面向综合力学环境预测的回归多任务学习研究

Aiming at reducing engineering cost and risk, the prediction of combined dynamic environment which roots on experimental data has become a key issue in the complex industrial fields of aeronautics and astronautics, mechanical manufacture and so on. However, it is still difficult to obtain accurate and robust predictive results of complex dynamic environment merely from a small number of experimental data. To solve this problem, different from the current approach which utilizes single mechanical object for testing and modeling, this project presents a novel multi-task learning based idea which plans to establish the prediction model by adopting multiple similar but not identical mechanical objects. This project focuses on the research on multi-task learning theory and algorithm. First, this project plans to introduce covering number theory to establish the generalization bound of regression multi-task learning machine, and the functional relationship between this bound and sample number as well as the ration of target/auxiliary tasks’ number. Based on this analysis, according to different engineering demands, this project plans to adopt multi-dimensional support vector machine as basic algorithm, and further construct a new regression multi-task learning machine and its model selection method. Moreover, a new task clustering algorithm and asymmetry multi-task learning machine are both proposed. Finally, a cylinder shell testing system will be constructed to evaluate the performance of the above proposed algorithms. The research results in this project will improve the precision and numerical stability of prediction of complex dynamic environment effectively, which is of important theoretical and engineering significance.

为降低工程代价和风险，综合力学环境预测期望从试验数据对复杂力学环境进行预测，已成为航空航天、机械制造等复杂工业领域的关键工程环节。然而，如何从少量试验数据对复杂力学环境进行准确而鲁棒的预测依然是困扰该行业的难点。为解决该问题，与以往对单体力学对象进行测试和建模的方法不同，本项目拟采用多个相似（而不是相同）力学对象进行辅助建模，着重对回归多任务学习理论和算法进行研究。首先，本项目拟引入覆盖数理论，建立回归多任务学习泛化误差界及其与任务样本数、目标/辅助任务样本数比值的函数关系。在此基础上，针对不同需求，本项目拟采用多输出支持向量机作为基础算法，构建新的回归多任务学习算法和相应的模型选择方法，并提出一种新的任务聚类算法和不对称多任务学习算法。最后，将建立圆柱壳力学环境试验系统，对上述算法的实际效果进行评价。研究成果可有效提高对复杂力学环境预测的精度和数值稳定性，具有重要的理论和工程意义。

从机器学习理论角度分析，综合力学环境预测是一个低维小样本的回归建模问题，可利用相似任务的信息提高整体建模效果。对回归多任务学习理论和算法的研究与改进，可有效提高该问题的预测精度和数值稳定性。本项目从以下三方面进行了研究：1）研究了回归多任务学习泛化误差界的理论表示，从两个角度构建了泛化误差估计方法与模型选择算法；2）针对不同的任务间结构特性，以多输出支持向量机和极限学习机为基础算法形式，提出了多种具体的结构化多任务学习和任务聚类算法，并对其训练过程、参数选择等进行了优化；3）构建了一系列基于多任务学习和多输入多输出回归的综合力学环境预测方法，在圆柱壳振动系统上验证了该类预示方法的有效性，并搭建了软件原型系统。基于上述工作，本项目取得了一批有价值的研究成果，发表论文19篇，其中SCI检索7篇、EI检索期刊论文3篇、权威会议论文2篇，及软件著作权4项。培养硕士研究生7人，其中1人获校级优秀硕士学位论文。该项目属于机器学习与力学领域的交叉研究，其成果对多任务学习的理论研究及在工业领域的应用研究均具有重要的参考价值。