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NASA NTRS2001

Data Reduction and Its Impact on Test-Analysis Correlation

A research project has been initiated to improve crash test and analysis correlation. The research has focused on two specimen types: simple metallic beams and plates; and a representative composite fuselage section. Impact tests were performed under carefully controlled conditions. In addition, the specimens were densely instrumented to enable not only correlation with finite element simulations, but to also assess the repeatability of the data. Simulations utilizing a detailed finite element model were executed in a nonlinear transient dynamic code. The results presented in this paper concentrate on the effect of several data reduction processes, to include filtering frequency and sampling rate, on the correlation accuracy.

Lyle, Karen H.↗

NASA NTRS1995

An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based on approximation of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

Fukumori, Ichiro↗

NASA NTRS1994

An Approximate Kalman Filter for Ocean Data Assimilation; An Example with an Idealized Gulf Stream Model

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based on approximations of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady-state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudo measurements is examined, including velocity, density, and volume transport at localized arrays, and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform a previous study that used an empirical nudging scheme. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

['Kalman↗

NASA NTRS2010

Predicting Failure Progression and Failure Loads in Composite Open-Hole Tension Coupons

Failure types and failure loads in carbon-epoxy [45n/90n/-45n/0n]ms laminate coupons with central circular holes subjected to tensile load are simulated using progressive failure analysis (PFA) methodology. The progressive failure methodology is implemented using VUMAT subroutine within the ABAQUS(TradeMark)/Explicit nonlinear finite element code. The degradation model adopted in the present PFA methodology uses an instantaneous complete stress reduction (COSTR) approach to simulate damage at a material point when failure occurs. In-plane modeling parameters such as element size and shape are held constant in the finite element models, irrespective of laminate thickness and hole size, to predict failure loads and failure progression. Comparison to published test data indicates that this methodology accurately simulates brittle, pull-out and delamination failure types. The sensitivity of the failure progression and the failure load to analytical loading rates and solvers precision is demonstrated.

Arunkumar, Satyanarayana↗

NASA NTRS1994

The Accuracy of Parameter Estimation in System Identification of Noisy Aircraft Load Measurement

This thesis focuses on the subject of the accuracy of parameter estimation and system identification techniques. Motivated by a complicated load measurement from NASA Dryden Flight Research Center, advanced system identification techniques are needed. The objective of this problem is to accurately predict the load experienced by the aircraft wing structure during flight determined from a set of calibrated load and gage response relationship. We can then model the problem as a black box input-output system identification from which the system parameter has to be estimated. Traditional LS (Least Square) techniques and the issues of noisy data and model accuracy are addressed. A statistical bound reflecting the change in residual is derived in order to understand the effects of the perturbations on the data. Due to the intrinsic nature of the LS problem, LS solution faces the dilemma of the trade off between model accuracy and noise sensitivity. A method of conflicting performance indices is presented, thus allowing us to improve the noise sensitivity while at the same time configuring the degredation of the model accuracy. SVD techniques for data reduction are studied and the equivalence of the Correspondence Analysis (CA) and Total Least Squares Criteria are proved. We also looked at nonlinear LS problems with NASA F-111 data set as an example. Conventional methods are neither easily applicable nor suitable for the specific load problem since the exact model of the system is unknown. Neural Network (NN) does not require prior information on the model of the system. This robustness motivated us to apply the NN techniques on our load problem. Simulation results for the NN methods used in both the single load and the 'warning signal' problems are both useful and encouraging. The performance of the NN (for single load estimate) is better than the LS approach, whereas no conventional approach was tried for the 'warning signals' problems. The NN design methodology is also presented. The use of SVD, CA and Collinearity Index methods are used to reduce the number of neurons in a layer.

Kong, Jeffrey↗

NASA NTRS1976

Alternative methods for the design of jet engine control systems

Various alternatives to linear quadratic design methods for jet engine control systems are discussed. The main alternatives are classified into two broad categories: nonlinear global mathematical programming methods and linear local multivariable frequency domain methods. Specific studies within these categories include model reduction, the eigenvalue locus method, the inverse Nyquist method, polynomial design, dynamic programming, and conjugate gradient approaches.

Sain, M. K.↗

NASA NTRS1991

A comparison of experimental observations and numerical predictions for the initiation of fiber microbuckling in notched composite laminates

The results of the present experimental study of fiber microbuckling indicates that free surfaces, ply orientations, and resin-rich regions affect the strain level for the initiation of in-plane fiber microbuckling. Nonlinear matrix constitutive behavior, in conjunction with initial fiber waviness, cause significant reductions of fiber microbuckling initiation strain level; these two factors generate nonlinear global stress-strain responses in the models. The fiber microbuckling initiation strains correlate well with the applied strain associated with asymptotic local shear strains.

Guynn, E. G.↗

NASA NTRS1999

Horizontal vestibuloocular reflex evoked by high-acceleration rotations in the squirrel monkey. II. Responses after canal plugging

The horizontal angular vestibuloocular reflex (VOR) evoked by high-frequency, high-acceleration rotations was studied in four squirrel monkeys after unilateral plugging of the three semicircular canals. During the period (1-4 days) that animals were kept in darkness after plugging, the gain during steps of acceleration (3, 000 degrees /s(2), peak velocity = 150 degrees /s) was 0.61 +/- 0.14 (mean +/- SD) for contralesional rotations and 0.33 +/- 0.03 for ipsilesional rotations. Within 18-24 h after animals were returned to light, the VOR gain for contralesional rotations increased to 0. 88 +/- 0.05, whereas there was only a slight increase in the gain for ipsilesional rotations to 0.37 +/- 0.07. A symmetrical increase in the gain measured at the plateau of head velocity was noted after animals were returned to light. The latency of the VOR was 8.2 +/- 0. 4 ms for ipsilesional and 7.1 +/- 0.3 ms for contralesional rotations. The VOR evoked by sinusoidal rotations of 0.5-15 Hz, +/-20 degrees /s had no significant half-cycle asymmetries. The recovery of gain for these responses after plugging was greater at lower than at higher frequencies. Responses to rotations at higher velocities for frequencies >/=4 Hz showed an increase in contralesional half-cycle gain, whereas ipsilesional half-cycle gain was unchanged. A residual response that appeared to be canal and not otolith mediated was noted after plugging of all six semicircular canals. This response increased with frequency to reach a gain of 0.23 +/- 0.03 at 15 Hz, resembling that predicted based on a reduction of the dominant time constant of the canal to 32 ms after plugging. A model incorporating linear and nonlinear pathways was used to simulate the data. The coefficients of this model were determined from data in animals with intact vestibular function. Selective increases in the gain for the linear and nonlinear pathways predicted the changes in recovery observed after canal plugging. An increase in gain of the linear pathway accounted for the recovery in VOR gain for both responses at the velocity plateau of the steps of acceleration and for the sinusoidal rotations at lower peak velocities. The increase in gain for contralesional responses to steps of acceleration and sinusoidal rotations at higher frequencies and velocities was due to an increase in the gain of the nonlinear pathway. This pathway was driven into inhibitory cutoff at low velocities and therefore made no contribution for rotations toward the ipsilesional side.

NASA Discipline Developmental Biology↗

NASA NTRS1991

Parallelized solvers for heat conduction formulations

Based on multilevel partitioning, this paper develops a structural parallelizable solution methodology that enables a significant reduction in computational effort and memory requirements for very large scale linear and nonlinear steady and transient thermal (heat conduction) models. Due to the generality of the formulation of the scheme, both finite element and finite difference simulations can be treated. Diverse model topologies can thus be handled, including both simply and multiply connected (branched/perforated) geometries. To verify the methodology, analytical and numerical benchmark trends are verified in both sequential and parallel computer environments.

Padovan, Joe↗

NASA NTRS1991

Coupled rotor-fuselage vibration reduction with multiple frequency blade pitch control

A nonlinear coupled rotor/flexible fuselage analysis has been developed and used to study the effects of higher harmonic blade pitch control on the vibratory hub loads and fuselage acceleration levels. Previous results, obtained with this model have shown that conventional higher harmonic control (HHC) inputs aimed at hub shear reduction cause an increase in the fuselage accelerations and vice-versa. It was also found that for simultaneous reduction of hub shears and fuselage accelerations, a pitch input representing a combination of two higher harmonic components of different frequencies was needed. Subsequently, it was found that this input could not be implemented through a conventional swashplate. This paper corrects a mistake originally made in the representation of the multiple frequency pitch input and shows that such a pitch input can be only implemented in the rotating reference frame. A rigorous mathematical solution is found, for the pitch input in the rotating reference frame, which produces simultaneous reduction of hub shears and fuselage acceleration. New insight on vibration reduction in coupled rotor/fuselage systems is obtained from the sensitivity of hub shears to the frequency and amplitude of the open loop HHC signal in the rotating reference frame. Finally the role of fuselage flexibility in this class of problems is determined.

Papavassiliou, I.↗

NASA NTRS1987

Model-size reduction for the non-linear dynamic analysis of quasi-symmetric structures

A numerical technique is developed to reduce the size of models describing the nonlinear dynamic response of quasi-symmetric structures (i.e., structures with unsymmetric geometry). The response vectors of the structure are approximated by a linear combination of the symmetric and antisymmetric vectors at each time step. The mathematical formulation and numerical implementation of the method are described in detail, and results for a shallow laminated anisotropic panel of quadrilateral planform are presented in graphs and normalized contour plots.

Noor, Ahmed K.↗

NASA NTRS1994

Nonlinear equilibration of localized instabilities on a baroclinic jet

Dynamical mechanisms underlying the equilibration of absolute instability are examined in a nonlinear, quasigeostrophic, two-layer model. The key to understanding the nonlinear equilibration is in recognizing that linear absolute instabilities can be stabilized both by a reduction of the vertical shear and by enhancement of the mean barotropic velocity. In a localized domain, the equilibration process proceeds with the creation of locally convectively unstable regions downstream, which encroach onto the locally absolutely unstable region until the local instability is suppressed. That local instabilities exist only if absolutely unstable regions span a minimum size is verified by eigenvalue calculations of three-dimensional flows. Numerical examples suggest that this critical size is at least 9000 km for a wide range of parameter values chosen to investigate the midlatitude storm tracks. Fluctuations arising from local absolute instability obtain maximum amplitude in the downstream convectively unstable regions rather than in the absolutely unstable regions themselves. Together, these results suggest that if an equilibrated absolute instability were to occur in midlatitudes, a zonal band of surface easterlies exceeding 900 km would be required and the associated enhanced variances would not be found coincident with the regions of absolute instability.

Delsole, Timothy M.↗

NASA NTRS1988

Dynamic analysis of nonlinear rotor-housing systems

Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.

Noah, Sherif T.↗

NASA NTRS2001

A Unified Development of Basis Reduction Methods for Rotor Blade Analysis

The axial foreshortening effect plays a key role in rotor blade dynamics, but approximating it accurately in reduced basis models has long posed a difficult problem for analysts. Recently, though, several methods have been shown to be effective in obtaining accurate,reduced basis models for rotor blades. These methods are the axial elongation method,the mixed finite element method, and the nonlinear normal mode method. The main objective of this paper is to demonstrate the close relationships among these methods, which are seemingly disparate at first glance. First, the difficulties inherent in obtaining reduced basis models of rotor blades are illustrated by examining the modal reduction accuracy of several blade analysis formulations. It is shown that classical, displacement-based finite elements are ill-suited for rotor blade analysis because they can't accurately represent the axial strain in modal space, and that this problem may be solved by employing the axial force as a variable in the analysis. It is shown that the mixed finite element method is a convenient means for accomplishing this, and the derivation of a mixed finite element for rotor blade analysis is outlined. A shortcoming of the mixed finite element method is that is that it increases the number of variables in the analysis. It is demonstrated that this problem may be rectified by solving for the axial displacements in terms of the axial forces and the bending displacements. Effectively, this procedure constitutes a generalization of the widely used axial elongation method to blades of arbitrary topology. The procedure is developed first for a single element, and then extended to an arbitrary assemblage of elements of arbitrary type. Finally, it is shown that the generalized axial elongation method is essentially an approximate solution for an invariant manifold that can be used as the basis for a nonlinear normal mode.

Ruzicka, Gene C.↗

DOE OSTI2025

Machine learning modeling and model predictive control of a closed-circuit reverse osmosis system

Closed-circuit reverse osmosis (CCRO) offers a flexible and energy-efficient alternative to conventional reverse osmosis by operating in a semi-batch mode that recycles brine, enabling higher recovery rates and reduced specific energy consumption (SEC). However, developing accurate, system-level dynamic models for CCRO remains challenging due to its nonlinear, multi-phase operation and sensitivity to variable feed water conditions. Traditional modeling approaches, such as NARMAX (nonlinear autoregressive moving average with exogenous inputs), often struggle to generalize across varying inlet feed concentrations, necessitating frequent parameter re-estimation and limiting their utility for real-time control applications. To address these limitations, we developed a long short-term memory (LSTM) neural network model trained on an extensive experimental data set from a CCRO pilot plant. The model accepts three inputs, feed flow rate, recirculation flow rate, and initial feed conductivity, and predicts three key outputs: reject conductivity, feed pump power draw, and recirculation pump power draw. We validated the LSTM model against experimental data, demonstrating its ability to distinguish between different feed conductivities and adapt to variable flow rates. Subsequently, we incorporated the LSTM model within a nonlinear model predictive control (MPC) scheme and conducted closed-loop simulations to optimize the integrated SEC (iSEC). In conclusion, the results project up to a 6% reduction in iSEC by using MPC to optimize performance over the entire experiment duration, without requiring any random excitation for data collection or parameter re-estimation.

Desalination↗

NASA NTRS1989

Computational fluid dynamic control

A general technique is presented for modeling fluid, or gas, dynamic systems specifically for the development of control systems. The numerical methods which are generally used in computational fluid dynamics are borrowed to create either continuous-time or discrete-time models of the particular fluid system. The resulting equations can be either left in a nonlinear form, or easily linearized about an operating point. As there are typically very many states in these systems, the usual linear model reduction methods can be used on them to allow a low-order controller to be designed. A simple example is given which typifies many internal flow control problems. The resulting control is termed computational fluid dynamic control.

Hartley, Tom T.↗

NASA NTRS1985

A method for high order linear system reduction and nonlinear system simplification

Least-squares-type algorithms for reducing the order of linear systems in the frequency domain and simplifying nonlinear systems in time domain are developed and demonstrated. The possible model structures are represented as nodes in a tree, and costs along the branches are assigned using the repeated-Gram-Schmidt orthogonalization procedure of Desrochers and Saridis (1980), permitting identification of the optimal n-term model by searching the tree to depth n, with no need for parameter identification. The efficiency and flexibility of the algorithms is shown in applications to the eighth-order linear system studied by Hsia (1972), a three-state eight-nonlinear-term aircraft-dynamics problem, and the related linear-controller problem (Garrard and Jordan, 1977).

Desrochers, A. A.↗

NASA NTRS1982

On making large nonlinear problems small

Reduction methods for solving large-scale nonlinear problems are considered. Attention is given to: (1) the selection of basis vectors for steady-state problems; (2) the identification and determination of bifurcation and limit points, including tracing post-limit-point and post-bifurcation-point paths using reduction methods; (3) the application of reduction methods to nonlinear problems with prescribed nonzero values of the fundamental unknowns; and (4) the use of reduction methods in conjunction with multifield (mixed) finite element models. The effectiveness of using reduction methods is demonstrated on the basis of several numerical examples including two-dimensional steady conduction in a square plate with temperature dependent thermal conductivity and a shallow spherical cap subjected to a central-point load and a ring load.

Noor, A. K.↗