Conjugate Gradient Method Of Minimization Research Articles

Estimation of thermal contact conductance using transient approach with inverse heat conduction problem

Precise evaluation of thermal contact conductance (TCC) is essential for the thermal and mechanical analysis of a thermal system found in different engineering applications. Inverse heat conduction method provides an effective tool for the estimation of thermal contact conductance at the interface of two bodies in contact. In this work, 1-D inverse heat conduction method has been employed for the estimation of thermal contact conductance for metallic contacts. Function estimation technique using conjugate gradient method of minimization with adjoint problem has been utilized. Transient temperature data at fixed axial locations in the contacting bodies, their thermophysical properties and boundary conditions at the two ends are provided as the input to the inverse problem. Initially, the inverse method has been applied with the simulated data for various boundary conditions and different test functions to check the validity of inverse problem. Subsequently, the experiment has been performed for various boundary conditions, under different environmental, and loading conditions for metallic specimens. Transient temperature data from the experiments are provided as an input in the inverse problem. Eventually, the effectiveness and reliability of the transient approach based on inverse analysis has been established by comparing the results with their corresponding steady state values of TCC. The accuracy of the inverse solutions has been demonstrated with the help of parity plots. Conclusively, the transient approach has been found to be successful in TCC estimation with short duration experimental runs as compared to long waiting period of steady state TCC run. In addition, the transient approach eliminates the need for the measurement of heat flux and temperature drop at the interface, encountered in steady state approach.

Fast Identification Method of Total Normal Surface Absorptances Using Inverse Techniques

This paper proposes a simple and fast method to identify the normal absorptance of various surfaces submitted to a radiation source, using inverse techniques. The method consists of imposing during a lap of a few seconds a radiative flux on the front face of a sample whose absorptance is to be identified. The time-dependent temperature on the rear face is measured, and the procedure of inversion is implemented to give a time function of absorbed flux. Only one time–temperature function is measured using a current type K thermocouple. The normal absorptance of the front face is obtained by comparing the time heat flux function of the source and the identified absorbed heat flux function. This method can be quickly and efficiently adopted for many practical applications without the need to use optical devices, which give accurate measurement but at substantial cost. The inverse technique using a conjugate gradient method of minimization with adjoint problem is implemented to estimate the absorbed heat flux. In order to achieve good values of radiative absorptances, reliable knowledge of thermal diffusivities and adequately manufactured samples are required.

A non-linear optimal control problem in obtaining homogeneous concentration for semiconductor materials

A non-linear optimal control algorithm is examined in this study for the diffusion process of semiconductor materials. The purpose of this algorithm is to estimate an optimal control function such that the homogeneity of the concentration can be controlled during the diffusion process and the diffusion-induced stresses for the semiconductor materials can thus be reduced. The validation of this optimal control analysis utilizing the conjugate gradient method of minimization is analysed by using numerical experiments. Three different diffusion processing times are given and the corresponding optimal control functions are to be determined. Results show that the diffusion time can be shortened significantly by applying the optimal control function at the boundary and the homogeneity of the concentration is also guaranteed. This control function can be obtained within a very short CPU time on a Pentium III 600 MHz PC.

Inverse estimation of the tapered probe-sample shear force of scanning near-field optical microscope

In this paper, the conjugate gradient method of minimization with an adjoint equation is successfully applied to solve the inverse problem in estimating the shear force between the tapered probe and sample during the scanning process of scanning near-field optical microscope (SNOM). While knowing the available deflection at the tapered probe tip, the determination of the interaction shear force is regarded as an inverse vibration problem. In the estimating processes, no prior information on the functional form of the unknown quantity is required. The accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements of deflection at the tapered probe tip. Numerical results show that good estimations on the interaction shear force can be obtained for all the test cases considered in this study.

AN OPTIMAL CONTROL PROBLEM FOR CRYOPRESERVATION OF CELLS USING ULTRARAPID FREEZING TECHNIQUE

An optimal control algorithm for cryopreservation of cells using ultrarapid freezing technique is applied successfully in the present study to determine the strength of optimal laser heating based on the desired limited temperature distribution of the cell. The validity of this optimal control analysis utilizing the conjugate gradient method of minimization is examined using numerical experiments. Three different heating times are given, and the corresponding optimal control heat fluxes are determined. Results show that the optimal boundary heat fluxes can be obtained with any arbitrary initial guesses within a very short CPU time on a Pentium III 600-MHz PC.

FUNCTION ESTIMATION IN PREDICTING TIME-DEPENDENT HEAT FLUX OF AN ANNULAR FIN

The conjugate gradient method of minimization with an adjoint equation is successfully used to solve the inverse problem in estimating the base heat flux of an annular fin. While knowing the temperature history at any point of the fin, the boundary time-varying base heat flux can be computed. In the analysis, the thermomechanical coupling effect is taken into account in the governing equation of heat conduction and the convection heat transfer coefficient is assumed to be a function of the radius of the fin. No prior information is available on the functional form of the unknown heat flux in the present study; thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined using simulated and inexact measurements obtained within the medium. Results show that an excellent estimation on the heat flux, temperature distributions, and thermal stress distributions can be obtained for all the test cases considered in this study.

Inverse algorithm for optimal processing of composite materials

During thermoset composite materials processing, the chemical reaction is highly exothermic and because of the low thermal conductivity of the material, significant temperature and state of cure gradients can be generated in thick parts. This creates non-uniform stresses that provoke defects. We propose to control the transformation by monitoring the temperature of the mold walls. A general inverse analysis based on the conjugate gradient method of minimization associated to the adjoint equations is used. After having detailed the method, we propose two examples. The first one presents an optimal cycle to obtain uniform conversion at the end of the curing of an epoxy/glass-fiber composite. The second example is concerned with the control of the temperature variations during the curing of a polyester/glass-fiber composite. The method is experimentally validated and proves to be very powerful and flexible.

INVERSE PROBLEMS IN AN AXISYMMETRIC MULTILAYER ANNULAR CLINDER WITH AN INTERLAYER THERMAL RESISTANCE

A numerical approach to estimate an unknown heat flux for axisymmetric multilayer annular cylinder with an interlayer thermal resistance is presented. The effects of interlayer thermal resistance upon temperature response to predict the subjected heat flux are investigated and discussed. The conjugate gradient method of minimization with an adjoint equation is successfully used to solve the inverse problem in estimating the unknown inner heat flux of multi-layer annular cylinder with an interlayer thermal resistance. While knowing the temperature history at any point of the annular cylinder, the inner boundary time-varying heat flux can be computed. In the analysis, the thermal resistance effect between interlayer is taken into account in the governing equation of heat conduction and the convection heat transfer. No prior information is available on the functional form of the unknown heat flux in the present study: thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using simulated and inexact measurements obtained within the medium

PREDICTION OF UNKNOWN BASE HEAT FLUX IN AN ANNULAR FIN BY STRAIN MEASUREMENT

The conjugate gradient method of minimization with an adjoint equation is successfully used to solve the inverse problem in estimating the base heat flux of an annular fin. As long as knowing the strain history at any point of the fin, the time-varying base heat flux can be computed. In the analysis, the thermomechanical coupling effect is taken into account in the governing equation of heat conduction, and the convection heat transfer coefficient is assumed to be a function of the radius of the fin. The accuracy of the inverse analysis is examined by using simulated and inexact measurements obtained within the medium

An optimal control algorithm for entrance concurrent flow problems

The conjugate gradient method of minimization is applied successfully in the present optimal control algorithm in determining the optimal boundary control function for a concurrent flow problem based on the desired thermal entry length and fluid temperatures. The validity of the present optimal control analysis is examined by means of numerical experiments. Different desired thermal entry length and fluid temperature distributions are given in three test cases and the corresponding optimal control heat fluxes are determined. The results show that the optimal boundary heat fluxes can be obtained with an arbitrary initial guess within seconds of CPU time on a Pentium III-600 MHz PC.

Inverse radiation problem of boundary incident radiation heat flux in semitransparent planar slab with semitransparent boundaries

An inverse method is presented for estimating the unknown boundary incident radiation heat flux on one side of one-dimensional semitransparent planar slab with semitransparent boundaries from the knowledge of the radiation intensities exiting from the other side. The inverse problem is solved using conjugate gradient method of minimization based on discrete ordinates method (DOM) of radiative transfer equation. The equations of sensitivity coefficients are derived and easily solved by DOM, with the result that the complicated numerical differentiation commonly used in solving sensitivity coefficients is avoided. The effects of anisotropic scattering, absorption coefficient, scattering coefficient, boundary reflectivity, fluid temperature outside the boundaries, convection heat transfer coefficients, conduction coefficient of semitransparent media and slab thickness on the accuracy of the inverse analysis are investigated. The results show that the boundary incident radiation heat flux can be estimated accurately, even with noisy data.

An inverse problem in predicting heat flux of M42 percussion primer

Experiment temperature profiles of M42 primer have been analysed with inverse methodology to obtain information of the heat flux. A one-dimensional heat transfer has been assumed in the copper plate with 0.5 mm thickness and 8 mm dia. The conjugate gradient method of minimization with adjoint problem is applied to estimate the transient heat flux of the primer by using discrete temperature measurements from a thermocouple on the opposite side of the plate. Analysis shows the thermal output decreasing with the increase of the distance from the primer. The temperature data and the estimated heat flux show the same trend as that of de Young's.

Estimation of inlet temperature profile in laminar duct flow

The inverse analysis using conjugate-gradient method of minimization with an adjoint equation is presented for estimating the transversal variation of inlet temperature from temperature measurements taken at downstream location in a parallel-plate duct. The advantage of the method is that no prior information is needed for the functional form of spacewise variation of the unknown inlet temperature. The effects of the number of measurements N as well as the distribution of the measurements in the transversal direction, axial locations of the sensor, measurement errors, and functional form of the unknown inlet temperature on the accuracy of estimations are investigated. Inlet temperature distribution involving slope discontinuities was found difficult to estimate.

Inverse problem of controlling the interface velocity in Stefan problems by conjugate gradient method

Abstract The conjugate gradient method of minimization with adjoint equation is used successfully to solve the inverse problem in estimating an appropriate boundary control function such that the phase front moves at a desired velocity in the Stefan problem. It is assumed that no prior information is available on the functional form of the unknown control function, therefore, it is classified as the function estimation in inverse calculation. The stability and accuracy of the inverse analysis using present algorithm are examined by comparing the results of the previous work by Voller [12]. Results show that the estimated control function by using conjugate gradient method did not exhibit oscillatory behavior in the inverse calculations for a broad range of front velocity while in [12] the inverse solutions are very sensitive to phase front velocity, therefore the application of future time stepping [2] is necessary in [12]. The advantage of applying this algorithm in inverse analysis lies in its stability...

The function estimation in measuring temperature-dependent thermal conductivity in composite material

An inverse analysis utilizing the conjugate gradient method of minimization and adjoint equation is used successfully to solve the inverse problem in estimating the temperature-dependent thermal conductivity of a composite material. No prior information is available on the functional form of the unknown thermal conductivity in the present study, thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements that were obtained within the medium.

An inverse problem in simultaneously measuring temperature-dependent thermal conductivity and heat capacity

An inverse analysis utilizing the conjugate gradient method of minimization and the adjoint equation is used for simultaneously estimating the temperature-dependent thermal conductivity and heat capacity per unit volume of a material. No prior information is used for the functional forms of the unknown thermal conductivity and heat capacity in the present study, thus, it is classified as the function estimation by inverse calculation. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements obtained within the medium. Results show that the CPU time used on a VAX-9420 computer is within 1.4–4.46 s for all the test cases considered here. Moreover, excellent estimations on the thermal properties can be obtained when a good initial guess of either thermal conductivity or heat capacity is given before the inverse calculations.

Function estimation in predicting temperature-dependent thermal conductivity without internal measurements

The conjugate gradient method of minimization with an adjoint equation is used successfully to solve the inverse problem in estimating the temperature-dependent thermal conductivity of the homogeneous as well as nonhomogeneous solid material. It is assumed that no prior information is available on the functional form of the unknown thermal conductivity in the present study, thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using simulated exact and inexact measurements obtained within the medium. Results show that an excellent estimation on the thermal conductivity can be obtained with any arbitrary initial guesses by using just boundary measurements (i.e., internal measurements are unnecessary) within 1 s CPU time in a VAX-9420 computer. The advantages of applying this algorithm in inverse analysis can greatly simplify the experimental setup, diminish the sensitivity to the measurement errors, and reduce the CPU time in inverse calculation, while the reliable predictions can still be achieved.

The estimation of surface thermal behavior of the working roll in hot rolling process

A two-dimensional inverse analysis utilizing the conjugate gradient method of minimization is applied to estimate the surface thermal behavior (i.e. heat flux and temperature) of a roll which was used in steel rolling mills with water cooling. No prior information is needed for the functional forms of timewise and spacewise variation of the surface heat flux and temperature. The transient temperature recordings inside the roll are modified from the existing experimental data and serve as the simulated experimental data for the inverse analysis. The results show that the estimation of surface heat flux and temperature becomes worse when the temperature measurements are taken too far away from the surface, due to a thin thermal layer. Once the surface heat flux is determined, the surface heat transfer coefficients can be calculated based on the Fourier law, provided that the ambient temperatures are known. After the surface heat transfer coefficients of the roll are determined, an evaluation of the cooling system of the roll can be performed.

An inverse analysis for estimating the time-varying inlet temperature in laminar flow inside a parallel plate duct

An inverse problem utilizing the conjugate gradient method of minimization with adjoint problem is used to estimate the timewise variation of the inlet temperature of a thermally developing, hydrodynamically developed laminar flow between parallel plates by utilizing transient temperature measurements from a single thermocouple located downstream of the entrance. It is assumed that there is no prior information available on the functional form of time dependence of the inlet temperature other than that which can be inferred from the measured downstream temperatures. The effects of functional form of the inlet temperature, sensor position, magnitude of measurement error and data sampling rate on the accuracy of estimates are examined. In order to examine the accuracy of the method under most strict conditions, timewise variations in the form of step changes were also studied. The inverse analysis considered here could predict the timewise variation of inlet temperature even under such strict conditions. The estimates are notably more accurate when the thermocouple is placed near the entrance.

The estimation of space and time dependent strength of a volumetric heat source in a one-dimensional plate

An inverse analysis utilizing the conjugate gradient method of minimization and the adjoint equation is used to estimate the space and time dependent strength of a volumetric heat source with no prior information for the functional forms of timewise and spatial variations of the source strength. Simulated experimental data, needed for the inverse analysis, are generated by adding random errors to the calculated exact temperatures for the boundaries and interior of the plate. In order to examine the accuracy of estimations under the most strict conditions, test cases such as sawtooth shaped spatial variation of the source strengths are considered. The effects of the number and location of temperature sensors on the accuracy of the estimations are systematically examined. The estimates are significantly improved when the thermocouples are positioned close to the locations where the source strength exhibits peaks and valleys.