Lightweight Deep Learning for Missing Data Imputation in Wastewater Treatment With Variational Residual Auto-Encoder

Deep variational residual auto-encoder (ResNet-VAE) has shown promising outcomes in missing imputation of wastewater quality data. Nevertheless, with its large storage size and computation overhead, it is of great difficulty to deploy wastewater treatment plant (WWTP) sensors for real-time missing imputation. To address this problem, we propose a novel approach called lightweight-ResNet-VAE to compress classical ResNet-VAE by network pruning, weight quantization, and relative indexing in this article. First, we develop a three-step network pruning method to sparsify the weight matrices by removing insignificant weights to reduce the time cost of model inference. Second, we develop weight quantization and use eight shared weights to compress the size of each weight from 32-bit to 3-bit. Finally, the relative indexing is adopted to further compress the size of the classical ResNet-VAE by compressed sparse row (CSR), which greatly accelerates the model computation and saves storage size. Experiments on the Beipai IoT influent quality data set demonstrate that lightweight-ResNet-VAE compresses the size of the classical ResNet-VAE from 301.88 to 26.24 kB with a compression rate of 11.50 times, and outperforms the baseline methods in terms of computation acceleration, storage saving and energy consumption with only a slight decrease on accuracy as 2.74% in MAPE of missing imputation for wastewater quality data due to pruning less significant weights and quantizing the remaining weights.