Composite Neural Network Research Articles

Operator learning for urban water clarification hydrodynamics and particulate matter transport with physics-informed neural networks

Computational fluid dynamics (CFD) can be a powerful tool for higher-fidelity water infrastructure planning and design. Despite decades of development and demonstration over a wide range of water systems such as clarification basins, activated sludge processes, ozone contactors, etc., CFD remains primarily used in academic research, with limited application in civil and environmental engineering practice. This limitation is contributed by its higher computational cost and demand for specialized user skills. This, however, need not be the case, if a robust and efficient surrogate model can be developed from CFD simulations and independently deployed for engineering purposes. Leveraging the emerging scientific machine learning (ML) techniques of physics-informed ML and operator learning, this study develops a composite neural network (CPNN) for learning the flow hydrodynamics and particulate matter (PM) transport and fate in clarification systems. The CPNN consists of a deep operator network (DeepONet) as an encoder and a physics-informed neural network (PINN) as a decoder. In contrast to common “black box” and lumped ML approaches, the developed CPNN directly incorporates physics principles into its architecture. Furthermore, the CPNN is designed for process-resolved and operator learning, enabling it to predict spatial hydrodynamics and PM concentration distribution (i.e., contours) across different basin geometrics and loading conditions. Compared to CFD simulation, the developed CPNN model has significantly higher computational efficiency (∼ milliseconds) while demonstrating robust predictive capability. For predicting basin hydrodynamics across 10,000 test cases, the trained CPNN model achieves an R2 above 0.8 for 66.4% of cases and an R2 above 0.4 for 89.2% of cases. A similar performance is also demonstrated by the CPNN in predicting basin PM concentration. Further investigation reveals that basin geometrics that trigger bi-modal flow solutions can be particularly challenging for ML. Additionally, this study visualizes the dependency of basin hydrodynamics and PM concentration on basin geometrics and loading conditions, providing valuable insights for optimizing basin configuration. Lastly, the potentials and benefits of web-based applications, e.g., DeepXtorm, as a user-friendly interface for the developed CPNN model is discussed. This study represents the initial step toward achieving real-time higher-fidelity water infrastructure planning, design, optimization, and regulation.

Hysteresis modeling and compensation of a piezoelectric fast steering platform using multiple NARMA-L2 models

The piezoelectric fast steering platform (PFSP) enhances the scanning capabilities of lidar systems for autonomous vehicles. However, hysteresis nonlinearity degrades the scanning accuracy of the PFSP. To meet this challenge, this paper proposes a novel approach for hysteresis modeling and compensation using multiple nonlinear autoregressive moving average (NARMA)-L2 models. First, the hysteresis model is partitioned into a collection of submodels based on the K-means methodology, where the feature vector stems from the classical Bouc–Wen (CBW) model. Each submodel describes the dynamics of a specific hysteresis segment by a single NARMA-L2 model. The composite neural network (CNN), formed by combining two multilayer perceptron (MLP) networks, is trained to estimate the hysteresis output of the single NARMA-L2 model. Compared to the submodels obtained by evenly partitioning according to the input range, the submodels obtained by K-means partitioning offer higher hysteresis modeling accuracy. To compensate for the hysteresis nonlinearity, a novel adaptive Multi-NARMA-L2 (AMNL2) controller is then designed by online adjusting the parameters of the CNN. Furthermore, an adaptive filter is proposed to alleviate the oscillation caused by high-frequency disturbances during switching. Finally, experiments demonstrate that the AMNL2 controller outperforms the traditional MNL2 controller and the proportional–integral–derivative (PID) controller.

A new feature selection algorithm and composite neural network for electricity price forecasting

In a competitive electricity market, the forecasting of energy prices is an important activity for all the market participants either for developing bidding strategies or for making investment decisions. In this paper, a new forecast strategy is proposed for day ahead prediction of electricity price, which is a complex signal with nonlinear, volatile and time dependent behavior. Our forecast strategy includes a new two stage feature selection algorithm, a composite neural network (CNN) and a few auxiliary predictors. The feature selection algorithm has two filtering stages to remove irrelevant and redundant candidate inputs, respectively. This algorithm is based on mutual information (MI) criterion and selects the input variables of the CNN among a large set of candidate inputs. The CNN is composed of a few neural networks (NN) with a new data flow among its building blocks. The CNN is the forecast engine of the proposed strategy. A kind of cross-validation technique is also presented to fine-tune the adjustable parameters of the feature selection algorithm and CNN. Moreover, the proposed price forecast strategy is equipped with a few auxiliary predictors to enrich the candidate set of inputs of the forecast engine. The whole proposed strategy is examined on the PJM, Spanish and Californian electricity markets and compared with some of the most recent price forecast methods.