Model-based methods require an accurate dynamic model to design the controller.However,the hydraulic parameters of nonlinear systems,complex friction,or actuator dynamics make it challenging to obtain accurate models....Model-based methods require an accurate dynamic model to design the controller.However,the hydraulic parameters of nonlinear systems,complex friction,or actuator dynamics make it challenging to obtain accurate models.In this case,using the input-output data of the system to learn a dynamic model is an alternative approach.Therefore,we propose a dynamic model based on the Gaussian process(GP)to construct systems with control constraints.Since GP provides a measure of model confidence,it can deal with uncertainty.Unfortunately,most GP-based literature considers model uncertainty but does not consider the effect of constraints on inputs in closed-loop systems.An auxiliary system is developed to deal with the influence of the saturation constraints of input.Meanwhile,we relax the nonsingular assumption of the control coefficients to construct the controller.Some numerical results verify the rationality of the proposed approach and compare it with similar methods.展开更多
Similar to many fields of sciences,recent deep learning advances have been applied extensively in geosciences for both small-and large-scale problems.However,the necessity of using large training data and the’black ...Similar to many fields of sciences,recent deep learning advances have been applied extensively in geosciences for both small-and large-scale problems.However,the necessity of using large training data and the’black box’nature of learning have limited them in practice and difficult to interpret.Furthermore,including the governing equations and physical facts in such methods is also another challenge,which entails either ignoring the physics or simplifying them using unrealistic data.To address such issues,physics informed machine learning methods have been developed which can integrate the governing physics law into the learning process.In this work,a 1-dimensional(1 D)time-dependent seismic wave equation is considered and solved using two methods,namely Gaussian process(GP)and physics informed neural networks.We show that these meshless methods are trained by smaller amount of data and can predict the solution of the equation with even high accuracy.They are also capable of inverting any parameter involved in the governing equation such as wave velocity in our case.Results show that the GP can predict the solution of the seismic wave equation with a lower level of error,while our developed neural network is more accurate for velocity(P-and S-wave)and density inversion.展开更多
Joint roughness is one of the most important issues in the hydromechanical behavior of rock mass.Therefore,the joint roughness coefficient(JRC)estimation is of paramount importance in geomechanics engineering applicat...Joint roughness is one of the most important issues in the hydromechanical behavior of rock mass.Therefore,the joint roughness coefficient(JRC)estimation is of paramount importance in geomechanics engineering applications.Studies show that the application of statistical parameters alone may not produce a sufficiently reliable estimation of the JRC values.Therefore,alternative data-driven methods are proposed to assess the JRC values.In this study,Gaussian process(GP),K-star,random forest(RF),and extreme gradient boosting(XGBoost)models are employed,and their performance and accuracy are compared with those of benchmark regression formula(i.e.Z2,Rp,and SDi)for the JRC estimation.To analyze the models’performance,112 rock joint profile datasets having eight common statistical parameters(R_(ave),R_(max),SD_(h),iave,SD_(i),Z_(2),R_(p),and SF)and one output variable(JRC)are utilized,of which 89 and 23 datasets are used for training and validation of models,respectively.The interpretability of the developed XGBoost model is presented in terms of feature importance ranking,partial dependence plots(PDPs),feature interaction,and local interpretable model-agnostic explanations(LIME)techniques.Analyses of results show that machine learning models demonstrate higher accuracy and precision for estimating JRC values compared with the benchmark empirical equations,indicating the generalization ability of the data-driven models in better estimation accuracy.展开更多
Knowledge-based engineering(KBE) has made success in automobile and molding design industry, and it is introduced into the ship structural design in this paper. From the implementation of KBE, the deterministic design...Knowledge-based engineering(KBE) has made success in automobile and molding design industry, and it is introduced into the ship structural design in this paper. From the implementation of KBE, the deterministic design solutions for both rules design method(RDM) and interpolation design method(IDM) are generated. The corresponding finite element model is generated. Gaussian process(GP) is then employed to build the surrogate model for finite element analysis, in order to increase efficiency and maintain accuracy at the same time, and the multi-modal adaptive importance sampling method is adopted to calculate the corresponding structural reliability.An example is given to validate the proposed method. Finally, the reliabilities of the structures' strength caused by uncertainty lying in water corrosion, static and wave moments are calculated, and the ship structures are optimized to resist the water corrosion by multi-island genetic algorithm. Deterministic design results from the RDM and IDM are compared with each separate robust design result. The proposed method shows great efficiency and accuracy.展开更多
Knowledge-Based Engineering （KBE） is introduced into the ship structural design in this paper. From the implementation of KBE, the design solutions for both Rules Design Method （RDM） and Interpolation Design Meth...Knowledge-Based Engineering （KBE） is introduced into the ship structural design in this paper. From the implementation of KBE, the design solutions for both Rules Design Method （RDM） and Interpolation Design Method （IDM） are generated. The corresponding Finite Element （FE） models are generated. Topological design of the longitudinal structures is studied where the Gaussian Process （GP） is employed to build the surrogate model for FE analysis. Multi-objective optimization methods inspired by Pareto Front are used to reduce the design tank weight and outer surface area simultaneously. Additionally, an enhanced Level Set Method （LSM） which employs implicit algorithm is applied to the topological design of typical bracket plate which is used extensively in ship structures. Two different sets of boundary conditions are considered. The proposed methods show satisfactory efficiency and accuracy.展开更多
高斯过程回归(Gaussian process regression, GPR)是一种广泛应用的回归方法,可以用于解决输入输出均为多元变量的人体姿态估计问题.计算复杂度是高斯过程回归的一个重要考虑因素,而常用的降低计算复杂度的方法为稀疏表示算法.在稀疏算...高斯过程回归(Gaussian process regression, GPR)是一种广泛应用的回归方法,可以用于解决输入输出均为多元变量的人体姿态估计问题.计算复杂度是高斯过程回归的一个重要考虑因素,而常用的降低计算复杂度的方法为稀疏表示算法.在稀疏算法中,完全独立训练条件(Fully independent training conditional, FITC)法是一种较为先进的算法,多用于解决输入变量彼此之间完全独立的回归问题.另外,输入变量的噪声问题是高斯过程回归的另一个需要考虑的重要因素.对于测试的输入变量噪声,可以通过矩匹配的方法进行解决,而训练输入样本的噪声则可通过将其转换为输出噪声的方法进行解决,从而得到更高的计算精度.本文基于以上算法,提出一种基于噪声输入的稀疏高斯算法,同时将其应用于解决人体姿态估计问题.本文实验中的数据集来源于之前的众多研究人员,其输入为从视频序列中截取的图像或通过特征提取得到的图像信息,输出为三维的人体姿态.与其他算法相比,本文的算法在准确性,运行时间与算法稳定性方面均达到了令人满意的效果.展开更多
时间序列早期分类(ETSC)有两个矛盾的目标:早期性和准确率。分类早期性的实现,总是以牺牲它的准确率为代价。现有基于优化的多变量时间序列(MTS)早期分类方法,虽然在成本函数中考虑了错误分类成本和延迟决策成本,却忽视了MTS数据集样本...时间序列早期分类(ETSC)有两个矛盾的目标:早期性和准确率。分类早期性的实现,总是以牺牲它的准确率为代价。现有基于优化的多变量时间序列(MTS)早期分类方法,虽然在成本函数中考虑了错误分类成本和延迟决策成本,却忽视了MTS数据集样本之间的局部结构对分类性能的影响。针对这个问题,提出一种基于正交局部保持映射(OLPP)和成本优化的MTS早期分类模型(OLPPMOAE)。首先,使用OLPP将MTS样本前缀映射到低维空间,保持原数据集的局部结构;其次,在低维空间训练一组高斯过程(GP)分类器,生成训练集每个时刻的类概率;最后,使用粒子群优化(PSO)算法从这些类概率中学习停止规则中的最优参数。在6个MTS数据集上的实验结果表明,在早期性基本持平的情况下,OLPPMOAE的准确率显著高于基于成本的R1_C_(lr)(stopping Rule and Cost function with regularization term l_(1)and l_(2))模型,平均准确率能够提升11.33%~15.35%,调和均值(HM)能够提升4.71%~9.01%。因此,所提模型能够以较高的准确率尽早地分类MTS。展开更多
文摘Model-based methods require an accurate dynamic model to design the controller.However,the hydraulic parameters of nonlinear systems,complex friction,or actuator dynamics make it challenging to obtain accurate models.In this case,using the input-output data of the system to learn a dynamic model is an alternative approach.Therefore,we propose a dynamic model based on the Gaussian process(GP)to construct systems with control constraints.Since GP provides a measure of model confidence,it can deal with uncertainty.Unfortunately,most GP-based literature considers model uncertainty but does not consider the effect of constraints on inputs in closed-loop systems.An auxiliary system is developed to deal with the influence of the saturation constraints of input.Meanwhile,we relax the nonsingular assumption of the control coefficients to construct the controller.Some numerical results verify the rationality of the proposed approach and compare it with similar methods.
文摘Similar to many fields of sciences,recent deep learning advances have been applied extensively in geosciences for both small-and large-scale problems.However,the necessity of using large training data and the’black box’nature of learning have limited them in practice and difficult to interpret.Furthermore,including the governing equations and physical facts in such methods is also another challenge,which entails either ignoring the physics or simplifying them using unrealistic data.To address such issues,physics informed machine learning methods have been developed which can integrate the governing physics law into the learning process.In this work,a 1-dimensional(1 D)time-dependent seismic wave equation is considered and solved using two methods,namely Gaussian process(GP)and physics informed neural networks.We show that these meshless methods are trained by smaller amount of data and can predict the solution of the equation with even high accuracy.They are also capable of inverting any parameter involved in the governing equation such as wave velocity in our case.Results show that the GP can predict the solution of the seismic wave equation with a lower level of error,while our developed neural network is more accurate for velocity(P-and S-wave)and density inversion.
文摘Joint roughness is one of the most important issues in the hydromechanical behavior of rock mass.Therefore,the joint roughness coefficient(JRC)estimation is of paramount importance in geomechanics engineering applications.Studies show that the application of statistical parameters alone may not produce a sufficiently reliable estimation of the JRC values.Therefore,alternative data-driven methods are proposed to assess the JRC values.In this study,Gaussian process(GP),K-star,random forest(RF),and extreme gradient boosting(XGBoost)models are employed,and their performance and accuracy are compared with those of benchmark regression formula(i.e.Z2,Rp,and SDi)for the JRC estimation.To analyze the models’performance,112 rock joint profile datasets having eight common statistical parameters(R_(ave),R_(max),SD_(h),iave,SD_(i),Z_(2),R_(p),and SF)and one output variable(JRC)are utilized,of which 89 and 23 datasets are used for training and validation of models,respectively.The interpretability of the developed XGBoost model is presented in terms of feature importance ranking,partial dependence plots(PDPs),feature interaction,and local interpretable model-agnostic explanations(LIME)techniques.Analyses of results show that machine learning models demonstrate higher accuracy and precision for estimating JRC values compared with the benchmark empirical equations,indicating the generalization ability of the data-driven models in better estimation accuracy.
基金the Project of Ministry of Finance andMinistry of Education of China(Nos.200512 and201335)the State Key Laboratory of Ocean Engineering Foundation of Shanghai Jiao Tong University(No.GKZD010053-10)
文摘Knowledge-based engineering(KBE) has made success in automobile and molding design industry, and it is introduced into the ship structural design in this paper. From the implementation of KBE, the deterministic design solutions for both rules design method(RDM) and interpolation design method(IDM) are generated. The corresponding finite element model is generated. Gaussian process(GP) is then employed to build the surrogate model for finite element analysis, in order to increase efficiency and maintain accuracy at the same time, and the multi-modal adaptive importance sampling method is adopted to calculate the corresponding structural reliability.An example is given to validate the proposed method. Finally, the reliabilities of the structures' strength caused by uncertainty lying in water corrosion, static and wave moments are calculated, and the ship structures are optimized to resist the water corrosion by multi-island genetic algorithm. Deterministic design results from the RDM and IDM are compared with each separate robust design result. The proposed method shows great efficiency and accuracy.
基金financially supported by the Project of Ministry of Education and Finance of China(Grant Nos.200512 and 201335)the Project of the State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University(Grant No.GKZD010053-10)
文摘Knowledge-Based Engineering （KBE） is introduced into the ship structural design in this paper. From the implementation of KBE, the design solutions for both Rules Design Method （RDM） and Interpolation Design Method （IDM） are generated. The corresponding Finite Element （FE） models are generated. Topological design of the longitudinal structures is studied where the Gaussian Process （GP） is employed to build the surrogate model for FE analysis. Multi-objective optimization methods inspired by Pareto Front are used to reduce the design tank weight and outer surface area simultaneously. Additionally, an enhanced Level Set Method （LSM） which employs implicit algorithm is applied to the topological design of typical bracket plate which is used extensively in ship structures. Two different sets of boundary conditions are considered. The proposed methods show satisfactory efficiency and accuracy.
文摘高斯过程回归(Gaussian process regression, GPR)是一种广泛应用的回归方法,可以用于解决输入输出均为多元变量的人体姿态估计问题.计算复杂度是高斯过程回归的一个重要考虑因素,而常用的降低计算复杂度的方法为稀疏表示算法.在稀疏算法中,完全独立训练条件(Fully independent training conditional, FITC)法是一种较为先进的算法,多用于解决输入变量彼此之间完全独立的回归问题.另外,输入变量的噪声问题是高斯过程回归的另一个需要考虑的重要因素.对于测试的输入变量噪声,可以通过矩匹配的方法进行解决,而训练输入样本的噪声则可通过将其转换为输出噪声的方法进行解决,从而得到更高的计算精度.本文基于以上算法,提出一种基于噪声输入的稀疏高斯算法,同时将其应用于解决人体姿态估计问题.本文实验中的数据集来源于之前的众多研究人员,其输入为从视频序列中截取的图像或通过特征提取得到的图像信息,输出为三维的人体姿态.与其他算法相比,本文的算法在准确性,运行时间与算法稳定性方面均达到了令人满意的效果.
文摘时间序列早期分类(ETSC)有两个矛盾的目标:早期性和准确率。分类早期性的实现,总是以牺牲它的准确率为代价。现有基于优化的多变量时间序列(MTS)早期分类方法,虽然在成本函数中考虑了错误分类成本和延迟决策成本,却忽视了MTS数据集样本之间的局部结构对分类性能的影响。针对这个问题,提出一种基于正交局部保持映射(OLPP)和成本优化的MTS早期分类模型(OLPPMOAE)。首先,使用OLPP将MTS样本前缀映射到低维空间,保持原数据集的局部结构;其次,在低维空间训练一组高斯过程(GP)分类器,生成训练集每个时刻的类概率;最后,使用粒子群优化(PSO)算法从这些类概率中学习停止规则中的最优参数。在6个MTS数据集上的实验结果表明,在早期性基本持平的情况下,OLPPMOAE的准确率显著高于基于成本的R1_C_(lr)(stopping Rule and Cost function with regularization term l_(1)and l_(2))模型,平均准确率能够提升11.33%~15.35%,调和均值(HM)能够提升4.71%~9.01%。因此,所提模型能够以较高的准确率尽早地分类MTS。
