An adaptive weighted-average Kriging method applied to monitoring of freshwater ecosystems
Qilu Liu
A # , Jingfang Shen A # and Yaohui Li A B *
A
B
Abstract
The prediction of freshwater quality is important for detecting pollution risks and assessing changes in freshwater ecosystems. As a high-precision interpolation method, Kriging was able to predict freshwater quality by using previously monitored data. However, how to select the key parameters, regression functions and correlation functions of Kriging method in the process of improving prediction accuracy is still a bottleneck.
This study aims to propose an adaptive weighted-average Kriging (AWAK) method to further enhance the accuracy of freshwater-quality predictions.
The AWAK method consists of four main steps. First, the key parameters influencing pollution indicators are selected by FPS method. Subsequently, six different Kriging candidate models are constructed by using regression and correlation functions with different characteristics. Then, an enhanced-likelihood function is used to determine the weights of the six Kriging candidate models. Finally, AWAK is built by weighted sum of these six Kriging models.
The AWAK outperformed traditional Kriging in predicting pH and dissolved oxygen, significantly reducing prediction errors.
By employing the AWAK method, this study successfully improved the accuracy of freshwater-quality predictions.
The introduction of the AWAK provides an effective approach in the field of freshwater ecology.
Keywords: adaptive weighting, correlation function, enhanced likelihood function, freshwater ecosystems, freshwater-quality prediction, Kriging, regression function, surrogate model.
References
Albert JS, Destouni G, Duke-Sylvester SM, Magurran AE, Oberdorff T, Reis RE, Winemiller KO, Ripple WJ (2021) Scientists’ warning to humanity on the freshwater biodiversity crisis. Ambio 50(1), 85-94.
| Crossref | Google Scholar | PubMed |
Barzegar R, Aalami MT, Adamowski J (2020) Short-term water quality variable prediction using a hybrid CNN–LSTM deep learning model. Stochastic Environmental Research and Risk Assessment 34(2), 415-433.
| Crossref | Google Scholar |
Basudhar A, Missoum S (2008) Adaptive explicit decision functions for probabilistic design and optimization using support vector machines. Computers & Structures 86(19–20), 1904-1917.
| Crossref | Google Scholar |
Bichon BJ, Eldred MS, Swiler LP, Mahadevan S, McFarland JM (2008) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA Journal 46(10), 2459-2468.
| Crossref | Google Scholar |
Biondi F, Kawamoto Y, Legay A, Traonouez L-M (2019) Hybrid statistical estimation of mutual information and its application to information flow. Formal Aspects of Computing 31, 165-206.
| Crossref | Google Scholar |
Blatman G, Sudret B (2010) An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis. Probabilistic Engineering Mechanics 25(2), 183-197.
| Crossref | Google Scholar |
Bouhlel MA, Martins JRRA (2019) Gradient-enhanced Kriging for high-dimensional problems. Engineering with Computers 35, 157-173.
| Crossref | Google Scholar |
Goel T, Haftka RT, Shyy W, Queipo NV (2007) Ensemble of surrogates. Structural and Multidisciplinary Optimization 33, 199-216.
| Crossref | Google Scholar |
Han Z-H, Zhang Y, Song C-X, Zhang K-S (2017) Weighted gradient-enhanced Kriging for high-dimensional surrogate modeling and design optimization. AIAA Journal 55(12), 4330-4346.
| Crossref | Google Scholar |
Huang H, Lin DKJ, Liu M-Q, Zhang Q (2020) Variable selection for Kriging in computer experiments. Journal of Quality Technology 52(1), 40-53.
| Crossref | Google Scholar |
Hung Y (2011) Penalized blind Kriging in computer experiments. Statistica Sinica 21(3), 1171-1190.
| Crossref | Google Scholar |
Joseph VR, Hung Y, Sudjianto A (2008) Blind Kriging: a new method for developing metamodels. Journal of Mechanical Design 130(3), 031102.
| Crossref | Google Scholar |
Liem RP, Oyetunde KS, Palar PS, Shimoyama K (2019) Kriging with mixed kernel (MK) for complex aerospace problems. In ‘Sixteenth International Conference on Flow Dynamics’, 6–8 November 2019, Sendai, Japan. (Institute of Fluid Science, Tohoku University) Available at https://www.researchgate.net/publication/338254592_Kriging_with_mixed_kernel_MK_for_complex_aerospace_problems
Mardia KV, Marshall RJ (1984) Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika 71(1), 135-146.
| Crossref | Google Scholar |
Mardia KV, Watkins AJ (1989) On multimodality of the likelihood in the spatial linear model. Biometrika 76(2), 289-295.
| Crossref | Google Scholar |
Marelli S, Sudret B (2018) An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis. Structural Safety 75, 67-74.
| Crossref | Google Scholar |
Mehmani A, Chowdhury S, Meinrenken C, Messac A (2018) Concurrent surrogate model selection (COSMOS): optimizing model type, kernel function, and hyper-parameters. Structural and Multidisciplinary Optimization 57(3), 1093-1114.
| Crossref | Google Scholar |
Nguyen TG, Huynh NTH (2023) Evaluating surface water quality using indexes of water quality and plankton diversity. Civil Engineering Journal 9(5), 1187-1202.
| Crossref | Google Scholar |
Palar PS, Shimoyama K (2018) Ensemble of Kriging with multiple kernel functions for engineering design optimization. In ‘Bioinspired optimization methods and their applications: 8th international conference, BIOMA 2018’, 16–18 May 2018, Paris, France. (Eds P Korošec, N Melab, EG Talbi) Lecture Notes in Computer Science10835, 211–222. (Springer) doi:10.1007/978-3-319-91641-5_18
Palar PS, Parussini L, Bregant L, Shimoyama K, Izzaturrahman MF, Baehaqi FA, Zuhal LR (2022) Composite Kernel functions for surrogate modeling using recursive multi-fidelity Kriging. In ‘AIAA SciTech Forum 2022 [AIAA 2022-0506] (AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2022)’, 3–7 January 2022, San Diego, CA, USA and held virtually. (American Institute of Aeronautics and Astronautics Inc., AIAA) doi:10.2514/6.2022-0506
Sakata S, Ashida F, Zako M (2004) An efficient algorithm for Kriging approximation and optimization with large-scale sampling data. Computer Methods in Applied Mechanics and Engineering 193(3–5), 385-404.
| Crossref | Google Scholar |
Sukri AS, M S, Karama R, Nasrul , Talanipa R, Kadir A, Aswad NH (2023) Utilization management to ensure clean water sources in coastal areas. Journal of Human, Earth, and Future 4(1), 23-35.
| Crossref | Google Scholar |
Sundar VS, Shields MD (2019) Reliability analysis using adaptive Kriging surrogates with multimodel inference. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems – A. Civil Engineering 5(2), 04019004.
| Crossref | Google Scholar |
Xu P, Wang D, Singh VP, Wang Y, Wu J, Wang L, Zou X, Liu J, Zou Y, He R (2018) A Kriging and entropy-based approach to raingauge network design. Environmental Research 161, 61-75.
| Crossref | Google Scholar | PubMed |
Zerpa LE, Queipo NV, Pintos S, Salager J-L (2005) An optimization methodology of alkaline–surfactant–polymer flooding processes using field scale numerical simulation and multiple surrogates. Journal of Petroleum Science and Engineering 47(3–4), 197-208.
| Crossref | Google Scholar |
Zhang Y, Yao W, Chen X, Ye S (2020) A penalized blind likelihood Kriging method for surrogate modeling. Structural and Multidisciplinary Optimization 61(2), 457-474.
| Crossref | Google Scholar |
Zhao L, Wang P, Song B, Wang X, Dong H (2020) An efficient Kriging modeling method for high-dimensional design problems based on maximal information coefficient. Structural and Multidisciplinary Optimization 61(1), 39-57.
| Crossref | Google Scholar |
Zhao D, Ma M, You X-Y (2022) A Kriging-based adaptive parallel sampling approach with threshold value. Structural and Multidisciplinary Optimization 65, 225.
| Crossref | Google Scholar |
Zounemat-Kermani M, Alizamir M, Keshtegar B, Batelaan O, Hinkelmann R (2022) Prediction of effluent arsenic concentration of wastewater treatment plants using machine learning and Kriging-based models. Environmental Science and Pollution Research International 29(14), 20556-20570.
| Crossref | Google Scholar | PubMed |
