Ching-yu Yang

A genetic algorithm for inverse radiation problems

Abstract An inverse radiation analysis for simultaneous estimation of the single scattering albedo, the optical thickness and the phase function, from the knowledge of the exit radiation intensities is presented. A genetic algorithm is adopted as the optimizer to search the parameters of the radiation system. The study shows that the single scattering albedo and the optical thickness can be estimated accurately even with noisy data. The estimation of the phase function is more difficult than that of the single scattering albedo and the optical thickness.

The boundary estimation in two-dimensional inverse heat conduction problems

A direct method is developed to estimate the boundary condition in two-dimensional inverse heat conduction problems. At the beginning of the study, finite-difference methods are employed to discretize the problem domain and then a linear inverse model is constructed to identify the boundary condition. The linear least-squares method is adopted for the linear model and thus iteration times can be limited to one cycle and the uniqueness of the solutions can be identified easily. Results from the examples confirm that the proposed method is effective and applicable to solution of multidimensional inverse heat conduction problems. In the example problems, three kinds of measuring methods are adopted to estimate the surface temperature. The result shows that only a few measuring points is sufficient to estimate the surface temperature when the measurement errors are neglected. When the measurement errors are considered, more measuring points are needed in order to increase the congruence of the estimated results to the exact solutions.

Estimation of the temperature-dependent thermal conductivity in inverse heat conduction problems

Abstract An iterative approach is presented to determine the temperature-dependent thermal conductivity from the temperature measurements taken at one side of boundary. On the basis of the proposed method, the undetermined thermal conductivity is first denoted as the unknown variables in a set of nonlinear equations, which are formulated from the measured temperature and the calculated temperature. Then, a linearization method is used to solve the set of nonlinear equations. In the examples, one sensor is used to measure the temperature profile whether the measurement errors are included or excluded. The results show that the speed of convergence is considerably fast, since the number of iterations to approach a satisfied solution is within nine to eleven times. Comparisons between the exact thermal conductivity and the estimated ones are made to confirm the validity of the proposed method. The close agreement between the exact solutions and the estimated results shows the potential of the proposed method in finding the accurate value of the temperature-dependent thermal conductivity in inverse heat conduction problem.

A linear inverse model for the temperature-dependent thermal conductivity determination in one-dimensional problems

Abstract A direct procedure is presented for the inverse determination of the thermal conductivity in the one-dimensional heat conduction problem. A linear inverse model is proposed to estimate the thermal conductivity. The model is constructed from the approximated model of the heat equation when the temperature measurements are available in the problem domain. Distinguishing features of the proposed model are that the iterations in the process can be done only once and that the inverse problem can be solved in a linear domain. This provides a contrast to the traditional approach, which needs numerous iterations in the computing process and is operated in a nonlinear domain. Results from the examples confirm that the proposed method is applicable in solving the thermal conductivity in inverse heat conduction problems. The result shows that the exact solution can be found when measurement errors are neglected. When measurement errors are considered, the close agreement between the exact solutions and the estimated results shows the potential of the proposed model in finding the accurate value of the thermal conductivity in one-dimensional heat conduction problems.

Solving the two-dimensional inverse heat source problem through the linear least squares error method

Abstract An inverse model is presented for determining the strength of the temporal dependent heat source when the prior knowledge of the source functions are not available in the two-dimensional heat conduction problem. This model is constructed from the finite difference approximation of the differential heat conduction equation based on the assumption that the temperature measurements are available over the problem domain. In contrast to the traditional approach, the iteration in the proposed model can be done only once and the inverse problem can be solved in a linear domain. Three examples are used to show the usage of the proposed method.

The determination of two heat sources in an inverse heat conduction problem

Abstract There are some restrictions in the two sources estimation problem in recent studies. One of the restrictions is that the estimated results are inaccurate when two sources have different shapes and close distance. Another is that the accuracy of the estimation is questioned when the duration of two heat sources has a significant difference. The third restriction is that the estimation becomes inaccurate when the ratio of the peak values of the two heat sources is too large. Therefore, it is necessary to develop a robust method to estimate the strengths of two heat sources in order to alleviate the problems in past research. In this paper, a numerical algorithm coupled with the concept of future time is proposed to determine the problem sequentially. A special feature about this method is that no preselect functional form for the unknown sources is necessary and no sensitivity analysis is needed in the algorithm. Three examples are used to demonstrate the characteristics of the proposed method. From the results, they show that the proposed method is an accurate and efficient method to determine the strength of the two sources in the inverse heat conduction problems.

A sequential method to estimate the strength of the heat source based on symbolic computation

Abstract A sequential method is proposed to determine the strength of the heat source in inverse heat conduction problems. This method uses symbols to represent the temporal source strength and then executes a computational method to calculate the temperature distribution. Consequently, a set of linear equations is constructed from the comparison between the calculated symbolic temperature and the measured numerical temperature. Thus, the inverse problem is solved through the linear least-squares error method, which leads to a solution of the unknown source strength at the present time step. Results from the examples confirm that the proposed method is applicable in solving the inverse heat source problem.

Estimation of Boundary Conditions in Nonlinear Inverse Heat Conduction Problems

A sequential method is proposed to estimate boundary conditions for nonlinear heat conduction problems. An inverse solution is deduced from a e nite element method, the concept of the future time, and a modie ed Newton‐ Raphson method. The undetermined boundary condition at each timestep is denoted as theunknown variablein a set of nonlinear equations, which are formulated from the measured temperature and the calculated temperature. Then, an iterative process is used to solve the set of nonlinear equations. No selected function isneeded to represent the undetermined function in advance. Two examples are used to demonstrate the characteristics of the proposed method. Thecloseagreementbetween theexactvaluesand theestimated resultscone rmsthevalidity and accuracy of the proposed method. The results show that the proposed method is an accurate, stable, and efe cient method to determine the boundary conditions in two-dimensional nonlinear inverse heat conduction problems.

Analysis and optimal control of time-varying systems via Fourier series

The Fourier series approximation approach is introduced into the analysis and optimal control of the time-varying linear systems. The operational properties of the coefficient, product matrices and forward and backward integration matrices of Fourier series are derived

Analysis and parameter identification of time-delay systems via polynomial series

Time delay frequently occurs in electrical and mechanical systems. In addition, systems such as population and economic growth, epidemic growth, and neural networks are commonly modelled by delay-differential equations. Although it is difficult to solve time-delay systems, we can apply the delay matrix L(s) to simplify the problem. As has been shown, Taylor series have the simplest operational properties. Therefore, we can apply the integration and delay matrix of Taylor series via transformation. As a result, we can derive all of the polynomial delay matrices with arbitrary time delay.