This paper is concerned with a novel integrated multi-step heuristic dynamic programming(MsHDP)algorithm for solving optimal control problems.It is shown that,initialized by the zero cost function,MsHDP can converge t...This paper is concerned with a novel integrated multi-step heuristic dynamic programming(MsHDP)algorithm for solving optimal control problems.It is shown that,initialized by the zero cost function,MsHDP can converge to the optimal solution of the Hamilton-Jacobi-Bellman(HJB)equation.Then,the stability of the system is analyzed using control policies generated by MsHDP.Also,a general stability criterion is designed to determine the admissibility of the current control policy.That is,the criterion is applicable not only to traditional value iteration and policy iteration but also to MsHDP.Further,based on the convergence and the stability criterion,the integrated MsHDP algorithm using immature control policies is developed to accelerate learning efficiency greatly.Besides,actor-critic is utilized to implement the integrated MsHDP scheme,where neural networks are used to evaluate and improve the iterative policy as the parameter architecture.Finally,two simulation examples are given to demonstrate that the learning effectiveness of the integrated MsHDP scheme surpasses those of other fixed or integrated methods.展开更多
Constant stress accelerated life tests(ALTs) can be applied to obtain a high estimation accuracy of reliability measure?ments, but these are time?consuming tests. Progressive stress ALTs can yield failures more quickl...Constant stress accelerated life tests(ALTs) can be applied to obtain a high estimation accuracy of reliability measure?ments, but these are time?consuming tests. Progressive stress ALTs can yield failures more quickly but cannot guaran tee the estimation accuracy of reliability measurements. In this paper, a progressive?constant combination stress ALT is proposed to combine the merits of both tests. The optimal plan, in which the design variables are the initial pro?gressive stress level, the progressive stress ramp rate, the sample allocation proportion of the progressive stress and the constant stress level, is determined using the principle of minimizing the asymptotic variance of the maximum likelihood estimator of the natural log reliable life for the connectors. A comparison between the optimal PCCSALT plan and the CSALT plan with the same sample size and estimation accuracy shows that the test time is reduced by 13.59% by applying the PCCSALT.展开更多
In this study, single and interactive effect of three parameters, pH, ferrous and pulp concentration has been investigated by a 2^3 full factorial CCRD （central composite rotatable design） composed of eight factoria...In this study, single and interactive effect of three parameters, pH, ferrous and pulp concentration has been investigated by a 2^3 full factorial CCRD （central composite rotatable design） composed of eight factorial points, six central and six axial points. Initially, ＂none＂ mode from transformation subsection was chosen as the default choice for both responses, i.e. %recovery and gram of recovered zinc. Box-Cox plots give the best Lambda for each response （y^Lambda= f （A, B, C .....）） which occur at 1.91 and 2.16 for %recovey and gram of recovered zinc, respectively. A linear （y^1.91 = f （linear）） and a quadratic （y^2. 16= f （quadratic）） equation were suggested by software as the model for %recovery and gram of recovered zinc, respectively. Analysis of variance （ANOVA） for both models shows a high coefficient of determination （R^2）. In order to optimize and find the best conditions under which three parameters occur appropriately, optimization was done numerically. Desirability plots indicate properly that the best conditions occur at pH = 1.46, ferrous = 6.67 g/L, %pulp = 7.1 （%w/v）, %recovery = 86.5, gram of recovered zinc = 0.63 g and desirability = 0.777. Finally, PRP （progressive route of the process） analysis donates us a proper insight of what is happening during these 30 days. PRP analysis categorizes flasks in two parts, 1- flasks worth economically, 2- flasks with one-time-usable feed materials.展开更多
基金the National Key Research and Development Program of China(2021ZD0112302)the National Natural Science Foundation of China(62222301,61890930-5,62021003)the Beijing Natural Science Foundation(JQ19013).
文摘This paper is concerned with a novel integrated multi-step heuristic dynamic programming(MsHDP)algorithm for solving optimal control problems.It is shown that,initialized by the zero cost function,MsHDP can converge to the optimal solution of the Hamilton-Jacobi-Bellman(HJB)equation.Then,the stability of the system is analyzed using control policies generated by MsHDP.Also,a general stability criterion is designed to determine the admissibility of the current control policy.That is,the criterion is applicable not only to traditional value iteration and policy iteration but also to MsHDP.Further,based on the convergence and the stability criterion,the integrated MsHDP algorithm using immature control policies is developed to accelerate learning efficiency greatly.Besides,actor-critic is utilized to implement the integrated MsHDP scheme,where neural networks are used to evaluate and improve the iterative policy as the parameter architecture.Finally,two simulation examples are given to demonstrate that the learning effectiveness of the integrated MsHDP scheme surpasses those of other fixed or integrated methods.
基金Supported by National Natural Science Foundation of China(Grant No.51405447)International Science&Technology Cooperation Program of China(Grant No.2015DFA71400)
文摘Constant stress accelerated life tests(ALTs) can be applied to obtain a high estimation accuracy of reliability measure?ments, but these are time?consuming tests. Progressive stress ALTs can yield failures more quickly but cannot guaran tee the estimation accuracy of reliability measurements. In this paper, a progressive?constant combination stress ALT is proposed to combine the merits of both tests. The optimal plan, in which the design variables are the initial pro?gressive stress level, the progressive stress ramp rate, the sample allocation proportion of the progressive stress and the constant stress level, is determined using the principle of minimizing the asymptotic variance of the maximum likelihood estimator of the natural log reliable life for the connectors. A comparison between the optimal PCCSALT plan and the CSALT plan with the same sample size and estimation accuracy shows that the test time is reduced by 13.59% by applying the PCCSALT.
文摘In this study, single and interactive effect of three parameters, pH, ferrous and pulp concentration has been investigated by a 2^3 full factorial CCRD （central composite rotatable design） composed of eight factorial points, six central and six axial points. Initially, ＂none＂ mode from transformation subsection was chosen as the default choice for both responses, i.e. %recovery and gram of recovered zinc. Box-Cox plots give the best Lambda for each response （y^Lambda= f （A, B, C .....）） which occur at 1.91 and 2.16 for %recovey and gram of recovered zinc, respectively. A linear （y^1.91 = f （linear）） and a quadratic （y^2. 16= f （quadratic）） equation were suggested by software as the model for %recovery and gram of recovered zinc, respectively. Analysis of variance （ANOVA） for both models shows a high coefficient of determination （R^2）. In order to optimize and find the best conditions under which three parameters occur appropriately, optimization was done numerically. Desirability plots indicate properly that the best conditions occur at pH = 1.46, ferrous = 6.67 g/L, %pulp = 7.1 （%w/v）, %recovery = 86.5, gram of recovered zinc = 0.63 g and desirability = 0.777. Finally, PRP （progressive route of the process） analysis donates us a proper insight of what is happening during these 30 days. PRP analysis categorizes flasks in two parts, 1- flasks worth economically, 2- flasks with one-time-usable feed materials.
