اصلاح مدل اجزاي محدود يك سيستم لوله‌ي Z‌شكل با استفاده از آزمايش مودال تجربي

FINITE ELEMENT MODEL UPDATING OF A Z-SHAPED PIPING SYSTEM BY MODAL TESTING

در اين پژوهش، مدل اجزاي محدود يك سيستم لوله‌ي انتقال گاز Z‌شكل با بهره‌گيري از داده‌هاي تجربي حاصل از آزمايش كيفي و با استفاده از روش بهينه‌سازي اجتماع ذرات، با هدف كمينه‌سازي اختلاف بين پارامترهاي كيفي مدل اجزاي محدود و مدل تجربي اصلاح مي‌شود. براي اصلاح ماتريس‌هاي جرم، سختي و ميرايي در مدل اجزاي محدود، 28 پارامتر طراحي در نظر گرفته شده ‌است كه با اِعمال روش بهينه‌سازي ذكر‌شده، يافتن‌ِ مقادير بهينه‌ براي اين پارامترها ميسر مي‌شود. با بهره‌گيري از اين مقادير بهينه در مدل اجزاي محدود، پارامترهاي كيفي حاصل از اين مدل ــ شامل فركانس هاي طبيعي ناميرا، فاكتورهاي ميرايي و شكل مودها ــ تطابق بيشتري با مقادير متناظر تجربي خواهند داشت.

In this study, the finite element (FE) model of a Z-shaped piping system is updated using experimental modal data via particle swarm optimization (PSO). PSO is a random search method that imitates social behaviors like fish schooling or birds flocking to solve optimization problems. Members of the swarm inform each other of good positions and adjust their own position and velocity based on these good positions. The best previous position of each member and the position of the best member among all the swarm are recorded and used to find the new velocities (i.e. the rate of the position change) and positions. Because of the random methodology of the PSO, and utilizing a population of solutions rather than a single point, it is more effective in finding the global optimum than the conventional gradient-based algorithms. Besides, the convergence of the PSO does not depend on the initial guess, while the convergence of the gradient-based methods is highly affected by the initial starting point. This paper deals with the modification of the mass, stiffness and damping matrices of the system, to bring the vibration response of the FE model closer to the experimental one. Having performed modal testing, the first six experimental modes of the system (i.e. natural frequencies, mode shapes and damping ratios) are extracted from the experimental FRF data. Then, considering the modification process as an optimization problem, the weighted sum of the squared error between the measured and computed modal parameters is minimized. Moreover, several physical parameters of the system with unknown values are considered as design parameters. In the following study, the design parameters are; Young’s modulus, density, proportional damping constants, and mass and stiffness of threaded joints. Then, PSO is applied to find the optimum values of the design parameters in the minimization problem. The study showed that the proposed approach is robust, accurate and easy to implement. Utilizing the optimum values of the design parameters, the FE model of the system better represents the vibration behavior of the piping system.