**1. Introduction**

During the development of new fan products, it is necessary to repeatedly experiment and test to optimize the product. However, the conventional design and development of a fan is usually limited by standard methods, and the fan is the best solution to study symmetry or asymmetry. This method consists of multiple rounds of simulations and experiments. When a designer comes up with a new idea, it takes a long time to test and verify the parameters of the impeller profile. During the research, the single fan uses an asymmetry concept and the singular blade is used as the design, while the double fans constitute an asymmetry concept. In order to optimize the best method of symmetry or asymmetry regarding the mechanical principle of the blades, a new statistical method of gray relational analysis (GRA) analysis and the optimization of specific fan design parameters are required. In 2012, Kim et al. [1] suggested that a detailed blade design and optimized tip clearance is important for performance, and the geometric parameters of a blade were calculated and the results served as the flow criteria. The geometric parameters of a blade were also determined by calculations and verified by the simulation results of Computational Fluid Dynamics (CFD) and experiments. In 2010, Hurault et al. [2] studied the impact of the turbulence in axial-flow fans, and the fans that had been studied were provided with radial, swept-forward, and swept-backward blades. He compared the results of experiments and CFD with those obtained by Rhee et al. [3]. However, there are many gray zones

for the blade parameters during the process of development, and therefore most of the parameters are difficult to determine. In 2009, Lai et al. [4] applied the method of gray relational analysis (GRA) to product design evaluation (PDE) models when designing new product models. The final results solved the problem of complicated probabilities in the application of ergonomics to human comfort. In 2011, Wei et al. [5] proposed an optimal alternative solution package with the concept of the largest gray correlation degree, and the package was used to determine the negative ideal solution with a minimal degree of gray relation. The method is simple and effective, and it is also easy to calculate. In 2012, Qiu et al. [6] applied GRA to the verification of simulation models and simulation techniques for modeling, and improved the technique of GRA by considering data curves' geometrical shape. The rationality and effectiveness of GRA have been further verified by case studies. Li et al. [7] proposed that the important achievements by the continuous and diverse values of the gray system theory can be predictable and controllable. Under indeterminate conditions, he applied GRA to typical gray matrix problems and solved the problem of indeterminate and gray zones. The theory of GRA is one of the most mature and most broadly utilized gray system theories. During the analysis, the calculations were conducted on the basis of value comparisons, and in general, the comparison of parameters was also an important index for the analysis. Gray relational analysis supplies a simple way of analyzing a sequence of relationships or behaviors of a system. The analysis has the characteristics of quantitative and sequential analysis, and it can be applied to a random sequence of major and minor factors. This approach can analyze and confirm the factors affecting the target factors or the factors' degrees of improvement. It substantially affects the quantitative analysis of the factors of a system with a trend of dynamic development [8].

Li's work aims to investigate the possibility of using tip nozzles on ducted fans under conditions of large blade pitch angles and high ruggedness. The aerodynamic performance and flow field of the hovering ducted fan are studied numerically at a certain range of blade pitch angles at three operating speeds. Numerical experiments were performed using a shear stress transfer k-ω turbulence model and a fine, high-quality structured grid. The maximum thrust, peak efficiency, and stall margin of a ducted fan with a sharp jet are the main objectives of this study. The results show that under the condition of stall margin, the thrust of the fan with the tip nozzle increased by 30%. The improvement in aerodynamics seems to increase with increasing blade pitch angle because the separation flow at the front of the blade becomes uniform and reattaches to the blade surface due to the entrainment of the tip jet. The nozzles that are angled in the downward flushing direction can increase the nozzle ejection efficiency at larger blade pitch angles. Tip nozzles are suitable for fans with large pitch angles and high ruggedness [9]. Wang research proposed an integrated device called a wind energy fan (WEF), which uses wind energy to directly drive a fan connected to a wind turbine through a drive shaft. This vertical wind turbine can achieve underground ventilation. A test platform was established to test the WEF performance, considering three transmission ratios and two wind turbines with three and five blades. The results show that the transmission ratio has a significant effect on the fan air volume and should be selected to obtain the rated air volume. A wind turbine with three blades is easier to start, and its air volume is 5.43–17.85% higher than a wind turbine with five blades. Based on the aerodynamic characteristics of vertical fans and axial fans, a method of matching power and speed was proposed. This scheme is an effective wind energy technology, which can realize the active utilization of wind energy [10]. Wu used CFD simulations to study the transient characteristics of blade forces in fans with uneven blade spacing. Based on this, a "[T] -h" model for predicting blade forces was developed, and then a prediction based on simulation results and CFD research was developed based on the Lowson model [11]. David evaluated the performance of these underground fan systems in four different deep gold mines in South Africa. Of the six systems, the overall efficiency of the auxiliary fan system was 5%, with an average fan efficiency of 33% of the 33 fans. The results show that these fans deviate significantly from the design operating point. Therefore, current underground fan practices have significant shortcomings. Our detailed studies have concluded that the combination of underground auxiliary fan systems can lead to significant energy inefficiencies. Therefore, maintaining

good underground fan operation (such as optimal fan selection, pipe design, and maintenance) is critical to the efficiency of the mine ventilation network [12].

It is clear from the above analysis that no one has yet attempted to apply GRA to fan design. Based on this observation, a new concept of applying GRA to fan design is proposed in this study. After the relationship between parameters of a fan design is determined by GRA, the performance of new fan designs can be improved by the optimization of parameters. To verify the performance improvement, the CFD software, FLUENT, is used to obtain numerical results of the fan's performance, including flow rate and static pressure [1].
