Mathematical modelling in the analysis and design of hard and soft measurement systems

This paper briefly looks into the role and extent of mathematical modelling in the design and analysis of measurement systems, especially measurement sub-systems in the form of instruments and instrument elements. These fall within the classical domain of hard measurement (physical, strongly-defined measurement). It also examines the role and use of mathematical modelling in the area of soft measurement (non-physical, weakly defined measurement). These constitute two sub-sets of widely-defined measurement. Based on a number of examples it demonstrates the use of modern modelling techniques in the design and analysis of sub-systems in measurement technology. In doing so, it focuses on the scope and importance of physical modelling at a sub-system level, which ultimately contributes to modelling activities at a global systems level.

[1]  Ludwik Finkelstein,et al.  Widely-defined measurement – An analysis of challenges , 2009 .

[2]  J. Raamachandran.  Boundary and Finite Elements: Theory and Problems , 2000 .

[3]  Michael Tiller,et al.  Introduction to Physical Modeling with Modelica , 2001 .

[4]  François E. Cellier,et al.  On the selection of variables for qualitative modelling of dynamical systems , 2002, Int. J. Gen. Syst..

[5]  Gernot Beer,et al.  Introduction to Finite and Boundary Element Methods for Engineers , 1993 .

[6]  Eckart Schnack,et al.  A hybrid coupled finite-boundary element method in elasticity , 1999 .

[7]  Sanowar H. Khan,et al.  Investigation of optimal parameters for finite element solution of the forward problem in magnetic field tomography based on magnetoencephalography , 2011 .

[8]  Roman Z. Morawski,et al.  An application-oriented mathematical meta-model of measurement , 2013 .

[9]  L. Finkelstein.  Widely, strongly and weakly defined measurement , 2003 .

[10]  L. Finkelstein,et al.  Modeling in measurement and instrumentation—An overview , 1994 .

[11]  Barr and Feigenbaum Edward A. Avron,et al.  The Handbook of Artificial Intelligence , 1981 .

[12]  J. D'Angelo.  Hybrid Finite Element/Boundary Element Analysis of Electromagnetic Fields , 1989 .

[13]  Sergey Edward Lyshevski,et al.  Micromechatronics: Modeling, Analysis, and Design with MATLAB , 2003 .

[14]  L. Finkelstein,et al.  Problems of measurement in soft systems , 2005 .

[15]  Gordon R. Hopkins.  Nonlinear Lumped Parameter Mathematical Model of Dynamic Response of the Human Body , 1971 .

[16]  K. Barker.  Economic Modelling: Theory, Reality, Uncertainty and Decision-Making , 2007 .

[17]  Ludwik Finkelstein,et al.  Advances and generic problems in instrument design methodology , 2007 .

[18]  C. Trowbridge,et al.  The Analytical and Numerical Solution of Electric and Magnetic Fields , 1992 .

[19]  Peter P. Silvester,et al.  Finite Elements for Electrical Engineers , 1983 .

[20]  Jean-Philippe Chancelier,et al.  Modeling and Simulation in Scilab/Scicos with ScicosLab 4.4 , 2009 .

[21]  Sanowar H. Khan,et al.  A new submodelling technique for multi-scale finite element computation of electromagnetic fields: Application in bioelectromagnetism , 2010 .

[22]  B. Barnes,et al.  Mathematical modelling with case studies : a differential equations approach using Maple and MATLAB , 2002 .

[23]  Singiresu S. Rao.  The finite element method in engineering , 1982 .

[24]  Giovanni Battista Rossi,et al.  MEASUREMENT RELATED TO HUMAN PERCEPTION AND INTERPRETATION - STATE OF THE ART AND CHALLENGES , 2009 .

[25]  J. Michell.  Measurement in psychology: A critical history of a methodological concept. , 1999 .

[26]  Peter A. Fritzson,et al.  Introduction to Modeling and Simulation of Technical and Physical Systems with Modelica , 2011 .

[27]  Thomas Rylander,et al.  Computational Electromagnetics , 2005, Electronics, Power Electronics, Optoelectronics, Microwaves, Electromagnetics, and Radar.

[28]  Klaas Sijtsma,et al.  Introduction to the measurement of psychological attributes , 2011 .

[29]  Mark R. Wilson.  The role of mathematical models in measurement: a perspective from psychometrics , 2011 .

[30]  Wolfgang Borutzky,et al.  Bond Graph Methodology: Development and Analysis of Multidisciplinary Dynamic System Models , 2009 .

[31]  Roald Taymanov,et al.  Improvement of Traceability of Widely-Defined Measurements in the Field of Humanities , 2010 .

[32]  S. Mukherjee,et al.  Boundary element techniques: Theory and applications in engineering , 1984 .

[33]  Javier Kypuros.  System Dynamics and Control with Bond Graph Modeling , 2013 .

[34]  Claes Johnson.  Numerical solution of partial differential equations by the finite element method , 1988 .

[35]  Yasuhito Takahashi,et al.  Large‐scale magnetic field analysis by the hybrid finite element‐boundary element method combined with the fast multipole method , 2006 .

[36]  Kenneth T. V. Grattan,et al.  Design and investigation of high-speed, large-force and longlifetime electromagnetic actuators by finite element modelling , 2005 .

[37]  A.I. Borovkov,et al.  Solution of the Forward Problem in Magnetic-Field Tomography (MFT) Based on Magnetoencephalography (MEG) , 2009, IEEE Transactions on Magnetics.

[38]  Anthony Finkelstein,et al.  Design theory advances and measurement science , 2000 .

[39]  G. Zingales.  Concise encyclopedia of measurement and instrumentation: edited by L. Finkelstein and K.T.V. Grattan, Pergamon, Oxford, 1993, 434 pp., ISBN 0-080-36212-5. , 1994 .

[40]  O. C. Zienkiewicz,et al.  The Finite Element Method: Its Basis and Fundamentals , 2005 .