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Kangkang Wang,Zurun Xu 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.1
In this paper, a generalized Shannon-McMillan theorem for the nonhomogeneous Markov chains indexed by an infinite tree which has a uniformly bounded degree is discussed by constructing a nonnegative martingale and analytical methods. As corollaries, some Shannon-Mcmillan theorems for the nonhomogeneous Markov chains indexed by a homogeneous tree and the nonhomogeneous Markov chain are obtained. Some results which have been obtained are extended.
Wang, Kangkang,Xu, Zurun The Korean Society for Computational and Applied M 2012 Journal of applied mathematics & informatics Vol.30 No.1
In this paper, a generalized Shannon-McMillan theorem for the nonhomogeneous Markov chains indexed by an infinite tree which has a uniformly bounded degree is discussed by constructing a nonnegative martingale and analytical methods. As corollaries, some Shannon-Mcmillan theorems for the nonhomogeneous Markov chains indexed by a homogeneous tree and the nonhomogeneous Markov chain are obtained. Some results which have been obtained are extended.
Luoke Hu,Wei Cai,Lianjie Shu,Kangkang Xu,Hao Zheng,Shun Jia 한국정밀공학회 2021 International Journal of Precision Engineering and Vol.8 No.2
Many studies have approved that optimising the cutting parameters is effective for reducing the energy consumption of machining operations of machine tools. However, this technique to reduce the end face turning energy consumption (EFTEC), where the material removal rate is variable, has not received attention. Besides, the energy consumed for the spindle speed changes was ignored in previous research. Aiming to fill these gaps, an integrated EFTEC model is developed considering the spindle speed changes. In terms of optimisation, the EFTEC model is discretised according to the allowable accuracy of the machine tool. Simulated annealing is adopted to search for the optimal values of cutting parameters that lead to the minimum EFTEC. In the case study, nine parts with changing diameters and cutting depths are machined by a lathe (CK6153i). According to the experiments, simulated annealing has more than 96% probability of obtaining the global optima. The optimum achieves a 14.03% EFTEC reduction for a case. The relationship between the design parameters and the optimal cutting parameters is discussed. A case shows that 2.43% of the machining time increases suffer from the EFTEC optimisation.
Jin Xi,Wu Daibiao,Yang Haidong,Zhu Chengjiu,Shen Wenjing,Xu Kangkang 한국CDE학회 2023 Journal of computational design and engineering Vol.10 No.3
Complex nonlinear distributed parameter systems (DPSs) exist widely in advanced industrial thermal processes. The modeling of such highly nonlinear systems is a challenge for traditional time/space-separation-based methods since they employ linear methods for the model reduction and spatiotemporal reconstruction, which may lead to an inefficient application of the nonlinear spatial structure features represented by the spatial basis functions. To overcome this problem, a novel spatiotemporal modeling framework composed of nonlinear temporal domain transformation and nonlinear spatiotemporal domain reconstruction is proposed in this paper. Firstly, local nonlinear dimension reduction based on the locally linear embedding technique is utilized to perform nonlinear temporal domain transformation of the spatiotemporal output of nonlinear DPSs. In this step, the original spatiotemporal data can be directly transformed into low-order time coefficients. Then, the extreme learning machine (ELM) method is utilized to establish a temporal model. Finally, through the spatiotemporal domain reconstruction based on the kernel-based ELM method, the prediction of the temporal dynamics obtained from the temporal model can be reconstructed back to the spatiotemporal output. The effectiveness and performance of the proposed method are demonstrated in experiments on the thermal processes of a snap curing oven and a lithium-ion battery.