The simulation-random statistics (SRS) method is one of the effective approaches to solving groundwater contamination source identification (GCSI) challenges. In this paper, we applied a heuristic search iterative process (HSIP) based on SRS to provide interval estimation and probability distribution for an unknown variable to enhance our understanding of the unknown variable. Posterior distribution has been a subject of interest in HSIP; therefore, it is imperative to update prior distributions using final iterations obtained from posterior distributions, which has been seldom considered in previous research. This paper first proposed such updates and subsequently designed an updating HSIP (UHSIP). This paper first proposed a feedback correction step and incorporated it into UHSIP to achieve feedback improvements and simultaneous updates of an unknown variable and prior distribution. In UHSIP, a surrogate system such as extreme learning machine (ELM) is usually established for a numerical simulation model to reduce computational cost. The particle swarm optimization (PSO) algorithm has been demonstrated to optimize input weights and hidden layer biases in ELM. However, the PSO algorithm is prone to premature convergence and its calculation accuracy does not satisfy precision requirements when optimizing complex functions. To enhance accuracy, this paper first proposed a new adaptive chaotic PSO (ACPSO) algorithm to establish ACPSO–ELM surrogate system. The two newly proposed approaches were tested in two case studies based on groundwater inorganic and organic contaminations. Results reveal that UHSIP can effectively enhance identification accuracy, and ACPSO–ELM surrogate system has a higher approximation accuracy to the simulation model than PSO–ELM. Overall, the two main innovations in this paper (UHSIP and ACPSO–ELM surrogate system) present promising and effective solutions to GCSI challenge.

模拟随机统计（SRS）方法是解决地下水污染源识别（GCSI）挑战的有效方法之一。在本文中，我们应用基于SRS的启发式搜索迭代过程（HSIP）为未知变量提供区间估计和概率分布，以增强我们对未知变量的理解。后分布一直是HSIP感兴趣的主题。因此，必须使用从后验分布获得的最终迭代来更新先前的分布，这在以前的研究中很少考虑。本文首先提出了这样的更新，然后设计了更新的HSIP（UHSIP）。本文首先提出了一个反馈校正步骤，并将其合并到UHSIP中以实现反馈改进以及未知变量和先验分布的同时更新。在UHSIP中，通常为数字仿真模型建立诸如极限学习机（ELM）之类的替代系统，以降低计算成本。粒子群优化（PSO）算法已被证明可优化ELM中的输入权重和隐藏层偏差。但是，PSO算法易于过早收敛，并且在优化复杂功能时其计算精度无法满足精度要求。为了提高精度，本文首先提出了一种新的自适应混沌PSO（ACPSO）算法，以建立ACPSO-ELM替代系统。在两个基于地下水无机和有机污染物的案例研究中，对这两种新提出的方法进行了测试。结果表明，UHSIP可以有效地提高识别精度，并且ACPSO-ELM替代系统对仿真模型的逼近精度比PSO-ELM高。总体而言，本文的两个主要创新（UHSIP和ACPSO-ELM代理系统）提出了应对GCSI挑战的有希望且有效的解决方案。