Perturbation stochastic model updating of a bolted structure / Mohamad Azam Shah Aziz Shah - Aziz Shah, Mohamad Azam Shah (2022)
The stochastic model updating (SMU) method based on perturbation theory offers many advantages in predicting the dynamic behaviour of an engineering structure under conditions of variability and uncertainty with high accuracy and at low cost solutions. However, the presence of high-dimensional uncertainty of the structural problem, such as a bolted structure, makes it difficult for the SMU method to provide an accurate prediction result, which usually leads to large errors, hard convergence and ill-condition problems. This high-dimensional uncertainty is due to the limited ability to obtain comprehensive knowledge about the bolted structure, especially about the initial properties of the contact interfaces. Moreover, it is almost impossible to determine the stiffness of the contact interfaces experimentally. In this study, a new scheme using the perturbation SMU method with multidimensional analysis was proposed to estimate appropriate initial values for the high-dimensional uncertain parameters in a FE model of a bolted structure. The scheme was developed by introducing a multidimensional analysis consisting of a systematic quasi-random sampling algorithm. The bolted structure used in this study was developed based on standard grade AISI 1020. The framework of this study includes systematic methods such as (1) identifying the measured dynamic behaviour of the components and the bolted structure using experimental modal analysis (EMA). The bolted structure was tested under deterministic and stochastic conditions. For the latter, the bolted structure was reassembled 100 times to evaluate the variability of the dynamic behaviour of the structure. Subsequently, (2) FE models of the structural components were developed and first updated using deterministic model updating (DMU), taking into account the experimental results, to minimise the uncertainties before reassembling them into the model of the bolted structure. Consequently, (3) FE models of the bolted structure were developed and an appropriate FE model was selected based on the EMA result counterpart. (4) The appropriate FE model was improved using multidimensional analysis by improving the poor correlation of the FE model with EMA, then the appropriate initial value of the high-dimensional uncertain parameters was extracted from the improved model. The SMU method based on the improved model was used to predict the variability of the dynamic behaviour of the structure. The accuracy of the predicted dynamic behaviour by the proposed scheme was evaluated from the EMA results and the high dimensional uncertain parameters in the bolted structure can be quantified. The comparison of the results between the updated dynamic behaviour of variability and EMA showed that the proposed scheme was highly able to improve the initial stochastic prediction of the bolted structure from 23.25 % to 1.5 % and 503.48 % to 9.69 % for mean and standard deviation respectively. The results show that the proposed scheme clearly highlights the ability of the SMU method to solve high-dimensional structural uncertainty problems, especially for bolted joints, which have rarely been reported before due to the difficulties in reducing dimensionality and identifiability uncertainties. In other words, the implementation of a multidimensional analysis to increase the knowledge of the uncertain parameters is undoubtedly necessary for the success of the SMU method. Moreover, the proposed scheme has demonstrated its ability to efficiently quantify the range of uncertainties in structural parameters. Finally, this study has a great impact on the engineering community by providing reliable analytical Big Data for the creation of intelligent prediction systems.