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This paper considers a low carbon supply chain consisting of a single manufacturer and a single retailer under the condition that the demand is uncertain. We first establish three games, including manufacturer Stackelberg (MS), retailer Stackelberg (RS) and Nash according to the different power structure of the firms. We then determine that the equilibrium stocking factors, emission reduction levels, wholesale prices and retail prices for the three models, respectively. After that, we demonstrate the effects of power structure. Results show that when the power shifts from the retailer to the manufacturer, the stocking factor decreases, whereas the wholesale price increases. Finally, we discuss the impacts of the random demand. We find that the expected profits of the firms, the emission reduction levels and the retail prices are increasing with respect to the market potential and low-carbon sensitivity coefficient, respectively. Meanwhile, they decrease with respect to the price sensitivity coefficient.

The detection of gas leaks using acoustic signals is often compromised by environmental noise, which significantly impacts the accuracy of subsequent leak identification. Current noise reduction algorithms based on non-negative matrix factorization (NMF) typically utilize the Euclidean distance as their objective function, which can exacerbate noise anomalies. Moreover, these algorithms predominantly rely on simple techniques like Wiener filtering to estimate the amplitude spectrum of pure signals. This approach, however, falls short in accurately estimating the amplitude spectrum of non-stationary signals. Consequently, this paper proposes an improved non-negative matrix factorization (INMF) noise reduction algorithm that enhances the traditional NMF by refining both the objective function and the amplitude spectrum estimation process for reconstructed signals. The improved algorithm replaces the conventional Euclidean distance with the Kullback–Leibler (KL) divergence and incorporates noise and sparse constraint terms into the objective function to mitigate the adverse effects of signal amplification. Unlike traditional methods such as Wiener filtering, the proposed algorithm employs an adaptive Minimum Mean-Square Error-Log Spectral Amplitude (MMSE-LSA) method to estimate the amplitude spectrum of non-stationary signals adaptively across varying signal-to-noise ratios. Comparative experiments demonstrate that the INMF algorithm significantly outperforms existing methods in denoising leakage acoustic signals. [ABSTRACT FROM AUTHOR]