## 1 Introduction  
With the rapid economic development, people have put forward new requirements for the ventilation and air-conditioning system. At the same time, the COVID-19 pandemic has further raised people's attention on this [1, 2]. Building electrical energy accounts for a large proportion of total energy consumption [3, 4], and ventilation and air-conditioning systems are important energy-consuming sections, accounting for about 40% of building energy consumption [5]. Fan is an important component of ventilation and air-conditioning system. The improvement in fan performance can reduce electricity consumption by itself, which is considerable in some ventilation use and help increase the efficiency of refrigeration system to decrease even more electric energy cost. Therefore, research on developing ventilation equipment with high efficiency, energy-saving and low noise has grown increasingly important [6]. From the user's point of view, the multi-blade centrifugal fan has the characteristics of small space occupation and low noise. These two unique advantages make it widely used in air conditioning, ventilation, building ventilation and other industries [7]. However, its low efficiency has always limited the market promotion of this type of fan [8]. Noiseand energy consumption problems in existing multi-blade centrifugal fan designs have grown increasingly problematic as modern demands for energy conservation and emissions reduction have intensified [9]. As the main working component of a building ventilation system, improving the efficiency of the fan can reduce the energy consumption of the entire system [10]. The increase in fan efficiency may also reduce the fan noise, which significantly affects users' experience on building ventilation and air conditioning systems [11]. As the power component of the multi-blade centrifugal fan, the aerodynamic performance and the acoustic characteristics of the fan were impacted by the impeller [12]. Multi-blade centrifugal fans usually have 60 blades, so by adjusting the structure of the blades, the performance of the fan can be greatly improved [13; 14]. In the conventional design, the blade profile of the multi-blade centrifugal fan is polynomial (and usually single) in the middle arc. The air performance of single arc blades is generally poor [15]. However, optimizing the design of the multi-segment curve of the blade profile may improve aerodynamic performance, the efficiency and acoustic characteristic of the fan. Many previous scholars have attempted to optimize the design of multi-blade centrifugal fan blades. In selecting multi-blade centrifugal fan airfoil, [PERSON] [16] explored a single-arc blade type multi-blade fan and a double-arc blade type multi-blade fan to find that the aerodynamic characteristics of the former are inferior to those of the latter. A double-arc blade type multi-blade fan with a larger arc radius shows favorable aerodynamic characteristics and low noise. Recently, researchers have developed bionic designs on a leaf (blade) surface, leading-edge and trailing edge by extracting the unique noise-reducing characteristic structure produced by natural organisms during evolution [17; 18]. [PERSON] [19] found that the A-level noise of non-smooth structured bionic blades, striped surface bionic blades and bionic serrated leading-edge blades are all lower than those of prototype blades. Early fluid machinery blade parameterization techniques mainly centered on the bump function method [20], which is convenient for airfoil design but requires approximately 10 control parameters. As the upper and lower surfaces are modified, the design volume grows excessive and it is difficult to intuitively reflect the influence of a single parameter on the design result. [PERSON] et al. [21] proposed a new parametric airfoil design method based on the Bessel curve and developed it into a generalized form of adjustable shape parameters.