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[Objective] With the implementation of the “dual carbon” strategic goals, China is experiencing a rapid increase in natural gas demand. However, the occurrence of leakage accidents in pipelines carrying this flammable and explosive gas poses potential threats, including casualties, environmental pollution, and economic losses. As a result, the research on detecting leaks in natural gas pipelines becomes particularly significant. [Methods] Utilizing the Gaussian plume model and Unmanned Aerial Vehicles (UAVs) equipped with methane concentration sensors, this study employed the Markov Chain Monte Carlo (MCMC) method based on Bayesian inference to determine the positions and rates of leakage sources along natural gas pipelines. The inverse computation method of gas source intensity, relying on probability statistics, was employed to calculate leakage parameter intervals with the highest probability. To verify the effectiveness of the MCMC algorithm in identifying leakage sources in natural gas pipelines, gas leakage simulations were conducted in a scenario featuring continuous leakage accidents of overhead natural gas pipelines. [Results] The MCMC algorithm demonstrated its effectiveness in calculating the positions and rates of leakage in natural gas pipelines. However, its success rate declined due to increasing overall errors. Nonetheless, data cleaning greatly enhanced the algorithm’s ability to adapt to errors, with a success rate exceeding 90% when supported by data cleaning. In contrast, the success rates gradually declined without any data processing. By applying inverse computation of hazardous gas source intensity to leakage detection, more accurate results were obtained regarding the positions and rates of pipeline leakage. It was observed that when the initial points were distant from the actual leakage source, the algorithm’s performance diminished. Hence,a rational selection of the initial point proved beneficial for the overall operation of the algorithm. [Conclusion] The combined approach involving the MCMC algorithm and UAVs equipped with methane concentration sensors effectively enables the simultaneous identification of leakage positions and rates in natural gas pipelines. The findings of this study hold significant importance for facilitating emergency response measures to leakage accidents.

Regarding the problems that the process of optimization is sensitive to the initial point and easily trapped into local optimum, we propose an improved collaborative optimization algorithm. The proposed algorithm takes into account of the distance between the disciplinary level design point and and the system level internal design point, as well as the disciplinary level's optimal design point. Besides, it can weaken the dependence of optimization results on the relaxing factor and the initial point, and find the optimal design point using the least times of optimization iteration. Two classical examples verify the effectiveness and stability of our proposal. [ABSTRACT FROM AUTHOR]

In view of the problem of optimizing the initial value in GM(1,1) model, as criterion of the objective function with the minimum of the square sum of the error and the model test with the minimum of average relative error is inconsistency, leads to the optimization effect is not very good. In this paper, optimizing the GM(1,1) model with the minimum of the square sum of the relative error as the target, respectively optimizing the initial condition and the initial point, the algorithm of optimize formula is given. It proved that under the criterion of minimum the square sum of the relative error in original sequence, the initial conditions optimization and the initial point optimization are unified. Examples show that the results of average relative error calculated by optimizing formula are in close proximity to the numerical solutions. Using the optimization formula to calculating is more convenient than the numerical solution. [ABSTRACT FROM AUTHOR]

Through the in-depth study of generalized accumulation grey model, it is found that the model actually is an uniform for GM(1,1) model (grey model), stage model, jump model and non-equidistance model. Then we research the influence of the parameters and the forecasting value on changing the initial point, the quantitative relationship between changed and before is deduced by matrix analysis. Whafs more, an optimization method for generalized accumulation grey model is proposed by combining the optimization of generalized accumulated generating matrix, the optimization of initial point and the optimization of the initial condition selection. Finally, an empirical study, the classic "TV sales problem", is investigated, it is certified that the combined optimization method is effective. [ABSTRACT FROM AUTHOR]