We discuss the discovery of causal mechanisms and identifiability of intermediate variables on a causal path. Different from variable selection, we try to distinguish intermediate variables on the causal path from oth...We discuss the discovery of causal mechanisms and identifiability of intermediate variables on a causal path. Different from variable selection, we try to distinguish intermediate variables on the causal path from other variables. It is also different from ordinary model selection approaches which do not concern the causal relationships and do not contain unobserved variables. We propose an approach for selecting a causal mechanism depicted by a directed acyclic graph （DAG） with an unobserved variable. We consider several causal networks, and discuss their identifiability by observed data. We show that causal mechanisms of linear structural equation models are not identifiable. Furthermore, we present that causal mechanisms of nonlinear models are identifiable, and we demonstrate the identifiability of causal mechanisms of quadratic equation models. Sensitivity analysis is conducted for the identifiability.展开更多
Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy,stiffness and workspace of machining equipment....Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy,stiffness and workspace of machining equipment.Therefore,a 5-DOF(degrees of freedom)parallel kinematic machine(PKM)with redundant constraints is proposed.Based on the kinematics analysis of the parallel mechanism using intermediate variables,the kinematics problems of the PKM are solved through equivalent kinematics model.The structural stiffness matrix method is adopted to model the stiffness of the parallel mechanism of the PKM,where the stiffness of each joint and branch component is obtained by stiffness formula and finite element analysis.And the stiffness model of the parallel mechanism is improved by correction coefficient matrix,each element of which is constructed as a polynomial function of three independent end variables of the parallel mechanism.The terminal stiffness matrices obtained by simulation result are used to determine the coefficients of polynomial function by least square fitting to describe the correction coefficient over the workspace of the parallel mechanism quantitatively.The experiment results prove that the modification method can greatly improve the stiffness model of the parallel mechanism.To enhance the machining accuracy of the PKM,the proposed kinematics model and the improved stiffness model are utilized to optimize the working stiffness of parallel machine by searching the best relative position of parallel machine and workpiece.A plate workpiece taken as example is examined in the case study section,which demonstrates the effectiveness of optimization method.展开更多
An approximate solution to Richards＇ equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method （DTM） with interm...An approximate solution to Richards＇ equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method （DTM） with intermediate variables. Two examples are given to demonstrate the accuracy of the presented solution.展开更多
文摘We discuss the discovery of causal mechanisms and identifiability of intermediate variables on a causal path. Different from variable selection, we try to distinguish intermediate variables on the causal path from other variables. It is also different from ordinary model selection approaches which do not concern the causal relationships and do not contain unobserved variables. We propose an approach for selecting a causal mechanism depicted by a directed acyclic graph （DAG） with an unobserved variable. We consider several causal networks, and discuss their identifiability by observed data. We show that causal mechanisms of linear structural equation models are not identifiable. Furthermore, we present that causal mechanisms of nonlinear models are identifiable, and we demonstrate the identifiability of causal mechanisms of quadratic equation models. Sensitivity analysis is conducted for the identifiability.
文摘Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy,stiffness and workspace of machining equipment.Therefore,a 5-DOF(degrees of freedom)parallel kinematic machine(PKM)with redundant constraints is proposed.Based on the kinematics analysis of the parallel mechanism using intermediate variables,the kinematics problems of the PKM are solved through equivalent kinematics model.The structural stiffness matrix method is adopted to model the stiffness of the parallel mechanism of the PKM,where the stiffness of each joint and branch component is obtained by stiffness formula and finite element analysis.And the stiffness model of the parallel mechanism is improved by correction coefficient matrix,each element of which is constructed as a polynomial function of three independent end variables of the parallel mechanism.The terminal stiffness matrices obtained by simulation result are used to determine the coefficients of polynomial function by least square fitting to describe the correction coefficient over the workspace of the parallel mechanism quantitatively.The experiment results prove that the modification method can greatly improve the stiffness model of the parallel mechanism.To enhance the machining accuracy of the PKM,the proposed kinematics model and the improved stiffness model are utilized to optimize the working stiffness of parallel machine by searching the best relative position of parallel machine and workpiece.A plate workpiece taken as example is examined in the case study section,which demonstrates the effectiveness of optimization method.
基金Project supported by the National Basic Research Program of China(973 Program)(No.2011CB013800)
文摘An approximate solution to Richards＇ equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method （DTM） with intermediate variables. Two examples are given to demonstrate the accuracy of the presented solution.
