural damage identification with piezoelectric admittance experimental signals. `The results highlight the capability of the algorithm to identify a small solution set with high accuracy to match the actual damage scenario.

Yang Zhang↗

NASA NTRS2003

Reliability Sensitivity Analysis and Design Optimization of Composite Structures Based on Response Surface Methodology

This report discusses the development and application of two alternative strategies in the form of global and sequential local response surface (RS) techniques for the solution of reliability-based optimization (RBO) problems. The problem of a thin-walled composite circular cylinder under axial buckling instability is used as a demonstrative example. In this case, the global technique uses a single second-order RS model to estimate the axial buckling load over the entire feasible design space (FDS) whereas the local technique uses multiple first-order RS models with each applied to a small subregion of FDS. Alternative methods for the calculation of unknown coefficients in each RS model are explored prior to the solution of the optimization problem. The example RBO problem is formulated as a function of 23 uncorrelated random variables that include material properties, thickness and orientation angle of each ply, cylinder diameter and length, as well as the applied load. The mean values of the 8 ply thicknesses are treated as independent design variables. While the coefficients of variation of all random variables are held fixed, the standard deviations of ply thicknesses can vary during the optimization process as a result of changes in the design variables. The structural reliability analysis is based on the first-order reliability method with reliability index treated as the design constraint. In addition to the probabilistic sensitivity analysis of reliability index, the results of the RBO problem are presented for different combinations of cylinder length and diameter and laminate ply patterns. The two strategies are found to produce similar results in terms of accuracy with the sequential local RS technique having a considerably better computational efficiency.

Rais-Rohani, Masoud↗