شناسايي فركانس‌هاي طبيعي بر‌ پايه تبديل ارتقا يافته هيلبرت- هوآنگ

Identification of Natural Frequencies Based on a New Enhanced Hilbert-Huang Transform

در مقاله حاضر، بر‌اساس تبديل ارتقا يافته هيلبرت- هوآنگ كه به‌تازگي به‌وسيله مولفان توسعه يافته، روشي خروجي-تنها براي شناسايي فركانس‌هاي طبيعي سازه‌هاي چند درجه آزاد پيشنهاد شده است. در روش پيشنهادي، با تحليل پاسخ سازه به‌وسيله تبديل ارتقا يافته هيلبرت- هوآنگ، يك طيف دامنه- فركانس موسوم به «طيف حاشيه‌اي ميانگين» براي سازه فراهم مي‌شود كه به‌وسيله آن فركانس‌هاي طبيعي سيستم سازه‌اي شناسايي مي‌شوند. براي ارزيابي كارايي روش شناسايي پيشنهادي، شتاب‌نگاشت‌هاي حاصل از آزمايش ارتعاش محيطي انجام گرفته روي يك پل و يك ساختمان در قالب دو مطالعه موردي تحليل شده‌اند كه در آن‌ها شش فركانس اول پل در جهت قايم و سه فركانس اول ساختمان در سه جهت شرق- غرب، شمال- جنوب و پيچشي شناسايي شده‌اند. با توجه به‌سادگي روش پيشنهادي و تطابق نتايج حاصل از آن با ديگر روش‌هاي معتبر شناسايي سيستم، زمينه كابرد آن به‌عنوان ابزاري كارامد در شناسايي سيستم‌هاي سازه‌اي فراهم است.

Hilbert-Huang transform (HHT) consists of two main parts: (1) empirical mode decomposition (EMD) to extract intrinsic mode functions (IMFs) and (2) Hilbert spectral analysis to obtain time-frequency characteristics of the IMFs through the Hilbert transform. Recently, a new enhanced HHT is proposed by the authors in which, two mathematical limitations that restrict the application of the Hilbert transform are circumvented and also an additional smoothing parameter is applied to decrease noise effects on the results. In this paper based on the HHT approach, a simple method for output-only identification of natural frequencies of linear structures is proposed in which HHT or enhanced HHT can be employed. In the proposed method, ambient response data measured at all degrees of freedom of the structure are used to obtain an averaged marginal spectrum. The averaged marginal spectrum is used for identifying the natural frequencies of the structure. In order to validate the effectiveness of the proposed identification method, ambient response data of an arch bridge and a 15-story building are examined. In the first case, the first six natural frequencies of the bridge in vertical direction are extracted. And in the second case, the first three natural frequencies of the building in East-West, North-South and torsional directions are identified. From the results, first, it is found that the enhanced HHT by employing the smoothing parameter is more efficient than the HHT in increasing the readability of the time-frequency-amplitude spectrum and also is capable to provide more accurate amplitude-frequency distribution; second, by comparing results of the proposed method with those obtained from other valid methods, it is concluded that the proposed identification method by using the enhanced HHT is accurately able to estimate the natural frequencies of structures. Regarding to simplicity of the proposed method, it can be applied as an efficient tool for identification of structures or employed to extract changes in frequencies due to occurrences of damages during strong ground motions.