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Gradient search procedures application for nonlinear system unknown parameters identification from system dynamic response observations
Research areas associated with digital signal processing and control and estimation theory are identified. Particular attention is given to image processing, system identification problems (parameter identification, linear prediction, least squares, Kalman filtering), stability analyses (the use of the Liapunov theory, frequency domain criteria, passivity), and multiparameter systems, distributed processes, and random fields.
This research proposes a sensitivity-based framework for selecting the optimal prescribed loading path for a biaxial cruciform specimen. Optimality here is determined by the direction and magnitude of the prescribed displacement that minimizes the influence of random noise on the material model parameter identification. Using simulated experimental data based on finite element simulation, in this work, we identify the material model parameters of a Ludwik hardening model and plane stress implementation of the Hill-48 yield criterion using finite element model updating (FEMU). Our analysis reveals that the identification (or estimator) uncertainty of model parameters depends on the displacement boundary conditions (i.e., loading sequence) and the ground-truth value of the individual parameters. Optimal experimental design (OED) criteria based on the Fisher information matrix were investigated to mitigate indecision in the choice of optimal load path when the identification uncertainty of different material model parameters optimized at different load paths. The determinant of the Fisher information matrix was chosen here as the more useful metric due to its ability to capture uncertainty of the most influential material model parameters. The proposed framework demonstrates potential for real-time automated load step selection using scalar criteria derived prior to mechanical loading. The framework can be generalized to other geometries, boundary conditions and material models, allowing this procedure to be utilized for different experimental configurations and materials.
Flexible-structure damage is presently addressed by a combined model- and parameter-identification approach which employs the AI methodologies of classification, heuristic search, and object-oriented model knowledge representation. The conditions for model-space search convergence to the best model are discussed in terms of search-tree organization and initial model parameter error. In the illustrative example of a truss structure presented, the use of both model and parameter identification is shown to lead to smaller parameter corrections than would be required by parameter identification alone.
Many papers relevant to reconfigurable flight control have appeared over the past fifteen years. In general these have consisted of theoretical issues, simulation experiments, and in some cases, actual flight tests. Results indicate that reconfiguration of flight controls is certainly feasible for a wide class of failures. However many of the proposed procedures although quite attractive, need further analytical and experimental studies for meaningful validation. Many procedures assume the availability of failure detection and identification logic that will supply adequately fast, the dynamics corresponding to the failed aircraft. This in general implies that the failure detection and fault identification logic must have access to all possible anticipated faults and the corresponding dynamical equations of motion. Unless some sort of explicit on line parameter identification is included, the computational demands could possibly be too excessive. This suggests the need for some form of adaptive control, either by itself as the prime procedure for control reconfiguration or in conjunction with the failure detection logic. If explicit or indirect adaptive control is used, then it is important that the identified models be such that the corresponding computed controls deliver adequate performance to the actual aircraft. Unknown changes in trim should be modelled, and parameter identification needs to be adequately insensitive to noise and at the same time capable of tracking abrupt changes. If however, both failure detection and system parameter identification turn out to be too time consuming in an emergency situation, then the concepts of direct adaptive control should be considered. If direct model reference adaptive control is to be used (on a linear model) with stability assurances, then a positive real or passivity condition needs to be satisfied for all possible configurations. This condition is often satisfied with a feedforward compensator around the plant. This compensator must be robustly designed such that the compensated plant satisfies the required positive real conditions over all expected parameter values. Furthermore, with the feedforward only around the plant, a nonzero (but bounded error) will exist in steady state between the plant and model outputs. This error can be removed by placing the compensator also in the reference model. Design of such a compensator should not be too difficult a problem since for flight control it is generally possible to feedback all the system states.
A project to identify a full-envelope model of the YAV-8B Harrier using flight-test and parameter identification techniques is described. As part of the research in advanced control and display concepts for V/STOL aircraft, a full-envelope aerodynamic model of the Harrier is identified, using mathematical model structures and parameter identification methods. A global-polynomial model structure is also used as a basis for the identification of the YAV-8B aerodynamic model. State estimation methods are used to ensure flight data consistency prior to parameter identification.Equation-error methods are used to identify model parameters. A fixed-base simulator is used extensively to develop flight test procedures and to validate parameter identification software. Using simple flight maneuvers, a simulated data set was created covering the YAV-8B flight envelope from about 0.3 to 0.7 Mach and about -5 to 15 deg angle of attack. A singular value decomposition implementation of the equation-error approach produced good parameter estimates based on this simulated data set.
The NASA F-15 Intelligent Flight Control System project team developed a series of flight control concepts designed to demonstrate neural network-based adaptive controller benefits, with the objective to develop and flight-test control systems using neural network technology to optimize aircraft performance under nominal conditions and stabilize the aircraft under failure conditions. This report presents flight-test results for an adaptive controller using stability and control derivative values from an online learning neural network. A dynamic cell structure neural network is used in conjunction with a real-time parameter identification algorithm to estimate aerodynamic stability and control derivative increments to baseline aerodynamic derivatives in flight. This open-loop flight test set was performed in preparation for a future phase in which the learning neural network and parameter identification algorithm output would provide the flight controller with aerodynamic stability and control derivative updates in near real time. Two flight maneuvers are analyzed - pitch frequency sweep and automated flight-test maneuver designed to optimally excite the parameter identification algorithm in all axes. Frequency responses generated from flight data are compared to those obtained from nonlinear simulation runs. Flight data examination shows that addition of flight-identified aerodynamic derivative increments into the simulation improved aircraft pitch handling qualities.
The NASA F-15 Intelligent Flight Control System project team has developed a series of flight control concepts designed to demonstrate the benefits of a neural network-based adaptive controller. The objective of the team is to develop and flight-test control systems that use neural network technology to optimize the performance of the aircraft under nominal conditions as well as stabilize the aircraft under failure conditions. Failure conditions include locked or failed control surfaces as well as unforeseen damage that might occur to the aircraft in flight. This report presents flight-test results for an adaptive controller using stability and control derivative values from an online learning neural network. A dynamic cell structure neural network is used in conjunction with a real-time parameter identification algorithm to estimate aerodynamic stability and control derivative increments to the baseline aerodynamic derivatives in flight. This set of open-loop flight tests was performed in preparation for a future phase of flights in which the learning neural network and parameter identification algorithm output would provide the flight controller with aerodynamic stability and control derivative updates in near real time. Two flight maneuvers are analyzed a pitch frequency sweep and an automated flight-test maneuver designed to optimally excite the parameter identification algorithm in all axes. Frequency responses generated from flight data are compared to those obtained from nonlinear simulation runs. An examination of flight data shows that addition of the flight-identified aerodynamic derivative increments into the simulation improved the pitch handling qualities of the aircraft.
The purpose of this document is to explore the use of adaptive routines in battery modeling. The adaptive routines consist of real-time state estimators combined with battery parameter model components that are adjusted in real-time as battery data becomes available. Several aspects are explored. It is shown that model parameter identification is possible for simple battery models using available input/output data measurements. The online system identification used is recursive least squares. Model identification may be combined with a state observer such as the extended Kalman filter or the unscented Kalman filter to form an adaptive model combined with state estimation. However, such a combination is found to be problematic due to uncertainty, observability and stability issues. This paper is organized as follows. Section 1 introduces adaptive routines and possible roles they play in battery modeling. In Section 2 real-time parameter identification is described with results based on battery data. Section 3 reviews various state estimators and results using a simple battery model. In Section 4 parameter identification and state estimation are combined to form an adaptive routine. Finally, in Section 5 conclusions are drawn and future work is suggested.
Linear distributed parameter system identification by stochastic approximation, obtaining constant parameters sequentially
Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.
The problem of estimating the state of a turbopump rotating assembly and identifying unknown products of inertia and unknown bearing parameters is considered. A linearized, extended Kalman filtering approach has been used and found to be successful for both state estimation and parameter identification in an inherently nonlinear problem. The input data were simulated Bently test data obtained from a verified 12-dimensional state-space model and were compared with real Bently test data obtained from NASA. The results prove the feasibility of using this model and this type of test data to obtain the hidden parameters of a typical turbopump rotating assembly.
The development of a 4-bladed model rotor is reported that can be excited with a simple eccentric mechanism in progressing and regressing modes with either harmonic or transient inputs. Parameter identification methods were applied to the problem of extracting parameters for linear perturbation models, including rotor dynamic inflow effects, from the measured blade flapping responses to transient pitch stirring excitations. These perturbation models were then used to predict blade flapping response to other pitch stirring transient inputs, and rotor wake and blade flapping responses to harmonic inputs. The viability and utility of using parameter identification methods for extracting the perturbation models from transients are demonstrated through these combined analytical and experimental studies.
Modern flight control research has improved spacecraft survivability as its goal. To this end we need to have a failure detection system on board. In case the spacecraft is performing imperfectly, reconfiguration of control is needed. For that purpose we need to have parameter identification of spacecraft dynamics. Parameter identification of a system is called system identification. We treat the system as a black box which receives some inputs that lead to some outputs. The question is: what kind of parameters for a particular black box can correlate the observed inputs and outputs? Can these parameters help us to predict the outputs for a new given set of inputs? This is the basic problem of system identification. The X33 was supposed to have the onboard capability of evaluating the current performance and if needed to take the corrective measures to adapt to desired performance. The X33 is comprised of both rocket and aircraft vehicle design characteristics and requires, in general, analytical methods for evaluating its flight performance. Its flight consists of four phases: ascent, transition, entry and TAEM (Terminal Area Energy Management). It spends about 200 seconds in ascent phase, reaching an altitude of about 180,000 feet and a speed of about 10 to 15 Mach. During the transition phase which lasts only about 30 seconds, its altitude may increase to about 190,000 feet but its speed is reduced to about 9 Mach. At the beginning of this phase, the Main Engine is Cut Off (MECO) and the control is reconfigured with the help of aerosurfaces (four elevons, two flaps and two rudders) and reaction control system (RCS). The entry phase brings down the altitude of X33 to about 90,000 feet and its speed to about Mach 3. It spends about 250 seconds in this phase. Main engine is still cut off and the vehicle is controlled by complex maneuvers of aerosurfaces. The last phase TAEM lasts for about 450 seconds and the altitude and speed, both are reduced to zero. The present attempt, as a start, focuses only on the entry phase. Since the main engine remains cut off in this phase, there is no thrust acting on the system. This considerably simplifies the equations of motion. We introduce another simplification by assuming the system to be linear after some non-linearities are removed analytically from our consideration. Under these assumptions, the problem could be solved by Classical Statistics by employing the least sum of squares approach. Instead we chose to use the Neural Network method. This method has many advantages. It is modern, more efficient, can be adapted to work even when the assumptions are diluted. In fact, Neural Networks try to model the human brain and are capable of pattern recognition.
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.
Results are given of remote sensing experiments conducted in the New York Bight between April 7-17, 1975, to evaluate the role of remote sensing technology to aid in monitoring ocean dumping. Remote sensors were flown on the C-54, U-2, and C-130 aircraft while the National Oceanic and Atmospheric Administration obtained concurrent in situ sea truth data using helicopters and surface platforms. The test site, aircraft platforms, experiments, and supporting sensors are described. The operation of each aircraft are discussed and aircraft flight lines, flight parameters, and data identification parameters are presented in figures and tables.
A conceptual design of a model based failure detection and diagnosis system is developed for the space shuttle main engine. This design relies on the accurate and reliable identification of the parameters of the highly nonlinear and very complex engine. The design approach is presented in some detail and results for a failed valve are presented. These preliminary results verify that the developed parameter identification technique together with a neural network classifier can be used for this purpose.
A conceptual design of a model based failure deeteection and diagnosis system is deeveloped for the Space Shuttle Main Engine. This design relies on the accurate and reliable identification of the parameters of the highly nonlinear and very complex engine. The design approach is presented in some detail and results for a failed valve are presented. These preliminary results verify that the developed parameter identification technique, together with a neural network classifier, can be used for this purpose.