Search NASA⌕ Search

SEARCH · Search NASA

Results for “design variables”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Numerical Optimization of Spray-Guided Spark Assistance for Cold Idle Operation in a Heavy-Duty Gasoline Compression Ignition Engine

This article describes the results of a response surface model (RSM)-based numerical optimization campaign for spray-guided spark assistance at cold operations in a heavy-duty gasoline compression ignition (GCI) engine. On the basis of an earlier work on spark-assisted GCI cold combustion, a space-filling design of experiments (DoE) method was first undertaken to investigate a multitude of hardware design variables and engine operating parameters. The main design variables included the number of injector nozzles, fuel split quantities and injection timings, and spark timing. The objective variables were engine combustion efficiency (ŋ c ), maximum pressure rise rate (MPRR), and engine-out nitrogen oxide (NO x ) emissions. A total of 150 design candidates were automatically generated using the Sobol sequence method provided by the commercial software package, CAESES. Then, closed-cycle computational fluid dynamic (CFD) spark-assisted GCI simulations under cold idling operations were performed. The outcomes from the CFD-DoE design campaign were utilized to construct high-fidelity RSMs that allowed for further design optimization of the spark plug- and fuel injector-related design variables, along with fuel injection strategy parameters. A merit function with respect to objective variables was formulated with an appropriate weight assignment on each objective variable. Finally, the best design candidate was identified from the RSM-based optimization process and further validated in the CFD analysis. The best design candidate showed the potential to significantly improve combustion efficiency (ŋ c > 90%) over the baseline at cold idle while satisfying MPRR and NOx emissions constraints (MPRR < 5 bar/CAD and NO x < 4.5 g/kWh).

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1992

Structural tailoring of aircraft engine blade subject to ice impact constraints

In this paper, results are presented for the minimum weight design of SR2 unswept blade made of (Titanium/Graphite-Epoxy/Titanium)s fiber composite. The blade which is rotating at high RPM is subject to ice impact. The root chord length, blade thicknesses at five stations, and graphite-epoxy ply orientation are chosen as design variables. The design constraints are placed on the behavior variables: leading edge strain and root damage parameter due to ice impact, maximum post-impact bending stress at the root due to rotation, first three natural frequencies and resonance margin after impact. The method of feasible directions is employed to solve the inequality constrained minimization problem. The effect of ice speed and the ice impact location on the final design are discussed.

Reddy, E. S.↗
NASA NTRS1991

Multidisciplinary optimization of controlled space structures with global sensitivity equations

A new method for the preliminary design of controlled space structures is presented. The method coordinates standard finite element structural analysis, multivariable controls, and nonlinear programming codes and allows simultaneous optimization of the structures and control systems of a spacecraft. Global sensitivity equations are a key feature of this method. The preliminary design of a generic geostationary platform is used to demonstrate the multidisciplinary optimization method. Fifteen design variables are used to optimize truss member sizes and feedback gain values. The goal is to reduce the total mass of the structure and the vibration control system while satisfying constraints on vibration decay rate. Incorporating the nonnegligible mass of actuators causes an essential coupling between structural design variables and control design variables. The solution of the demonstration problem is an important step toward a comprehensive preliminary design capability for structures and control systems. Use of global sensitivity equations helps solve optimization problems that have a large number of design variables and a high degree of coupling between disciplines.

Padula, Sharon L.↗
NASA NTRS2000

Optimization of Car Body under Constraints of Noise, Vibration, and Harshness (NVH), and Crash

To be competitive on the today's market, cars have to be as light as possible while meeting the Noise, Vibration, and Harshness (NVH) requirements and conforming to Government-man dated crash survival regulations. The latter are difficult to meet because they involve very compute-intensive, nonlinear analysis, e.g., the code RADIOSS capable of simulation of the dynamics, and the geometrical and material nonlinearities of a thin-walled car structure in crash, would require over 12 days of elapsed time for a single design of a 390K elastic degrees of freedom model, if executed on a single processor of the state-of-the-art SGI Origin2000 computer. Of course, in optimization that crash analysis would have to be invoked many times. Needless to say, that has rendered such optimization intractable until now. The car finite element model is shown. The advent of computers that comprise large numbers of concurrently operating processors has created a new environment wherein the above optimization, and other engineering problems heretofore regarded as intractable may be solved. The procedure, shown, is a piecewise approximation based method and involves using a sensitivity based Taylor series approximation model for NVH and a polynomial response surface model for Crash. In that method the NVH constraints are evaluated using a finite element code (MSC/NASTRAN) that yields the constraint values and their derivatives with respect to design variables. The crash constraints are evaluated using the explicit code RADIOSS on the Origin 2000 operating on 256 processors simultaneously to generate data for a polynomial response surface in the design variable domain. The NVH constraints and their derivatives combined with the response surface for the crash constraints form an approximation to the system analysis (surrogate analysis) that enables a cycle of multidisciplinary optimization within move limits. In the inner loop, the NVH sensitivities are recomputed to update the NVH approximation model while keeping the Crash response surface constant. In every outer loop, the Crash response surface approximation is updated, including a gradual increase in the order of the response surface and the response surface extension in the direction of the search. In this optimization task, the NVH discipline has 30 design variables while the crash discipline has 20 design variables. A subset of these design variables (10) are common to both the NVH and crash disciplines. In order to construct a linear response surface for the Crash discipline constraints, a minimum of 21 design points would have to be analyzed using the RADIOSS code. On a single processor in Origin 2000 that amount of computing would require over 9 months! In this work, these runs were carried out concurrently on the Origin 2000 using multiple processors, ranging from 8 to 16, for each crash (RADIOSS) analysis. Another figure shows the wall time required for a single RADIOSS analysis using varying number of processors, as well as provides a comparison of 2 different common data placement procedures within the allotted memories for each analysis. The initial design is an infeasible design with NVH discipline Static Torsion constraint violations of over 10%. The final optimized design is a feasible design with a weight reduction of 15 kg compared to the initial design. This work demonstrates how advanced methodology for optimization combined with the technology of concurrent processing enables applications that until now were out of reach because of very long time-to-solution.

Kodiyalam, Srinivas↗
NASA NTRS1990

New evidence favoring multilevel decomposition and optimization

A new multilevel optimization technique based on a global sensitivity matrix which uses behavior variables in addition to design variables and constraints to decompose the problem is proposed. The technique simplifies the decomposition of the design problem and the programming task and improves the convergence speed of multilevel optimization compared to conventional optimization. The technique is particularly well suited to problems with large numbers of design variables and with computationally expensive constraints.

Padula, Sharon L.↗
DOE OSTI2021

Optimal design of acoustic metamaterial cloaks under uncertainty

In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. The design variable is taken as an infinite-dimensional spatially-varying field that represents the material property, while an additive infinite-dimensional random field represents the variability of the material property or the manufacturing error. Discretization of this optimal design problem results in high-dimensional design variables and uncertain parameters. To solve this problem, we develop a computational approach based on a Taylor approximation and an approximate Newton method for optimization, which is based on a Hessian derived at the mean of the random field. We show our approach is scalable with respect to the dimension of both the design variables and uncertain parameters, in the sense that the necessary number of acoustic wave propagations is essentially independent of these dimensions, for numerical experiments with up to one million design variables and half a million uncertain parameters. Additionally, we demonstrate that, using our computational approach, an optimal design of the acoustic cloak that is robust to material uncertainty is achieved in a tractable manner. The optimal design under uncertainty problem is posed and solved for the classical circular obstacle surrounded by a ring-shaped cloaking region, subjected to both a single-direction single-frequency incident wave and multiple-direction multiple-frequency incident waves. Finally, we apply the method to a deterministic large-scale optimal cloaking problem with complex geometry, to demonstrate that the approximate Newton method’s Hessian computation is viable for large, complex problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

The role of under-determined approximations in engineering and science application

There is currently a great deal of interest in using response surfaces in the optimization of aircraft performance. The objective function and/or constraint equations involved in these optimization problems may come from numerous disciplines such as structures, aerodynamics, environmental engineering, etc. In each of these disciplines, the mathematical complexity of the governing equations usually dictates that numerical results be obtained from large computer programs such as a finite element method program. Thus, when performing optimization studies, response surfaces are a convenient way of transferring information from the various disciplines to the optimization algorithm as opposed to bringing all the sundry computer programs together in a massive computer code. Response surfaces offer another advantage in the optimization of aircraft structures. A characteristic of these types of optimization problems is that evaluation of the objective function and response equations (referred to as a functional evaluation) can be very expensive in a computational sense. Because of the computational expense in obtaining functional evaluations, the present study was undertaken to investigate under-determinined approximations. An under-determined approximation is one in which there are fewer training pairs (pieces of information about a function) than there are undetermined parameters (coefficients or weights) associated with the approximation. Both polynomial approximations and neural net approximations were examined. Three main example problems were investigated: (1) a function of one design variable was considered; (2) a function of two design variables was considered; and (3) a 35 bar truss with 4 design variables was considered.

Carpenter, William C.↗
NASA NTRS2012

Adaptive Aft Signature Shaping of a Low-Boom Supersonic Aircraft Using Off-Body Pressures

The design and optimization of a low-boom supersonic aircraft using the state-of-the- art o -body aerodynamics and sonic boom analysis has long been a challenging problem. The focus of this paper is to demonstrate an e ective geometry parameterization scheme and a numerical optimization approach for the aft shaping of a low-boom supersonic aircraft using o -body pressure calculations. A gradient-based numerical optimization algorithm that models the objective and constraints as response surface equations is used to drive the aft ground signature toward a ramp shape. The design objective is the minimization of the variation between the ground signature and the target signature subject to several geometric and signature constraints. The target signature is computed by using a least-squares regression of the aft portion of the ground signature. The parameterization and the deformation of the geometry is performed with a NASA in- house shaping tool. The optimization algorithm uses the shaping tool to drive the geometric deformation of a horizontal tail with a parameterization scheme that consists of seven camber design variables and an additional design variable that describes the spanwise location of the midspan section. The demonstration cases show that numerical optimization using the state-of-the-art o -body aerodynamic calculations is not only feasible and repeatable but also allows the exploration of complex design spaces for which a knowledge-based design method becomes less effective.

Ordaz, Irian↗
NASA NTRS1974

Approximate techniques of structural reanalysis

A study is made of two approximate techniques for structural reanalysis. These include Taylor series expansions for response variables in terms of design variables and the reduced-basis method. In addition, modifications to these techniques are proposed to overcome some of their major drawbacks. The modifications include a rational approach to the selection of the reduced-basis vectors and the use of Taylor series approximation in an iterative process. For the reduced basis a normalized set of vectors is chosen which consists of the original analyzed design and the first-order sensitivity analysis vectors. The use of the Taylor series approximation as a first (initial) estimate in an iterative process, can lead to significant improvements in accuracy, even with one iteration cycle. Therefore, the range of applicability of the reanalysis technique can be extended. Numerical examples are presented which demonstrate the gain in accuracy obtained by using the proposed modification techniques, for a wide range of variations in the design variables.

Noor, A. K.↗
NASA NTRS1994

Parallel Calculation of Sensitivity Derivatives for Aircraft Design using Automatic Differentiation

Sensitivity derivative (SD) calculation via automatic differentiation (AD) typical of that required for the aerodynamic design of a transport-type aircraft is considered. Two ways of computing SD via code generated by the ADIFOR automatic differentiation tool are compared for efficiency and applicability to problems involving large numbers of design variables. A vector implementation on a Cray Y-MP computer is compared with a coarse-grained parallel implementation on an IBM SP1 computer, employing a Fortran M wrapper. The SD are computed for a swept transport wing in turbulent, transonic flow; the number of geometric design variables varies from 1 to 60 with coupling between a wing grid generation program and a state-of-the-art, 3-D computational fluid dynamics program, both augmented for derivative computation via AD. For a small number of design variables, the Cray Y-MP implementation is much faster. As the number of design variables grows, however, the IBM SP1 becomes an attractive alternative in terms of compute speed, job turnaround time, and total memory available for solutions with large numbers of design variables. The coarse-grained parallel implementation also can be moved easily to a network of workstations.

Bischof, c. H.↗
DOE OSTI2021

Objective and algorithm considerations when optimizing the number and placement of turbines in a wind power plant

Abstract. Optimizing turbine layout is a challenging problem that has been extensively researched in the literature. However, optimizing the number of turbines within a given boundary has not been studied as extensively and is a difficult problem because it introduces discrete design variables and a discontinuous design space. An essential step in performing wind power plant layout optimization is to define the objective function, or value, that is used to express what is valuable to a wind power plant developer, such as annual energy production, cost of energy, or profit. In this paper, we demonstrate the importance of selecting the appropriate objective function when optimizing a wind power plant in a land-constrained site. We optimized several different wind power plants with different wind resources and boundary sizes. Results show that the optimal number of turbines varies drastically depending on the objective function. For a simple, one-dimensional, land-based scenario, we found that a wind power plant optimized for minimal cost of energy produced just 72 % of the profit compared to the wind power plant optimized for maximum profit, which corresponded to a loss of about USD 2 million each year. This paper also compares the performance of several different optimization algorithms, including a novel repeated-sweep algorithm that we developed. We found that the performance of each algorithm depended on the number of design variables in the problem as well as the objective function.

17 WIND ENERGY↗
DOE OSTI2025

A Dual-Mode Hybrid System Combining Solar Thermal With Pumped Thermal Energy Storage

A hybrid system that delivers renewable electricity generation and electricity storage capabilities is introduced. This dual-mode hybrid system is based on Pumped Thermal Energy Storage (PTES) which uses a heat pump to convert electricity into thermal energy that is trans-ferred to silica particles which are stored in concrete silos. The stored heat is later converted back to electricity in a heat engine. The heat pump and heat engine use a closed Joule-Brayton cycle and fluidized bed heat exchangers. If the PTES system is co-located with an array of concentrating solar mirrors and a particle receiver, then the silica particles may also be heated up by the concentrating solar power (CSP) system. The PTES heat engine may also be used to convert the stored solar heat into electricity, thereby sharing this system between the PTES and CSP systems and reducing costs. However, this requires careful management of the heat engine off-design parameters. A thermodynamic model is used to evaluate the performance of the dual mode PTES-CSP hybrid system. The model accounts for turbomachinery effi-ciency, and approach temperature and pressure loss in heat exchangers, as well as other sources of inefficiency, such as motor-generator losses, and air fan power. The hybrid system also requires the evaluation of the turbomachinery efficiency and pressure ratio at off-design conditions since the CSP system operates over different temperature ratios than the Carnot Battery. Several design variables and design modifications are investigated, such as pressure ratios and maximum temperatures.

14 SOLAR ENERGY↗
NASA NTRS1974

Earth Observatory Satellite system definition study. Report no. 3: Design/cost tradeoff studies

The key issues in the Earth Observatory Satellite (EOS) program which are subject to configuration study and tradeoff are identified. The issue of a combined operational and research and development program is considered. It is stated that cost and spacecraft weight are the key design variables and design options are proposed in terms of these parameters. A cost analysis of the EOS program is provided. Diagrams of the satellite configuration and subsystem components are included.

Source record↗
NASA NTRS1978

An algorithm for optimal structural design with frequency constraints

The paper presents a finite element method for minimum weight design of structures with lower-bound constraints on the natural frequencies, and upper and lower bounds on the design variables. The design algorithm is essentially an iterative solution of the Kuhn-Tucker optimality criterion. The three most important features of the algorithm are: (1) a small number of design iterations are needed to reach optimal or near-optimal design, (2) structural elements with a wide variety of size-stiffness may be used, the only significant restriction being the exclusion of curved beam and shell elements, and (3) the algorithm will work for multiple as well as single frequency constraints. The design procedure is illustrated with three simple problems.

Kiusalaas, J.↗
NASA NTRS1984

Skin-stiffener interface stresses in composite stiffened panels

A model and solution method for determining the normal and shear stresses in the interface between the skin and the stiffener attached flange were developed. An efficient, analytical solution procedure was developed and incorporated in a sizing code for stiffened panels. The analysis procedure described provides a means to study the effects of material and geometric design parameters on the interface stresses. These stresses include the normal stress, and the shear stresses in both the longitudinal and the transverse directions. The tendency toward skin/stiffener separation may therefore be minimized by choosing appropriate values for the design variables. The most important design variables include the relative bending stiffnesses of the skin and stiffener attached flange, the bending stiffness of the stiffener web, and the flange width. The longitudinal compressive loads in the flange and skin have significant effects on the interface stresses.

Wang, J. T. S.↗
NASA NTRS1985

Structural Tailoring of SSME Blades (vanes)

The engine blade design optimization program STAEBL (Structural Tailoring of Engine Blades) is available at the NASA Lewis computer facility. The analysis capabilities of this program were extended to typical loading conditions for SSME turbopump blades including thermal and pressure loading. Input files for representative SSME blade designs were developed and sample optimization studies for these blades completed. The structural tailoring program combines a general optimization package and a finite element blade analysis package. The analysis package's capabilities include natural frequency, maximum stress, and forced response computation, and fatigue life and flutter analysis. Optimization is performed using the feasible directions method. The current design is modified by perturbing the design variables so that the design constraints are satisfied while the objective function, such as blade weight, is reduced at the maximum rate. The program's geometric design variables include blade thickness distribution, thickness to chord ratios, and root chord.

Rubinstein, R.↗
NASA NTRS1991

Design of a blade-stiffened composite panel with a hole

A procedure is developed analytically to design and produce an optimized stiffened panel with a centrally located hole. The PASCO panel-buckling analysis and sizing code is employed with the Engineering Analysis Language (EAL) code for finite-element analysis to optimize the design variables. Important design considerations are stiffener height and ply thicknesses in the skin and the stiffener laminates. The EAL code calculates the maximum strains around the hole boundary, and the resulting constraints are combined with the buckling constraint developed by the PASCO code. Cooptimization of the two codes is effected until convergence on the optimal solution is achieved. Results of the analytical procedure are experimentally verified by applying a compressive end-load to graphite-fiber laminated plates with center holes. The experimental results support the analytical procedure, and it is found that for the same weight, the soft-skin designs tested are found to have the best tolerance characteristics and resistance to failure.

Nagendra, S.↗
NASA NTRS1993

Optimal design of a composite structure

This paper presents a design methodology for a laminated composite stiffened panel, subjected to multiple in-plane loads and bending moments. Design variables include the skin and stiffener ply orientation angles and stiffener geometry variables. Optimum designs are sought which minimize structural weight and satisfy mechanical performance requirements. Two types of mechanical performance requirements are placed on the panel, maximum strain and minimum strength. Minimum weight designs are presented which document that the choice of mechanical performance requirements cause changes in the optimum design. The effects of lay-up constraints which limit the ply angles to user specified values, such as symmetric or quasi-isotropic laminates, are also investigated.

Graesser, D. L.↗