Implementing machine learning to optimize the cost-benefit of urban water clarifier geometrics
Graphical abstract
Introduction
Current clarification basin design guidance imposes significant costs to stakeholders. The total cost of a single clarification basin ranges from hundreds of thousands to tens of millions United States dollar (USD) (Li, Sansalone, 2022, South Carolina Sea Grant Consortium, 2019) as shown in Fig. S1 (see online Supplemental Materials). A critical factor that escalates basin cost is the current adoption of presumptive basin performance based on residence time (RT, or hydraulic residence time [HRT]) or surface overflow rate (SOR) models (Li, Sansalone, 2022, Spelman, Sansalone, 2021). To provide a model alternative, a more robust algebraic model for basin clarification has recently been proposed based on symbolic regression (SR) and computational fluid dynamics (CFD) simulations (Li and Sansalone, 2022a). However, this model did not address (1) basin geometrics (e.g. horizontal aspect ratio, baffle geometry) or (2) geometric optimization for basin planning or retrofit. A frequent impetus for geometric optimization or retrofits is where basin expansion is not spatially viable or economical due to infrastructure constraints.
RT and SOR models are inadequate to provide robust guidance for clarification basin performance, nor do these models accurately reproduce the physical scaling behavior for clarification basin and similar systems (e.g., primary and secondary clarifiers, hydrodynamic separators) (Li and Sansalone, 2022b). As a result, the cost-effectiveness of basins is compromised. Specifically, the total cost of clarification systems scales non-linearly and exponentially with system performance (measured as total PM separation , as defined in Section 2). This exponential scaling behavior of a clarification system is suggested by Li and Sansalone (2022a), Spelman and Sansalone (2021), Stamou et al. (1989), Howard et al. (2012). Such exponential scaling behavior of a clarification system has major implications for the geometrics and retrofit of urban water basins. Improving basin PM clarification (and PM-partitioned contaminants) by simply enlarging system dimension is not an economical and sustainable approach, irrespective of conflicts with proximate land/infrastructure and lost opportunity costs resulting from basin expansion.
A potential solution to overcome the current cost barrier of basin design/geometrics (e.g., a common and generalizable plain polygon basin shape) is to enhance system performance through beneficial manipulation of intra-basin dynamics. Such intra-basin geometric retrofits can be implemented by internal structures such as baffles, as compared to expanding the bulk dimensions (increased basin surface area and volume). Studies demonstrate that through configuring internal baffles, basin transport dynamics can be manipulated and trained to generate conditions for enhancing PM and PM-associated contaminant separation (Ahmed, Kamel, Abdel Jawad, 1996, Asgharzadeh, Firoozabadi, Afshin, 2011, Garofalo, Sansalone, 2018, Goula, Kostoglou, Karapantsios, Zouboulis, 2008, Howard, Mohseni, Gulliver, Stefan, 2011, Jamshidnia, Firoozabadi, 2010, Li, Balachandar, Sansalone, 2021). Despite the potential benefits, configuring baffled clarification systems is challenging. Li, Balachandar, Sansalone, 2021, Li, Balachandar, Sansalone, 2021, Li and Sansalone (2021a) elucidate the nonlinearity in the iterations between turbulence structure and PM fate in response to internal baffle placement. As a result, the solution to baffle configuration within a basin is not trivial. There is not a singular set of baffle geometrics that guarantees enhanced PM clarification compared to an unbaffled basin of the same shape, surface area and volume. Li and Sansalone (2021b) demonstrates that a conventional baffling approach (e.g., array of parallel baffles) may yield neither the optimal system clarification performance nor the optimal design cost-benefit, especially for basin with a high horizontal aspect ratio (i.e., a long-linear basin). In addition, there is not a singular and/or universal baffle configuration that can be implemented across disparate basin geometrics and loadings. Optimal baffle configurations for PM separation are dependent on basin geometrics and loadings (Li et al., 2021a). A baffle configuration that improves system clarification for one set of basin geometry and loading conditions does not ensure the same level of clarification enhancement for another system geometry and loadings. In some cases, adverse effects of baffling are observed (Imam, McCorquodale, Bewtra, 1983, Li, Balachandar, Sansalone, 2021, Li, Sansalone, 2022, Li, Spelman, Sansalone, 2021, Liu, Ma, Luo, Bai, Wang, Zhang, 2010).
Currently, no tool exists to robustly and efficiently plan, optimize, and/or retrofit basin infrastructure for urban water management. Common tools (e.g., RT-based empirical models, surface overflow rate [SOR] models, lumped dynamic models such as Storm Water Management Model [SWMM]) are easy-to-use but are inadequate to guide basin optimization because basin transport dynamics are unresolved with these tools. More advanced CFD-based design methods (e.g., CFD models coupled with optimization algorithm) (Li and Sansalone, 2021b), while demonstrating significant benefits in scientific research, are complex and computationally expensive for routine engineering application (Liu et al., 2020) (e.g., an estimated wall time [the actual time taken to execute the computation] of 0.46 to 2.7 years for 2000 design optimization evaluations with an Intel Xeon E5-2698 v3 processor of 16 cores). There is a pressing need for a tool to provide cost-effective basin geometrics including intra-basin baffles or retrofit implementation as green infrastructure and accelerate the translation of research outcomes to engineering practice.
To address this need, this study presents an efficient and robust basin geometrics optimization and retrofit framework and tool with machine learning (ML) based on a deep learning library PyTorch (Paszke et al., 2019) and an optimization library of Dakota (Adams et al., 2020). ML offers a wealth of solutions to extract information and patterns from data that can be translated into knowledge and inform the engineering design of basin infrastructure. ML has been increasingly applied to the water science field such as water chemistry load prediction (Chen, Chen, Zhou, Huang, Qi, Shen, Liu, Zuo, Zou, Wang, Zhang, Chen, Chen, Deng, Ren, 2020, Huang, Ma, Ma, Huangfu, He, 2021, Li, Qiao, Yu, Wang, Li, Liao, Zhu, 2022, Thompson, Dickenson, 2021) and real-time flooding control (Bartos, Kerkez, 2021, Bartos, Mullapudi, Troutman, 2019, Mullapudi, Lewis, Gruden, Kerkez, 2020). ML can also be used to develop surrogate models for higher-fidelity models. Compared to higher-fidelity models, ML models, once trained, are more computationally efficient. Trained ML models can serve as robust “stands-in” for applications where a large number of iterations/computations are needed, such as parameter space exploration and design optimization (Adams et al., 2020). ML-based surrogate modeling approach recently has been applied to urban hydrology (Bermúdez, Ntegeka, Wolfs, Willems, 2018, Yang, Yang, Chen, Santisirisomboon, Lu, Zhao, 2020, Zahura, Goodall, Sadler, Shen, Morsy, Behl, 2020), aircraft wing design (Li, Zhang, 2021, Li, Zhang, 2021), hydro-power turbine design (Masood et al., 2021), and fusion plasma simulation (Dong et al., 2021). Building on this previous research, this study develops and extends the ML-based surrogate modeling approach to basin infrastructure design and optimization.
The specific objectives/tasks and methodology of this study are: (1) creating a diverse and robust database for ML model training with CFD simulations of PM separation in baffled basins over a wide range of basin geometries (e.g., length, width, depth etc.), loading conditions, and baffle configurations (e.g., length, spacing, angle), (2) training and assessing the predictive capability of developed ML model for basin PM separation inference, (3) developing a framework for robust and efficient basin optimization by leveraging and coupling the automatic differentiation (AD) in PyTorch with a optimization library of Dakota, and (4) examining the effectiveness of proposed basin geometric planning and optimization method with respect to the existing guidance and common basin configurations.
Section snippets
Materials and methods
As an outline of Materials and Methods, Section 2.1 provides background information, mathematical conceptualization and generalization of basin design as a nonlinear constrained optimization problem. Section 2.2 and 2.3 illustrate the methodology that solves this constrained optimization problem. Specifically, Section 2.2 presents the detailed development of the ML model as an efficient basin design performance evaluation engine. Section 2.3 formulates a basin cost model based on life cycle
Predictive capability of developed ML models
The predictive capability of the developed ANN model (i.e., the optimal ANN model determined from hyperparameter optimization, see online Supplemental Materials) was first examined for PM separation (, Eq. (2)). The developed ANN model demonstrates high predictive capability with the coefficient of determination of 0.998, 0.998, and 0.998 for training, validation, and test dataset, as illustrated in Fig. S14 (see online Supplemental Materials). Note that this is a conservative estimate
Need for methodological evolution for basin design and implementation
Functioning as a unit operation (UO), basins are widely implemented to sequester particulate matter (PM) as well as PM-bound chemicals and pathogens, whether for storm-, waste-, potable water or combined sewer overflow treatment. In recent decades, there has been a worldwide increase in the implementation of (wet detention or retention) as a type of green infrastructure for urban water cycle management. Despite the ubiquitous implementation of basins in the built environs, the practice of basin
Conclusion
This study developed a machine learning (ML)-based tool of basin design geometrics and retrofit for cost-effective clarification basin implementation in urban water management. This tool was developed in three stages: (1) generation of a basin performance database through computational fluid dynamics (CFD) simulations; (2) formulation of an artificial neural network (ANN) model based on dynamic similarity and trained for basin performance inference using the CFD-generated database; (3)
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by the University of Florida Informatics Institute (UFII) SEED Funds, and in part by the Florida Department of Transportation under Contract No. BDV31 977-112.
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