利用长短期记忆神经网络的改进POD-Galerkin降阶模型及其在流场预测中的应用  

Improved POD-Galerkin Reduced Order Model with Long Short-Term Memory Neural Network and Its Application in Flow Field Prediction

作　　者：张译文 王志恒[1] 邱睿贤 席光[1] ZHANG Yiwen;WANG Zhiheng;QIU Ruixian;XI Guang(School of Energy and Power Engineering,Xi’an Jiaotong University,Xi’an 710049,China)

机构地区：[1]西安交通大学能源与动力工程学院,西安710049

出　　处：《西安交通大学学报》2024年第2期12-21,共10页Journal of Xi'an Jiaotong University

基　　金：国家重大科技专项资助项目(2017-Ⅱ-0004-0016);国家自然科学基金资助项目(52176044)。

摘　　要：针对标准POD-Galerkin降阶模型在流场快速预测中存在误差而导致精度不高的问题,提出了一种利用长短期记忆神经网络的改进POD-Galerkin降阶模型。使用本征正交分解对流场进行降维,投影得到低维降阶模型,引入两个长短期记忆神经网络,建立从POD-Galerkin降阶模型到实际POD模态时间系数之间的修正映射、低阶模态时间系数与高阶模态时间系数之间的扩展映射,分别用于消除标准POD-Galerkin降阶模型的误差累积和扩展降阶模型的阶数,从而实现物理驱动与数据驱动混合的流动降阶模型的构建。将改进POD-Galerkin降阶模型应用于二维圆柱绕流的流场预测,通过与原始标准POD-Galerkin降阶模型的对比,分析了所提模型的精度和计算速度。结果表明:添加神经网络修正项后的降阶模型相较于标准POD-Galerkin降阶模型,有效提升了降阶模型的精度,预测各阶模态时间系数的均方根误差能够减小1~2个数量级,预测的流场更接近原始流场;在预测相同阶数的情况下,计算时间显著减小,基于4阶和6阶扩展的8阶改进降阶模型相较于原始8阶POD-Galerkin降阶模型预测速度分别提高了约56%和25%。Aiming at the issue of low accuracy in rapid prediction of flow field caused by errors in the standard POD-Galerkin reduced order model,an improved POD-Galerkin model using long short-term memory(LSTM)neural networks is proposed.In this method,based on the reduced order model obtained by dimensionality reduction and projection of the flow field using proper orthogonal decomposition(POD),two LSTM neural networks are introduced to establish a corrective mapping from the POD-Galerkin model to the actual POD coefficients,and an expansion mapping between the low-order mode time coefficients and the high-order mode time coefficients,so as to eliminate the error accumulation of the standard POD-Galerkin model and extend the order of reduced order model.This method enables the construction of a hybrid reduced order model that combines physics-driven and data-driven approaches.The improved POD-Galerkin model is applied to flow field prediction of a two-dimensional flow around a cylinder.A comparison with the original standard POD-Galerkin model is performed to analyze the model accuracy and computational speed.The results show that,with the addition of neural network correction terms,the accuracy of the reduced order model is effectively improved compared with the standard POD-Galerkin model.The root mean square error of the predicted mode time coefficients is reduced by one to two orders of magnitude compared with the original model,and the predicted flow field is closer to the original flow field.The improved model achieves a significant reduction in computation time while predicting the same order.The improved 8-order improved reduced order model based on 4-and 6-order expansions improves the prediction speed by approximately 56%and 25%,respectively,compared with the original 8-order POD-Galerkin model.

关 键 词：本征正交分解 降阶模型 神经网络 流场预测 

分 类 号：O357.1[理学—流体力学]