روشي نوين براي توليد شتاب‌نگاشت مصنوعي زلزله با استفاده از تبديل ويولت پاكت و شبكه‌‌هاي عصبي رگرسيون تعميم‌يافته

NEW METHOD FOR GENERATION OF ARTIFICIAL EARTHQUAKE ACCELEROGRAMS USING WAVELET PACKET TRANSFORM AND GENERALIZED REGRESSION NEURAL NETWORKS

براي طرح سازه‌‌هاي مقاوم در مقابل زلزله، يكي از مسايل و موارد مهم تحليل ديناميكي اين سازه‌ها براساس طيف طرح يا روش تاريخچه زماني است. با توجه به استفاده‌ي روز‌افزون از تحليل ديناميكي تاريخچه زماني براي محاسبه‌ي پاسخ سازه‌ها، توليد شتاب‌نگاشت‌‌هاي مصنوعيِ مناسب به‌علت كمبود ركورد‌هاي ثبت‌شده‌ي زلزله و نيز محدوديت و اشكالات موجود در آنها، امروزه امري ضروري به نظر مي‌رسد. در اين نوشتار با استفاده از توانايي يادگيري شبكه‌ي عصبي و همچنين با استفاده از تحليل وِيولِت به‌همراه الگوريتم بهترين پايه، روشي براي توليد شتاب‌نگاشت مصنوعي زلزله ارايه شده است. در روش پيشنهادي با استفاده از شبكه‌ي عصبي رگرسيون تعميم‌يافته ((GRNN اقدام به ساخت شبكه‌يي شده كه ورودي آن طيف پاسخ شبه سرعت، و خروجي آن ضرايب وِيولِت پاكت بهترين پايه‌ي شتاب‌نگاشت متناظر با آن است. در اين مدل با آموزش شبكه‌ي شتاب‌نگاشت‌‌هاي ثبت‌شده در ايران و طيف پاسخ آنها به‌كمك الگوريتم معرفي‌شده به‌روش معكوس با ارايه‌ي طيف پاسخ يا طيف طرح به شتاب‌نگاشت متناظر با آن دسترسي خواهيم يافت.

For earthquake resistant design of critical structures, a dynamic analysis, either response spectrum or time history, is frequently required. Owing to the lack of recorded data and the randomness of earthquake ground motion that may be experienced by structures in the future, it is usually difficult to obtain recorded data that fit the requirements well. Therefore, artificial seismic waves are widely used in seismic design, in verification of seismic capacity and in the seismic assessment of structures. The purpose of this paper is to develop a numerical method using generalized regression neural networks and the wavelet packet in the best basis method, which is presented for the computation of artificial earthquake records consistent with any arbitrarily specified target response spectra requirement. Earthquake ground motion has been modeled as a non-stationary process using a wavelet packet. In this study, a new neural-network-based methodology, with a wavelet packet best-basis transform, for the generation of artificial accelerograms from the pseudo-velocity response spectra, has been proposed. The wavelet packets can be used for numerous expansions of a given signal. The most suitable decomposition of a given signal, with respect to an entropy-based criterion, was selected. A single wavelet packet decomposition gives many bases, from which one can look for the best representation, with respect to a design objective. It can be done by using an entropy-based criterion to select the most suitable decomposition of a given signal. The best basis algorithm, described by Wickerhauser, uses a minimum entropy criterion and gives the most concise description for a signal for the dictionary in hand. This can be done by finding the "best tree" based on an entropy criterion. The best basis search algorithm uses wavelet packets in this approach; the signal is expressed as a linear combination of time-frequency atoms. The atoms are obtained by dilations of the analyzing functions, and are organized into dictionaries as wavelet packets. This method shows, by computation of the best-tree for given entropy, that the optimal wavelet packet tree is computed to balance the amount of compression and retained energy. By using this method, the results can be optimized. The presented method also uses the learning capabilities of neural networks to develop the knowledge of inverse mapping from response spectra to earthquake accelerogram. In the proposed method, the neural networks learn the inverse mapping directly from the actual recorded earthquake accelerograms and their response spectra. The proposed method is validated using Iranian earthquake accelerograms to train the neural networks. The trained neural network was tested with the earthquake accelerograms from both the training set and the novel cases from the test set. The generated accelerogram is plausible, with similar characteristics to those in the training set, and its response spectrum is very close to the input design spectrum. This is a useful property of the neural network based methodology; it will enable the generation of accelerograms compatible with any specified design spectra. The generated accelerograms can then be used in time history analysis of linear and nonlinear structures. Finally, with the proposed method, an artificial earthquake accelerogram, compatible with a single design spectrum, is generated. This study shows that the procedure, using the neural network-based model and wavelet packets in a best-basis method, is applicable for generating artificial earthquakes compatible with any response spectra.