Numerical solution of the parabolic partial differential equations with an unknown parameter play a very important role in engineering applications. In this study we present a high order scheme for determining unknown...Numerical solution of the parabolic partial differential equations with an unknown parameter play a very important role in engineering applications. In this study we present a high order scheme for determining unknown control parameter and unknown solution of two-dimensional parabolic inverse problem with overspe- cialization at a point in the spatial domain. In this approach, a compact fourth-order scheme is used to discretize spatial derivatives of equation and reduces the problem to a system of ordinary differential equations （ODEs）. Then we apply a fourth order boundary value method to the solution of resulting system of ODEs. So the proposed method has fourth order of accuracy in both space and time components and is unconditionally stable due to the favorable stability property of boundary value methods. The results of numerical experiments are presented and some comparisons are made with several well-known finite difference schemes in the literature. Also we will investigate the effect of noise in data on the approximate solutions.展开更多
This paper deals with instrumenting a mechatronic system,through the incorporation of suitable sensors,actuators,and other required hardware.Sensors(e.g.,semiconductor strain gauges,tachometers,RTD temperature sensors...This paper deals with instrumenting a mechatronic system,through the incorporation of suitable sensors,actuators,and other required hardware.Sensors(e.g.,semiconductor strain gauges,tachometers,RTD temperature sensors,cameras,piezoelectric accelerometers)are needed to measure(sense)unknown signals and parameters of a system and its environment.The information acquired in this manner is useful in operating or controlling the system,and also in process monitoring;experimental modeling(i.e.,model identification);product testing and qualification;product quality assessment;fault prediction,detection and diagnosis;warning generation;surveillance,and so on.Actuators(e.g.,stepper motors,solenoids,dc motors,hydraulic rams,pumps,heaters/coolers)are needed to"drive"a plant.Control actuators(e.g.,control valves)perform control actions,and in particular they drive control devices.Micro-electromechanical systems(MEMS)use microminiature sensors and actuators.MEMS sensors commonly use piezoelectric,capacitive,electromagnetic and piezoresistive principles.MEMS devices provide the benefits of small size and light weight(negligible loading errors),high speed(high bandwidth),and convenient mass-production(low cost).The process of instrumentation involves the identification of proper sensors,actuators,controllers,signal modification/interface hardware,and software with respect to their functions,operation,parameters,ratings,interaction with each other,so as to achieve the performance requirements of the overall system,and interfacing/integration/tuning of the selected devices into the system,for a given application.This paper presents the key steps of instrumenting a mechatronic system,in a somewhat general and systematic manner.Examples are described to illustrate several key procedures of instrumentation.展开更多
基金Supported by the Foundation of University of Kashn(Grant No.258499/5)
文摘Numerical solution of the parabolic partial differential equations with an unknown parameter play a very important role in engineering applications. In this study we present a high order scheme for determining unknown control parameter and unknown solution of two-dimensional parabolic inverse problem with overspe- cialization at a point in the spatial domain. In this approach, a compact fourth-order scheme is used to discretize spatial derivatives of equation and reduces the problem to a system of ordinary differential equations （ODEs）. Then we apply a fourth order boundary value method to the solution of resulting system of ODEs. So the proposed method has fourth order of accuracy in both space and time components and is unconditionally stable due to the favorable stability property of boundary value methods. The results of numerical experiments are presented and some comparisons are made with several well-known finite difference schemes in the literature. Also we will investigate the effect of noise in data on the approximate solutions.
基金supported by the Natural Sciences and Engineering Research Council of Canadathe India-Canada Centre of Excellence for Innovative Multidisciplinary Partnership to Accelerate Community Transformation and Sustainability(IC-IMPACTS)research grantsary D.Eng.degree from University of Waterloo,Canada(2008).He has been a Professor of Mechanical Engineering and Senior Canada Research Chair and NSERC-BC Packers Chair in Industrial Automation,at the University of British Columbia,Vancouver,Canada since 1988.He has authored 24 books and about 540 papers,approximately half of which are in joumals.His recent books published by Taylor&Francis/CRC are:Modeling of Dynamic Systems-with Engineering Applications(2018),Sensor Systems(2017),Sensors and Actuators-Engineering System Instrumentation,2nd edition(2016),Mechanics of Materials(2014),Mechatronics-A Foundation Course(2010),Modeling and Control of Engineering Systems(2009),VIBRATION-Fundamentals and Practice,2nd Ed.(2007),and by Addison Wesley:Soft Computing and Intelligent Systems Design-Theory,Tools,and Applications(with F.Karray,2004).Email:desilva@mech.ubc.ca.
文摘This paper deals with instrumenting a mechatronic system,through the incorporation of suitable sensors,actuators,and other required hardware.Sensors(e.g.,semiconductor strain gauges,tachometers,RTD temperature sensors,cameras,piezoelectric accelerometers)are needed to measure(sense)unknown signals and parameters of a system and its environment.The information acquired in this manner is useful in operating or controlling the system,and also in process monitoring;experimental modeling(i.e.,model identification);product testing and qualification;product quality assessment;fault prediction,detection and diagnosis;warning generation;surveillance,and so on.Actuators(e.g.,stepper motors,solenoids,dc motors,hydraulic rams,pumps,heaters/coolers)are needed to"drive"a plant.Control actuators(e.g.,control valves)perform control actions,and in particular they drive control devices.Micro-electromechanical systems(MEMS)use microminiature sensors and actuators.MEMS sensors commonly use piezoelectric,capacitive,electromagnetic and piezoresistive principles.MEMS devices provide the benefits of small size and light weight(negligible loading errors),high speed(high bandwidth),and convenient mass-production(low cost).The process of instrumentation involves the identification of proper sensors,actuators,controllers,signal modification/interface hardware,and software with respect to their functions,operation,parameters,ratings,interaction with each other,so as to achieve the performance requirements of the overall system,and interfacing/integration/tuning of the selected devices into the system,for a given application.This paper presents the key steps of instrumenting a mechatronic system,in a somewhat general and systematic manner.Examples are described to illustrate several key procedures of instrumentation.
