Hooke–Jeeves Method-used Local Search in a Hybrid Global Optimization Algorithm

Modern methods for optimization investigation of complex systems are based on development and updating the mathematical models of systems because of solving the appropriate inverse problems. Input data desirable for solution are obtained from the analysis of experimentally defined consecutive characteristics for a system or a process. Causal characteristics are the sought ones to which equation coefficients of mathematical models of object, limit conditions, etc. belong. The optimization approach is one of the main ones to solve the inverse problems. In the main case it is necessary to find a global extremum of not everywhere differentiable criterion function. Global optimization methods are widely used in problems of identification and computation diagnosis system as well as in optimal control, computing to-mography, image restoration, teaching the neuron networks, other intelligence technologies. Increasingly complicated systems of optimization observed during last decades lead to more complicated mathematical models, thereby making solution of appropriate extreme problems significantly more difficult. A great deal of practical applications may have the problem con-ditions, which can restrict modeling. As a consequence, in inverse problems the criterion functions can be not everywhere differentiable and noisy. Available noise means that calculat-ing the derivatives is difficult and unreliable. It results in using the optimization methods without calculating the derivatives.An efficiency of deterministic algorithms of global optimization is significantly restrict-ed by their dependence on the extreme problem dimension. When the number of variables is large they use the stochastic global optimization algorithms. As stochastic algorithms yield too expensive solutions, so this drawback restricts their applications. Developing hybrid algo-rithms that combine a stochastic algorithm for scanning the variable space with deterministic local search method is a promising way. A new hybrid algorithm that integrates a multiple Metropolis algorithm and the Hooke–Jeeves method for the local search is proposed. Some results on solving the global optimization benchmark are presented.</p

Theoretical background of hydraulic drive control system analysis for testing piston hydraulic cylinders

Introduction. The durability and performance of hydraulic machines is determined through life tests. At that, various braking devices (mechanical, electric, hydraulic, etc.) are used for strength loading of the hydraulic motor, as a result of which a significant amount of energy is lost. This can be avoided if the method of rotational motion with energy recovery is used during life tests. This approach is applicable for hydraulic pumps, motors, and hydraulic cylinders.Materials and Methods. A test bench is presented, the design of which provides recreation of the conditions most appropriate for the field operation of hydraulic cylinders. In this case, energy recovery is possible. To solve the research problems, methods of mathematical modeling were used, the basic functional parameters of the proposed design were calculated. The determination of the pressure increment at various points in the hydraulic system is based on the theory of volumetric rigidity. When modeling the motion of the moving elements of the bench hydraulic system, the laws of rotor motion are used.Research Results. In the structure of the test bench, the cylinders in question are located in the pressure main between the hydraulic pump and the hydraulic motor. This enables to significantly reduce the bench itself and to save a significant amount of energy due to its recovery. A basic hydraulic diagram of the test bench for piston hydraulic cylinders is presented, in which the operation of the moving elements of the system is shown. A mathematical modeling of the hydraulic system of the bench is performed. A kinematic diagram of the mechanism for transmitting motion between test cylinders is shown.Discussion and Conclusions. The system of equations presented in the paper shows how the increment of pressure at the selected nodal points of the energy recovery system is determined (in particular, how the increment depends on time, reduced coefficient of volumetric rigidity, operating fluid consumption, and piston areas). The velocities of the hydraulic pistons are determined according to the kinematic scheme of the mechanical transmission of the bench. Thus it can be argued that, thanks to the solution presented in the paper, the life test results of hydraulic cylinders will adequately reflect their operation under rated duties