LEANS(ID:7029/lea008)Lehigh Pactolusfor LEhigh ANalog Simulator Implementation of Pactolus Partial differential equation simulation language Related languages
References: in Simulation 6(8) August 1966 view details The paper first describes in detail the simulation of a nonlinear chemical reaction. The second part is devoted to a discussion of the relative merits of analog computation vs. a digital simulator program as an educational tool. The authors are to be commended for their work in introducing and using computers in their instructional programs. in ACM Computing Reviews 8(01) January-February 1967 view details in Proceedings of the 1972 Summer Computer Simulation Conference, San Diego, California July, 1972. view details Extract: Introduction Introduction The simulation of physical systems requires the implementation of a mathematical model characterizing the system under study. In a broad class of physical systems, the basic governing equations are known but the system parameters must be identified using experimental observations of the system. This is the case in such environment- orientated areas as air pollution, water pollution etc. A number of problem-oriented programming languages have been developed to facilitate simulation. For discrete-time systems, GPSS and SIMSCRIPT are widely used. For continuoustime systems characterized by ordinary differential equations, CSSL and CSMP are particularly helpful. PDEL and LEANS have been introduced for distributed parameter systems characterized by partial differential equations. In all of these languages, the mathematical model must be completely specified as they are intended for direct rather than inverse problems. A number of language extensions suitable for parameter identification in lumped (ordinary differential equations) systems have been described in recent years. These include MOBSSL-UAF and SLANG. The present paper describes a major extension of the partial differential equation language PDEL so as to make it useful for the identification of parameters in distributed parameter systems. Extract: PDEL-ID LAnguage Language Facilities There are four major language facilities provided by the implemented PDEL-ID system. They are: 1. System model specification 2. Observation data input 3. Parameter identification 4. Print-out control The system model specification facility, which for the most part is the same as in PDEL, enables the user to describe the distributed parameter system model to the computer. This is done through the use of the dimension, equation, parameter assignment, geometry, boundary condition and initial condition statements. The syntax of all these statements had already been described by Cardenas and Karplus. In addition, for system identification problems, unknown parameter identifiers, defined in Section 4.2.1, are used to specify those system parameters which have to be identified. The print-out control facility allows the user to specify interval sizes in space and time for both the numerical solution print-outs and solution plots. This facility has already been designed and implemented in PDEL. 3.1 Observation Data Input Facility For a simulation language designed for system identification such as PDEL-ID, the design of facility to handle observation data input deserves careful considerations. In system identification problems involving distributed parameter systems, the observation data used for identification contain the following attributes: 1. Field locations of observation points. 2. Measurement values of the variables observed. 3. Time corresponding to each measurement value. 4. Weight of the measurement value (sometimes). The observation data input facility is designed to provide flexible and simple data attribute specification with clear and complete problem documentation. The syntax of the statements in this facility is described in Section 4.1. 3.2 Parameter Identification Facility Since PDEL-ID is designed for distributed parameter system identification, the facility for parameter identification forms the heart of the entire language. The design of such facility is based on the following characteristics: 1. The design of the facility is aimed at slmple problem specification, programming ease, and natural syntax. 2. The use of the facility does not require detailed knowledge of the identification process involved. 3. Several identification schemes are available so that the most suitable one can be used. (Two are available at present, the quasilinearizatlon technique and the Fletcher-Powell technique). 4. The identification schemes are implemented in modular form and the language statements are completely compatible with all the identification modules. 5. Default conditions are available. If some necessary information is not specified by the user, some predetermined information is assumed. 6. The sensitivity of the criterion function value with respect to each of the parameters to be identified is calculated to give an indication of the reliability of the identlfied parameter value. Language statements are divided into identification initialization and identification control statements. The syntax of these statements are given in Section 4.2. in Proceedings of the ACM SIGPLAN symposium on Very high level languages, March 28-29, 1974, Santa Monica, California, United States view details |