ABSTRACT This paper deals with the solution of an inverse problem for the heat equation aimed at nondestructive evaluation of fractures, emerging on the accessible surface of a slab, by means of Active Thermography. In real life, this surface is heated with a laser and its temperature is measured for a time interval by means of an infrared camera. A fundamental step in iterative inversion methods is the numerical solution of the underlying direct mathematical model. Usually, this step requires specific techniques in order to limit an abnormal use of memory resources and computing time due to excessively fine meshes necessary to follow a very thin fracture in the domain. Our contribution to this problem consists in decomposing the temperature of the damaged specimen as a sum of a term (with known analytical form) due to an infinite virtual fracture and the solution of an initial boundary value problem for the heat equation on one side of the fracture (i.e. on a rectangular domain). The depth of the fracture is a variable parameter in the boundary conditions that must be estimated from additional data (usually, measurements of the surface temperature). We apply our method to the detection of simulated cracks in concrete and steel specimens.

中文翻译：

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使用激光点热成像技术表征垂直裂纹

摘要 本文通过主动热成像法解决了热方程的逆问题，该问题旨在对出现在板坯可触及表面上的裂缝进行无损评估。在现实生活中，这个表面是用激光加热的，它的温度是通过红外摄像机测量一段时间的。迭代反演方法的一个基本步骤是基础直接数学模型的数值解。通常，这一步需要特定的技术，以限制内存资源和计算时间的异常使用，这是由于在域中遵循非常细的裂缝所必需的过细网格。我们对这个问题的贡献在于将损坏试样的温度分解为由于无限虚拟断裂引起的项（具有已知的解析形式）和热方程一侧的初始边界值问题的解的总和。断裂（即在矩形域上）。裂缝深度是边界条件中的一个可变参数，必须根据附加数据（通常是表面温度的测量值）进行估计。我们将我们的方法应用于检测混凝土和钢试样中的模拟裂缝。表面温度测量）。我们将我们的方法应用于检测混凝土和钢试样中的模拟裂缝。表面温度测量）。我们将我们的方法应用于检测混凝土和钢试样中的模拟裂缝。