The identification method based on the traditional Proper Orthogonal Decomposition (POD) reduced-order model has the problem of low efficiency, due to the large amount of both data and computation, when dealing with complicated problems with a large number of spatially distributed nodes. To deal with this issue, an improved POD reduced-order model is proposed in this work. The improved POD reduced-order model only requires the establishment of a three-dimensional (3D) database of training samples varied with both time and measurement locations. Therefore, the amount of data and computation is independent of the total number of spatially distributed nodes, which enables the amount of data and computation to be greatly reduced. To identify thermal parameters in heat conduction problems, a database of transient temperature field is constructed with different training parameters and space nodes by using polygonal boundary element method, and a set of POD basis vectors is obtained by the POD reduced-order model. Then, a surrogate model combined with the improved particle swarm optimization (PSO) is employed for the identification of thermal parameters. Three different inverse heat conduction problems are designed and analyzed to verify the performance of the improved methodology. The results show that the efficiency of the modified method is superior to the traditional POD method with comparable accuracy. The more of the number of spatially distributed nodes, the more obvious advantages of the efficiency. Furthermore, this method has been tested on noisy data, proving its reliability in dealing with problems arising from measurement errors.

中文翻译：

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一种基于改进的 POD 和粒子群优化的热参数识别快速方法及其应用


基于传统正交分解 （POD） 降阶模型的识别方法在处理大量空间分布节点的复杂问题时，由于数据和计算量大，存在效率低下的问题。为了解决这个问题，这项工作提出了一种改进的 POD 降阶模型。改进的 POD 降阶模型只需要建立一个随时间和测量位置变化的训练样本的三维 （3D） 数据库。因此，数据量和计算量与空间分布节点的总数无关，这使得数据量和计算量可以大大减少。为了识别热传导问题中的热参数，采用多边形边界元法构建了具有不同训练参数和空间节点的瞬态温度场数据库，并通过 POD 降阶模型获得了一组 POD 基向量。然后，采用代理模型结合改进的粒子群优化 （PSO） 进行热参数的识别。设计并分析了三种不同的逆热传导问题，以验证改进方法的性能。结果表明，改进后的方法的效率优于传统的POD方法，精度相当。空间分布的节点数量越多，效率优势越明显。此外，该方法已在噪声数据上进行了测试，证明了它在处理测量误差引起的问题方面的可靠性。