人工智慧已成為目前科技發展中不可或缺的議題，在工業發展中也導入許多
人工智慧的元素，如在半導體產線中導入神經網路做缺陷識別，以及在傳統石化產
業中運用神經網路對生產過程做預測及監控。然而在一般數據驅動的神經網路中，
數據透過向前傳遞以及倒傳遞不斷對預測值及真實值進行最小化誤差的工作，為
加強神經網路對未知數據預測的能力以及將數據背後之物理意義納入考慮，物理
信息神經網路(PINN)被提出。
物理信息神經網路將神經網路預測代入描述已知系統的微分方程式，在訓練
時加入微分方程的誤差，幫助加強神經網路在預測上的表現及外插能力，即為所謂
正演問題；如果系統方程的參數未知，也可以在訓練過程在進而辨識出系統產生，
是為反演問題。
本研究利用單軸主動磁浮軸承系統探討利用物理信息神經網路建立非線性閉
環系統數位分身及在閉環條件下辨識出系統參數，並以此作為系統監控的手法對
系統故障做辨識。物理信息神經網路可以閉環條件利用少數隨機設定調整激勵下
正確辨識參數，並可以辨識出，物理信息神經網路可辨識出正常數據及故障數據。

The study of artificial intelligence is now fundamental to the advancement of science
and technology. Numerous aspects of artificial intelligence have also been incorporated
into industrial development, such as the use of neural networks in traditional
petrochemical sectors and the integration of neural networks for defect detection into
semiconductor production lines. Plan ahead and keep an eye on the production process.
In contrast, a broad data-driven neural network uses forward and backward transmission
to constantly minimize the error between the prediction and the actual value. To improve
the neural network's capacity to forecast data and incorporate the physical law, physics
informed neural network (PINN) is proposed.
PINN incorporates the neural network's prediction into the differential equation
describing the known system, and incorporates the differential equation's error during
training to help strengthen the neural network's performance and extrapolation ability in
prediction, which is known as the forward problem; if the system equations' parameters
are unknown, the system can also be identified during the training procedure and it is
known as inverse problem.
In order to build a nonlinear closed-loop system digital twin, identify system
parameters under closed-loop conditions, and use this as a system monitoring tool to
identify system failures, this study uses a single-axis active magnetic bearing system.
Under closed-loop conditions, the physical information neural network may modify the
proper identification parameters using a limited number of random configurations and be
recognized. PINN shows ability to distinguish between normal and faulty input.

目錄
摘要 .................................................................................................................................. ii
Abstract ............................................................................................................................. ii
致謝 ................................................................................................................................. iv
目錄 .................................................................................................................................. v
圖目錄 ............................................................................................................................ vii
表目錄 ............................................................................................................................. ix
第一章 緒論 .................................................................................................................... 1
1.1 研究背景 ............................................................................................................ 1
1.2 物理信息神經網路 ............................................................................................ 2
1.3 懸浮式軸承系統 ................................................................................................ 3
1.4 研究動機 ............................................................................................................ 3
1.5 章節安排 ............................................................................................................ 4
第二章 物理信息神經網路之實驗案例 ........................................................................ 5
2.1 懸浮式軸承系統微分方程式 ............................................................................ 5
2.2 物理信息神經網路架構 .................................................................................... 6
2.3 龍格．庫塔法 .................................................................................................... 8
2.4 神經網路初始化 ................................................................................................ 9
第三章 閉環數據模擬 .................................................................................................. 11
3.1 單軸懸浮式軸承系統線性化 .......................................................................... 11
3.2 白噪音擾動結果 .............................................................................................. 16
3.3 比例積分微分控制器參數調整 ...................................................................... 19
3.4 單軸懸浮式軸承非線性模型 .......................................................................... 21
第四章 正演問題及反演問題 ...................................................................................... 27


vi

4.1 正演問題 .......................................................................................................... 27
4.2 反演問題 .......................................................................................................... 30
第五章 系統監控 .......................................................................................................... 32
5.1 監控數據 .......................................................................................................... 32
5.2 監控結果 .......................................................................................................... 38
第六章 結論 .................................................................................................................. 43
文獻參考 ........................................................................................................................ 44

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