基于蒙特卡洛模拟算法的化工装置失效概率估算

Estimation of the chemical device failure probability based on Monte Carlo simulationalgorithm

分别采用分析算法和蒙特卡洛模拟算法计算装置的瞬时失效概率。首先对瞬时失效概率进行理论研究,依据可靠度理论进行分析,得到瞬时失效概率理论计算公式,但此方法存在理论公式复杂以及计算误差等问题;其次利用蒙特卡洛模拟分析构建化工装置失效概率估算方法,得出利用矩阵实验室(MATLAB)运行的程序流程;最后通过实例计算某个装置的瞬时失效概率,比较分析算法和蒙特卡洛模拟算法所得结果。结果表明,蒙特卡洛算法就整体性而言是可以接受的,而且随着装置数量的增加,装置的瞬时失效概率下降速率加快,这一情况与实际相符。

In this paper, we would like to propose a new method based on Monte Carlo Simulation （MCS） theory for chemical device failure probability estimation, particularly that of the chemical facilities failure characteristic of domino effect. As is seen, in petroleum chemical works, it is often the case that chemical device failure often leads to domino effect, which might be not only affected by the inter- nal factors, but also by external factors, such as domino effect brought about from the outside. Therefore, it is of great necessity to consider the domino effect when we come to the case of such kinds of device failure. Needless to say, chemical equipment accidents with domino effect usually take place in a complicated manner due to the diversified reasons or unexpected or expected causes. Great knowl- edge and vast experience are needed to make a sound assessment or estimation of such events based on the probability theory. Even if the situation was made clear, errors in calculation, such as round-off er- ror, things would remain suspicious because the data used for such assessment may not be adequate in size and accuracy for the number of likely scenarios is too huge. Therefore, at the first stage （initial- ization）, it is necessary to specify the data and information of the number of pieces of equipment （n）, the failure rates （2i） for any e- quipment in isolation, escalation probabilities （ Pji ）, number of itera- tions （N）, time step （At） and the final time （tf）, etc. It is also necessary to initialize a matrix, named F, which can show the failure probability of each component at each respective time step from 0. Then, for each time step and each component （i） （which can be chosen randomly, which should not be chosen in favor of the higher failure chance of any particular component, rather than done objec- tively） ; And, next, it is needed to work out the instantaneous proba- bility of failure （Pi） and compare the probability with a randomly generated number （ r1 ）, in case that Pi 〉 r1 means that the compo- nent under study fails at the time step, whose related position in F can be turned to one. In this case, it is assumed that in each At as a component is likely to fail for the sake of being too simple. In the in- nermost loop component, j is to be checked it is likely to cause any domino effect, i.e. for each component （j） if Pji is greater than a randomly generated number （ r3） , when the Domino effect is prone to occur （based on the concept of MCS） and therefore its position in F can be changed to one. Such tracing steps should be repeated for N times to make up for the stochastic nature of MC algorithm. For a random number to be quoted, it is necessary to use the algorithm in two steps, a predefined function in the software named MATLAB. Since the random numbers involved here are by nature a set of vari- ables with their values uniformly distributed between 0 and 1, differ- ent algorithms are to be used to generate such random numbers. And, as a result, we have made efforts in assessing the applicability and flexibility of the method while applying it for our estimation. From what is described above, it can be seen that the simulation method we have developed enjoys great advantages in comparison with the purely analytical probability methods. The major advantage of our method is independent of the accuracy of the results of the complexity of the system. In addition, when it is used, it is possible to work out the failure probability as a function of time.