Keith A. Woodbury

Inverse problems and parameter estimation: integration of measurements and analysis

The main purpose of this paper is to introduce the five following papers on inverse problems, and to relate the field of inverse problems to measurements. Inverse techniques are an emerging suite of methods which, when fully embraced, promise to provide better experiments and improved understanding of physical processes. This paper provides an overview of the general procedure and concepts related to identification of parameters or functions by inverse techniques. A discussion of errors and their implication for an appropriate function for minimization in inverse procedures is presented, and two methods for achieving this minimization are discussed. Some sequential concepts for parameter estimation are presented, along with a discussion of residuals and confidence intervals. Experiment design and optimization are reviewed, and a discussion of residuals and their relation to model building is presented.

GENETIC ALGORITHM IN SOLUTION OF INVERSE HEAT CONDUCTION PROBLEMS

Abstract This report demonstrates the use of a genetic algorithm search in the solution of an inverse problem. The genetic algorithm is used to solve the one-dimensional inverse heat conduction problem using numerical data generated by solution of the corresponding direct problem. Both “pure” and noisy data are considered. If used with regularization, the method is shown to yield reasonable results even in the face of noisy data. Although only a simple one-dimensional case is presented to demonstrate the method, the genetic algorithm approach is expected to excel in the solution of complicated multidimensional inverse problems.

Effect of thermocouple sensor dynamics on surface heat flux predictions obtained via inverse heat transfer analysis

Abstract A simple thermocouple model is used in this paper to generate data by simulating the imposition of a triangular heat flux history on a one-dimensional domain. A general inverse heat conduction (IHC) analysis computer program is developed and used to estimate the heat flux history based on the generated data. The results show that the effect of the thermocouples time constant is to diminish the magnitude of the predicted heat flux history and displace its distribution in time.

Assessment of strategies and potential for neural networks in the inverse heat conduction problem

The inverse heat conduction problem (IHCP) has been identified as a good candidate for solution using artificial neural networks (ANNs) [5, 9]. Reasons that have been cited include the ability of A...

Redundant data and future times in the inverse heat conduction problem

This paper considers a case study focusing on the use of redundant data and the trade between data density and number of future time steps used in Becks Sequential Function Specification Method (SFSM) [1] for solving the Inverse Heat Conduction Problem (IHCP). The effect of the number of future time steps (r) and size of data time difference (Δt) have been observed and are presented in this paper. The results indicate that use of redundant sensors can improve heat flux estimates in the one-dimensional IHCP. Furthermore, it is demonstrated that the number of future time steps used r and the size of the time step in the data Δt should be combined into a new parameter, the “look-ahead” time period, p = rΔt. Different applications of the method with the same value of p are seen to give correspondingly similar results. A subsequent numerical experiment is used to give guidelines on the selection of the parameter “p” for the method.

Using parallelization and hardware concurrency to improve the performance of a genetic algorithm

Genetic algorithms (GAs) are powerful tools for solving many problems requiring the search of a solution space having both local and global optima. The main drawback for GAs is the long execution time normally required for convergence to a solution. This paper discusses three different techniques that can be applied to GAs to improve overall execution time. A serial software implementation of a GA designed to solve a task scheduling problem is used as the basis for this research. The execution time of this implementation is then improved by exploiting the natural parallelism present in the algorithm using a multiprocessor. Additional performance improvements are provided by implementing the original serial software GA in dedicated reconfigurable hardware using a pipelined architecture. Finally, an advanced hardware implementation is presented in which both pipelining and duplicated hardware modules are used to provide additional concurrency leading to further performance improvements. Copyright

Thermocouple Data in the Inverse Heat Conduction Problem

The presence of thermocouples inside a heat-conducting body will distort the temperature field in the body and may lead to significant bias in the temperature measurement. If temperature histories obtained from thermocouples are used in the inverse heat conduction problem (IHCP), errors are propagated into the IHCP results. The bias in the thermocouple measurements can be removed through use of appropriate detailed thermocouple models to account for the dynamics of the sensor measurement. The results of these models can be used to generate correction kernels to eliminate bias in the thermocouple reading, or can be applied as sensitivity coefficients in the IHCP directly. Three-dimensional and axisymmetric models are compared and contrasted and a simple sensitivity study is conducted to evaluate the significance of thermal property selection on the temperature correction and subsequent heat flux estimation. In this paper, a high-fidelity thermocouple model is used to account for thermocouple bias in an experiment to measure heat fluxes from solidifying aluminum to a sand mold. Correction kernels are obtained that are used to demonstrate the magnitude of the temperature measurement bias created by the thermocouples. The corrected temperatures are used in the IHCP to compute the surface heat flux. A comparison to IHCP results using uncorrected temperatures shows the impact of the bias correction on the computed heat fluxes.

A simple 1D sensor model to account for deterministic thermocouple errors (bias) in the solution of the inverse heat conduction problem

This article demonstrates the deterministic errors in thermocouple measurements, or bias, through numerical simulation and illustrates the impact of these erroneous measurements on inverse heat conduction problem solutions. No experimental data are considered in this article. The case of molten metal solidifying through cooling in a sand mold is simulated to demonstrate the measurement bias effect. Temperature histories from these simulations are used to demonstrate the effect of biased data on the solution of the inverse problem. A simple one-dimensional (1D) sensor wire model suitable for integration into a numerical solver to account for temperature measurement bias is presented. The importance of the coupling between the wire and the surrounding domain is illustrated by an example.

Vertical Integration of Excel in the Thermal Mechanical Engineering Curriculum

Microsoft Excel is a ubiquitous tool used frequently by practicing engineers. A recent survey of alumni from The University of Alabama’s Department of Mechanical Engineering regarding software tools revealed that 100% of the respondents used Microsoft Excel regularly on their jobs, while a low percentage used standard packages such as ANSYS or MATLAB, and that none used software tools which had been bundled with textbooks. The spreadsheet environment offers a great platform for computation and organization of engineering work, and the Visual Basic engine allows for great extensibility of Excel through the development of special functions and add-in modules. This paper reports on a proof-of-concept project to implement sustained emphasis on Microsoft Excel in the thermal mechanical curriculum at The University of Alabama. Specific add-in modules for use in thermodynamic analysis and heat transfer analysis have been developed and are continually being refined. These add-in modules have been utilized in a sequence of courses Thermo I, Heat Transfer, Thermo II, and Energy Systems Design. Features of the add-in modules are detailed in this report and feedback from students and teachers are given.Copyright

Developing an Inverse Heat Conduction Analysis Tool for Real Time Heat Flux Estimation in Directional Flame Thermometer Application

Accurate measurement of heat flux and temperature can significantly affect the energy usage in several industrial applications, including furnace operation, metal processing, fire safety tests and more. Directional Flame Thermometers, or DFTs, offer the ability to use both temperature and heat flux measurements for furnace control. Currently, analysis of dynamic temperature data from the DFTs to compute heat flux information must be performed off-line at the conclusion of data-gathering by using software tools such as IHCP1D. Availability of a near real-time algorithm for accurate reduction of the data will allow for continual monitoring of the furnace during operation. This will result in better control over the process and significant savings in energy and cost. In this paper, a filter form of the inverse heat conduction algorithm is developed for utilization in DFTs. The algorithm is based on linearized solutions of the direct heat equation, and non-linear effects introduced by temperature dependent thermal properties are accounted for by interpolating of the resulting filter coefficients. The developed method is tested through several numerical experiments and also ANSYS model. A graphical user interface is developed in LabVIEW to provide a friendly interface for the end user. The temperature data measured by thermocouples on the DFT are transmitted to the computer through data acquisition card and the developed tool in LabView display the heat flux in a near real time fashion.© 2014 ASME