Mohamed Hussien

The self-organizing map (SOM), which is a type of artificial neural network (ANN), was formulated as an optimal control problem. Its objective function is to minimize the mean quantization error, and the state equation is the weight updating equation of SOM. Based on the objective function and the state equations, the Hamiltonian equation based on Pontryagin’s minimum principle (PMP) was formed. This study presents two models of SOM formulated as an optimal control problem. In the first model, called SOMOC1, the design is based on the state equation representing the weight updating equation of the best matching units of the SOM nodes in each iteration, whereas in the second model, called SOMOC2, it considers the weight updating equation of all the nodes in the SOM as the state updating equation. The learning rate is treated as the control variable. Based on the solution of the switching function, a bang-bang control was applied with a high and low learning rate. The proposed SOMOC2 model performs better than the SOMOC1 model and conventional SOM as it considers all the nodes in the Hamiltonian equation, and the switching function obtained from it is influenced by all the states, which provides one costate variable for each. The costate determines the marginal cost of violating the constraint by the state equations, and the switching function is influenced by this, hence producing a greater improvement in terms of the mean quantization error at the final iteration. It was found that the solution leads to an infinite order singular arc. The possible solutions for the suitable learning rates during the singular arc period are discussed in this study.

Solar thermal energy-powered air conditioning technologies are receiving increased attention. Among the solar energy-driven cooling technologies, open type liquid desiccant air conditioning (AC) system is emerging as a promising technology, which has a solar driven desiccant solution regenerator. In this type of system, the evaporation of water and concentrating the desiccant or regenerator performance determines the cooling performance of the AC system, which necessitates its development and experimental performance testing under actual operating conditions. The setup is made of a black painted corrugated solar collector of area 0.8 m × 1.84 m covered with glass, and a liquid desiccant solution tank and distribution system over the absorber. Solar regeneration experiments on calcium chloride–water solution were carried out on the setup and a total of five sets of meteorological, collector and solution property data were collected through concentrating the desiccant from 32.9 initially to 51.3% in five days. The evaporation of water from the regenerator was analyzed using energy and desiccant mass conservation. For a typical day, the mass of water evaporated was estimated to be 3.10 and 3.16 kg over a day, as estimated by conservation of mass and energy principles from a 34.8 kg of calcium chloride solution with initial desiccant concentration of 43.6% stored in the tank.