線性二次調節器(Linear-Quadratic Regulator, LQR)為結構振動控制常見的最佳化控制器之一，其透過最小化成本函數的權重矩陣來達成最佳控制。然而，用於LQR回饋運算的結構狀態，在實際應用中並無法直接量測，必須設計狀態估測器來提供狀態回饋給LQR進行控制。狀態估測器的設計方式往往取決於工程上的設計經驗，需要花費額外時間成本，在狀態回饋控制時亦需要額外的計算時間。此外，若狀態估測器性能不佳，會降低LQR的控制性能。在本研究中，以十層樓結構作為基準模型，應用生物共生演算法來最佳化LQR的權重矩陣得到狀態回饋增益後，使用機器學習的兩種類神經網路模型-多層感知器與帶有外源輸入的自回歸模型，以學習LQR控制器產生的控制力。進行數值模擬時以14組地震加速度進行結構受震之動力分析，以驗證回饋控制器的性能。結果顯示，類神經網路模型能夠直接根據結構加速度響應計算出與LQR相似的控制力，降低實務上使用狀態估測器實現最佳控制的依賴。最後，透過在實驗室進行振動台測試，對基於機器學習的控制方法進行了實驗驗證。實驗的結構試體配置了主動質量阻尼器以實現控制力，並以LQR控制器以及兩種類神經控制器進行多組地震的控制測試，透過實驗控制性能的比較過程中可得知，使用加速度回饋的類神經控制器和帶有卡爾曼濾波器的LQR控制器具有極度相似的控制效果。
此外，本研究提出以主動激振的方式，以主動設備對結構施力可得到各樓層的加速度反應，使用機器學習來取得兩者之間的反向關係，並且做為結構控制器。將此方法稱為主動激振法，其優點在於實務應用上無需對結構物進行系統識別，即可設計出控制器。在數值模擬時以頂層配置主動質量阻尼的10層樓結構模型進行地震測試，結果顯示經過適當調整的主動激振控制器，其結構加速度的控制效果與LQR相似。最後，以即時複合實驗技術對10層樓結構進行測試，並使用稱作主動慣質阻尼器的新型減震裝置，實現目標控制力，以驗證主動激振方法的耐震性能。實驗結果顯示，在降低結構加速度響應的程度上，主動激振法的控制性能與LQR相近。表示在不需事先對結構進行系統識別的情況下，主動激振法具有競爭優勢。後續研究將針對加速度計的不同安裝配置，並使用主動激振法之控制效果探討。

Linear-quadratic regulator (LQR) has been considered an optimal structural control approach which minimizes a cost function formulated by weighted states and control inputs. LQR control has been applied to active structural control which requires structural states as feedback signals; however, structural states may not be measurable in real application. As a result, state estimation is essential which inevitably takes additional computation time. Time delay and state estimate error could affect the control performance. In this study, two neural network models in machine learning have been applied to learn the control force generated from a LQR with weighting matrices optimized by applying symbiotic organisms search algorithm. The two models were a multilayer perceptron (MLP) model and an autoregressive with exogenous inputs (ARX) model. A 10-story building was adopted as a benchmark model for training and validation of the MLP and ARX models. Numerical simulation results demonstrate that the MLP and ARX models are able to emulate the LQR control force from the acceleration response directly, indicating that state estimation is not essential for optimal control implementation in real application. Finally, the two machine-learning based controllers were experimentally validated by conducting shake table testing in the laboratory in which the structural model is controlled by an active mass damper. Experimental results validate that the seismic control performance of the MLP and ARX models are particularly similar to that of the LQR with a Kalman filter.
In addition, an alternative machine learning approach which aims to learn the inverse relationship between the active control excitation to the structural acceleration responses. This approach is named as direct excitation method which can be implemented in a building without conducting system identification priorly in real application. Numerical simulation desmonstrates that the seismic control performance of direct excitation method with proper modification is similar with that of LQR. Finally, real-time hybrid simulation of the 10-story building are conducted to investigate the seismic control performance of direct excitation method using a novel active control device called active inerter damper. Experimental results desmonstrate that the control performance of direct excitation method is competitive with that of LQR regarding the mitigation of structural acceleration. Further studies will be focused on the optimization of direct excitation method with respect to various sensor location.

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