With the increasing attention given to environmentalism, designing a green closed-loop supply chain network has been recognized as an important issue. In this paper, we consider the facility location problem, in order to reduce the total costs and CO₂ emissions under an uncertain demand and emission rate. Particularly, we are more interested in the risk-averse method for providing more reliable solutions. To do this, we employ a coherent risk measure, conditional value-at-risk, to represent the underlying risk of uncertain demand and CO₂ emission rate. The resulting optimization problem is a 0-1 mixed integer bi-objective programming, which is challenging to solve. We develop an improved reformulation-linearization technique, based on decomposed piecewise McCormick envelopes, to generate lower bounds efficiently. We show that the proposed risk-averse model can generate a more reliable solution than the risk-neutral model, both in reducing penalty costs and CO₂ emissions. Moreover, the proposed algorithm outperforms and classic reformulation-linearization technique in convergence rate and gaps. Numerical experiments based on random data and a ‘real’ case are performed to demonstrate the performance of the proposed model and algorithm.

Maximum second-order cyclostationary blind deconvolution (CYCBD) is a good signal denoising method, which can be employed for gear fault diagnosis. However, CYCBD is highly dependent on the pre-period of the measured signal, which needs to be appropriately predetermined. To address this issue, a new method based on the multi-point kurtosis (MKurt) spectrum and CYCBD is proposed, which can be used for extracting fault features in a gearbox. First, deconvolution period T, the key parameter of CYCBD, is accurately selected using the MKurt spectrum. Then, according to the selected key parameter, CYCBD is employed to process the gearbox signals and identify the fault type. This proposed method is applied to the analysis of single and compound fault signals of a gearbox; the large gear and pinion fault signals under strong background noise are separated. Finally, the fault signals obtained by CYCBD are analysed using an envelope spectrum to extract the fault features. The two case studies demonstrate that the proposed method can effectively identify the gear faults. Moreover, the results show the superior effectiveness and reliability of this proposed method compared with the maximum correlation kurtosis deconvolution (MCKD) method.

A groundswell of opinion in utilizing environmentally friendly energy technologies has been put forth worldwide. In this paper, we consider an energy generation plant distribution and allocation problem under uncertainty to get the utmost out of available developments, as well as to control costs and greenhouse emissions. Different clean and traditional energy technologies are considered in this paper. In particular, we present a risk-averse stochastic mixed-integer linear programming (MILP) model to minimize the total expected costs and control the risk of CO₂ emissions exceeding a certain budget. We employ the conditional value-at-risk (CVaR) model to represent risk preference and risk constraint of emissions. We prove that our risk-averse model can be equivalent to the traditional risk-neutral model under certain conditions. Moreover, we suggest that the risk-averse model can provide solutions generating less CO₂ than traditional models. To handle the computational difficulty in uncertain scenarios, we propose a Lagrange primal-dual learning algorithm to solve the model. We show that the algorithm allows the probability distribution of uncertainty to be unknown, and that desirable approximation can be achieved by utilizing historical data. Finally, an experiment is presented to demonstrate the performance of our method. The risk-averse model encourages the expansion of clean energy plants over traditional models for the reduction CO₂ emissions.