A hybrid model combining mode decomposition and deep learning algorithms for detecting TP in urban sewer networks

Timely and accurately grasping total phosphorus (TP) concentration in sewer networks is crucial for urban phosphorus flow management and shock load early warning of sewage treatment facilities. Modeling-based methods are cleaner and more energy-saving than traditional methods requiring digestion procedures. However, the TP time series' strong nonlinearity and complexity result in unsatisfactory accuracy in these methods. This work proposes a hybrid model named CEEMDAN-SE-VMD-LSTM that combines complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), sample entropy (SE), variational mode decomposition (VMD), and long short-term memory (LSTM) neural network to improve the accuracies of modeling-based methods. In proposed hybrid model, the two-stage decomposition procedure can decompose the TP time series into several lower-complexity modes, and the powerful nonlinear mapping ability of the LSTM neural network enables accurate prediction of these modes. In case study, the proposed hybrid model achieves excellent detection accuracy with an average R2 of 0.9460 ± 0.0243. Compared with the hybrid models formed by combining other decomposition procedures (i.e., CEEMDAN, VMD, singular spectrum analysis (SSA), CEEMDAN-SE-SSA) and LSTM neural network, the proposed hybrid model has the highest detection accuracy (1.36–3.94 % higher Nash-Sutcliffe efficiency, 1.28–4.58 % higher R2, 12.14–24.86 % lower RMSE). The strategy of setting the mode decomposition procedure based on a comprehensive analysis of the decomposition algorithms and the obtained modes ensures high detection accuracy of the proposed hybrid model while avoiding costly computational burdens. This work is enlightening for improving the accuracy and modeling efficiency of soft detection methods, which are expected to reduce energy consumption and pollution caused by water quality detection.