基于稀疏正则化的稳态热源识别

Steady-state heat source identification based on sparse regularization

热源识别属于热传导反问题,目的在于识别热源的空间位置和强度,及时掌握实际工程结构的热源属性。热源问题一般具有非适定性,即当测量数据不够充分时,识别结果对测量噪声十分敏感。为克服非适定性,需要引入额外的约束条件。考虑点热源在空间上呈现稀疏性的特点,提出了一种新的基于稀疏正则化的点热源识别方法。考虑测量噪声的存在,通过罚函数将测量数据以弱形式施加到目标函数。接着,采用交替优化方法对温度和热源两个分离的变量进行迭代求解,并提出了一种快速确定正则化参数的阈值法。二维薄板稳态热传导数值算例表明,该方法能快速准确地识别热源的位置和强度,并且具有较好的抗噪性。

The heat source identification problem that aims to identify the spatial locations and strengths of point heat sources and know well about the heat source properties of actual engineering structure in time belongs to the field of Inverse Heat Conduction Problem(IHCP).The heat source identification problem is generally ill-posed,that is,the identified results are very sensitive to the measurement noise when the measured data is insufficient.In order to overcome the ill-posedness,additional constraints need to be introduced.In this paper,a novel point heat source identification approach based on sparse regularization is proposed where the sparsity of point heat sources in space is mainly considered.Due to the existence of measurement noise,a weak enforcement of measured data through a penalty term is introduced into the objective function.Moreover,to well corporate with the sparse regularization,the alternating minimization is used to iteratively solve the separated variables of temperature and heat source,and the threshold setting method is proposed to quickly and accurately find an appropriate regularization parameter.At last,a numerical example on a two-dimensional steady-state case shows that the proposed approach can quickly and accurately identified both the locations and the strengths of heat source and is insensitive to measurement noise.