This paper proposes a new variant of particle swarm optimization, namely adaptive particle swarm optimization with population diversity control (APSO-PDC), to improve the performance of particle swarm optimization. APSO-PDC is formulated based on adaptive selection of particle roles, population diversity control, and adaptive control of parameters. The adaptive selection of particle roles which combines the evolutionary state and dynamic particle state estimation method will sort the particles into three roles to let different particles execute different search tasks during optimization process. The adaptive control of parameters which is created based on the evolutionary state and particle roles encourages the exploitation ability and enhances the algorithm’s convergence speed. The population diversity control which combines comprehensive learning strategy of the comprehensive learning particle swarm optimizer with evolutionary state to update the individual best position strengthens exploration ability and thus increases the algorithm’s robustness toward the premature convergence issue. The performance of APSO-PDC is comprehensively evaluated by 21 unimodal and multimodal functions with or without rotation. The results indicate APSO-PDC has more preferable searching accuracy, searching reliability, and convergence speed than the other well-established particle swarm optimization variants. Finally, compared with other six particle swarm optimization variants, APSO-PDC shows satisfactory performance in optimizing tandem blade. This excellent performance proves that APSO-PDC has a better control of swarm exploration and exploitation abilities.
To improve the design quality of high-turning tandem blade, a coupling optimization system for the shape and relative position of tandem blades was developed based on an improved particle swarm optimization algorithm and NURBS parameterization. First of all, to increase convergence speed and avoid local optima of particle swarm optimization (PSO), an improved particle swarm optimization (IPSO) is formulated based on adaptive selection of particle roles, adaptive control of parameters and population diversity control. Then experiments are carried out using test functions to illustrate the performance of IPSO and to compare IPSO with some PSOs. The comparison indicates IPSO can obtain excellent convergence speed and simultaneously keep the best reliability. In addition, the coupling optimization system is validated by optimizing a large-turning tandem blade. Optimization results illustrate IPSO can obviously increase the optimization speed and reduce the time and cost of optimization. After optimization, at design condition, the total pressure loss coefficient of the optimized blade is decreased by 40.4%, and the static pressure ratio of optimized blade is higher and the total pressure loss coefficient is smaller at all incidence angles. In addition, properly reducing the gap area of tandem blade can effectively reduce the friction loss of the blade boundary layer and the mixing loss created by mixing the gap fluid and the mainstream fluid.
To improve the flow performance of tandem cascades on design and off design incidence angle and increase the stable operation range, an optimization system for tandem cascades was developed based on an adaptive particle swarm optimization (APSO-PDC). Firstly, APSO-PDC was proposed based on adaptive selection of particle roles and population diversity control. The adaptive selection of particle roles which combines the evolutionary state and dynamic particle state estimation (DPSE) method will sort the particles into three roles to help different particles execute different search tasks during optimization process. The population diversity control, which combines comprehensive learning strategy of the comprehensive learning particle swarm optimizer (CLPSO) with evolutionary state, pretty strengthens the exploration ability and avoids falling into the local optima. The performance of APSO-PDC is evaluated by 11 unimodal and multimodal functions. Compared with the other six PSOs, the results indicate APSO-PDC has better performance in terms of algorithm accuracy and algorithm reliability. In addition, APSO-PDC is validated by optimizing two large-turning tandem cascades, including low-dimension (5 optimization variables) and high-dimension problems (34 optimization variables). Compared with the other six PSOs, the optimization results demonstrate APSO-PDC has the fastest convergence speed and simultaneously controls well the population diversity.
To explore the flow mechanism and improve the performance of supersonic tandem rotor blades, the supersonic rotor Rotor37 is taken as the prototype and redesigned to an original supersonic tandem rotor. Then, based on the Kriging model, the physical programming method, and improved particle swarm optimization algorithm, a multi-objective optimization methodology is developed and applied to achieve the multi-objective optimization of the supersonic tandem rotor blades. Compared with Rotor37, the mass flow and surge margin of the original tandem rotor obviously increased. However, the efficiency of the original tandem rotor was slightly lower than Rotor37. After multi-objective optimization, compared with the original tandem rotor, the total pressure ratio and efficiency of the optimized tandem rotor significantly increased, and the efficiency increased by 1.6%. Further, the surge margin increased by 2.75%. The range and intensity of the high-loss region in the middle section of the optimized tandem rotor significantly decreased, and the range of the low-loss area in the middle region and tip region significantly increased, but the range and strength of the high-loss area in the tip region changed a little. The reason for the decrease of total pressure loss in the middle region and tip region is that the three-dimensional optimization of the blade significantly reduced the shock loss and boundary layer separation loss of the front blade. At the same time, the mixing loss between low energy fluid and the main flow in blade wake also reduced. Besides, the three-dimensional optimization of the blade had little impact on the leakage flow and the secondary flow generated by the mutual interference of the leakage flow and shock wave.
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