基于统计矩理论和贝叶斯方法的框架结构损伤识别方法研究

Damage identification method of frame structure based on statistical moment theory and Bayesian method

基于统计矩理论,以融合位移四阶统计矩和加速度八阶统计矩作为损伤指标,结合贝叶斯混合采样算法,提出了仅通过单次采样即可进行框架结构损伤识别的方法。该方法将标准MH算法和Gibbs算法相结合,以正交设计试验为基础研究单次采样的最佳时长。通过改进的位移四阶统计矩和加速度八阶统计矩损伤指标,快速识别模型结构损伤位置,然后结合贝叶斯MH-Gibbs混合采样算法基于模型分析快速识别结构损伤程度。建立12层标准框架结构数值模型,在信噪比40、30 dB条件下,针对不同损伤识别方法进行识别效果及效率研究对比。通过已有振动台试验对该识别方法进行验证,结果表明:改进的位移四阶统计矩和加速度八阶统计矩损伤指标相较于采用单一加速度八阶统计矩损伤指标识别效果更精准,根据正交设计试验得到的单次采样最佳时长避免贝叶斯方法多次采样的局限性,因此该方法在识别结构损伤时收敛快耗时短,识别精度高且只需一次采样即可对框架结构进行损伤诊断。

Based on the statistical moment theory, a method for damage identification of frame structures by only single sampling was proposed by fusing the fourth-order statistical moment of displacement and the eighth-order statistical moment of acceleration as damage indicators, combined with the Bayesian hybrid sampling algorithm. The method combined the standard MH algorithm and Gibbs algorithm, and investigated the optimal duration of single sampling based on orthogonal design of experiments. By improving the fourth-order statistical moment of displacement and the eighth-order statistical moment of acceleration damage indicators, the damage location of the model structure was quickly identified, and then the hybrid Bayesian MH-Gibbs sampling algorithm was combined with the model-based analysis to quickly identify the degree of structural damage. A numerical model of the 12-story standard frame structure was established, and the identification effect and efficiency were studied and compared with different damage identification methods under the conditions of signal-to-noise ratio of 40 dB and 30 dB. The results show that the improved fourth-order statistical moment of displacement and eighth-order statistical moment of acceleration damage indicators are more accurate than the single eighth-order statistical moment of acceleration, and the optimal duration of single sampling based on orthogonal design of tests avoid the limitation of multiple samplings by Bayesian method. Therefore, the method can be used for damage diagnosis of frame structures with only one sampling, characterized by quick convergence, less time and high precision.