# The Optimization of the Geometry of the Centrifugal Fan at Different Design Points
## 1 Introduction
An optimal design algorithm for centrifugal fans was analyzed by [PERSON] and [PERSON] [12]. They examined the centrifugal fan shape design problem, estimating the optimal shape of a centrifugal-flow fan based on knowledge of the desired volume flow rate of air using commercial CFD-ACE+ code and the Levenberg-Marquardt method. The angle-resolved velocity measurements in the impeller passages of a model bio-centrifugal pump were presented by [PERSON] et al. [13]. They mentioned that modifying the curvature of the center cone may provide a better match between the inlet flow angles and the impeller leading-edge angles. Some insights about similar investigations related to impeller material can be mentioned. Advanced elasto-plastic topology optimization of steel beams under elevated temperatures was reported by [PERSON] et al. [14]. Their results highlight the significance of integrating temperature effects in achieving optimal and robust steel beam designs. Structural optimization under the cutting stock problem was described by [PERSON] et al. [15]. Their considerations were discussed by comparing the solution obtained by the traditional weight-minimization approach with that obtained by the stock-constrained approach. Size and shape optimization of a guyed mast structure under wind, ice, and seismic loading was reported by [PERSON] et al. [16]. They mentioned that the entire optimization process seemed not to be sensible to the pole diameter, which was chosen as the input parameter of the design vector. Enhanced multi-strategy particle swarm optimization for constrained problems with an evolutionary-strategies-based unfeasible local search operator was reported by [PERSON] et al. [17]. They mentioned that the most extensively used method in many different practical applications is the penalty function method. An optimal preliminary design criterion of variable section beams was proposed by [PERSON] et al. [18]. The paper explored the optimal shape solution for a non-prismatic planar beam using the Timoshenko kinematics hypothesis. The proposed solution utilizes an analytical solution to analyze deformations and stresses under different constraints, considering load and the section variability of a rectangular cross-section. The study compared various solutions and evaluated sensitivity to key parameters and concludes that neglecting the arch effect and curvature is not possible beyond a certain threshold, investigating the relevance of beam span, emptying function level, and maximum allowable stress. The authors stated that meta-heuristics are currently very interesting techniques in structural optimization domains, in addition to the fact that there are no prior constraints on the objective function differentiability conditions and constraints. Reliability-based bi-directional evolutionary topology optimization of geometric and material nonlinear analysis with imperfections was featured by [PERSON] et al. [19]. In this paper, a novel computational technique was introduced to incorporate reliability-based design with the consideration of geometrically and materially nonlinear imperfect analysis. A new bi-directional evolutionary structural optimization scheme was developed and compared with perfect and imperfect analysis topology optimization designs for both deterministic and probabilistic analysis. The numerical examples demonstrated the effectiveness of the proposed method in finding optimal topologies for reliability-based design, with the results influenced by the introduction of a reliability index as a governing bound. The optimization of structural topology design through consideration of fatigue crack propagation was presented by [PERSON] and [PERSON] [20]. This paper introduced an advanced approach to structural topology optimization that incorporates fatigue crack propagation analysis.