Abstract
Groundwater contamination source estimation (GCSE) involves an inverse process to match time-series monitoring data in sparse observation wells. It is commonly accompanied by a search task in high-dimensional space and huge computational burden brought about by massive callings of the simulation model. Particle filters can provide accurate estimation for a high-dimensional search task in source estimation, but the process suffers from particle degradation and huge computational load brought about by repeatedly solving the transport simulation model. To tackle the particle degradation, an iterative ensemble smoother was introduced to provide a proper proposal distribution, improving the search efficiency of the traditional particle filter. Moreover, to relieve the computational burden, a deep residual neural network was proposed to perform the surrogate task for the highly nonlinear and long-running-time original simulation model. In general, a refined particle filter with a deep-learning-method surrogate was proposed as an inverse framework for GCSE, which was evaluated by estimation tasks for a point-source contamination case and an areal-source contamination case, respectively, under different levels of observation errors. The results indicated that the deep-residual-neural-network surrogate model achieved the performance R2 of 0.993 and 0.995, respectively for point-source and aerial-source contamination, to substitute the simulation models with a swift invoking process. Furthermore, the iterative ensemble smoother evidently improved the estimation efficiency of the particle filter. The proposed inverse framework can provide reliable and stable estimation of the groundwater contamination source and aquifer hydraulic conductivity.
Résumé
L’estimation de la source de contamination des eaux souterraines (GCSE) implique un processus inverse pour faire correspondre les données de surveillance de séries temporelles dans des puits d’observation épars. Elle s’accompagne généralement d’une tâche de recherche dans un espace à haute dimension et d’une énorme charge de calcul due aux appels massifs du modèle de simulation. Les filtres à particules peuvent fournir une estimation précise pour une tâche de recherche à haute dimension dans l’estimation des sources, mais le processus souffre de la dégradation des particules et de l’énorme charge de calcul engendrée par la résolution répétée du modèle de simulation de transport. Pour remédier à la dégradation des particules, un lisseur d’ensemble itératif a été introduit pour fournir une distribution appropriée des propositions, améliorant ainsi l’efficacité de la recherche du filtre à particules traditionnel. En outre, pour alléger la charge de calcul, un réseau neuronal résiduel profond a été proposé pour effectuer la tâche de substitution pour le modèle de simulation original hautement non linéaire et à long temps de calcul. En général, un filtre à particules raffiné avec un substitut de méthode d’apprentissage profond a été proposé comme cadre inverse pour le GCSE, lequel a été évalué par des tâches d’estimation pour un cas de contamination de source ponctuelle et un cas de contamination de source surfacique diffuse, respectivement, considérant différents niveaux d’erreurs d’observation. Les résultats indiquent que le modèle de substitution à base de réseau neuronal résiduel profond a atteint une performance R2 de 0.993 et 0.995, respectivement pour la contamination de source ponctuelle et de source surfacique diffuse, afin de remplacer les modèles de simulation par un processus d’invocation rapide. En outre, le lisseur d’ensemble itératif permet manifestement d’améliorer l’efficacité de l’estimation du filtre à particules. Le cadre inverse proposé peut fournir une estimation fiable et stable de la source de contamination des eaux souterraines et de la conductivité hydraulique de l’aquifère.
Resumen
La estimación de la fuente de contaminación de las aguas subterráneas (GCSE) implica un proceso inverso para cotejar los datos de seguimiento de las series temporales en escasos pozos de observación. Por lo general, va acompañada de una tarea de búsqueda en un espacio de alta dimensión y una enorme carga computacional provocada por las peticiones masivas del modelo de simulación. Los filtros de partículas pueden proporcionar una estimación precisa para una tarea de búsqueda de alta dimensión en la estimación de la fuente, pero el proceso sufre una degradación de partículas y una enorme carga computacional provocada por la resolución repetida del modelo de simulación de transporte. Para hacer frente a la degradación de las partículas, se introdujo un conjunto iterativo de suavización para proporcionar una distribución de propuestas adecuada, mejorando la eficiencia de la búsqueda del filtro de partículas tradicional. Además, para aliviar la carga computacional, se propuso una red neuronal residual profunda para realizar la tarea de sustitución del modelo de simulación original, altamente no lineal y de largo plazo. En general, se propuso un filtro de partículas refinado con un método de aprendizaje profundo como marco inverso para el GCSE, que se evaluó mediante tareas de estimación para un caso de contaminación de fuente puntual y un caso de contaminación de fuente areal, respectivamente, bajo diferentes niveles de errores de observación. Los resultados indicaron que el modelo sustituto de la red neuronal profunda alcanzó un rendimiento R2 de 0.993 y 0.995, respectivamente, para la contaminación de fuentes puntuales y aéreas, para sustituir los modelos de simulación con un proceso de invocación rápido. Además, el suavizador iterativo de conjuntos mejoró evidentemente la eficacia de la estimación del filtro de partículas. El marco inverso propuesto puede proporcionar una estimación confiable y estable de la fuente de contaminación del agua subterránea y de la conductividad hidráulica del acuífero.
摘要
地下水污染源估计(GCSE)是拟合稀疏观测井的时间序列监测数据的求逆过程。它通常需要高维空间的搜索任务和大量调用模拟模型的巨大计算负荷。粒子滤波器可以为源估计中的高维搜索任务提供准确的估计, 但该过程受到粒子退化和重复求解运移模拟模型产生的巨大计算量的影响。为了解决粒子退化问题, 引入了迭代集合平滑器以提供合适的源分布, 从而提高了传统粒子滤波器的搜索效率。此外, 为了减轻计算负担, 提出了深度残差神经网络来执行高度非线性和长时间运行的原模拟模型的替代任务。总体上, 本文提出了具有深度学习方法替代的细化粒子滤波器作为 GCSE 的求逆框架, 分别通过观察误差的不同水平的点源污染和面源污染案例的污染源估计。结果表明, 深度残差神经网络替代模型对点源和地表污染的性能 R2 分别为 0.993 和 0.995, 可以用快速调用过程替代模拟模型。此外, 迭代集合平滑器显著提高了粒子滤波器的解析效率。所提出的反演框架可以提供对地下水污染源和含水层导水率的可靠和稳定的估计。
Resumo
A estimativa de fontes de contaminação de águas subterrâneas (EFCAS) envolve um processo inverso para combinar dados de monitoramento de séries temporais em poços de observação esparsos. É comumente acompanhado por uma tarefa de busca em espaço de alta dimensão e enorme carga computacional trazida por chamadas massivas do modelo de simulação. Os filtros de partículas podem fornecer estimativas precisas para uma tarefa de busca de alta dimensão na estimativa de fontes, mas o processo sofre com a degradação das partículas e uma enorme carga computacional provocada pela resolução repetida do modelo de simulação de transporte. Para combater a degradação das partículas, um suavizador de ensemble iterativo foi introduzido para fornecer uma distribuição adequada da proposta, melhorando a eficiência de busca do filtro de partículas tradicional. Além disso, para aliviar a carga computacional, uma rede neural residual profunda foi proposta para realizar a tarefa substituta para o modelo de simulação original altamente não linear e de longa duração. Em geral, um filtro de partículas refinado com um substituto do método de aprendizado profundo foi proposto como uma estrutura inversa para EFCAS, que foi avaliada por tarefas de estimativa para um caso de contaminação de fonte pontual e um caso de contaminação de fonte de área, respectivamente, sob diferentes níveis de erros de observação. Os resultados indicaram que o modelo substituto de rede neural residual profunda alcançou o desempenho R2 de 0.993 e 0.995, respectivamente para contaminação por fonte pontual e fonte aérea, para substituir os modelos de simulação por um processo de invocação rápido. Além disso, a suavização do conjunto iterativo evidentemente melhorou a eficiência de estimativa do filtro de partículas. A estrutura inversa proposta pode fornecer estimativa confiável e estável da fonte de contaminação da água subterrânea e da condutividade hidráulica do aquífero.
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Pan, Z., Lu, W. & Bai, Y. Groundwater contamination source estimation based on a refined particle filter associated with a deep residual neural network surrogate. Hydrogeol J 30, 881–897 (2022). https://doi.org/10.1007/s10040-022-02454-z
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DOI: https://doi.org/10.1007/s10040-022-02454-z