关键词: 探测器布设优化, 极小碰集问题, 冗余度, 启发式算法

Abstract: In the production of oil and gas on offshore platforms, there may be leaks in their production and transportation devices. Once leaked, it not only pollutes the marine ecological environment, but also causes explosions when the concentration reaches a certain value, posing a threat to the safety of personnel and equipment. In order to closely monitor the leakage and concentration of gas, combustible gas detectors are usually installed on the platform. The detection range of each combustible gas detector is limited and the detectors are expensive, so it is necessary to optimize the layout of the detector to minimize economic costs while ensuring safety. In the past, the layout of detectors was mostly determined based on empirical criteria in actual production, lacking scientific and systematic methods. This article establishes a mathematical model and designs a heuristic for the optimization of the layout of combustible gas detectors on offshore oil extraction platforms, in order to provide a more scientific and systematic layout plan.
Based on the mechanism and characteristics of the layout optimization problem of combustible gas detector, a mathematical programming theoretical model is first established. Then, based on production practice, the theoretical model is dimensionally reduced and simplified: (1)Due to the layout height of detectors is decided by the density of the gas to be leaked, the layout height can be determined in advance, thus the model can be simplified from three-dimensional to two-dimensional. (2)Lower limit of concentration and upper limit of response time are considered for deciding whether the monitoring system will alarm, so the modeling can just consider the state at a certain time, thereby omitting the consideration of time dimension. (3)By digitizing graphics using grids, continuous optimization problems can be transformed into discrete optimization problems, simplifying the problem while also improving operability. Through the above processing, an approximate application model is obtained, which can be regarded as a variant of the minimal hitting set problem, that is, the minimal hitting set problem with redundancy. The computational complexity of minimal hitting set problems with redundancy greater than or equal to 2 are proved to be NP complete by using the method of polynomial reduction. Combined with the application background of layout optimization of combustible gas detectors, a heuristic is designed to solve the minimal hitting set problem, whose redundancy is 2. The heuristic prioritizes the situation where detectors have to be layout, and then takes a series of measures to maximize the number of leakage points that each detector may cover, that is, to achieve the sharing of leakage points with detectors as much as possible, aiming to minimize the number of required detectors while ensuring redundancy.
In the simulation experiment, a CHARM 3D simulation model is established based on the Navisworks 3D model of a certain oil extraction platform structure in the South China Sea, and diffusion simulation is conducted,assuming that the gas to be leaked is methane, gas diffusion simulation is conducted in 6 wind directions, and the heuristic is implemented using C language programming. The simulation results show that this heuristic can detect any potential leak point in any wind direction by at least two detectors without significantly increasing or reducing the number of detectors installed, thereby greatly improving the security of the platform.
Our next step is to conduct systematic research on the minimum hitting set problem considering redundancy and design a complete algorithm.

Key words: detector layout optimization, minimal hitting set problem, redundancy, heuristic