تشخيص آسيب در تيرها با كمك اندازه‌گيري خيز استاتيكي و آزمون فرض‌آماري

Damage Detection in Beams Using Static Deflection measurements and Statistical Hypothesis Testing

تشخيص آسيب‌هاي ايجاد شده در اعضاي ساختماني از اهميت بسيار زيادي برخوردار است. در اين مقاله، روشي جديد براي تشخيص آسيب‌هاي رخ داده در تيرها، با كمك خيز تير در اثر اعمال بار استاتيكي، ارايه شده است. براي اين منظور، جابه‌جايي تير، تحت اثر بار استاتيكي تعيين شده و با كمك آزمون فرض‌آماري، محل آسيب رخ داده در تير مشخص شده است. گفتني است كه آزمون فرض آماري، جز روش‌هاي مناسب استنباط آماري بوده و مي‌تواند در مورد ادعاي مطروحه پيرامون يك قضيه، با بررسي حالات مختلف و محتمل، اظهارنظر كند. ادعاي آماري مورد استفاده در اين مقاله، وجود آسيب در يك المان از تير است كه اين ادعا با عنوان «فرض مقابل يا Alternative Hypothesis» در نظر گرفته مي‌شود. در پايان براي بررسي كارآيي روش پيشنهادي، سناريوهاي خرابي مختلفي مطالعه شده است. نتايج به دست آمده حاكي از آن است كه با روش پيشنهاد شده، مي‌توان محل آسيب در تير را با دقت بسيار زيادي تعيين كرد. هم چنين نتايج به دست آمده، بيانگر حساسيت بسيار كم روش پيشنهادي به وجود نوفه‌هاي اتفاقي است.

Building structures begin to deteriorate once they are built due to harsh environment such as earthquake. To inspect present buildings and bridges following major disastrous events, such as earthquakes and hurricanes is often time-consuming and of high expense. This is also the case in regular operating conditions. Indeed critical members and connections are hidden under cladding and other architectural surface covers. This study aims to propose a novel method for identification of damages occurred in beams based on deflection under static loading. In this paper damage location on a beam is determined using statistical hypothesis testing applied on the deflection of the beam. It is worth mentioning that the statistical hypothesis testing is an appropriate method for statistical inference which can be used to judge a claim concerning an event in regards to different scenarios and possibilities. The statistical claim which would be analyzed is that damage is present among elements of the beam. Deflection of beam as a derivation of stiffness will be utilized here. Hence the basic idea in this study; to locate damages, is behind of calculating the difference between measured and estimated deflection of nodes of each element in both intact and damaged structures. Elements damage can be specified by applying damage index which is defined as D(x). Element’s damages can be judged through the damage index sign in two nodes of every element: The element will be considered damaged if the index is positive for both nodes of middle element or it is positive in only one node of element leading edges of fulcrums. To illustrate the efficiency and robustness of proposed method three different examples are considered. First example is a simple beam with five different scenarios including single and multiple damages. Second example is also presented to show comparison of the proposed method with the study by Abdo [18] and finally third instant is considered for showing reliability of the method in different beam types. For all of the examples, the deflection of damaged beams is recorded via sensors under only one state of static loading and the statistical parameters of the undamaged beams are generated under several static loading. Then by calculation of damage index, we can decide about damage locations. All examples show good performance of the novel method in damage localization. The most important result obtained from these examples is that, the more fine mesh, the better and the more accurate performance of the method. Of course this assertion is more important in the elements leading edges of fulcrums. Further, the performance of this method is demonstrated through damage simulation where the measured data are contaminated with noise and hence to evaluate the stability of the proposed method against various noise levels, scenarios are considered with different such levels.