Minimization of the weight of the blade of the aerial installation by an adaptive hybrid optimization method

Abstract

In various fields of engineering practice, such as turbine building, power engineering, elements of thin-walled structures are widely used, which operate under increased loads when interacting with air or water. These include blades of impellers of radial-axial and rotary-blade hydraulic turbines, blades of wind power plants. Designing highly efficient machines and structures with the required level of reliability requires determining their optimal characteristics. The article proposes an adaptive method for finding the minimum of an arbitrary smooth multivariable function. The method was used to solve the benchmark optimization problem of a function in the form of a valley. The essence of the proposed algorithm lies in the sequential approach to the bottom of the valley and the subsequent movement in the direction of decreasing the objective function. Comparison of the results of calculating the minimum point of the function is performed using both non-gradient and gradient methods, namely: Powell, Hook-Jeeves, the steepest descent method and the developed method. It was found that the effectiveness of the proposed method is greater than the usual search algorithms, but it is not without its drawbacks. The method is proposed that represents a number of hybrid methods, which form a hybrid coalition Proposed hybrid algorithm does not provide a satisfactory result in the "single" search. The search algorithm reaches a point where all the values of the function at the surrounding points are greater than the values at the obtained point, and the algorithm cannot overcome the barrier. To solve the problem, it is necessary to take the obtained point as a new starting point and repeat the algorithm for finding the minimum of the function, that is, use the multistart method. The proposed method was used to solve the problem of optimizing the blade of an air installation, which was reduced to the problem of unconditional optimization using the method of penalty functions, but the goal function had a significantly valley structure. The optimal values of section thicknesses were obtained, which made it possible to build a blade with improved characteristics.