贝叶斯学习框架下非线性制造过程建模及多目标优化关键技术研究
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摘要
非线性过程多目标优化和建模是制造领域两个重要而联系密切的研究课题。基于机器学习和计算智能的非线性过程建模方法,仅利用离散样本数据,可以建立多响应曲面,对非线性过程本身数理机理要求不高,算法适应性强,在制造过程优化中得到广泛应用。与其他方法相比,贝叶斯框架下的机器学习方法使用概率表示所有形式的不确定性,可以在模型中包含先验知识,隐含地避免过拟合,通过贝叶斯定理实现学习和推理过程,提供基于模型解释的方差信息,同时还为模型选择提供了一套完整的理论。因此贝叶斯学习框架下的非线性过程建模及其多目标优化研究具有重要理论价值和经济意义。
本文以非线性制造过程对研究对象,利用获取的含噪数据集,以小样本和实时性场合为研究切入点,从概率测度的角度,在贝叶斯统计学习框架下对非线性过程建模及多目标优化关键技术进行了深入研究。其主要研究内容和成果如下:
1、论文首先采用组件描述方式,给出了面向制造过程的多目标优化系统框架。该框架包括先验知识或先验模型、过程采样与数据预处理、非线性过程建模与模型验证和基于模型的多目标优化与控制以及Pareto。多解决策。该系统化视角可用于分析比较现有优化系统,也可用于选择新组件组合成新集成系统用于特定非线性过程的多目标优化。
2、依据上述系统框架,建立了一种基于相关向量机和遗传算法的混合智能方法来解决非线性制造过程中的工艺参数优化问题。基于稀疏贝叶斯学习的建模方法能够使模型具有更好的推广性,同时该建模方法有目前最稀疏的模型结构,因而更容易实现实时系统的建模要求。应用上述优化范式,本文给出了以物料分选系统优化调控为例的个案研究,实验结果证明了该混合智能方法的有效性,并且与其他的学习算法相比,在非线性系统辨识过程中,当相关向量集具备描述问题分布的能力后,即使训练样本增加,相关向量集数目仍然能够保持很好的稀疏性和稳定性。这对于需要不断给出适应度值计算的遗传算法的快速搜索过程和实时搜索近优工艺参数非常有利。
3、通过扩展核方法中常用的高斯核的函数形式,提出基于自适应超球形高斯核函数相关向量机回归算法以获得更稀疏回归模型。在此类核函数中,每个相关向量对应一个问题空间上独立的超球。针对引入的新高斯核,本文提出了分阶段最大化贝叶斯证据算法用于推断相关向量机超参数。该算法能够自动根据非线性系统的响应信号的变化频率调整高斯核宽度的大小。在基准数据集上的仿真和EDM过程建模实验表明该方法能够获得比传统相关向量机更稀疏的解和更高逼近精度,因而适合实时性要求更高的非线性建模的情况。
4、针对非线性过程建模中存在的小样本、脏数据的问题,以高速电火花线切割过程为应用对象,建立了一种基于高斯过程回归模型解释的可靠多目标优化方法。基于高斯过程回归的建模方法更适合制造过程建模的特点,能够使模型在小样本上具有很好的推广性,同时该建模方法有目前最好的预测精度。在可靠优化过程中,由预测响应的概率方差作为对预测不确定性的度量与高斯过程回归模型的响应一起构成了多个目标函数,从而使多目标优化的解具有一定的基于模型解释的可靠性。获得的Pareto前沿聚类后以交互的方式选出最有利的解。实验结果表明该建模方法在小样本上的模型精度、特征标度和预测模型的不确定性概率度量上有优势。并且在多目标优化过程中,通过设定可调整参数可以控制优化过程以获得更可靠的优化预测解。
5、针对非线性过程建模中,存在具有专业领域专家过程知识而要建立的制造过程数据量严重不足时的矛盾,着眼于融合粗糙模糊系统和非常稀少的噪声样本,本文提出了基于模糊先验模型的分段相关性迁移插值算法,融合高斯过程回归算法对非线性过程建模以提高建模精度。在两个基准数据集和电火花线切割机床上的实验研究证明了该算法的可行性和有效性。实验结果表明即使是在非常有限的训练数据集上,结合非常粗糙的模糊先验知识仍能够大大提高预测性能。对于给定具有推广意义的模糊先验模型,基于改融合算法的高斯过程回归建模对样本的需求可大大降低并同时保持精度。由于该方法独立于模糊模型,因而也适用其他智能模型融合。
6、给出了面向制造过程的非线性系统优化软件的系统架构以及各模块的功能。系统使用Matlab程序作为模型与算法程序运算的核心组件,集成于.net框架。为进一步研究与开发先进建模和优化算法提供一个良好的研究仿真平台。
Multi-objective optimization and modeling of nonlinear process are two significant and closely relational research topics in manufacturing. Machine learning and computational intelligence based nonlinear process modeling approach, only using discrete sample data, could generate multiple responses hypersurface, where it may be hardly to establish an exact or even approximate mathematical relationship between the input and output variables. Due to its flexibility and simplicity, extensive nonlinear process optimizations are applied in manufacturing. Compared with other methods, the general Bayesian learning framework approach denotes all forms of uncertainty with probability. The predictive model can be encoded prior knowledge to avoid overfitting, and realizing the inference and learning process through the Bayesian theorem, and supporting the variance based on the model representation, and also providing theories for model selection. Therefore the nonlinear process modeling under the Bayesian learning framework and multi-objective optimization of nonlinear process research has theoretical and economic significance.
The main contents of this dissertation are focused on nonlinear manufacturing process with few noisy samples and realtime scenario. Some key issues of nonlinear process modeling at the perspective of probability measure and under Bayesian statistical learning framework, and multi-objective optimization are studied. This dissertation makes some creative researches on the following aspects:
1. A general multi-objective optimization framework of nonlinear manufacturing process in systemic perspective firstly is described. The framework is constituted by five components including the prior knowledge or prior model about nonlinear process, the sampling strategy and data preprocessing, data-driven based nonlinear process modeling and model verification and model-based multi-objective optimization and its control, as well as Pareto solutions decision-making method. The systemic view can be used for the systematic analysis of the existing optimization system, and also can be used to generate a tuple of components into a new integrated system for specific nonlinear process optimization.
2. According to the framework mentioned above, a hybrid intelligent approach based on relevance vector machine (RVM) and genetic algorithm (GA) has been developed for optimal control of parameters of nonlinear manufacturing processes. Modeling method based on the sparse Bayesian learning could make the predictive model with competitive generalization, as well as it has state of the art sparseness, which could be more esaily to realize the real-time optimization system. Applied above optimization paradigm, as a case study, the optimization of control parameters of seed separator system is used for evaluating the proposed intelligent approach. The experimental results show the effectiveness of the proposed hybrid approach. Compared with other learning algorithm, in the nonlinear system identification, the number of relevance vectors of RVM keeps sparseness and stability after the relevance vectors have ability to describe the distribution of the dataset, which is very favorable to fast search process of genetic algorithm for time consuming of fitness computation and the finding of near-optimal control parameters.
3. Through extending conventional Gaussian kernel function in kernel based machine learning, a novel adaptive spherical Gaussian kernel is utilized by RVM for more sparseness predictive model in nonlinear process regression. The new class of kernel function has indepentent kernel width of relevance vector corresponding to problem space. For this new kernel function, a stagewise optimization algorithm for maximizing Bayesian evidence in sparse Bayesian learning framework is proposed for model selection. The attractive ability of this approach is to automatically choose the right kernel widths locally fitting RVs from the training dataset, which could keep right level smoothing at each scale of signal. Extensive empirical study, on artificial and real-world benchmark datasets and EDM process modeling, shows its effectiveness and flexibility of model on representing regression problem with higher levels of sparsity and better performance than classical RVM. Therefore, it is more suitable to real-time application.
4. For small and nosiy samples modeling of nonlinear process, reliable multi-objective optimization based on Gaussian process regression (GPR) is developed to optimize the WEDM-HS process, GPR based modeling methods make the model more suitable for modeling the characteristics of manufacturing process, and the model has competitive generalization in small samples, as well as state of the art prediction accuracy. Objective functions of predictive reliability multi-objectives optimization are built by probabilistic variance of predictive response used as empirical reliability measurement and responses of GPR models. Finally, the cluster class centers of Pareto front are the optional solutions to be chosen. Experiments on WEDM-HS are conducted to evaluate the proposed intelligent approach in terms of optimization process accuracy and reliability. The experimental result shows that GPR models have the advantage over other regressive models in terms of model accuracy and feature scaling and probabilistic variance. Given the regulable coefficient parameters, the experimental optimization and optional solutions show the effectiveness of controlling optimization process to acquire more reliable optimum predictive solutions.
5. For solving the contradiction in nonlinear process modeling with prior knowledge from field experts and serious shortage of process samples, and focusing on the fusion between rough fuzzy system and very scarce noisy samples, a effective re-sampling algorithm based on piecewise relational transfer interpolation is presented and it is integrated with GPR to improve modeling accuracy. An empirical study on two benchmark and WEDM datasets demonstrates the feasibility and effectiveness of this approach. The experimental result shows that combining very rough fuzzy prior model with training examples still significantly improves the predictive performance of WEDM process modeling, even with very limited training dataset. That is, given the generalized prior model, the samples needed by GPR model could be reduced greatly meanwhile keeping precise. Since this method is independent of the fuzzy model, which also applies to other intelligent model of fusiion.
6. Oriented manufacturing process, the architecture of nonlinear optimization system and the function of each module is developed to provide a good research platform for further development of advanced modeling and optimization algorithms. Matlab procedures as a model and algorithms processing the core computing components are integrated to .net framework.
本文以非线性制造过程对研究对象,利用获取的含噪数据集,以小样本和实时性场合为研究切入点,从概率测度的角度,在贝叶斯统计学习框架下对非线性过程建模及多目标优化关键技术进行了深入研究。其主要研究内容和成果如下:
1、论文首先采用组件描述方式,给出了面向制造过程的多目标优化系统框架。该框架包括先验知识或先验模型、过程采样与数据预处理、非线性过程建模与模型验证和基于模型的多目标优化与控制以及Pareto。多解决策。该系统化视角可用于分析比较现有优化系统,也可用于选择新组件组合成新集成系统用于特定非线性过程的多目标优化。
2、依据上述系统框架,建立了一种基于相关向量机和遗传算法的混合智能方法来解决非线性制造过程中的工艺参数优化问题。基于稀疏贝叶斯学习的建模方法能够使模型具有更好的推广性,同时该建模方法有目前最稀疏的模型结构,因而更容易实现实时系统的建模要求。应用上述优化范式,本文给出了以物料分选系统优化调控为例的个案研究,实验结果证明了该混合智能方法的有效性,并且与其他的学习算法相比,在非线性系统辨识过程中,当相关向量集具备描述问题分布的能力后,即使训练样本增加,相关向量集数目仍然能够保持很好的稀疏性和稳定性。这对于需要不断给出适应度值计算的遗传算法的快速搜索过程和实时搜索近优工艺参数非常有利。
3、通过扩展核方法中常用的高斯核的函数形式,提出基于自适应超球形高斯核函数相关向量机回归算法以获得更稀疏回归模型。在此类核函数中,每个相关向量对应一个问题空间上独立的超球。针对引入的新高斯核,本文提出了分阶段最大化贝叶斯证据算法用于推断相关向量机超参数。该算法能够自动根据非线性系统的响应信号的变化频率调整高斯核宽度的大小。在基准数据集上的仿真和EDM过程建模实验表明该方法能够获得比传统相关向量机更稀疏的解和更高逼近精度,因而适合实时性要求更高的非线性建模的情况。
4、针对非线性过程建模中存在的小样本、脏数据的问题,以高速电火花线切割过程为应用对象,建立了一种基于高斯过程回归模型解释的可靠多目标优化方法。基于高斯过程回归的建模方法更适合制造过程建模的特点,能够使模型在小样本上具有很好的推广性,同时该建模方法有目前最好的预测精度。在可靠优化过程中,由预测响应的概率方差作为对预测不确定性的度量与高斯过程回归模型的响应一起构成了多个目标函数,从而使多目标优化的解具有一定的基于模型解释的可靠性。获得的Pareto前沿聚类后以交互的方式选出最有利的解。实验结果表明该建模方法在小样本上的模型精度、特征标度和预测模型的不确定性概率度量上有优势。并且在多目标优化过程中,通过设定可调整参数可以控制优化过程以获得更可靠的优化预测解。
5、针对非线性过程建模中,存在具有专业领域专家过程知识而要建立的制造过程数据量严重不足时的矛盾,着眼于融合粗糙模糊系统和非常稀少的噪声样本,本文提出了基于模糊先验模型的分段相关性迁移插值算法,融合高斯过程回归算法对非线性过程建模以提高建模精度。在两个基准数据集和电火花线切割机床上的实验研究证明了该算法的可行性和有效性。实验结果表明即使是在非常有限的训练数据集上,结合非常粗糙的模糊先验知识仍能够大大提高预测性能。对于给定具有推广意义的模糊先验模型,基于改融合算法的高斯过程回归建模对样本的需求可大大降低并同时保持精度。由于该方法独立于模糊模型,因而也适用其他智能模型融合。
6、给出了面向制造过程的非线性系统优化软件的系统架构以及各模块的功能。系统使用Matlab程序作为模型与算法程序运算的核心组件,集成于.net框架。为进一步研究与开发先进建模和优化算法提供一个良好的研究仿真平台。
Multi-objective optimization and modeling of nonlinear process are two significant and closely relational research topics in manufacturing. Machine learning and computational intelligence based nonlinear process modeling approach, only using discrete sample data, could generate multiple responses hypersurface, where it may be hardly to establish an exact or even approximate mathematical relationship between the input and output variables. Due to its flexibility and simplicity, extensive nonlinear process optimizations are applied in manufacturing. Compared with other methods, the general Bayesian learning framework approach denotes all forms of uncertainty with probability. The predictive model can be encoded prior knowledge to avoid overfitting, and realizing the inference and learning process through the Bayesian theorem, and supporting the variance based on the model representation, and also providing theories for model selection. Therefore the nonlinear process modeling under the Bayesian learning framework and multi-objective optimization of nonlinear process research has theoretical and economic significance.
The main contents of this dissertation are focused on nonlinear manufacturing process with few noisy samples and realtime scenario. Some key issues of nonlinear process modeling at the perspective of probability measure and under Bayesian statistical learning framework, and multi-objective optimization are studied. This dissertation makes some creative researches on the following aspects:
1. A general multi-objective optimization framework of nonlinear manufacturing process in systemic perspective firstly is described. The framework is constituted by five components including the prior knowledge or prior model about nonlinear process, the sampling strategy and data preprocessing, data-driven based nonlinear process modeling and model verification and model-based multi-objective optimization and its control, as well as Pareto solutions decision-making method. The systemic view can be used for the systematic analysis of the existing optimization system, and also can be used to generate a tuple of components into a new integrated system for specific nonlinear process optimization.
2. According to the framework mentioned above, a hybrid intelligent approach based on relevance vector machine (RVM) and genetic algorithm (GA) has been developed for optimal control of parameters of nonlinear manufacturing processes. Modeling method based on the sparse Bayesian learning could make the predictive model with competitive generalization, as well as it has state of the art sparseness, which could be more esaily to realize the real-time optimization system. Applied above optimization paradigm, as a case study, the optimization of control parameters of seed separator system is used for evaluating the proposed intelligent approach. The experimental results show the effectiveness of the proposed hybrid approach. Compared with other learning algorithm, in the nonlinear system identification, the number of relevance vectors of RVM keeps sparseness and stability after the relevance vectors have ability to describe the distribution of the dataset, which is very favorable to fast search process of genetic algorithm for time consuming of fitness computation and the finding of near-optimal control parameters.
3. Through extending conventional Gaussian kernel function in kernel based machine learning, a novel adaptive spherical Gaussian kernel is utilized by RVM for more sparseness predictive model in nonlinear process regression. The new class of kernel function has indepentent kernel width of relevance vector corresponding to problem space. For this new kernel function, a stagewise optimization algorithm for maximizing Bayesian evidence in sparse Bayesian learning framework is proposed for model selection. The attractive ability of this approach is to automatically choose the right kernel widths locally fitting RVs from the training dataset, which could keep right level smoothing at each scale of signal. Extensive empirical study, on artificial and real-world benchmark datasets and EDM process modeling, shows its effectiveness and flexibility of model on representing regression problem with higher levels of sparsity and better performance than classical RVM. Therefore, it is more suitable to real-time application.
4. For small and nosiy samples modeling of nonlinear process, reliable multi-objective optimization based on Gaussian process regression (GPR) is developed to optimize the WEDM-HS process, GPR based modeling methods make the model more suitable for modeling the characteristics of manufacturing process, and the model has competitive generalization in small samples, as well as state of the art prediction accuracy. Objective functions of predictive reliability multi-objectives optimization are built by probabilistic variance of predictive response used as empirical reliability measurement and responses of GPR models. Finally, the cluster class centers of Pareto front are the optional solutions to be chosen. Experiments on WEDM-HS are conducted to evaluate the proposed intelligent approach in terms of optimization process accuracy and reliability. The experimental result shows that GPR models have the advantage over other regressive models in terms of model accuracy and feature scaling and probabilistic variance. Given the regulable coefficient parameters, the experimental optimization and optional solutions show the effectiveness of controlling optimization process to acquire more reliable optimum predictive solutions.
5. For solving the contradiction in nonlinear process modeling with prior knowledge from field experts and serious shortage of process samples, and focusing on the fusion between rough fuzzy system and very scarce noisy samples, a effective re-sampling algorithm based on piecewise relational transfer interpolation is presented and it is integrated with GPR to improve modeling accuracy. An empirical study on two benchmark and WEDM datasets demonstrates the feasibility and effectiveness of this approach. The experimental result shows that combining very rough fuzzy prior model with training examples still significantly improves the predictive performance of WEDM process modeling, even with very limited training dataset. That is, given the generalized prior model, the samples needed by GPR model could be reduced greatly meanwhile keeping precise. Since this method is independent of the fuzzy model, which also applies to other intelligent model of fusiion.
6. Oriented manufacturing process, the architecture of nonlinear optimization system and the function of each module is developed to provide a good research platform for further development of advanced modeling and optimization algorithms. Matlab procedures as a model and algorithms processing the core computing components are integrated to .net framework.
引文
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