In the present paper,a so-called epsilon-continuation approach is proposed for the solution of singular optimum in truss topology optimization problems.This approach is an improved version of the epsilon-relaxed appro...In the present paper,a so-called epsilon-continuation approach is proposed for the solution of singular optimum in truss topology optimization problems.This approach is an improved version of the epsilon-relaxed approach developed by the authors previously.In the proposed approach, we start the optimization process from a relaxation parameter with a relatively large value and obtain a solution by applying the epsilon-relaxed approach.Then we decrease the value of the relaxation parameter by a small amount and choose the optimal solution found from the previous optimization process as the initial design for the next optimization.This continuation process is continued until a small termination value of the relaxation parameter is reached.Convergence analysis of the proposed approach is also presented.Numerical examples show that this approach can alleviate the dependence of the final solution on the initial choice of the design variable and enhance the probability of finding the singular optimum from rather arbitrary initial designs.展开更多
The experimental processes are difficult to model by physical laws, because a multitude of factors can intervene simultaneously and are responsible for their instabilities and their random variations. Two types of fac...The experimental processes are difficult to model by physical laws, because a multitude of factors can intervene simultaneously and are responsible for their instabilities and their random variations. Two types of factors are to be considered;those that are easy to manipulate according to the objectives, and those that can vary randomly (uncontrollable factors). These could eventually divert the system from the desired target. It is, therefore, important to implement a system that is insensitive to fluctuations in factors that are difficult to control. The aim of this study is to optimize the synthesis of an apatitic calcium carbonate phosphate characterized with a Ca/P ratio equal to 1.61 by using the experimental design method based on the Taguchi method. In this process, five factors are considered and must be configured to achieve the previously defined objective. The temperature is a very important factor in the process, but difficult to control experimentally, so considered to be a problem factor (noise factor), forcing us to build a robust system that is insensitive to the last one. Therefore, a much simpler model to study the robustness of a synthetic solution with respect to temperature is developed. We have tried to parameterize all the factors considered in the process within a wide interval of temperature variation (60˚C - 90˚C). Temperature changes are no longer considered as a problem for apatitic calcium carbonate phosphate synthesis. In this finding, the proposed mathematical model is linear and efficient with very satisfactory statistical indicators. In addition, several simple solutions for the synthesis of carbonate phosphate are proposed with a Ca/P ratio equal to 1.61.展开更多
基金The project supported by the National Natural Science Foundation of China (10102003,10032010 and 10032030)
文摘In the present paper,a so-called epsilon-continuation approach is proposed for the solution of singular optimum in truss topology optimization problems.This approach is an improved version of the epsilon-relaxed approach developed by the authors previously.In the proposed approach, we start the optimization process from a relaxation parameter with a relatively large value and obtain a solution by applying the epsilon-relaxed approach.Then we decrease the value of the relaxation parameter by a small amount and choose the optimal solution found from the previous optimization process as the initial design for the next optimization.This continuation process is continued until a small termination value of the relaxation parameter is reached.Convergence analysis of the proposed approach is also presented.Numerical examples show that this approach can alleviate the dependence of the final solution on the initial choice of the design variable and enhance the probability of finding the singular optimum from rather arbitrary initial designs.
文摘The experimental processes are difficult to model by physical laws, because a multitude of factors can intervene simultaneously and are responsible for their instabilities and their random variations. Two types of factors are to be considered;those that are easy to manipulate according to the objectives, and those that can vary randomly (uncontrollable factors). These could eventually divert the system from the desired target. It is, therefore, important to implement a system that is insensitive to fluctuations in factors that are difficult to control. The aim of this study is to optimize the synthesis of an apatitic calcium carbonate phosphate characterized with a Ca/P ratio equal to 1.61 by using the experimental design method based on the Taguchi method. In this process, five factors are considered and must be configured to achieve the previously defined objective. The temperature is a very important factor in the process, but difficult to control experimentally, so considered to be a problem factor (noise factor), forcing us to build a robust system that is insensitive to the last one. Therefore, a much simpler model to study the robustness of a synthetic solution with respect to temperature is developed. We have tried to parameterize all the factors considered in the process within a wide interval of temperature variation (60˚C - 90˚C). Temperature changes are no longer considered as a problem for apatitic calcium carbonate phosphate synthesis. In this finding, the proposed mathematical model is linear and efficient with very satisfactory statistical indicators. In addition, several simple solutions for the synthesis of carbonate phosphate are proposed with a Ca/P ratio equal to 1.61.
