Inverse Problems in Engineering Mechanics III (eBook)

G.S. Dulikravich, Mana Tanaka (Autoren)

eBook Download: PDF | EPUB

2001 | 1. Auflage
432 Seiten
Elsevier Science (Verlag)
978-0-08-053514-2 (ISBN)

Infos

Inverse Problems are found in many areas of engineering mechanics and there are many successful applications e.g. in non-destructive testing and characterization of material properties by ultrasonic or X-ray techniques, thermography, etc. Generally speaking, inverse problems are concerned with the determination of the input and the characteristics of a system, given certain aspects of its output. Mathematically, such problems are ill-posed and have to be overcome through development of new computational schemes, regularization techniques, objective functionals, and experimental procedures.

This volume contains a selection of peer-reviewed papers presented at the International Symposium on Inverse Problems in Engineering Mechanics (ISIP2001), held in February of 2001 in Nagano, Japan, where recent development in inverse problems in engineering mechanics and related topics were discussed.

The following general areas in inverse problems in engineering mechanics were the subjects of the ISIP2001: mathematical and computational aspects of inverse problems, parameter or system identification, shape determination, sensitivity analysis, optimization, material property characterization, ultrasonic non-destructive testing, elastodynamic inverse problems, thermal inverse problems, and other engineering applications. These papers can provide a state-of-the-art review of the research on inverse problems in engineering mechanics.

Inhalt

Front Cover 1
Inverse Problems in Engineering Mechanics III 4
Copyright Page 5
Contents 10
Preface 6
Symposium Chairpersons 8
International Scientific Committee 8
Organizing Committee 9
Part I: Inverse Thermal Problems 14
Chapter 1. Simultaneous estimation of thermophysical properties and heat and mass transfer coefficients of a drying body 16
Chapter 2. Effects of lateral heat losses on the parameter estimation problem in moist capillary porous media 26
Chapter 3. Solution of some inverse heat conduction problems by the dynamic programming filter and BEM 36
Chapter 4. The time-to-arrival problem for reconstruction of multidimensional heat flux 42
Chapter 5. Estimation of the heat flux at the surface of ablating materials 52
Chapter 6. Estimation of thermal properties of ablating materials 62
Part II: Boundary Data and Parameters Identification 72
Chapter 7. Solution to shape optimization problems of continua on thermal elastic deformation 74
Chapter 8. A 3-D finite element formulation for the determination of unknown boundary conditions in heat conduction 80
Chapter 9. Alternating boundary element inversion scheme for solving inverse boundary value problem from noisy data and its regularization 90
Chapter 10. Solution of inverse geometry problems using Bezier splines and sensitivity coefficients 100
Chapter 11. Identification of boundary conditions by iterative analyses of suitably refined subdomains at biomaterials interfaces 110
Chapter 12. Domain characterization by tomography and material parameter identification for geological surveying 120
Chapter 13. Determination of material property of functionally graded cylinder using genetic algorithm 130
Part III: Damage or Defect Detection 138
Chapter 14. Inversion of vibration mode of an immersion ultrasonic transducer 140
Chapter 15. Three dimensional shape reconstruction of defects from measured backscattering waveforms 150
Chapter 16. Modeling of grain pullout in fatigued polycrystalline alumina 158
Chapter 17. Structural damage identification of frame model based on filtering algorithm 166
Chapter 18. Crack identification of elastically supported beam by genetic algorithm 174
Part IV: Inverse Problems in Solid Mechanics 180
Chapter 19. Parameters identification of an elastic plate subjected to dynamic loading by inverse analysis using BEM and Kalman filter 182
Chapter 20. A parameter identification method using observational boundary conditions and wavelet transform 194
Chapter 21. Stress distribution within granular body 198
Chapter 22. Stress distribution determination scheme for elastic plastic material based on equivalent inclusion method 206
Chapter 23. An inverse approach for constructing the residual stress caused by welding 214
Part V: Numerical and Computational Algorithms 222
Chapter 24. Parameter identification for evolution hemivariational inequalities and applications 224
Chapter 25. Direct method for solution of inverse boundary value problems of the Laplace equation 232
Chapter 26. A variational approach for finding the source function of the wave equation 240
Chapter 27. Ill-posed problems and a priori information 248
Chapter 28. A parameter estimation problem and its regularization by the conjugate gradient method 258
Chapter 29. Nonlinear inverse problems of vibrational spectroscopy 264
Chapter 30. Coefficient identification of the wave equation using the alternating directions method 274
Part VI: Applications of Computational Algorithms 282
Chapter 31. Construction of neural network using cluster analysis and Voronoi diagram 284
Chapter 32. General optimiser for continuous inverse analysis 294
Chapter 33. Inversion method using spectral decomposition of Green's function 304
Chapter 34. Application of stress inversion method to develop crustal deformation monitor of Japanese Islands 314
Chapter 35. Optical multilayer coating synthesis by simultaneous optimization of number of layers, refractive index, and thickness 324
Chapter 36. Adaptive parallel genetic clustering in parameter inverse problems 328
Part VII: Inverse Problems in Aeronautics and Fluid Dynamics 338
Chapter 37. The application of modified output error method on ALFLEX flight data 340
Chapter 38. Flight trajectory tracking system applied to inverse control for aerobatic maneuvers 350
Chapter 39. Stochastic optimization of parameters and control laws of the aircraft gas-turbine engines – A step to a robust design 358
Chapter 40. Sensitivity of aerodynamic optimazation to parameterized target functions 368
Chapter 41. Using the gasdynamic knowledge base for aerodynamic design and optimization in the sonic speed regime 378
Chapter 42. Design of a cascade airfoil shape using the discretized Navier-Stokes equations 388
Chapter 43. Application of constrained target pressure specification to Takanashi's inverse design method 394
Part VIII: Inverse Problems in Electromagnetics 404
Chapter 44. Approximate identification method for material integrity related to electromagnetic nondestructive evaluation 406
Chapter 45. On identification of magnetic sources in materials 416
Chapter 46. 3D electric impedance prospecting simulation based on the dual reciprocity boundary element modelling 424
Author Index 432

Textauszug

Simultaneous Estimation of Thermophysical Properties and Heat and Mass Transfer Coefficients of a Drying Body

G.H. Kanevce    Macedonian Academy of Sciences and Arts Skopje, Macedonia

L.P. Kanevce    Faculty of Technical Sciences St. Kliment Ohridski University, Bitola, Macedonia

G.S. Dulikravich    Department of Mechanical and Aerospace Engineering, UTA Box 19018 The University of Texas at Arlington, Arlington, Texas 76019, USA

ABSTRACT

This paper presents a solution method for the inverse problem of simultaneous estimation of moisture content and temperature-dependent moisture diffusivity together with other thermophysical properties of a drying body as well as the heat and mass transfer coefficients using only temperature measurements. Instead of the actual temperature measurements, the temperature response during convective drying is obtained from the numerical solution of the non-linear one-dimensional Luikov’s equations. In order to simulate real measurements, a normally distributed random error was added to the numerical temperature response. Thus, using the simulated experimental data resulted in a parameter estimation problem that was solved via the Levenberg-Marquardt method of minimization of the least-squares norm. As a representative drying body, a mixture of bentonite and quartz sand with known thermophysical properties has been chosen. An analysis of the influence of the drying parameters needed for the design of the proper experiment is presented. In order to perform this analysis, the sensitivity coefficients and the sensitivity matrix determinant were calculated.

KEYWORDS

Inverse approach

drying

thermophysical properties

heat and mass transfer coefficients

INTRODUCTION

Inverse approach to parameter estimation in last few decades has become widely used in various scientific disciplines. Kanevce, Kanevce and Dulikravich [5, 6, 7] and Dantas, Orlande and Cotta [2, 3] recently analysed application of inverse approaches to estimation of a drying body parameters.

There are several methods for describing the complex simultaneous heat and moisture transport processes within drying material. In the approach proposed by Luikov [9], the drying body moisture content and temperature field are expressed by a system of two coupled partial differential equations. The system of equations incorporates coefficients that are functions of temperature and moisture content, and must be determined experimentally. For many practical calculations the influence of the temperature and moisture content on all transport coefficients except for the moisture diffusivity is small and can be neglected. The moisture diffusivity dependence on moisture content and temperature exerts a strong influence on the drying process calculation. This effect cannot be ignored for the majority of practical cases. All the coefficients except for the moisture diffusivity can be relatively easily determined by experiments. The main problem in the moisture diffusivity determination by classical or inverse methods is the difficulty of moisture content measurements. Local moisture content measurements are practically unfeasible especially for small drying objects. Standard drying curves measurements (body mean moisture content during the drying) are complex and have low accuracy. Instead, accurate and easy to perform thermocouple temperature measurements can be used.

The main idea of the present method is to take advantage of the relation between the heat and mass (moisture) transport processes within the drying body and from its surface to the surroundings. Then, the moisture diffusivity estimation can be performed on the basis of a temperature response by using an inverse approach. Kanevce, Kanevce and Dulikravich [5, 6] recently analysed this idea of the moisture diffusivity estimation by temperature response of a drying body. An analysis of the sensitivity of this method of moisture diffusivity estimation to the heat and mass transfer coefficients accuracy showed [7] that perturbations (simulated errors) in heat and mass transfer coefficients produce reduced errors of estimated moisture diffusivity parameters.

The objective of this paper is an analysis of the possibility of simultaneous estimation of several thermophysical properties of a drying body and the heat and mass transfer coefficients. An analysis of the influence of the drying air parameters and the drying body dimensions is presented as well. In order to perform this analysis, the sensitivity coefficients and the sensitivity matrix determinant were calculated.

MATHEMATICAL MODEL OF DRYING

In the case of an infinite flat plate of thickness 2 L, if the shrinkage of the material can be neglected (ρs = const), the temperature, T, and moisture content, X, in the drying body are expressed by the following system of coupled nonlinear partial differential equations

ρs∂T∂t=∂∂xk∂T∂x+ερsΔH∂X∂t

  (1)

X∂t=∂∂xD∂X∂x+Dδ∂T∂x

  (2)

Here, t, x, c, k, ΔH, ε, δ, D, ρs are time, distance from the mid-plane of the plate, heat capacity, thermal conductivity, latent heat of vaporization, ratio of water evaporation rate to the reduction rate of the moisture content, thermo-gradient coefficient, moisture diffusivity, and density of the dry plate material, respectively.

From the experimental and numerical examinations of the transient moisture and temperature profiles [4] it was concluded that for practical calculations, the influence of the thermodiffusion, δ, is small and can be ignored. It was also concluded that the system of two simultaneous partial differential equations could be used by treating the transport coefficients as constants except for the moisture diffusivity, D. Consequently, the resulting system of equations for the temperature and moisture content prediction is

T∂t=kcρs∂2T∂x2+εΔHc∂X∂t

  (3)

X∂t=∂∂xD∂X∂x

  (4)

As initial conditions, uniform temperature and moisture content profiles are assumed

=0Tx0=T0,Xx0=X0

  (5)

The boundary conditions on the free plate surface (x = L) are

k∂T∂xx=L+jq−ΔH1−εjm=0Dρs∂X∂xx=L+jm=0

  (6)

In the case of convective drying of the sample, the convective heat flux, jq(t), and mass flux, jm(t), on the surface of evaporation are

q=hTa−Tx=Ljm=hDCx=L−Ca

  (7)

where h is the convection heat transfer coefficient and hD is the mass transfer coefficient, while Ta is the drying air bulk temperature. The water vapor concentration in the drying air, Ca is calculated from

a=φ⋅psTa/461.9/Ta+273

  (8)

The water vapor concentration of the air in equilibrium with the free surface of the body is calculated from

x=L=aTx=LXx=L⋅psTx=L/461.9/Tx=L+273

  (9)

The water activity, a, or the equilibrium relative humidity of the air in contact with the surface at temperature Tx = L and moisture content Xx = L is calculated from experimental water sorption isotherms. Equilibrium water vapor concentration was calculated from the experimental water sorption isotherms as a function of the free surface temperature and moisture content.

Since the problem is symmetric, boundary conditions on the mid-plane of the plate are

T∂xx=0=0,∂X∂xx=0=0

  (10)

ESTIMATION OF PARAMETERS

The estimation methodology used is based on minimization of the ordinary least squares norm

P=[Y−TPTY−TP

  (11)

Here, YT = [Y1,Y2, …, Yimax] is the vector of measured temperatures, TT = [T1(P), T2(P), …, Timax(P)] is the vector of estimated temperatures at times ti (i = 1, 2, …, imax) at the measurement locations j = 1,2 (at the mid-plane and at the free plane surface, respectively), PT = [P1,P2, …,PN] is the vector of unknown parameters, imax is the total number of measurements, and N is the total number of unknown parameters (imax ≥ N).

A version of Levenberg-Marquardt method was applied to obtain the solution of the presented parameter estimation problem [10]. This method is quite stable, powerful, and straightforward and has been applied to a variety of inverse problems [2,3,5, 6, 7, 8,11]. It belongs to a class of damped least squares methods [1]. The solution for vector P is achieved using the following iterative procedure

r+1=Pr+JrTJr+μrI−1JrTY−TPr

  (12)

where I is the identity matrix, μ is the damping parameter, and J is the...

Produkt-Details

• Erscheint lt. Verlag: 20.11.2001
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-053514-3 / 0080535143
• ISBN-13: 978-0-08-053514-2 / 9780080535142