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A REVIEW AND DISCUSSION OF SOME METHODS FOR SYSTEM IDENTIFICATION AND modelING

MEDICAL & BIOLOGICAL ENGINEERING 1968年第3期6卷 231-+页

作者： REID, MH MACKAY, RS Present address: Boston University Medical Center Boston Massachusetts University of California Berkeley California

Mathematically testing the validity of a theoretical model with an observed physical system is an important step in understanding and utilizing such a system. Perhaps even more useful is the generation of computational techniques which use input-output data from physical systems to automatically construct mathematical models which, in some sense, provide the ''best'' descriptions of the real systems. This paper briefly discusses a few of the more recent mathematical techniques available for model generation and testing. A new identification method based upon convex and linear programming is discussed in detail and a number of examples indicating its applicability are given. The linear programming method is basically an approximation to a convex programming problem, the solution of which determines the coefficients of the differential equation describing the observed system data. A number of extensions of the identification method indicate some of its most useful properties. The order of the assumed model differential equation can be larger than that of the unknown system and the identification process will either assign zero values to the superfluous coefficients of the model or pole-zero cancellations will occur in the factored form of the Laplace transform of the model transfer function. ''Best'' lowest order models may be selected automatically. Linear constraints among the coefficients of the model differential equation may be used to restrict the allowable ranges of the coefficients. Multiple sets of data for a single system may be used simultaneously in the indentification process. Multiple input-output systems or systems described by difference equations or with transportation lag can also be identified. Coefficients of time varying and/or nonlinear models may be determined. Review on some recent identification methods and a new convex and linear programming method is presented which is particularly applicable to biological and medical experimentation.

关键词： Simplex Algorithm model transfer function Convex Programming Problem Linear Programming Method Basic Feasible Solution

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APPLICATIONS OF A NEW TECHNIQUE FOR SYSTEM IDENTIFICATION TO DOLPHIN TEMPERATURE REGULATION AND RABBIT INTRAOCULAR PRESSURE CONTROL

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MEDICAL & BIOLOGICAL ENGINEERING 1968年第3期6卷 269-&页

作者： REID, MH MACKAY, RS Present address: Boston University Medical Center Boston Massachusetts University of California Berkeley California

This study illustrates the application of system identification by linear programming (see page 231) to two diverse biological problems, namely incremental deep body temperature regulation in dolphins, recorded by radio telementry from a swallowed temperature sensitive transmitter, and intraocular pressure control in rabbits. An interesting result of the dolphin experiment is that the animal's internal temperature rises following a transfer from warmer to colder water. The temperature transient indicates an overshoot phenomena followed by a return to the original equilibrium temperature in approximately 1 hr. A theory of the operation of the ‘counter-flow heat exchanger’ of the dolphin is presented in conjunction with a linear model for thermal regulation. The mechanism of intraocular pressure control in a rabbit is also briefly investigated. Pressure transients resulting from injection of small amounts of fluid into a rabbit's eye are presented and a comparison is made between the formulated mathematical model and existing electrical analogs for intraocular pressure regulation. The pressure transient and model for an eye in a recently killed rabbit are significantly different from those of a live rabbit.

关键词： Intraocular Pressure Step Change Pressure Transient Metabolic Heat Production model transfer function

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