Purpose

This paper aims to discuss inverse problems that arise in a variety of practical thermal processes and systems. It presents some of the approaches that may be used to obtain results that lie within a small region of uncertainty. Therefore, the non-uniqueness of the solution is reduced so that the final design and boundary conditions may be determined. Optimization methods that may be used to reduce the uncertainty and to select locations for experimental data and for minimizing the error are presented. A few examples of thermal systems are given to illustrate the applicability of these methods and the challenges that must be addressed in solving inverse problems.

Design/methodology/approach

In most analytical and numerical solutions, the basic equations that describe the process, as well as the relevant and appropriate boundary conditions, are known. The interest lies in obtaining a unique solution that satisfies the equations and boundary conditions. This may be termed as a direct or forward solution. However, there are many problems, particularly in practical systems, where the desired result is known but the conditions needed for achieving it are not known. These are generally known as inverse problems. In manufacturing, for instance, the temperature variation to which a component must be subjected to obtain desired characteristics is prescribed, but the means to achieve this variation are not known. An example of this circumstance is the annealing, tempering or hardening of steel. In such cases, the boundary and initial conditions are not known and must be determined by solving the inverse problem to obtain the desired temperature variation in the component. The solutions, thus, obtained are generally not unique. This is a review paper, which discusses inverse problems that arise in a variety of practical thermal processes and systems. It presents some of the approaches or strategies that may be used to obtain results that lie within a small region of uncertainty. It is important to realize that the solution is not unique, and this non-uniqueness must be reduced so that the final design and boundary conditions may be determined with acceptable accuracy and repeatability. Optimization techniques are often used for minimizing the error. This review presents several methods that may be applied to reduce the uncertainty and to select locations for experimental data for the best results. A few examples of thermal systems are given to illustrate the applicability of these methods and the challenges that must be addressed in solving inverse problems. By considering a variety of systems, the paper also shows the importance of solving inverse problems to obtain results that may be used to model and design thermal processes and systems.

Findings

The solution of inverse problems, which frequently arise in thermal processes, is discussed. Different strategies to obtain the conditions that lead to the desired result are given. The goal of these approaches is to reduce uncertainty and obtain essentially unique solutions for different circumstances. The error of the method can be checked against known conditions to see if it is acceptable for the given problem. Several examples are given to illustrate the use of these methods.

Originality/value

The basic strategies presented here for solving inverse problems that arise in thermal processes and systems, as well as the optimization techniques used to reduce the domain of uncertainty, are fairly original. They are used for certain challenging problems that have not been considered in detail earlier. Several methods are outlined for considering different types of problems.

中文翻译：

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解决热过程和系统中的逆问题的策略

目的

本文旨在讨论各种实际热过程和系统中出现的逆问题。它介绍了一些可用于获得位于不确定性小区域内的结果的方法。因此，减少了解的非唯一性，从而可以确定最终设计和边界条件。介绍了可用于减少不确定性和选择实验数据位置和最小化误差的优化方法。给出了一些热系统的例子来说明这些方法的适用性以及在解决逆问题时必须解决的挑战。

设计/方法/方法

在大多数解析解和数值解中，描述过程的基本方程以及相关和适当的边界条件都是已知的。兴趣在于获得满足方程和边界条件的唯一解。这可以称为直接或正向解决方案。然而，存在许多问题，特别是在实际系统中，期望的结果是已知的，但实现它所需的条件是未知的。这些通常被称为逆问题。例如，在制造过程中，规定了部件必须经受的温度变化才能获得所需的特性，但实现这种变化的方法尚不清楚。这种情况的一个例子是钢的退火、回火或硬化。在这种情况下，边界和初始条件未知，必须通过求解逆问题来确定，以获得所需的组件温度变化。因此，获得的解通常不是唯一的。这是一篇综述论文，讨论了各种实际热过程和系统中出现的逆问题。它提出了一些方法或策略，可用于获得位于不确定性小区域内的结果。重要的是要认识到解不是唯一的，必须减少这种非唯一性，以便以可接受的精度和可重复性确定最终设计和边界条件。优化技术通常用于最小化误差。本综述介绍了几种可用于降低不确定性和选择实验数据位置以获得最佳结果的方法。给出了一些热系统的例子来说明这些方法的适用性以及在解决逆问题时必须解决的挑战。通过考虑各种系统，本文还展示了求解逆问题以获得可用于对热过程和系统进行建模和设计的结果的重要性。

发现

讨论了热过程中经常出现的逆问题的解决方案。给出了获得导致预期结果的条件的不同策略。这些方法的目标是减少不确定性并针对不同情况获得本质上独特的解决方案。可以根据已知条件检查该方法的错误，以查看对于给定问题是否可以接受。给出了几个例子来说明这些方法的使用。

原创性/价值

这里提出的用于解决热过程和系统中出现的逆问题的基本策略，以及用于减少不确定性域的优化技术，都是相当原始的。它们用于解决之前未详细考虑的某些具有挑战性的问题。概述了用于考虑不同类型问题的几种方法。