The restarted FOM method presented by Simoncini[7]according to the natural collinearity of all residuals is an efficient method for solving shifted systems,which generates the same Krylov subspace when the shifts are ...The restarted FOM method presented by Simoncini[7]according to the natural collinearity of all residuals is an efficient method for solving shifted systems,which generates the same Krylov subspace when the shifts are handled simultaneously.However,restarting slows down the convergence.We present a practical method for solving the shifted systems by adding some Ritz vectors into the Krylov subspace to form an augmented Krylov subspace. Numerical experiments illustrate that the augmented FOM approach(restarted version)can converge more quickly than the restarted FOM method.展开更多
Industry 4.0 and Cyber Physical Production Systems (CPPS) are often discussed and partially already sold. One important feature of CPPS is fault tolerance and as a consequence self-configuration and restart to increas...Industry 4.0 and Cyber Physical Production Systems (CPPS) are often discussed and partially already sold. One important feature of CPPS is fault tolerance and as a consequence self-configuration and restart to increase Overall Equipment Effectiveness. To understand this challenge at first the state of the art of fault handling in industrial automated production systems (aPS) is discussed as a result of a case study analysis in eight companies developing aPS. In the next step, metrics to evaluate the concept of self-configuration and restart for aPS focusing on real-time capabilities, fault coverage and effort to increase fault coverage are proposed. Finally, two different lab size case studies prove the applicability of the concepts of self-configuration, restart and the proposed metrics.展开更多
基金Supported-by the National Natural Science Foundation of China(19971057)the Science and Technology Developing Foundation of University in Shanghai of China(02AK41).
文摘The restarted FOM method presented by Simoncini[7]according to the natural collinearity of all residuals is an efficient method for solving shifted systems,which generates the same Krylov subspace when the shifts are handled simultaneously.However,restarting slows down the convergence.We present a practical method for solving the shifted systems by adding some Ritz vectors into the Krylov subspace to form an augmented Krylov subspace. Numerical experiments illustrate that the augmented FOM approach(restarted version)can converge more quickly than the restarted FOM method.
文摘Industry 4.0 and Cyber Physical Production Systems (CPPS) are often discussed and partially already sold. One important feature of CPPS is fault tolerance and as a consequence self-configuration and restart to increase Overall Equipment Effectiveness. To understand this challenge at first the state of the art of fault handling in industrial automated production systems (aPS) is discussed as a result of a case study analysis in eight companies developing aPS. In the next step, metrics to evaluate the concept of self-configuration and restart for aPS focusing on real-time capabilities, fault coverage and effort to increase fault coverage are proposed. Finally, two different lab size case studies prove the applicability of the concepts of self-configuration, restart and the proposed metrics.
