پديد آورندگان :
پورقلي، مهران دانشگاه آزاد اسلامي - دانشكده فني، سراب، ايران , محمدزاده گيلارلو، محسن دانشگاه آزاد اسلامي - دانشكده فني، سراب، ايران , قنادي، مهين دانشگاه آزاد اسلامي - دانشكده فني، سراب، ايران
كليدواژه :
شناسائي سيستم , عدد شرطي , ماتريس هانكل , بعد سيستم مطلوب , نمودار پايداري
چكيده فارسي :
در روشهاي زيرفضاي تصادفي مهترين عامل تاثيرگذار بر مشخصات ديناميكي مستخرج، ابعاد ماتريس هانكل بوده كه شامل تعداد سطرها و ستون هاي آن است. استفاده از ابعاد كوچك ماتريس احتمال عدم شناسائي قطبهاي پايدار را داشته و انتخاب ابعاد بسيار بزرگ علاوه برآنكه احتمال بوجود آمدن قطبهاي مجازي و باياس را افزايش داده، باعث افزايش هزينه محاسباتي نيز ميگردد. از اينرو در اين تحقيق قصد براين است كه تعداد سطرهاي بلوكي و ستون هاي مطلوب ماتريس هانكل در روش زيرفضاي تصادفي متعادل طوري محاسبه شود كه ضمن پوشش قطبهاي موجود، هزينه محاسباتي حداقلي نيز داشته باشد. براي اين منظور از معيار عدد شرطي ماتريس هانكل و انديكاتور انرژي استفاده خواهد شد. مراحل كار بدين طريق است كه با استفاده از انديكاتور انرژي، حداكثر مرتبه موثر سيستم براي سطرهاي بلوكي مختلف ماتريس هانكل استخراج گرديده و سپس نمودار ماكزيمم عدد شرطي براي آنها رسم ميشود. تعداد سطرهاي بلوكي مطلوب ماتريس هانكل از همگرائي معيار عدد شرطي با توجه به تعريف اين معيار استخراج ميشود. به منظور صحتسنجي روش پيشنهادي، از نتايج آزمايش ارتعاش محيطي پل روگذر شهر نمين كه توسط محققين اين مقاله انجام گرفته، استفاده شده است. نتايج اين تحقيق نشان دهنده اين است كه از بُعد 352، نمودار عدد شرطي نسبت به تغيير سطرها بلوكي حساسيت خود را از دست داده كه بعنوان بعد مطلوب انتخاب شده است. همچنين در بعد بهينه با استفاده از تغييرات انحناي نمودار انديكاتور انرژي مرتبه 66 بعنوان مرز بد-شرطيدگي ماتريس سيستم، محاسبه گرديده كه پيدايش مودهاي باياس و محاسباتي در نمودار پايداري، مويد مرتبه محاسبه شده است
چكيده لاتين :
In stochastic subspace methods, the most important factor influencing the dynamic specifications is the dimensions of the Hankel matrix include the number of rows and columns. Using small matrix dimensions is unlikely to identify existing poles, and selecting very large dimensions not only increases the likelihood of virtual and bias poles but also increases computational costs. In this study, it is intended that the optimal dimensions of the Hankel matrix in the balanced stochastic subspace method be calculated in such a way that in addition to covering the existing poles, it also has a minimum computational cost. For this purpose, the condition number of the Hankel Matrix and Energy Indicator is used in two steps. The steps are as follows: First, calculate the optimal order of each cycle, and then use the optimal order to draw the condition number of the system matrix for different dimensions and calculate the desired dimension from its convergence. To verify the accuracy of the proposed method, the ambient vibration test of the Namin Entrance Bridge has been used. This bridge is located at the entrance of Namin city, 25 km from the center of Ardabil province, Iran, which includes two spans of 27.10m with a concrete deck. The deck of the bridge is located on beams with I sections, which are 2.5m away from each other, and the whole set of beams and deck is located on a system of foundations and piles with a diameter of 120cm. This bridge being the only entrance to the city and is exposed to various traffic loads, it was necessary to monitor the dynamic characteristics of the bridge as modal frequencies and damping ratios to evaluate the performance and ensure the health of the bridge structure. According to the numerical analysis and the length of the data (12000), the minimum order and the maximum number of cycles are 22 and 55, respectively. By diverging the curvature of the energy indicator graph, the optimal order is determined in the initial 5-12% of the singular values of cycles. For example, the maximum order of the 6th cycles was obtained, 28-62. Also, from the convergence of the maximum condition number of cycles from the 8th cycle, the optimal dimension was selected 352. In a general summary, it can be said that the use of the energy indicator concept in finding the effective order of the stability diagram has a significant effect on reducing the uncertainty of the extracted results. So that from the three identified stable poles, two poles have been extracted in the effective-order area. Also, using the concept of conditional number to find the optimal dimension of the system was effective, so that by drawing a stability diagram for the 15th cycle, it was found that the identified modal characteristics were not significantly different from the results of the optimal cycle (8th). Finally, the extracted modal properties have an acceptable agreement with the numerical model and frequency domain decomposition method (FDD). The modal frequencies of both methods (FDDand B-SSI) have a good correlation but the damping ratios were very different. In frequency domain methods the damping ratios being very sensitive to the quality of data collection, one can expect that the results of the subspace method are closer to reality
