A Neural Network Approach to Estimate the Frequency of a Cantilever Beam with Random Multiple Damages

Natural frequency is an important parameter in the structural health monitoring (SHM) system. Any changes in this parameter indicate structural alteration due to damage. This study provides a neural network (NN) solution as an alternative to the finite element (FE) method to measure the natural frequencies of a cantilever beam with random multiple damage. It is based on a statistical dataset of a free vibration test obtained from the APDL (Ansys parametric design language) simulation using a MATLAB (matrix laboratory) script. The script can generate an unlimited number of possible damage combinations for any given parameters with the help of the Monte Carlo (MC) technique. MC helps to generate a random number of damages in random locations at each simulation. Damage conditions are controlled by three parameters including damage severity and damage size (in terms of the mean and standard deviation of damage). Moreover, the method proposes a curve-fitting equation to validate the predicted natural frequency for the first three modes obtained from the neural network model. Both methods are in good agreement with each other, having minimal errors in the range of 0.2-3% for each mode. The frequency result shows that the beam frequency is 8.6486 Hz if the area reduction is 10%, whereas it comes down to 7.2338 Hz if there is a 30% area reduction. A two-level factorial test shows that damage severity is the most impactful factor compared to the damage sizes on the frequency shift event. This indicates that damage alters the composition of the beam and has an impact on its frequency change with the assumed damage parameters. Therefore, the proposed NN model can estimate the frequency shift for various damage scenarios. It can be utilized in the vibration-based damage identification process to predict the frequency changes of the damaged beam without any computational burden.