Simulation-optimization model for estimating hydraulic conductivity: a numerical case study of the Lu Dila hydropower station in China

Abstract

A simulation-optimization model (ADINA-MMRDE) has been developed using the commercial finite-element software ADINA coupled with an improved differential evolution algorithm (MMRDE) to estimate the hydraulic conductivity of the aquifer of the Lu Dila hydropower project in China. The ADINA-MMRDE model employed the sum of the weighted square difference between the simulated value and the observed value as the objective function. To evaluate the accuracy of the MMRDE, the ADINA software was also coupled with a classical differential evolution (DE) algorithm and particle swarm optimization (PSO). Before estimating the initial seepage field of the Lu Dila hydropower station, the performance of the ADINA-MMRDE model was first tested using a boundary-simplified model based on the initial seepage field model. The effects of different objective functions, measurement errors and population sizes on the performance of ADINA-MMRDE were investigated. Then the ADINA-MMRDE model was applied to the Lu Dila hydropower project by considering water levels in 20 boreholes. The results showed that the head calculated using the estimated parameters was very close to its observed value. The water levels of 13 monitoring boreholes were used for further confirmation of the parameters obtained by the inversion. The results revealed that the calculated values of the monitoring borehole water levels were generally well fitted to the measured values. This study demonstrated the effectiveness of the ADINA-MMRDE model for practical and complex parameter inversion tasks.

Résumé

Un modèle de simulation et d’optimisation (ADINA-MMRDE) a été développé en utilisant le logiciel à éléments finis du commerce ADINA, couplé à un algorithme amélioré à évolution différentielle (MMRDE) pour estimer la conductivité hydraulique de l’aquifère du projet de centrale hydroélectrique de Lu Dila en Chine. Le modèle ADINA-MMRDE a utilisé la somme des écarts quadratiques pondérés entre les valeurs simulées et les valeurs observées, comme fonction objectif. Pour évaluer la fiabilité de MMRDE, le logiciel ADINA a été également couplé à un algorithme à évolution différentielle (ED) classique et à une optimisation par essaim de particules (OEP). Avant d’estimer le champ d’infiltration initial de la centrale hydroélectrique de Lu Dila, la performance du modèle ADINA-MMRDE a d’abord été testée à l’aide d’un modèle à limites simplifiées basé sur le modèle de champ d’infiltration initial. Les effets des différentes fonctions objectif, des erreurs de mesure et de la taille des populations sur la performance de ADINA-MMRDE ont été étudiés. Ensuite, le modèle ADINA-MMRDE a été appliqué au projet de la centrale hydroélectrique de Lu Dila en prenant en compte les niveaux d’eau de 20 forages. Les résultats ont montré que la charge hydraulique calculée en utilisant les paramètres estimés était très proche des valeurs observées. Les niveaux d’eau de 13 des forages de suivi ont été utilisés pour confirmer davantage les paramètres obtenus par inversion. Les résultats ont montré que les valeurs calculées des niveaux d’eau du forage de suivi étaient généralement bien ajustées aux valeurs mesurées. Cette étude a démontré l’efficience du modèle ADINA-MMRDE pour des tâches pratiques et complexes d’inversion des paramètres.

Resumen

Se ha desarrollado un modelo de simulación-optimización (ADINA-MMRDE) utilizando el software comercial de elementos finitos ADINA junto con un algoritmo de evolución diferencial mejorado (MMRDE) para estimar la conductividad hidráulica del acuífero del proyecto hidroeléctrico Lu Dila en China. El modelo ADINA-MMRDE empleaba la suma de la diferencia cuadrada ponderada entre el valor simulado y el valor observado como función objetiva. Para evaluar la precisión del MMRDE, el software ADINA también se combinó con un algoritmo clásico de evolución diferencial (DE) y optimización de la nube de partículas (PSO). Antes de estimar el campo de infiltración inicial de la central hidroeléctrica Lu Dila, se probó el rendimiento del modelo ADINA-MMRDE utilizando un modelo simplificado de límites basado en el modelo del campo de infiltración inicial. Se investigaron los efectos de diferentes funciones objetivas, errores de medición y tamaños de población sobre el desempeño de ADINA-MMRDE. Luego se aplicó el modelo ADINA-MMRDE al proyecto hidroeléctrico Lu Dila, considerando los niveles de agua en 20 pozos. Los resultados mostraron que la altura calculada utilizando los parámetros estimados estaba muy cerca de su valor observado. Los niveles de agua de 13 pozos de monitoreo se utilizaron para confirmar los parámetros obtenidos por la inversión. Los resultados revelaron que los valores calculados de los niveles de agua de la perforación de monitoreo estaban generalmente bien ajustados a los valores medidos. Este estudio demostró la eficacia del modelo ADINA-MMRDE para tareas prácticas y complejas de inversión de parámetros.

摘要

在这项研究中, 开发了一个模拟优化模型(ADINA-MMRDE), 使用商业有限元软件ADINA结合改进的差分进化算法(MMRDE)来估算中国鲁地拉水电项目含水层的渗透系数。在ADINA-MMRDE模型中, 使用模拟值和观测值之间的加权平方差之和作为目标函数。为了评估MMRDE的准确性, 还将ADINA软件与经典差分进化(DE)算法和粒子群优化(PSO)进行了结合。在估算鲁地拉水电站的初始渗流场之前, 首先使用基于初始渗流场模型的边界简化模型测试了ADINA-MMRDE模型的性能。研究了不同目标函数、测量误差和种群大小对ADINA-MMRDE性能的影响。然后通过考虑20个钻孔水位作为观测数据, 将ADINA-MMRDE模型应用于鲁地拉水电项目。结果显示使用估计参数计算的水头非常接近其观测值。13个监测孔的水位用于进一步验证反演得到的参数。结果表明, 监测孔水位的计算值总体上与其测量值吻合良好。本研究证明了ADINA-MMRDE模型对实际和复杂参数反演任务的有效性。

Resumo

Foi desenvolvido um modelo de simulação-otimização (ADINA-MMRDE) utilizando-se o programa comercial de elementos finitos ADINA acoplado a um algoritmo evolucionário diferencial modificado (MMRDE) para estimar a condutividade hidráulica do maciço do projeto da usina hidroelétrica Lu Dila na China. O modelo ADINA-MMRDE empregou a soma dos quadrados das diferenças ponderadas entre os valores simulados e os valores observados como expressão da função objetivo. Para avaliar a acurácia do MMRDE, o programa ADINA foi também acoplado ao clássico algoritmo de evolução diferencial (DE) e ao de otimização de enxame de partículas (PSO). Antes de estimar o campo de exfiltração inicial da usina hidroelétrica Lu Dila, o desempenho do modelo ADINA-MMRDE foi primeiro testado utilizando uma condição de contorno simplificada baseada no modelo de campo de exfiltração inicial. Foram investigados os efeitos de diferentes funções objetivos, erros de medições e dimensionamentos de populações no desempenho do ADINA-MMRDE. Em seguida o modelo ADINA-MMRDE foi aplicado ao projeto hidroelétrico Lu Dila a partir dos níveis de água de 20 poços piezométricos. Os resultados demonstraram que as cargas hidráulicas calculadas utilizando-se os parâmetros estimados foram significativamente próximas aos respectivos valores observados. O nível de água de 13 poços de monitoramento foi utilizado para a validação dos parâmetros obtidos pela modelagem inversa. Os resultados revelaram que os valores calculados para as cargas hidráulicas dos poços de monitoramento foram geralmente bem ajustados aos valores medidos. Este estudo demonstrou a efetividade do modelo ADINA-MMRDE para modelagem inversa de parâmetros práticos e complexos.

Appendix: model development

The intelligent optimization algorithm can be employed to optimize both continuous and noncontinuous problems. Even if the equations are unknown, as long as there is a “black box” problem for input-output relations, the problem can be optimized using intelligent optimization algorithms. The process of parameter inversion is an iterative method and requires continuous calculation of the objective function. It is necessary to continuously build numerical models, input parameters, apply loads, calculate models, and extract and analyze results. Therefore, the coupling of an intelligent optimization algorithm with a numerical model is an indispensable step in inversion analysis. FEM is an effective engineering analysis method, and ADINA is one of the most popular large-scale universal FEM software programs. In this paper, ADINA was used to build the numerical model, which was created in the ADINA user interface (AUI) using the “-cmd” option. Commands were read from a given file so that ADINA can run automatically.

Steps before inversion

The AUI generates various files with different functions during the preprocessing, analysis, calculation, and postprocessing stages. The types of documents used in this study are explained in Table 9.

Table 9 Inversion-related ADINA file types

Each calculation of the objective function includes the creation of a numerical model, the input of parameters, the application of loads, the analysis of the model, and the processing of results. This process can be divided into the three processes of model parameter input, model calculation, and processing of results.

Parameter input

ADINA supports the input of stream files by command, and the command stream files can be opened in text formats. The preprocessing database file (*.idb) contains the complete information of the model. As a binary file, it opens much faster in the AUI than does the preprocessed command stream file (*.in). To save time in solving the model each time, set up the numerical model in advance and store it as an *.idb file, so it only needs to add a command to open the *.idb file at the beginning of the *.in file. The statement is written as: DATABASE OPEN …\*.idb, where …\ represents the full path of the *.idb file. Whenever the optimization algorithm needs to pass a set of parameters to be solved to ADINA, it must first be written into the *.in file in a specific format. The *.dat file must be generated before the ADINA solver is called. A command statement is inserted in the end of the *.in file to generate the *.dat file. The command statement for the ADINA Structure module to generate the *.dat file is written as: ADINA FILE = ‘*.dat’ OVERWRIT = YES. For different calculation modules, replace ADINA with the corresponding module. For example, for ADINA Thermal, ADINA should be replaced with ADINA-T.

Model calculation

Since the command stream for generating the *.dat file has been added at the end of the *.in file, the *.dat file will be automatically generated when the AUI reads the *.in file. Therefore, the model calculation can be completed by using a batch command to connect the ADINA solver to open the file, and the calculation generates a result file in the *.por format.

Result output

The postprocessing command stream is used to open the results file (*.por), and some postprocessing methods (e.g., smooth processing) are employed to output the corresponding results to appropriate locations. When the model contains a large number of nodes and only a few nodes are to be outputted, the “ZONE” command is used to place the corresponding nodes in the newly created “ZONE” groups; thus, this command saves time in reading results. The command used to complete the output of the target node is written as: FILELIST OPTION=FILE FILE=’…\*.txt’. The output file is read in a specific format and compared with the observed data. Finally, the objective function is calculated, and its corresponding parameters are obtained.

Run ADINA-AUI by batch

The coupling between ADINA and intelligent optimization algorithms is a process of information transfer. Each calculation of the objective function is performed in four steps.

• 1. The intelligent optimization algorithm writes the parameters to be evaluated to the preprocessed command stream file (*.in); uses the batch command to open the AUI in the background; and, finally, reads the *.in file to generate the solution file (*.dat).

• 2. A batch command is used to open a specific solver in the background to solve the *.dat file and generate a result file (*.por).

• 3. The batch command opens the AUI to read the postprocess command stream file (*.plo) and outputs the calculation result in a *.txt file.

• 4. The *.txt file is processed in an objective function subroutine to calculate the objective function.

The entire process is continuous, and the search direction of the parameters to be estimated is controlled by the intelligent optimization algorithm.

The batch command (ADINA R & D 2013) to start the AUI is expressed as follows:

…\aui.exe -b -m < MTOT> < file>. [in|plo], where …\ refers to the full path of aui.exe. The command stream file (*.in or *.plo) can be read using the AUI startup options (−s (UNIX version) or -b (Windows version). If the -b option is not included in the command section, the model will open during the opening of the AUI. The memory allocation MTOT for ADINA should be specified at just high enough, and MTOT is measured in MW or MB. -m. <file> represents the full path of the *.in or *.plo file.

The batch command to run the ADINA solver to solve the solution file is as follows:

…\ < prog>.exe - b- s- m < MTOT>[b|w] – M < MSPR>[b|w]- t < #cpu > <file>.dat, where ...\ refers to the full path of <prog>.exe and < prog>.exe represents the solver (adina, adinaf, and adinat) of ADINA. Option -M < MSPR> indicates the memory value assigned to the sparse solver, and Option - t < #cpu > is the core number of CPUs used for the calculation.

The subroutine ‘system ()’ was used in this study to call the ADINA batch file (*.bat) in the external control procedure, and ADINA then calculated the input parameters and outputted the results. For example, if ADINA is installed in “C:\ADINA90” and all file names are set to “test”, the schematic diagram of using batch command in ADINA is illustrated in Fig. 14.

Fig. 14

Batch process diagram of ADINA