Presenting a new method and X-index based on Choi-Williams distribution and matrix density methods to detect damage in concrete beams

One of the most critical issues in the field of construction, which has gained significant attention, particularly in the last two decades, is the monitoring of structural conditions. Over time, structures may experience damage to their components during use, which can worsen if not addressed. Various factors, such as the application of larger-than-expected forces, unfavorable environmental conditions, severe weathering, design flaws, impacts, fatigue, and corrosion, can cause damage to structures, leading to substantial changes in their dynamic properties. In this research, a new method, along with a novel damage index, is introduced for detecting damage in concrete beams. The method processes structural response signals using the ChoiWilliams time-frequency function. Then, damage is identified using the X-index, and its location is determined. To assess the proposed method, a reinforced concrete beam was constructed in the laboratory, and vibration tests were conducted under various damage scenarios. The results demonstrate that the proposed method not only detects the presence of damage but also accurately identifies its location and determines the damage's relative severity. In the proposed method, there is no need to develop an analytical model, measure the input force, or remove noise from the signals. Another advantage of this method is the relatively small number of sensors required.