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The following paper is presented in viewgraph format and covers topics including: (1) linear state feedback control system; (2) Kalman filter state estimation; (3) relation between residual and stochastic part of output; (4) obtaining Kalman filter gain; (5) state estimation under unknown system model and unknown noises; and (6) relationship between filter Markov parameters and system Markov parameters.
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A vortex model of winds associated with clear-air turbulence (CAT) is shown to be useful for characterizing actual airline CAT encounters. The model consists of an array of vortices with solid-body cores embedded in a potential flow field. Parameters such as the size and strength of the vortices and their locations are identified using a modified Newton-Raphson algorithm. A manual identification start-up scheme is used to minimize errors in the initial parameter estimates, and the identification algorithm is found to be robust in regard to the remaining errors. The analysis of a CAT encounter involving a commercial airliner demonstrates the success of the model and estimation procedure. The analysis finds vortices with core diameters of 1000 ft and tangential velocities of 87 ft/sec in this encounter.
Background and Motivation - Low Order Equivalent System (LOES) - From handling qualities analysis - Traditionally simplifying complex control law and plant - More easily understood form - Extend LOES to a complex model due to aeroelasticity - Maximum likelihood (Filter Error) System Identification - Z = H_loes (U + W) + V - There are a lot of parameters - Estimate noise parameters - Extra outputs mean extra parameters to estimate - Usually assume noise model to simplify - Output Error and Equation Error - Results in biased estimates of the parameters - Sensing flexible aircraft have many outputs - Quasi maximum likelihood exploits redundancy of outputs
Background and Motivation - Low Order Equivalent System (LOES) - From handling qualities analysis - Traditionally simplifying complex control law and plant - More easily understood form - Extend LOES to a complex model due to aeroelasticity - Maximum likelihood (Filter Error) System Identification - Z = H_loes (U + W) + V - There are a lot of parameters - System identification usually simplifies by assuming a value - Output Error and Equation Error - Results in biased estimates of the parameters - We are proposing a new method to solving this problem
A methodology is proposed for testing, modal identification, and model correlation of structures which are assembled in an evolutionary manner. The methodology prescribes initial testing of a base structure without any attached components. The experimental modal properties are used to update the physical properties of the base structure finite element model using a Bayesian Estimation Technique (BET). The BET is implemented in METLAB using IMOS functions. As components are added to the base structure, additional tests are performed. Three testing options are proposed, all of which enable estimation of the physical parameters of the components alone. Furthermore, improvements to the original BET implementation have been made, which contribute to higher fidelity models and more efficient computational times.
Many system identification algorithms produce models in modern state variable form. When a mechanical system is identified one knows that there must be a model in second order form. In structural dynamics one is interested in either a modal model of the system, or in a model including a mass matrix, stiffness matrix and a damping matrix. In this paper, algorithms are developed that convert a modern state space realization into the above two representations of interest in mechanical systems. The algorithm can be used with any identification methods that produce a modern state variable representation such as the Eigensystem Realization Algorithm (ERA), its modified version by data correlation (ERA/DC), and combinations of these with Observer/Kalman Filter Identification (OKID). An algorithm is developed that allows one to identify the damping matrix in a model representation, so that one determines how near to modal the damping is in the system, and can therefore understand the degree to which the modes are coupled by the damping in the system. A second algorithm produced the mass, damping, and stiffness matrices, given the input and output matrices. It is assumed that the number of sensors (or the number of actuators) is greater than or equal to the number of modes in the system, and it is proved that this is a necessary condition to be able to uniquely identify these matrices. Experience with examples suggests that a singular value truncation involved in these algorithms can help one determine the true system order. This truncation has the benefit of knowledge of the correct form for a mechanical system model, which is not present in the modern control identification algorithm.
The state-space presentation of an aerodynamic vortex model is considered from a classical and system identification perspective. Using an aerodynamic vortex model as a numerical simulator of a wing tunnel experiment, both full state and limited state data or measurements are considered. Two possible approaches for system identification are presented and modal controllability and observability are also considered. The theory then is applied to the system identification of a flow over an aerodynamic delta wing and typical results are presented.
The importance of recognizing that each lower-order model used for rotorcraft parameter identification has a limited range of applicability is illustrated in some detail. Examples are given to illustrate the use of conditioning the test input signals and the potential of using multi-axis test inputs to enhance the parameter identifiability. The paper discusses the benefits and limitations of using frequency sweeps as flight-test input signals for identification of frequency response for rotorcraft and for the subsequent fitting of parametric transfer-function models. This paper demonstrates the major role played by analytical modeling and the understanding of the physics involved in the rotorcraft flight dynamics, particularly understanding the limit of lower-order models, in achieving successful rotorcraft parameter identification.
The determination of the torsional constants of three blade models having NACA four-digit symmetrical airfoil cross sections is presented. Values were obtained for these models analytically and experimentally. Results were also obtained for three other models having rectangular, elliptical, and parabolic cross sections. Complete modal analyses were performed for five blade models. The identification of modal parameters was done for cases when the blades were modeled as either undamped or damped multi-degree-of-freedom systems. For the experimental phase of this study, the modal testing was performed using a Dual Channel FFT analyzer and an impact hammer (which produced an impulsive excitation). The natural frequency and damping of each mode in the frequency range up to 2 kHz were measured. A small computer code was developed to calculate the dynamic response of the blade models for comparison with the experimental results. A comparison of the undamped and damped cases was made for all five blade models at the instant of maximum excitation force. The program was capable of handling models where the excitation forces were distributed arbitrarily along the length of the blade.
Structural damage identification based on physical models is often transformed into an optimization problem that minimizes the difference between measurement information of structure being monitored and the model prediction in the parametric space. However, the objective function in this context often exhibits multimodality, involving high-dimensional variables due to the reliance on finite element models for damage identification. These features pose challenges to optimization algorithms, where entrapment in local solutions can lead to false positives and false negatives in damage identification. In this research, we propose a reinforcement learning based multi-swarm optimizer to tackle such challenges in pursuit of a small yet diverse solution set that can capture the true damage scenario as one of the solutions. The proposed method leverages the flexibility of the particle swarm optimizer and incorporates novel strategies of metaheuristics to realize targeted improvement. To enable the particle swarm to adaptively select the appropriate search strategy based on the current environment, we adopt the learning automata technique, which sidesteps the need for reward strategy selection that is usually ad hoc at each step of the search. The integration harnesses the automatic learning and self-adaptation capabilities of learning automata, enabling the particles to navigate based on environmental signals. This leads to accumulated probabilities tied to advantageous movements, fostering an adaptive exploration of particles in the search space. The proposed approach is first validated through implementing into benchmark test cases with comparisons. It is then applied to structural damage identification with piezoelectric admittance experimental signals. `The results highlight the capability of the algorithm to identify a small solution set with high accuracy to match the actual damage scenario.
Identification and control of flexible space structures were studied. Exploration of the most advanced modeling estimation, identification and control methodologies to flexible space structures was discussed. The following general areas were discussed: space platforms, antennas, and flight experiments; control/structure interactions - modeling, integrated design and optimization, control and stabilization, and shape control; control technology; control of space stations; large antenna control, dynamics and control experiments, and control/structure interaction experiments.
Primary lithium cells which use LiAlCl4/SOCl2 electrolyte exhibit high energy density and long life. Currently these cells pose a safety problem since they have been found to vent or explode. This paper summarizes experiments to resolve the safety problem of Li-SOCl2 cells by thermal modeling and identification of possibly hazardous intermediates formed during discharge of these cells. A thermal model and mechanism for the reduction of SOCl2 are presented, as well as a discussion of their application to Li-SOCl2 cell safety.
A high gain steering controller to compensate for limitations in a handicapped driver's range of motion is employed when adapting vehicle to his use. A driver/vehicle system can become unstable as vehicle speed is increased, therefore it is desirable to use a computer simulation of the driver/vehicle combination as a design tool to investigate the system response prior to construction of a controller and road testing. Unknown driver parameters must be identified prior to use of the model for system analysis. A means to collect the data necessary for identification of these driver model parameters without extensive instrumentation of a vehicle to measure and record vehicle states is addressed. Initial tests of the procedure identified all of the driver parameters with errors of 6% or less.
The equation error for a class of systems modeled by input/output differential operator equations has the potential to be integrated exactly, given the input/output data on a finite time interval, thereby opening up the possibility of using an explicit least squares estimation technique for system parameter identification. The paper delineates the class of models for which this is possible and shows how the explicit least squares cost function can be obtained in a way that obviates dealing with unknown initial and boundary conditions. The approach is illustrated by two examples: a second order chemical kinetics model and a third order system of Lorenz equations.
The following constitutes a summary of this paper: on-orbit identification methodology starts with nonparametric techniques for a priori system identification; development of the nonparametric identification and model determination experiment software has been completed; the validation experiments to be performed on the JPL Control and Identification Technology Validation Laboratory have been designed.
A method for using system identification techniques to improve airframe finite element models was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory.
A method for using system identification techniques to improve airframe finite element models using test data has been developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in the total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all of the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory.