支持向量回归机模型选择研究及在综合力学环境预示中的应用
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摘要
在航天航空、汽车制造等领域中，有效地预示结构响应对于现实应用有着重要意义。预测结构响应的关键问题之一在于如何有效地分析和模拟结构所处的力学环境。由于结构在工作状态中常处于包含振动、冲击、噪声、气动等不同形式载荷的综合力学环境，此时常用的有限元、统计能量法等数值方法由于无法准确再现复杂环境而难以有效地预测振动响应，直接进行试验测量又往往由于环境的复杂性而导致难以多次重复。
由于线性系统在不同边界条件下的响应之间存在着映射关系，因此可用一种边界条件下的振动响应预测另一种边界条件下的振动响应。基于映射关系的环境预示的关键是对未知数据的预测能力，即泛化能力，同时考虑到小样本问题，因此采用支持向量回归机（SVR）建立映射关系模型。为了提高映射关系的预测精度，本文从提高映射关系模型泛化能力的角度入手，对SVR模型选择算法进行了深入研究，目的在于提高映射关系的预测效果，获得更加准确和鲁棒的映射关系模型。主要工作和贡献如下：
1.提出了一种加权SVR求解路径算法，以有效提取响应数据中的映射关系模型信息。该方法可根据样本的重要性，设置不同的权值，在模型选择过程中根据权值大小调整模型。为了得到合理的权值，进一步提出了一种基于PSO优化的权重动态优化方法，将寻找最优权重的问题转化为一个以泛化误差界为优化目标的两维优化问题，从而确定最优求解路径模型，实验结果表明该算法有效提高了映射关系模型的泛化能力。
2.针对映射关系模型的参数选择问题，本文提出了一种实数制的小世界优化算法，该算法采用禁忌搜索构建局域搜索算子，具有良好的全局收敛性，在分析了LS-SVM留一法泛化误差界作为回归模型泛化性能度量方式的合理性的基础上，提出了基于小世界优化策略的LS-SVM回归机模型选择算法。实验结果表明，该算法可有效避免超参数陷入局部极值，从而获得更好的模型泛化能力。
3.为提高含噪实验数据的预测效果，本文从迁移学习的角度对含噪声的映射关系建模问题进行研究，提出了一种基于主曲线的回归迁移学习算法。该算法将主曲线作为多个相似回归任务的共有部分，并采用加权学习算法进行模型选择。利用该算法，可将具有简单形式的响应数据中蕴含的映射关系模型知识进行迁移，有效提高了含较高噪声响应数据的建模效果。
4.针对结构多信息源的传递特征，本文提出了一种基于SVR特征选择的多输入多输出建模方法。该方法将映射关系建模视作多输入多输出问题，将全时（频）段的响应数据作为输入特征，并采用基于SVR泛化误差界的特征选择算法排除冗余的响应数据，实验结果表明该方法可有效提高映射关系模型的泛化能力。
5.为了能根据响应预测数据制定试验条件，本文提出了一种新的载荷识别方法，该方法采用SVR求解路径算法作为建模算法，可适用于不同谱型形式的载荷反求，避免了传统频域法由于病态矩阵而产生的误差扰动，实验结果表明该方法具有较好的识别精度和数值稳定性。
Effective prediction of structural response always plays a important role in the fields ofaeronautics, astronautics, car-manufacturing and so on. One of the key questions is how toanalyze and simulate the true mechanical environment of structure. Because structures inworking condition are regularly excited by different kinds of loads, for example, vibration,shock, noise and so on, traditional numerical methods such as finite element method,statistical energy analysis, etc could not predict structural response effectively becausecombined dynamical environment is hard to reproduce. Moreover, direct experimentalmeasurement is hard to repeat many times because of the complexity of environment.
There exists a mapping relationship between responses of one linear system under differentboundary conditions. Therefore, the structural vibration response under one boundarycondition can be predicted by the response under another condition. The key part ofenvironmental prediction based on mapping relationship is the predictive power for new data,i.e. generalization ability. Besides, considering the small sample size, this thesis utilizessupport vector regression(SVR) to establish mapping relationship. Aiming at improving thepredictive precision of mapping relationship model, this thesis studies the model selectionalgorithms of SVR. It is of great importance to improve generalization ability as well aspredictive performance of mapping relationship model. The main works and contributionsare listed as follows.
1. To withdraw the model information from response data distribution, a weighted SVRsolution path algorithm is proposed. According to the sample’s importance, this algorithmsets different weight of error penalty parameter on each sample and optimizes the model bymeans of modifying the value of weights. Furthermore, a heuristic weight-settingoptimization algorithm is proposed to compute the optimal weights by using particle swarmoptimization(PSO). The idea of this algorithm is to transfer the primal problem to a globaloptimization problem with two variables. After solve this optimization, the optimal solutionpath model is determined. Experimental results show that the proposed algorithm canimprove the generalization ability of mapping relationship model effectively.
2. Aiming at choosing the optimal SVR parameters, a new decimal-coding small-world optimization algorithm is proposed. This algorithm employs tabu search to construct localsearch operator and has good global convergence. Furthermore, based on the analysis ofeffectiveness of leave-one-out bound of LS-SVM on regression problems, a new modelselection algorithm based on small-world strategy is proposed for LS-SVM regression.Experimental results show that the proposed algorithm can avoiding premature of parametersand has better generalization ability than traditional methods.
3. To improve the predictive performance from noisy experimental data, a new regressiontransfer learning algorithm based on principal curve is proposed from aspect of transferlearning. This algorithm utilizes non-parametric approach to seek the common-across-tasksrepresentation among multiple related regression tasks by computing the principal curve, andthen weights the samples by means of this curve. Numerical results demonstrate that thisalgorithm can withdraw the model information of mapping relationship from low noisy data,and improve the model performance from high noisy response data.
4. Accoring to the transfer characteristic of multiple information sources, a newmultiple-input multiple-output(MIMO) modeling method is proposed based on SVR featureselection. This method treats the modeling procedure of mapping relationship as MIMOproblem, and reconstructs input feature by adopt whole-brand frequency or time responsedata. For eliminating the negative influence of redundant response data, the feature selectionalgorithm based on SVR generalization error bound is integrated into MIMO modelingprocedure. Experimental results show this method can improve the generalization abilityeffectively.
5. To formulate experimental condition by means of response data, a new dynamical loadidentification approach is proposed. This approach utilizes SVR solution path algorithm asmodeling algorithm, and can be applied to identify inversely a wide variety of mechanicalloads which have different forms. Numerical results demonstrate that this approach canavoid error disturbances caused by ill-posed matrix in traditional frequency domain method,and outperforms greatly the common methods in terms of identification accuracy andnumerical stability.
由于线性系统在不同边界条件下的响应之间存在着映射关系，因此可用一种边界条件下的振动响应预测另一种边界条件下的振动响应。基于映射关系的环境预示的关键是对未知数据的预测能力，即泛化能力，同时考虑到小样本问题，因此采用支持向量回归机（SVR）建立映射关系模型。为了提高映射关系的预测精度，本文从提高映射关系模型泛化能力的角度入手，对SVR模型选择算法进行了深入研究，目的在于提高映射关系的预测效果，获得更加准确和鲁棒的映射关系模型。主要工作和贡献如下：
1.提出了一种加权SVR求解路径算法，以有效提取响应数据中的映射关系模型信息。该方法可根据样本的重要性，设置不同的权值，在模型选择过程中根据权值大小调整模型。为了得到合理的权值，进一步提出了一种基于PSO优化的权重动态优化方法，将寻找最优权重的问题转化为一个以泛化误差界为优化目标的两维优化问题，从而确定最优求解路径模型，实验结果表明该算法有效提高了映射关系模型的泛化能力。
2.针对映射关系模型的参数选择问题，本文提出了一种实数制的小世界优化算法，该算法采用禁忌搜索构建局域搜索算子，具有良好的全局收敛性，在分析了LS-SVM留一法泛化误差界作为回归模型泛化性能度量方式的合理性的基础上，提出了基于小世界优化策略的LS-SVM回归机模型选择算法。实验结果表明，该算法可有效避免超参数陷入局部极值，从而获得更好的模型泛化能力。
3.为提高含噪实验数据的预测效果，本文从迁移学习的角度对含噪声的映射关系建模问题进行研究，提出了一种基于主曲线的回归迁移学习算法。该算法将主曲线作为多个相似回归任务的共有部分，并采用加权学习算法进行模型选择。利用该算法，可将具有简单形式的响应数据中蕴含的映射关系模型知识进行迁移，有效提高了含较高噪声响应数据的建模效果。
4.针对结构多信息源的传递特征，本文提出了一种基于SVR特征选择的多输入多输出建模方法。该方法将映射关系建模视作多输入多输出问题，将全时（频）段的响应数据作为输入特征，并采用基于SVR泛化误差界的特征选择算法排除冗余的响应数据，实验结果表明该方法可有效提高映射关系模型的泛化能力。
5.为了能根据响应预测数据制定试验条件，本文提出了一种新的载荷识别方法，该方法采用SVR求解路径算法作为建模算法，可适用于不同谱型形式的载荷反求，避免了传统频域法由于病态矩阵而产生的误差扰动，实验结果表明该方法具有较好的识别精度和数值稳定性。
Effective prediction of structural response always plays a important role in the fields ofaeronautics, astronautics, car-manufacturing and so on. One of the key questions is how toanalyze and simulate the true mechanical environment of structure. Because structures inworking condition are regularly excited by different kinds of loads, for example, vibration,shock, noise and so on, traditional numerical methods such as finite element method,statistical energy analysis, etc could not predict structural response effectively becausecombined dynamical environment is hard to reproduce. Moreover, direct experimentalmeasurement is hard to repeat many times because of the complexity of environment.
There exists a mapping relationship between responses of one linear system under differentboundary conditions. Therefore, the structural vibration response under one boundarycondition can be predicted by the response under another condition. The key part ofenvironmental prediction based on mapping relationship is the predictive power for new data,i.e. generalization ability. Besides, considering the small sample size, this thesis utilizessupport vector regression(SVR) to establish mapping relationship. Aiming at improving thepredictive precision of mapping relationship model, this thesis studies the model selectionalgorithms of SVR. It is of great importance to improve generalization ability as well aspredictive performance of mapping relationship model. The main works and contributionsare listed as follows.
1. To withdraw the model information from response data distribution, a weighted SVRsolution path algorithm is proposed. According to the sample’s importance, this algorithmsets different weight of error penalty parameter on each sample and optimizes the model bymeans of modifying the value of weights. Furthermore, a heuristic weight-settingoptimization algorithm is proposed to compute the optimal weights by using particle swarmoptimization(PSO). The idea of this algorithm is to transfer the primal problem to a globaloptimization problem with two variables. After solve this optimization, the optimal solutionpath model is determined. Experimental results show that the proposed algorithm canimprove the generalization ability of mapping relationship model effectively.
2. Aiming at choosing the optimal SVR parameters, a new decimal-coding small-world optimization algorithm is proposed. This algorithm employs tabu search to construct localsearch operator and has good global convergence. Furthermore, based on the analysis ofeffectiveness of leave-one-out bound of LS-SVM on regression problems, a new modelselection algorithm based on small-world strategy is proposed for LS-SVM regression.Experimental results show that the proposed algorithm can avoiding premature of parametersand has better generalization ability than traditional methods.
3. To improve the predictive performance from noisy experimental data, a new regressiontransfer learning algorithm based on principal curve is proposed from aspect of transferlearning. This algorithm utilizes non-parametric approach to seek the common-across-tasksrepresentation among multiple related regression tasks by computing the principal curve, andthen weights the samples by means of this curve. Numerical results demonstrate that thisalgorithm can withdraw the model information of mapping relationship from low noisy data,and improve the model performance from high noisy response data.
4. Accoring to the transfer characteristic of multiple information sources, a newmultiple-input multiple-output(MIMO) modeling method is proposed based on SVR featureselection. This method treats the modeling procedure of mapping relationship as MIMOproblem, and reconstructs input feature by adopt whole-brand frequency or time responsedata. For eliminating the negative influence of redundant response data, the feature selectionalgorithm based on SVR generalization error bound is integrated into MIMO modelingprocedure. Experimental results show this method can improve the generalization abilityeffectively.
5. To formulate experimental condition by means of response data, a new dynamical loadidentification approach is proposed. This approach utilizes SVR solution path algorithm asmodeling algorithm, and can be applied to identify inversely a wide variety of mechanicalloads which have different forms. Numerical results demonstrate that this approach canavoid error disturbances caused by ill-posed matrix in traditional frequency domain method,and outperforms greatly the common methods in terms of identification accuracy andnumerical stability.
引文
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