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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Model reduction in integrated controls-structures design

It is the objective of this paper to present a model reduction technique developed for the integrated controls-structures design of flexible structures. Integrated controls-structures design problems are typically posed as nonlinear mathematical programming problems, where the design variables consist of both structural and control parameters. In the solution process, both structural and control design variables are constantly changing; therefore, the dynamic characteristics of the structure are also changing. This presents a problem in obtaining a reduced-order model for active control design and analysis which will be valid for all design points within the design space. In other words, the frequency and number of the significant modes of the structure (modes that should be included) may vary considerably throughout the design process. This is also true as the locations and/or masses of the sensors and actuators change. Moreover, since the number of design evaluations in the integrated design process could easily run into thousands, any feasible order-reduction method should not require model reduction analysis at every design iteration. In this paper a novel and efficient technique for model reduction in the integrated controls-structures design process, which addresses these issues, is presented.

Maghami, Peiman G.↗
NASA NTRS1983

A meteorologically-driven yield reduction model for spring and winter wheat

A yield reduction model for spring and winter wheat was developed for large-area crop condition assessment. Reductions are expressed in percentage from a base yield and are calculated on a daily basis. The algorithm contains two integral components: a two-layer soil water budget model and a crop calendar routine. Yield reductions associated with hot, dry winds (Sukhovey) and soil moisture stress are determined. Input variables include evapotranspiration, maximum temperature and precipitation; subsequently crop-stage, available water holding percentage and stress duration are evaluated. No specific base yield is required and may be selected by the user; however, it may be generally characterized as the maximum likely to be produced commercially at a location.

Ravet, F. W.↗
NASA NTRS2019

Parameters Inference and Model Reduction for the Single-Particle Model of Li Ion Cells

The Single-Particle Model (SPM) of Li ion cell is a computationally efficient model for simulating Li ion cell for weak to moderate currents. The model depends n a number of parameters describing the geometry and material properties of a cell components. In order to apply the model to simulating a cell, the best-fit parametric values have to be inferred from a constant discharge data. We report our efforts to determine the best-fit set for 18650 LP batteries. We found that rather than being best-fit by a particular point in the parametric space the data is fit equally well by an ensemble of points clustering about an effective multidimensional manifold in the parametric space. This property of the SPM is known to be shared by a multitude of the so-called "sloppy models" of complex systems, characterized by a few stiff directions in the parametric space, in which the predicted behavior varies significantly, and a number of sloppy directions in which the behavior doesn't change appreciably. Only the stiff parameters combinations are identifiable. Geometrical features of the BFM give insights to possible reduction of the SPM to a model having fewer sloppy parameters. We have constructed a hierarchy of such models. The fully reduced model depends on only stiff effective parameters which are identifiable and can be used for characterization of the battery's state of health.

Khasin, Michael↗
NASA NTRS1989

Component model reduction via the projection and assembly method

The problem of acquiring a simple but sufficiently accurate model of a dynamic system is made more difficult when the dynamic system of interest is a multibody system comprised of several components. A low order system model may be created by reducing the order of the component models and making use of various available multibody dynamics programs to assemble them into a system model. The difficulty is in choosing the reduced order component models to meet system level requirements. The projection and assembly method, proposed originally by Eke, solves this difficulty by forming the full order system model, performing model reduction at the the system level using system level requirements, and then projecting the desired modes onto the components for component level model reduction. The projection and assembly method is analyzed to show the conditions under which the desired modes are captured exactly; to the numerical precision of the algorithm.

Bernard, Douglas E.↗
NASA NTRS1989

Model reduction for flexible spacecraft with clustered natural frequencies

Two approaches to the problem of model reduction for flexible spacecraft that have proved very useful are balancing and model truncation. Furthermore, it is well known that a model representation of a lightly damped flexible structure with widely spaced natural frequencies is approximately balanced. Consequently, reduction in either coordinate system gives similar results for this case. It is important to note, however, that flexible space structures typically have clusters of closely spaced frequencies. In such cases, reduction in model coordinates can give large errors, while the error obtained using balancing is generally much smaller. A new reduction procedure which combines the best features of model and balanced reduction is therefore developed. It is more efficient than balanced reduction of the full system, as it only involves balancing those subsystems of close modes that are highly correlated, yet is shown to yield results which are essentially as good.

Williams, T. W. C.↗
NASA NTRS1989

Model reduction for flexible space structures

This paper presents the conditions under which modal truncation yields a near-optimal reduced-order model for a flexible structure. Next, a robust model reduction technique to cope with the damping uncertainties typical of flexible space structure is developed. Finally, a flexible truss and the COFS-1 structure are used to give realistic applications for the model reduction techniques studied in the paper.

Gawronski, Wodek↗
NASA NTRS1991

Discrete-time model reduction in limited frequency ranges

A mathematical formulation for model reduction of discrete time systems such that the reduced order model represents the system in a particular frequency range is discussed. The algorithm transforms the full order system into balanced coordinates using frequency weighted discrete controllability and observability grammians. In this form a criterion is derived to guide truncation of states based on their contribution to the frequency range of interest. Minimization of the criterion is accomplished without need for numerical optimization. Balancing requires the computation of discrete frequency weighted grammians. Close form solutions for the computation of frequency weighted grammians are developed. Numerical examples are discussed to demonstrate the algorithm.

Horta, Lucas G.↗
NASA NTRS1992

Laboratory for Engineering Man/Machine Systems (LEMS): System identification, model reduction and deconvolution filtering using Fourier based modulating signals and high order statistics

Several important problems in the fields of signal processing and model identification, such as system structure identification, frequency response determination, high order model reduction, high resolution frequency analysis, deconvolution filtering, and etc. Each of these topics involves a wide range of applications and has received considerable attention. Using the Fourier based sinusoidal modulating signals, it is shown that a discrete autoregressive model can be constructed for the least squares identification of continuous systems. Some identification algorithms are presented for both SISO and MIMO systems frequency response determination using only transient data. Also, several new schemes for model reduction were developed. Based upon the complex sinusoidal modulating signals, a parametric least squares algorithm for high resolution frequency estimation is proposed. Numerical examples show that the proposed algorithm gives better performance than the usual. Also, the problem was studied of deconvolution and parameter identification of a general noncausal nonminimum phase ARMA system driven by non-Gaussian stationary random processes. Algorithms are introduced for inverse cumulant estimation, both in the frequency domain via the FFT algorithms and in the domain via the least squares algorithm.

Pan, Jianqiang↗
NASA NTRS1987

Model reductions using a projection formulation

A new methodology for model reduction of MIMO systems exploits the notion of an oblique projection. A reduced model is uniquely defined by a projector whose range space and orthogonal to the null space are chosen among the ranges of generalized controllability and observability matrices. The reduced order models match various combinations (chosen by the designer) of four types of parameters of the full order system associated with (1) low frequency response, (2) high frequency response, (3) low frequency power spectral density, and (4) high frequency power spectral density. Thus, the proposed method is a computationally simple substitute for many existing methods, has an extreme flexibility to embrace combinations of existing methods and offers some new features.

De Villemagne, Christian↗
NASA NTRS1990

An iterative algorithm combining model reduction and control design

A design strategy which integrates model reduction by modal cost analysis and a multiobjective controller design is proposed. The necessary modeling and control algorithms are easily programmed in Matlab standard software. Hence, this method is very practical for controller design for large space structures. The design algorithm also solves the very important problem of tuning multiple loop controllers (multi-input, multi-output, or MIMO). Instead of the single gain change that is used in standard root locus and gain and phase margin theories, this method tunes multiple loop controllers from low to high gain in a systematic way in the design procedure. This design strategy is applied to NASA's Mini-Mast system.

Hsieh, C.↗
NASA NTRS1994

Model reduction of nonsquare linear MIMO systems using multipoint matrix continued-fraction expansions

This paper deals with the multipoint Cauer matrix continued-fraction expansion (MCFE) for model reduction of linear multi-input multi-output (MIMO) systems with various numbers of inputs and outputs. A salient feature of the proposed MCFE approach to model reduction of MIMO systems with square transfer matrices is its equivalence to the matrix Pade approximation approach. The Cauer second form of the ordinary MCFE for a square transfer function matrix is generalized in this paper to a multipoint and nonsquare-matrix version. An interesting connection of the multipoint Cauer MCFE method to the multipoint matrix Pade approximation method is established. Also, algorithms for obtaining the reduced-degree matrix-fraction descriptions and reduced-dimensional state-space models from a transfer function matrix via the multipoint Cauer MCFE algorithm are presented. Practical advantages of using the multipoint Cauer MCFE are discussed and a numerical example is provided to illustrate the algorithms.

Guo, Tong-Yi↗
NASA NTRSDate not supplied

Alternate Methods of Model Reduction to Avoid Dynamic Modal Truncation Error

Loads analysis is traditionally performed using dynamically reduced models, which provides the benefit to reduce run time. If the reduced model frequency cutoff is not chosen appropriately, the model will lack the dynamic content required to fully represent the response of the non-reduced model. Standard guidance for reduced model frequency content, provided in NASA-STD-5002, is to solve fixed base modes up to a minimum of 1.5x the model frequency content of interest and to employ static modal truncation methods such as residual vectors, the mode acceleration method, and the residual flexibility method to account for the truncated flexibility of the missing modes. Fixed base modes require the selection of a set of degrees of freedom to be constrained which, if not properly selected, may affect the accuracy of the reduced model by excluding some of the dynamic characteristic of the full model. In this case, the standard NASA guidance would be insufficient, but it may not be readily apparent that a portion of the reduced model response is missing. This error was encountered during an independent verification and validation (IV&V) effort, where it was observed that the resulting dynamic response was lower than the inline analysis. In this specific case, despite following the standard NASA model reduction guidelines in the selection of the frequency cutoff, the inline model still did not fully capture the necessary dynamic content. As part of the IV&V, an alternate reduction methodology was employed using an unconstrained mode acceleration method. The original model initially performed a constrained reduction to twice the frequency content of interest before doing a free-free run, employing the mode acceleration method to account for the truncated modes. In contrast in the IV&V, the unconstrained model reduced directly to the needed frequency content of the free-free run, avoiding any interactions between constraints and dynamic content. To verify the model, the original reduction methodology was used to generate a series of Hurty-Craig-Bampton reductions, each with a higher frequency cutoff than the previous. The results were shown to converge once the frequency cutoff increased past eight times the frequency content of interest. At the same frequency cutoff, the results of the Hurty-Craig-Bampton model converged with the results of the unconstrained mode acceleration model. This comparative study provided confidence that the results of the unconstrained modal acceleration reduced model were correct and that the Hurty-Craig-Bampton needed to increase its frequency cutoff to fully capture the dynamic response.

Erin Simmons↗
NASA NTRSDate not supplied

Alternate Methods of Model Reduction to Avoid Dynamic Modal Truncation Error

Loads analysis is traditionally performed using dynamically reduced models, which provides the benefit to reduce run time. If the reduced model frequency cutoff is not chosen appropriately, the model will lack the dynamic content required to fully represent the response of the non-reduced model. Standard guidance for reduced model frequency content, provided in NASA-STD-5002, is to solve fixed base modes up to a minimum of 1.5x the model frequency content of interest and to employ static modal truncation methods such as residual vectors, the mode acceleration method, and the residual flexibility method to account for the truncated flexibility of the missing modes. Fixed base modes require the selection of a set of degrees of freedom to be constrained which, if not properly selected, may affect the accuracy of the reduced model by excluding some of the dynamic characteristic of the full model. In this case, the standard NASA guidance would be insufficient, but it may not be readily apparent that a portion of the reduced model response is missing. This error was encountered during an independent verification and validation (IV&V) effort, where it was observed that the resulting dynamic response was lower than the inline analysis. In this specific case, despite following the standard NASA model reduction guidelines in the selection of the frequency cutoff, the inline model still did not fully capture the necessary dynamic content. As part of the IV&V, an alternate reduction methodology was employed using an unconstrained mode acceleration method. The original model initially performed a constrained reduction to twice the frequency content of interest before doing a free-free run, employing the mode acceleration method to account for the truncated modes. In contrast in the IV&V, the unconstrained model reduced directly to the needed frequency content of the free-free run, avoiding any interactions between constraints and dynamic content. To verify the model, the original reduction methodology was used to generate a series of Hurty-Craig-Bampton reductions, each with a higher frequency cutoff than the previous. The results were shown to converge once the frequency cutoff increased past eight times the frequency content of interest. At the same frequency cutoff, the results of the Hurty-Craig-Bampton model converged with the results of the unconstrained mode acceleration model. This comparative study provided confidence that the results of the unconstrained modal acceleration reduced model were correct and that the Hurty-Craig-Bampton needed to increase its frequency cutoff to fully capture the dynamic response.

Erin Simmons↗
NASA NTRS1980

Cost decomposition of linear systems with application to model reduction

A means is provided to assess the value or 'cst' of each component of a large scale system, when the total cost is a quadratic function. Such a 'cost decomposition' of the system has several important uses. When the components represent physical subsystems which can fail, the 'component cost' is useful in failure mode analysis. When the components represent mathematical equations which may be truncated, the 'component cost' becomes a criterion for model truncation. In this latter event component costs provide a mechanism by which the specific control objectives dictate which components should be retained in the model reduction process. This information can be valuable in model reduction and decentralized control problems.

Skelton, R. E.↗
NASA NTRS1990

Model reduction for flexible structures

Several conditions for a near-optimal reduction of general dynamic systems are presented focusing on the reduction in balanced and modal coordinates. It is shown that model and balanced reductions give very different results for the flexible structure with closely-spaced natural frequencies. In general, balanced reduction is found to give better results. A robust model reduction technique was developed to study the sensitivity of modeling error to variations in the damping of a structure. New concepts of grammians defined over a finite time and/or a frequency interval are proposed including computational procedures for evaluating them. Application of the model reduction technique to these grammians is considered to lead to a near-optimal reduced model which closely reproduces the full system output in the time and/or frequency interval.

Gawronski, Wodek↗
NASA NTRS1992

Krylov vector methods for model reduction and control of flexible structures

Krylov vectors and the concept of parameter matching are combined here to develop model-reduction algorithms for structural dynamics systems. The method is derived for a structural dynamics system described by a second-order matrix differential equation. The reduced models are shown to have a promising application in the control of flexible structures. It can eliminate control and observation spillovers while requiring only the dynamic spillover terms to be considered. A model-order reduction example and a flexible structure control example are provided to show the efficacy of the method.

Su, Tzu-Jeng↗
NASA NTRS1990

Component model reduction via the projection and assembly method

This paper explains the projection and assembly model reduction method which has been used to derive reduced order component models for the Galileo spacecraft. Assembly of reduced order component models produces a reduced order system model which can then be used in multibody simulation codes for efficient run times. The methodology is explained and a proof is given showing the exact reproduction of selected significant system modes. Frequency bounds are obtained for all modes produced when the reduced order components are assembled. The projection and assembly method is demonstrated on two examples. The first example is a simplified model of the Galileo spacecraft, while the second example is the model of the Galileo spacecraft in its early mission configuration. When articulation of components is allowed, the method may not reproduce all system modes precisely. Remedies for this problem are suggested.

Kissel, Glen J.↗