The problem of localizing two leaks using only flow rate and pressure measurements at the boundaries of a pipeline, and under steady-state flow conditions, is ill-posed due to the undetermined nature of the inverse problem, which involves two coupled equations with four unknowns associated with the presence of the leaks: two emitter coefficients and two locations. Therefore, attempting to solve this problem using any method without imposing additional constraints leads to an unbounded solution space, which contains solutions that may be physically meaningless. In this article, we propose a four-algorithm method that incorporates both spatial and hydraulic constraints to filter out physically infeasible solutions. The proposed method is based on Monte Carlo simulations, which use input data from hydraulic instruments installed at the boundaries of the pipeline, as well as random values with predefined probabilities that are bounded by the hydraulic-spatial constraints. The outputs of the method are probability distributions for the four unknowns. To demonstrate the feasibility of the method, results obtained through simulations and experimental testing on a test bed are presented.

中文翻译：

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通过蒙特卡罗模拟和水力空间约束对管道中的两个泄漏进行定位估计


在稳态流动条件下，仅使用管道边界处的流量和压力测量来定位两个泄漏的问题是不适定的，因为反演问题的性质不确定，涉及两个具有四个未知数的耦合方程与泄漏的存在相关：两个发射器系数和两个位置。因此，尝试使用任何方法解决此问题而不施加额外的约束会导致无限的解决方案空间，其中包含可能在物理上无意义的解决方案。在本文中，我们提出了一种四算法方法，该方法结合了空间和水力约束来过滤掉物理上不可行的解决方案。所提出的方法基于蒙特卡罗模拟，该模拟使用来自安装在管道边界的液压仪器的输入数据，以及具有受水力空间约束限制的预定义概率的随机值。该方法的输出是四个未知数的概率分布。为了证明该方法的可行性，给出了通过模拟和试验台上的实验测试获得的结果。