Showing papers in "AIAA Journal in 1994"

Two-equation eddy-viscosity turbulence models for engineering applications

Abstract: Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-ω model of Wilcox in the inner region of the boundary layer and switches to the standard k-e model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity

Simulation of Transition with a Two-Equation Turbulence Model

Abstract: This paper demonstrates how well the A>co turbulence model describes the nonlinear growth of flow instabilities from laminar flow into the turbulent flow regime. Viscous modifications are proposed for the A>co model that yield close agreement with measurements and with direct numerical simulation results for channel and pipe flow. These modifications permit prediction of subtle sublayer details such as maximum dissipation at the surface, k ~ y2 as y —> 0, and the sharp peak value of k near the surface. With two transition specific closure coefficients, the model equations yield a realistic description of a transitional incompressible flat-plate boundary layer. A new concept known as the numerical roughness strip is introduced that permits triggering transition at a desired location. A series of transitional boundary-layer applications, including effects of surface heat transfer, pressure gradient and freestream Mach number, verify that the numerical roughness strip is very effective in triggering transition and that flow in the transitional region is realistically described.

Intelligent structures for aerospace - A technology overview and assessment

Abstract: HIS article presents an overview and assessment of the technology leading to the development of intelligent structures. Intelligent structures are those which incorporate actuators and sensors that are highly integrated into the structure and have structural functionality, as well as highly integrated control logic, signal conditioning, and power amplification electronics. Such actuating, sensing, and signal processing elements are incorporated into a structure for the purpose of influencing its states or characteristics, be they mechanical, thermal, optical, chemical, electrical, or magnetic. For example, a mechanically intelligent structure is capable of altering both its mechanical states (its position or velocity) or its mechanical characteristics (its stiffness or damping). An optically intelligent structure could, for example, change color to match its background.17 Definition of Intelligent Structures Intelligent structures are a subset of a much larger field of research, as shown in Fig. I.123 Those structures which have actuators distributed throughout are defined as adaptive or, alternatively, actuated. Classical examples of such mechanically adaptive structures are conventional aircraft wings with articulated leading- and trailing-edge control surfaces and robotic systems with articulated manipulators and end effectors. More advanced examples currently in research include highly articulated adaptive space cranes. Structures which have sensors distributed throughout are a subset referred to as sensory. These structures have sensors which might detect displacements, strains or other mechanical states or properties, electromagnetic states or properties, temperature or heat flow, or the presence or accumulation of damage. Applications of this technology might include damage detection in long life structures, or embedded or conformal RF antennas within a structure. The overlap structures which contain both actuators and sensors (implicitly linked by closed-loop control) are referred to as controlled structures. Any structure whose properties or states can be influenced by the presence of a closed-loop control system is included in this category. A subset of controlled structures are active structures, distinguished from controlled structures by highly distributed actuators which have structural functionality and are part of the load bearing system.

Optimization of coupled systems: a critical overview of approaches

Abstract: A unified overview is given of problem formulation approaches for the optimization of multidisciplinary coupled systems. The overview includes six fundamental approaches upon which a large number of variations may be made. Consistent approach names and a compact approach notation are given. The approaches are formulated to apply to general nonhierarchic systems. The approaches are compared both from a computational viewpoint and a managerial viewpoint. Opportunities for parallelism of both computation and manpower resources are discussed. Recommendations regarding the need for future research are advanced.

Computational methods for efficient structural reliability and reliability sensitivity analysis

Abstract: This paper presents recent developments in efficient structural reliability analysis methods. The paper proposes an efficient, adaptive importance sampling (AIS) method that can be used to compute reliability and reliability sensitivities. The AIS approach uses a sampling density that is proportional to the joint PDF of the random variables. Starting from an initial approximate failure domain, sampling proceeds adaptively and incrementally with the goal of reaching a sampling domain that is slightly greater than the failure domain to minimize over-sampling in the safe region. Several reliability sensitivity coefficients are proposed that can be computed directly and easily from the above AIS-based failure points. These probability sensitivities can be used for identifying key random variables and for adjusting design to achieve reliability-based objectives. The proposed AIS methodology is demonstrated using a turbine blade reliability analysis problem.

Stochastic approach to noise modeling for free turbulent flows

Abstract: A new approach to noise modeling for free turbulent flows is presented. The equations governing the sound field are obtained in two steps. The first step consists of treating the mean and turbulent components of the flow while the acoustic perturbations are neglected. In the second step, a set of equations is derived for the acoustic variables. On the left-hand side of this system, one finds the linearized Euler equations, whereas the right-hand side exhibits source terms related to the turbulent fluctuations and their interactions with the mean flow. These terms are modeled using a stochastic description of the three-dimensional turbulent motion. This is achieved by synthesizing the velocity field at each point in space and for all times with a collection of discrete Fourier modes. The synthesized field posesses the suitable one- and two-point statistical moments and a reasonable temporal power spectral density. The linearized Euler equations including a stochastic description of noise sources are solved numerically with a scheme based on a fractional step treatment. Each one-dimensional problem is solved with a weak formulation. A set of calculations are carried out for a simple freejet. Comparisons between calculations and experiments indicate that a spatial filtering of the source terms is required to obtain the expected level in the far field. Realistic pressure signals, power spectral densities, and sound field patterns are obtained. It is indicated that the stochastic noise generation and radiation (SNGR) approach may be applied to more complex flows because the numerical codes used to calculate the mean flowfield and the wave propagation are not specific of jet configurations. The limitations of the present model lie in the statistical properties of the synthetic turbulent field and in the use of an axisymmetric modeling of the acoustic propagation.

Eigenanalysis of unsteady flow about airfoils, cascades, and wings

Abstract: A general technique for constructing reduced order models of unsteady aerodynamic flows about twodimensional isolated airfoils, cascades of airfoils, and three-dimensional wings is developed. The starting point is a time domain computational model of the unsteady small disturbance flow. For illustration purposes, we apply the technique to an unsteady incompressible vortex lattice model. The eigenmodes of the system, which may be thought of as aerodynamic states, are computed and subsequently used to construct computationally efficient, reduced order models of the unsteady flowfield. Only a handful of the most dominant eigenmodes are retained in the reduced order model. The effect of the remaining eigenmodes is included approximately using a static correction technique. An important advantage of the present method is that once the eigenmode information has been computed, reduced order models can be constructed for any number of arbitrary modes of airfoil motion very inexpensively. Numerical examples are presented that demonstrate the accuracy and computational efficiency of the present method. Finally, we show how the reduced order model may be incorporated into an aeroelastic flutter model.

Structural damage assessment using a generalized minimum rank perturbation theory

Abstract: Recently, the authors proposed computationally attractive algorithms to determine the location and extent of structural damage for undamped structures assuming damage results in a localized change in stiffness properties. The algorithms make use of a finite-element model and a subset of measured eigenvalues and eigenvectors. The developed theories approach the damage location and extent problem in a decoupled fashion. First, a theory is developed to determine the location of structural damage. With location determined, a damage extent theory is then developed. The damage extent algorithm is a minimum rank perturbation, which is consistent with the effects of many classes of structural damage on a finite-element model. In this work, the concept of the minimum rank perturbation theory (MRPT) is adopted to determine the damage extent on the mass properties of an undamped structure. In addition, the MRPT is extended to the case of proportionall y damped structures. For proportionally damped structures, the MRPT is used to find the damage extent in any two of the three structural property matrices (mass, damping, or stiffness). Finally, illustrative case studies using both numerical and actual experimental data are presented. HE advent of the Space Shuttle has prompted considerable attention to the design and control of large space structures. Due to the large size and complexity of envisioned structures, as well as the use of advanced materials to reduce structural weight, it may become necessary to develop a structural health monitoring system to detect and locate structural damage as it occurs. From experience gained in the machinery health monitoring field, one would expect the vibration signature of the structure, either frequency response functions and/or modal parameters, to provide useful information in determining the location and extent of structural damage. Assume that a refined finite element model (FEM) of the structure has been developed before damage has occurred. By refined, we mean that the measured and analytical modal properties are in agreement. Next, assume that at a later date some form of structural damage has occurred. If significant, the damage will result in a change in the structures modal parameters. The question is: can the discrepancy between the original FEM modal properties and postdamage modal properties be used to ascertain structural damage? Most prior work in damage detection has used the general framework of FEM refinement (system identification) in the development of damage assessment algorithms. The motivation behind the development of FEM refinement techniques is based on the need to validate engineering FEMs before their acceptance as the basis for final design analysis. The standard problem has been to seek a refined FEM that is as close to the original FEM and whose modal properties are in agreement with those that are measured subject to various constraints such as symmetry and sparsity preservation. A considerable amount of work in this area has been

Supersonic and hypersonic shock/boundary-layer interaction database

Abstract: An assessment is given of existing shock wave/tubulent boundary-layer interaction experiments having sufficient quality to guide turbulence modeling and code validation efforts. Although the focus of this work is hypersonic, experiments at Mach numbers as low as 3 were considered. The principal means of identifying candidate studies was a computerized search of the AIAA Aerospace Database. Several hundred candidate studies were examined and over 100 of these were subjected to a rigorous set of acceptance criteria for inclusion in the data-base. Nineteen experiments were found to meet these criteria, of which only seven were in the hypersonic regime (M is greater than 5).

Numerical investigations of transitional H2/N2 jet diffusion flames

Abstract: A numerical method for accurate simulation of the time and spatial characteristics of the inner and outer vortex structures in transitional H 2 /N 2 jet diffusion flames is presented. The direct numerical simulation, incorporating buoyancy, a simple one-step chemistry model, coefficients that depend on temperature and species concentration, is described in detail. The species and energy equations are simplified by introducing two conserved scalars β 1 and β 2 and by assuming that the Lewis number of the flow is equal to unity. An implicit, third-order-accurate, upwind numerical scheme having very low numerical diffusion is used to simulate the inner small-scale structures and the outer large-scale structures simultaneously

Structural damage detection and identification using neural networks

Abstract: A novel methodology is presented for on-line damage identification of discrete structural systems. The damage characteristic (location and severity) of the system first can be detected and then identified from the change of its dynamic properties (eigenvalues and mode shapes) through a backward-propa gation neural network. The neural network is constructed by three multilayer subnets that perform the tasks of input pattern generation, damage location identification, and damage severity determination, respectively. The methodology is demonstrated on two spring-mass systems. The effectiveness and limitations of the methodology are discussed. Nomenclature C = damping matrix of the discrete structural system di = dynamic residual vector K = stiffness matrix of the discrete structural system M = mass matrix of the discrete structural system \//» vdj = generalized eigenvalue and eigenvector of damaged system

Turbulent Mixing Noise from Supersonic Jets

Abstract: There is now a substantial body of theoretical and experimental evidence that the dominant part of the turbulent noise of supersonic jets is generated directly by the large turbulence structures/instability waves of the jet flow. Earlier, Tam and Burton provided a description of the physical mechanism by which supersonically traveling instability waves can generate sound efficiently. They used the method of matched asymptotic expansions to construct an instability wave solution which is valid in the far field. The present work is an extension of the theory of Tam and Burton. It is argued that the instability wave spectrum of the jet may be regarded as generated by stochastic white noise excitation at the nozzle lip region. The reason why the excitation has white noise characteristics is that near the nozzle lip region the flow in the jet mixing layer has no intrinsic length and time scales. The present stochastic wave model theory of supersonic jet noise contains a single unknown multiplicative constant. Comparisons between the calculated noise directivities at selected Strouhal numbers and experimental measurements of a Mach 2 jet at different jet temperatures have been carried out. Favorable agreements are found.

Automatic choice of measurement locations for dynamic testing

Abstract: This paper examines the problem of choosing an optimum set of measurement locations for experimental modal testing and suggests criteria whereby the suitability of the chosen locations can be assessed. Two methods of coordinate selection are used: one based on Guyan reduction and the other on the Fisher information matrix. Each begins with a detailed finite element model of the structure being tested. Both procedures reduce this model by one degree of freedom at a time until the number of degrees of freedom in the reduced model equals the number of measurement locations required. The choice of the eliminated coordinates is generally automatic, and the coordinates of the reduced model are those used for modal testing

Edge-based finite element scheme for the Euler equations

Abstract: We describe the development, validation, and application of a new finite element scheme for the solution of the compressible Euler equations on unstructured grids. The implementation of the numerical scheme is based on an edge-based data structure, as opposed to a more traditional element-based data structure. The use of this edge-based data structure not only improves the efficiency of the algorithm but also enables a straightforward implementation of upwind schemes in the context of finite element methods. The algorithm has been tested and validated on some well-documented configurations. A flow solution about a complete F-18 fighter is shown to demonstrate the accuracy and robustness of the proposed algorithm

Some recent results for nonlinear acoustics in combustion chambers

Abstract: Conditions of high energy densities and low losses in combustion chambers encourage the excitation and sustenance of organized unsteady motions generically called combustion instabilities The fluctuations, common in propulsion systems, often reach sufficient amplitudes to cause excessive rates of heat transfer to exposed surfaces and unacceptable structural vibrations, causing failure in extreme cases In many cases, to avoid the occurrence of instabilities, combustion chambers are operated below their maximum performance Considerable effort has been spent, for more than four decades, on experimental and analytical programs devoted to solving problems of combustion instabilities Much of the work has been required to measure quantities which, because of the complex processes involved, cannot be predicted accurately from first principles Analytical work has been concerned largely with linear behavior, the chief purpose being to predict stability of small disturbances in combustion chambers Many useful results have been obtained, serving in practice to help design experiments, correlate data, and predict the stability of new systems However, linear behavior is only a small part of the general problem A combustion chamber is an isolated system so far as its stability is concerned, and unstable disturbances evolve as 'self-excited' motions Hence their amplitudes will grow indefinitely unless nonlinear processes are effective Complete understanding of observed behavior will therefore be reached only by treating nonlinear behavior In the recent past, increased attention has been paid to nonlinear combustion instabilities It is particularly important for practical purposes to explain the existence of limit cycles and the occurrence of unstable motions in linearly stable systems exposed to large initial disturbances These matters are far from closed, and although substantial progress has been accomplished, little impact has been made on the development of new systems The chief purpose of this paper is to provide a brief review of work on nonlinear combustion instabilities, largely in the framework of an approximate analysis Some connections will be made with the modern theory of nonlinear dynamical systems, including very recent and incomplete attempts by others to assess the possible chaotic behavior observed in laboratory tests

Structural damage detection of space truss structures using best achievable eigenvectors

Abstract: A method is presented by which measured modes and frequencies from a modal test can be used to determine the location and magnitude of damage in a space struss structure. The damage is located by computing the Euclidean distances between the measured mode shapes and the best achievable eigenvectors. The best achievable eigenvectors are the projection of the measured mode shapes onto the subspace defined by the refined analytical model of the structure and the measured frequencies. Loss of both stiffness and mass properties can be located and quantified. To examine the performance of the method when experimentally measured modes are employed, various damage detection studies using a laboratory eight-bay truss structure were conducted. The method performs well even though the measurement errors inevitably make the damage location more difficult.

Second-order structural identification procedure via state-space-based system identification

Abstract: A theory is presented for transforming the system-theory-based realization models into the corresponding physical-coordinate-based structural models The theory has been implemented into a computational procedure and applied to several example problems The results show that the present transformation theory yields an objective model basis possessing a unique set of structural parameters from an infinite set of equivalent system realization models For proportionally damped systems, the transformation directly and systematically yields the normal modes and modal damping When nonproportional damping is present, the relative magnitude and phase of the damped mode shapes are separately characterized, and a corrective transformation is then employed to capture the undamped normal modes and nondiagonal modal damping matrix namics equations has hampered the application (and acceptance) of the system-theory-based structural identification techniques and can eventually curtail the progress of hybrid experimental/analyti- cal modeling and design efforts The present paper offers a theory for transforming the system- theory-based realization models into the corresponding physical- coordinate-based structural models Since a key idea employed in the development of the present theory is an objective common basis normalization, it is designated as a common basis-normal- ized structural identification (CBSI) procedure The resultant model is unique for a given sequence of Markov parameters, which in turn are uniquely determined for a linear structure with given inputs and outputs Therefore, the realized model, after transformation, has a one-to-one correspondence with the physical parameters of the system and can either yield data for finite ele- ment model correlation or alternatively for direct calculation of mass, stiffness, and damping matrices of the original structure Specifically, we begin with the so-called McMillan transformation employed by Longman and Juang9 and show that the McMillan transformation does not in general yield the desired structural nor- mal modes To arrive at an objective transformation basis of gener- alized coordinates, we invoke two invariance properties The first is the output invariance property, viz, the outputs are invariant with respect to any choice of generalized coordinates The second is the normal mode identity, viz, for proportionally damped cases the mode shapes for the displacement, velocity, and acceleration vectors are the same There are several byproducts that the present theory provides, primarily due to the common basis normalization employed in the theory First, the present transformation theory allows the integra- tion of different realized models with varying actuator and sensor locations if they arise from the same structure Second, each sensor and actuator or groups of sensors and actuators can be processed in parallel and combined concurrently or sequentially for the con- struction of a global model Third, it can facilitate a decentralized real-time control implementation From a structural dynamics point of view, the transformation to an objective basis provides a state- space model coinciding with the canonical form of the second- order equations of motion, thus extracting the classical real-valued parameters of interest to modal testing, mass-normalized normal modes, and the general modal damping matrix, while maintaining the system equivalence properties of the state-space form

Linear disturbances in hypersonic, chemically reacting shock layers

Abstract: The effects of equilibrium- and nonequilihrium-air chemical reactions on the linear stability of a Mach 25, 10-deg half-angle sharp-cone shock layer are investigated. First, the basic state is computed using the parabolized Navier-Stokes equations with a shock-fitting scheme. This eliminates spurious numerical oscillations that could adversely affect the stability analysis. Spatial stability analyses are then described for three different approximations of the physics: perfect gas, air in local chemical equilibrium, and air in chemical nonequilibrium. It is shown in both the equilibrium- and nonequilibrium-air calculations that the second mode of Mack is shifted to lower frequencies

Unsteady flow phenomena over delta wings at high angle of attack

Abstract: Experiments show that coherent pressure fluctuations observed on delta wings are due to the helical mode instability of the vortex breakdown flowfield. No dominant frequency in the spectra of pressure fluctuations on the wing surface was observed after the breakdown reached the apex of the wing, although the vortex shedding could be detected in the wake. Measurements of pressure fluctuations at different streamwise locations on the wing suggest that the dimensionless frequency fx/U^ is nearly constant for a given geometry, which implies increasing wavelength in the streamwise direction. For different wings, this nondimensional frequency is shown to be a function of nondimensional circulation T/U^x only. Both the wavelength of the disturbances and the core radius increase with the nondimensional circulation at a fixed streamwise location. The wavelength normalized by the core radius is around 3-4, which is much smaller than the predictions for the Q vortex.

Collisional quenching corrections for laser-induced fluorescence measurements of NO A2Sigma(+)

Abstract: Quantitative combustion diagnostics using laser-induced fluorescence require a knowledge of energy transfer and quenching rates at elevated temperatures. Such information is critical both for experimental design and for subsequent reduction of measured signals to measurements of temperature and species concentrations. We present the results of a study of electronic energy transfer in NO A2S+. These results are cast in the form of empirical correlations which have been developed to facilitate the practical applications of quenching corrections. The choice of particular functional forms for these correlations is based on a classical collisional model of the process. This model has been calibrated against an extensive set of measured cross sections. Results are presented for a number of species of interest in combustion and aerothermodynamic applications.

New higher order plate theory in modeling delamination buckling of composite laminates

Abstract: A new higher order plate theory for modeling delamination buckling and postbuckling of composite laminates is developed Delaminations between layers of composite plates are modeled by jump discontinuity conditions, in both lower and higher order terms of displacements, at the delaminated interfaces Some higher order terms are identified at the beginning of the formulation by using the conditions that shear stresses vanish at all free surfaces including the delaminated interfaces Therefore, all boundary conditions for displacements and stresses are satisfied in the present theory Geometric nonlinearity is included in computing layer buckling The general governing equations, along with all boundary and continuity conditions of plates, are derived for predicting the delamination buckling and postbuckling behavior The associated delamination growth problem is also examined by the use of Griffith-type fracture criterion A numerical example is presented to validate the theory The results are also compared with experimentally obtained data

Numerical investigation of separated nozzle flows

Abstract: A numerical study of axisymmetric overexpanded nozzle is presented. The flow structure of the startup and throttle-down processes are examined. During the impulsive startup process, observed flow features include the Mach disk, separation shock, Mach stem, vortex core, contact surface, slip stream, initial shock front, and shocklet. Also the movement of the Mach disk is not monotonical in the downstream direction. For a range of pressure ratios, hysteresis phenomenon occurs; different solutions were obtained depending on different processes. Three types of flow structures were observed. The location of separation point and the lower end turning point of hysteresis are closely predicted. A high peak of pressure is associated with the nozzle flow reattachment. The reversed vortical structure and affects engine performance.

Unstructured viscous grid generation by the advancing-layers method

Abstract: A new method of generating unstructured triangular/tetrahedral grids with high-aspect-ratio cells is proposed. The method is based on new grid-marching strategy referred to as 'advancing-layers' for construction of highly stretched cells in the boundary layer and the conventional advancing-front technique for generation of regular, equilateral cells in the inviscid-flow region. Unlike the existing semi-structured viscous grid generation techniques, the new procedure relies on a totally unstructured advancing-front grid strategy resulting in a substantially enhanced grid flexibility and efficiency. The method is conceptually simple but powerful, capable of producing high quality viscous grids for complex configurations with ease. A number of two-dimensional, triangular grids are presented to demonstrate the methodology. The basic elements of the method, however, have been primarily designed with three-dimensional problems in mind, making it extendible for tetrahedral, viscous grid generation.

Computation of oscillating airfoil flows with one- and two-equation turbulence models

Abstract: The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds-averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. One- and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading-edge and where natural transition was allowed to occur naturally are considered. The more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are observed. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading-edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall.

Fast multigrid method for solving incompressible hydrodynamic problems with free surfaces

Abstract: We develop of a finite-volume multigrid Euler scheme for solving three-dimensional, fully nonlinear ship wave problems. The flowfield and the a priori unknown free surface location are calculated by coupling the free surface kinematic and dynamic equations with the equations of motion for the bulk flow. The evolution of the free surface boundary condition is linked to the evolution of the bulk flow via a novel iteration strategy that allows temporary leakage through the surface before the solution is converged. The method of artificial compressibility is used to enforce the incompressibility constraint for the bulk flow. A multigrid algorithm is used to accelerate convergence to a steady state

Turbulent Drag Reduction Mechanism Above a Riblet Surface

Abstract: The structure of a turbulent flowfield along a riblet surface was investigated with the aid of a three-dimensional particle tracking velocimetry. The statistics of all three velocity components were measured and compared with those above a smooth wall. Under a drag-reducing condition, all of the turbulent velocity fluctuations and the Reynolds shear stress were decreased near the riblet surface, although the flow characteristics in most of the flowfield were quite similar to those above the smooth wall. It was also found that the redistribution mechanism of the turbulent kinetic energy from the streamwise component to the spanwise one was considerably suppressed in the region above the riblet valley. On the other hand, under a neutral drag condition, a cross-stream secondary flow was apparent near the ribs. This fluid motion should enhance the turbulent momentum transport and deteriorate the drag-reducing effect of the riblet.

Nonprobabilistic, convex-theoretic modeling of scatter in material properties

Abstract: Nonprobabilistic, convex modeling of uncertain material properties for viscoelastic structures is developed in this paper. In particular, the problem of forced vibrations of viscoelastic beams is studied. First the analytic solution by Inman is generalized for a deterministic set of variables, describing material properties. Next, these variables are treated as varying in a solid "ball" in the four-dimensional space, thus modeling the scatter in material properties. The least favorable response needed for the design of the structure is determined.

Approximation in nonhierarchic system optimization

Abstract: This paper reports on the effectiveness of a nonhierarchic system optimization algorithm in application to complex coupled systems problems. A second-order nonhierarchic system optimization algorithm developed in earlier studies is modified in this study to provide for individual constraint/state modeling. A cumulative constraint formulation was used in previous implementation studies. The test problems in this study are each complex coupled systems. Complex coupled systems require an iterative solution strategy to evaluate system states. Nonhierarchic algorithm development is driven by these types of problems, and their study is imperative. The algorithm successfully optimizes each of the complex coupled systems. A significant reduction in the number of system analyses required for optimization is observed as compared with conventional optimization using the generalized reduced-gradient method. in the design database. The design database stores design site information generated during the subspace optimizations. A quadratic polynomial approximation to the design is formed using the strategy of Vanderplaats. 6 A weighted least-squares solution strategy is employed to solve for the second-order terms in Vanderplaats' strategy. Exact data in the design data- base are more heavily weighted in the least-squares solution procedure. The resulting quadratic polynomial forms the basis function of accumulated approximation replacing the linear basis used in the original formulation. In Renaud and Gabriele5 improved convergence is observed for the welded beam test problem. The improved convergence is attributed to the im- proved accuracy of cumulative constraint approximations when using second-order-based approximating functions. Additional studies using the second-order-based coordina- tion procedure of system approximation indicated that replac- ing the cumulative constraints with their component con- straints may improve algorithm performance. Implementation of the second-order-based coordination procedure of system approximation was less effective in reducing cycling when applied to the Golinski speed reducer problem. The speed reducer cumulative constraints were composed of a large num- ber of individual constraints as compared with the cumulative constraints in the welded beam test problem. With a larger number of individual constraints assigned to a cumulative constraint, it will more likely undergo a change in its active set during the coordination procedure. It is difficult to approxi- mate these changes in the cumulative constraints. Inaccurate cumulative constraint approximations reduce algorithm per- formance and delay convergence. Approximating individual constraints/states in the coor-