Many studies on pressure sensor (PS) placement and pressure reducing valve (PRV) localization in water distribution systems (WDSs) have been made with the objective of improving water leakage detection and pressure reduction, respectively. However, due to varying operation conditions, it is expected to realize pressure control using a number of PSs and PRVs to keep minimum operating pressure in real-time. This study aims to investigate the PS placement and PRV localization for the purpose of pressure control system design for WDSs. For such a control system, a PS should be positioned to represent the pressure patterns of a region of the WDS. Correspondingly, a PRV should be located to achieve a maximum pressure reduction between two neighboring regions. According to these considerations, an approach based on the k-means++ method for simultaneously determining the numbers and positions of both PSs and PRVs is proposed. Results from three case studies are presented to demonstrate the effectiveness of the suggested approach. It is shown that the sensors positioned have a high accuracy of pressure representation and the valves localized lead to a significant pressure reduction.

As science and technology advance, industrial manufacturing processes get more complicated. Back Propagation Neural Network (BPNN) convergence is comparatively slower for processing nonlinear systems. The nonlinear system used in this study to evaluate the optimization of BPNN based on the LM algorithm proved the algorithm’s efficacy through a MATLAB simulation analysis. This paper examined the application impact of the enhanced approach using the Continuous stirred tank reactor (CSTR) control system as an example. The study’s findings demonstrate that the LM optimization algorithm’s identification error exceeds 10-5. The research’s suggested control approach for reactant concentration CA in CSTR systems provides a better tracking effect and a stronger anti-interference capacity. Compared to the PI control method, the overall control effect is superior. As a result, the optimization model for nonlinear systems has a greatly improved processing accuracy. With some data support for the accuracy study of neural network models and the application of nonlinear systems, the suggested LM-BP optimization algorithm is evidently more appropriate for nonlinear systems.

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