چكيده به لاتين
This thesis studies simultaneous vibration control and on-line system identification of structures. Modal parameters are estimated by means of blind source separation (BSS) methods which have been highly regarded by researchers. BSS procedures recover a set of independent sources from their unknown linear mixtures when only mixtures are observed. Batch data is required for the separation in traditional blind source separation methods. These algorithms are however unfavorable, as some sets of data are observed one after another. In this study, an adaptive blind source separation technique - equivariant adaptive separation via independence (EASI) - is introduced to overcome the mentioned disadvantage within the structures to extract modal matrix and modal coordinates. The EASI algorithm is beneficial as it can provide solutions to real time problems, while also update the modal matrix for each step. EASI not only avoids increases in size of the relevant matrices and vectors, but also decreases the analysis time. A synthetic example and a benchmark structure have been used in this study to better investigate the efficiency of the proposed method. The simulation results demonstrate the effectiveness of the EASI algorithm in on-line identification of modal parameters of structures. It should be noted that this algorithm is not able to estimate the modal parameters (natural frequencies and modal damping ratios) alone. Therefore, EASI-Teager method is proposed to be a combination of EASI and DESA-1 (discrete energy separation algorithm) algorithms. In the proposed approach, firstly, the EASI method is used to decompose structural responses into independent sources at each instance. Secondly, the TEO based demodulation method with discrete energy separation algorithm (DESA-1) is applied to each independent source, and the instantaneous frequencies and damping ratios are extracted. The DESA-1 method can provide the fast time response and has high resolution so it is suitable for online problems. This thesis also compares the performance of DESA-1 algorithm with Hilbert transform (HT) method. Compared to HT method, the DESA-1 method requires smaller amounts of samples to estimate and has a smaller computational complexity and faster adaption due to instantaneous characteristic. Furthermore, due to high resolution of the DESA-1 algorithm, it is very sensitive to noise and outliers. The effectiveness of the proposed approach has been validated using synthetic examples and a benchmark structure.
Despite the advantages of the EASI algorithm, it is encountered by some drawbacks. It uses a constant step-size parameter and needs to establish a tradeoff between the misadjustment in the steady-state and the convergence rate. So, the current study proposes a new variable step-size equivariant adaptive source separation via independence (VS-EASI) algorithm for online blind modal identification of structures. Unlike the traditional EASI algorithm, the proposed algorithm adaptively updates its step-size based on the input signals and the un-mixing matrix, through establishing a new function between the step-size and the separating indicator. This will lead to better performance of the proposed method and the fast convergence speed is reached while the steady-state error is low. Furthermore, this algorithm mitigates the irrelevant noise making it more suitable than the EASI algorithm for practical application. Simulation results of synthetic examples and a benchmark structure verify the superior convergence and better performance of the proposed algorithm in the steady-state over conventional EASI with fixed step-size in stationary environments as well as non-stationary ones.
All research on BSS has been conducted in structures without the presence of a control force. Because the presence of the control force in the structure disrupts the main condition for using blind resource separation methods. Therefore, in order to achieve the main goal of this thesis, which is to apply these methods to controlled structures and create smart structures, we are looking for a control method that can satisfy the conditions of blind resource separation methods. So that when the structure damaged under external forces such as earthquakes, we can detect the amount of damage without interrupting the control force and apply the appropriate and optimal control force to the structure.
The best way to handle this situation is through independent modal control. Thus, the proposed process consists of an online estimator of the blind resource separation type and a controller of the independent modal control method. When external excitations are applied to the structure, control forces are applied to control the structural vibrations; if damage occurs during the excitations to the structure, this estimator estimates new modal parameters and then these new parameters enter the control section and the controller gain matrix is updated to optimize the control forces.
