Engineering topics
Publications and source records attributed to Bekey, G. A..
Paper introduces concept of near equivalence in probability between different parameters or mathematical models of physical system. One in series of papers, each establishes different part of rigorous theory of mathematical modeling based on concepts of structural error, identifiability, and equivalence. This installment focuses upon effects of additive structural errors on degree of bias in estimates parameters.
Errors and previously implicit assumptions treated explicitly. Paper discusses errors in mathematical models of physical systems and problem of identifying model from system input and output. Problem approached by explicitly taking account of erroneous choices of model structure. Paper concerned specifically with linear or weakly nonlinear models.
Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.
On-line pulse control for vibration suppression in a flexible spacecraft was evaluated. A continuous beam vs. a truss was modeled. A linear finite element model was used to determine the truss characteristics. Control issues outlined are ED pulse actuator development, pseudo pulse algorithm development, and large nonlinear simulation problems.
This paper is concerned with the identification of a system in the presence of several error sources. Following some basic definitions, the notion of 'near-equivalence in probability' is introduced using the concept of near-equivalence between a model and process. Necessary and sufficient conditions for the identifiability of system parameters are given. The effect of structural error on the parameter estimates for both deterministic and stochastic cases are considered.
In this paper, the notion of 'near-equivalence in probability' is introduced for identifying a system in the presence of several error sources. Following some basic definitions, necessary and sufficient conditions for the identifiability of parameters are given. The effects of structural error on the parameter estimates for both the deterministic and stochastic cases are considered.
A simple yet effective method is presented for the on-line vibration control of nonlinear distributed parameter systems, with constant or time-varying properties, responding to a wide class of dynamic environments. The control procedure uses pulse generators located at selected positions throughout a given system. The degree of system oscillation near each controller determines the controller's activation time and pulse amplitude. The direct method of Liapunov is used to establish that the response of the controlled nonlinear system is Lagrange stable. Analytical and experimental studies of a wing-like plate demonstrate the feasibility, reliability, and robustness of the proposed vibration-suppression method.
In most identification problems, the possibility of identifying a model from the observation of input and output is approached by first assuming that the model is an exact representation of the process. Since models are only approximations to a real process, this paper presents a concrete way of taking into account the difference in structure between the model and the process it represents. The identifiability problem is reformulated on the basis of equivalence and near-equivalence between model and process. Necessary and sufficient conditions under which the differences between the outputs of the process and a model remains within a desired bound in the presence of modeling error are given. Necessary and sufficient conditions for the identifiability of parameters are presented.
An approach to system identification is presented which explicitly takes structure errors into account and hence provides a systematic way for answering questions concerning the magnitude of estimated parameter errors resulting from structural errors. It is indicated that, from this point of view, it is possible to define near equivalence between process and model and to obtain meaningful theoretical results on solution error system identification. It remains to apply these results to large realistic problems such as those involving models of complex man machine systems.
The following topics are covered in view graph form: (1) pulse control strategy; (2) stability analysis and digital simulations; (3) digital/analog and analog/digital conversions, and analog simulation; and (4) experimental studies.
An extensive computer market survey was made to determine those available systems suitable for current and future flight simulation studies at Ames Research Center. The primary requirement is for the computation of relatively high frequency content (5 Hz) math models representing powered lift flight vehicles. The Rotor Systems Research Aircraft (RSRA) was used as a benchmark vehicle for computation comparison studies. The general nature of helicopter simulations and a description of the benchmark model are presented, and some of the sources of simulation difficulties are examined. A description of various applicable computer architectures is presented, along with detailed discussions of leading candidate systems and comparisons between them.
An approach to modeling human driver behavior in single-lane car following which is based on a finite-state decision structure is considered. The specific strategy at each point in the decision tree was obtained from observations of typical driver behavior. The synthesis of the decision logic is based on position and velocity thresholds and four states defined by regions in the phase plane. The performance of the resulting assumed intuitively logical model was compared with actual freeway data. The match of the model to the data was optimized by adapting the model parameters using a modified PARTAN algorithm. The results indicate that the heuristic model behavior matches actual car-following performance better during deceleration and constant velocity phases than during acceleration periods.
The man machine interface between the human driver and his automobile during car following tasks was examined. A direct connection between models of the human operator and the theory of optimal control was established for car following situations involving both linear and nonlinear car dynamics. Results obtained from several types of mathematical models are discussed. Conventional parameter identification techniques were used to obtain the parameters of these models by comparing their performance to data obtained by aerial photogrammetry. The results indicate that there are two general classes of model structures: models assumed to have preview information and models without preview.
Studies are summarized on the application of advanced analytical and computational methods to the development of mathematical models of human controllers in multiaxis manual control systems. Specific accomplishments include the following: (1) The development of analytical and computer methods for the measurement of random parameters in linear models of human operators. (2) Discrete models of human operator behavior in a multiple display situation were developed. (3) Sensitivity techniques were developed which make possible the identification of unknown sampling intervals in linear systems. (4) The adaptive behavior of human operators following particular classes of vehicle failures was studied and a model structure proposed.
Human operator models parameter estimation by stochastic approximation, considering continuous and sampled data models
Applying statistical decision theory to manual adaptive control systems
On-line parameter tracking algorithm, obtaining parameters in mathematical relation between full wave rectified EMG and human triceps muscle force during isometric task
Skeletal muscle force generation stochastic model based on motor unit, discussing Poission distribution and dynamic force response