自迴歸時間序列與貝氏分類法於結構物健康診斷之應用

Structural Health Monitoring by AR-ARX Time Series Analysis with Bayesian Classification

林偉淞(Wei-Sung Lin)

指導教授 ： 張國鎮

國立臺灣大學/工學院/土木工程學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.01739

摘要

有別於傳統的結構物健康診斷方法，皆須耗費許多時間與人力進行診斷結果分析與判斷。本研究主要目的，著眼於為未來開發的新一代結構物健康診斷方法，進行診斷理論方法初步的可行性驗證。以期本研究能成功適用於實際結構物健康診斷中，並以統計理論的機率運算為基礎簡易呈現最有可能之結構物破壞類別，免除需大量人力與時間投入分析與判斷。本研究乃是以結構物日常條件下微震動反應的量測紀錄為診斷原始資料，同時採用AR-ARX自迴歸時間序列作為結構物破壞情狀表徵之『結構物特徵時間序列』，運算理論則是引進生物資訊領域中應用於診斷細胞癌症基因的『貝氏分類診斷邏輯方法』作為結構物破壞類別的分類工具。

『貝氏分類診斷邏輯方法』即所謂圖像識別概念之結構物健康診斷方法，藉由瞭解已知結構物破壞情況的資料樣本係數機率密度分佈函數模型，推斷當前處於未知破壞情況條件下量測的結構物動力反應記錄最有可能的損傷程度。本研究診斷系統的理論驗證方法，以重複樣本空間與非重複樣本空間兩種比對手段，前者由於比對與被比對樣本空間是完全相同，故可作為檢驗『結構物特徵時間序列』在不同的破壞種類是否具差異性，亦即序列資料對該破壞情況具代表性；後者由於比對與被比對樣本空間是完全相異，故可模擬本研究結構健康診斷方法於實際應用上的診斷情況。而驗證步驟，則是最初以有限元素程式模擬結構物發生破壞的情況，再輸出分析得到的結構數值反應資料進行健康診斷分析。緊接著，著手進行結構物夜間微震動與震動台實驗，以真實量測得到的結構反應資料再次進行健康診斷分析，藉此瞭解現實環境中雜訊或其他不可預期因素對本研究理論方法診斷結果的影響程度。最後階段則是以貝氏分類法的最佳化理論，輔以兩階段聯集每一筆資料的診斷結果，藉以提升本研究方法的診斷準確性。

關鍵字

結構物健康診斷 ； AR-ARX結構物特徵時間序列 ； 貝氏機率理論

並列摘要

For the research interest on this thesis, preliminary feasibility study on the application of the purposed Structure Health Monitoring (SHM) diagnosis algorithm on detecting structural damage was carried out. The fundamental theory of this applied SHM diagnosis algorithm, Bayesian Classification, was developed based on the mathematical theory of Probability and Statistics. Hence, the diagnosis results can be indicated as what sort of damage level the structure most likely suffered instead of pointing out the real damage symptoms or reasons.

This purposed SHM diagonal prototype system involves the contents including the structural health presentation techniques of AR-ARX Time Series, DNA Array comparison concept originated from bioinformation science, and the mainly integrated and computational diagnosis theory of the purposed system, the Bayesian Classification Algorithm, which is commonly used to deal with the data stream classification or digital image pattern recognition problems on the region of computer and information science. Accordingly, the integrated diagnosis procedure of this developed algorithm theory can be applied in the future to providing the near real time SHM automatically with only one electronic microprocessor set installed in-situ. Moreover, the principle diagnosis philosophy of Bayesian Classification Theory is totally relied on the comparison procedure of the measured structural intact and damaged response data in AR-ARX time series format under the day night ambient vibration condition, then the evaluation report will finally come out by choosing the one which is representing the most probably damage situation of the existing structure and simultaneously which is equivalent meaning to corresponding to the highest damage occurrence probability score among several presumed damage cases.

Hereafter on this thesis, the phrase of pattern recognition SHM diagnosis is named after the property of comparing intact and damage AR-ARX structural response time series through the Bayesian Classification Algorithm. For the research methodology of theory feasibility, two examination processes – Independent and Dependent Sample Classification – and three verification stages – numerical simulation, experiment verification, union optimization – must to be checked in order to prove whether the Bayesian diagnosis algorithm can successfully detect the exact damage situation of existing structures. On the other hand, conducting the examination processes of independent and dependent sample classification on every stage can primarily, respectively, verify the theory feasibility of algorithm and the significance or discrimination degree of collected data for each damage case. Moreover, as the three verification stages arranged is aimed to gradually include the uncertainty of environment effects involved as well as to optimize the structural health diagnosis precision and accuracy by means of likelihood selection and union optimization concept.

At the end, the contribution of this thesis can provide sufficient sound evidences to prove that this purposed SHM system is not only theoretical feasibility on detecting the existing structural damage situation under the day night ambient condition, but also providing the new SHM alternatives with high diagnosis precision and accuracy, otherwise, which can totally eliminate the labor effort and objective human judgment involved at analysis step unlike the traditional methods.

並列關鍵字

Structural Health Monitoring ； AR-ARX Time Series ； Bayesian Theory

參考文獻

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3. Christopher Chatfield, “The Analysis of Time Series: An Introduction”, 3rd Edition, Chapman and Hall, New York (1984).

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6. S.W. Doebling, “Damage Detection and Modal Refinement Using Elemental Stiffness Perturbations with Constrained Connectivity”, Proceedings of AIAA/ASME/AHS Adaptive Structure Forum, AIAA-96-1307, pp. 360-370. (1996).