Real-life civil structures often stay in a grey situation due to lack of knowledge and measurements. In a poor information condition, classic Bayesian inference is practically difficult to perform owing to intractable likelihood functions. Under such circumstance, a structure should be defined as a grey system. Thereby, a grey Bayesian inference framework has been proposed by incorporating the grey theory with approximate Bayesian computation for damage assessment purposes. Structural parameters are represented by interval grey variables, whose grey kernels and degrees of greyness are used to define probability distributions for sampling. A grey population Monte Carlo sampler has also been developed by introducing interval grey numbers and an evolutionary particle pool into the particle filtering process. A novel particle interchange mechanism is simultaneously proposed for effective particle interflow. Meanwhile, stochastic response surfaces are used to correlate structural parameters with responses for fast response computation. Also, likelihood calculation is replaced with a distance measure between simulated and measured samples. Lastly, the proposed inference strategy has been verified against both the numerical and experimental beams having the different damage scenarios. The damage locations and severities were successfully identified by the changes in the grey intervals and kernels.

中文翻译：

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用于结构损伤评估的灰色贝叶斯推理框架

由于缺乏知识和衡量标准，现实生活中的土木结构经常处于灰色状态。在信息不佳的情况下，由于似然函数难以处理，经典的贝叶斯推理实际上难以执行。在这种情况下，结构应该被定义为灰色系统。因此，通过将灰色理论与近似贝叶斯计算相结合，提出了一种灰色贝叶斯推理框架，用于损伤评估。结构参数由区间灰度变量表示，其灰度内核和灰度等级用于定义采样的概率分布。通过在粒子过滤过程中引入区间灰度数和进化粒子池，还开发了一个灰色种群 Monte Carlo 采样器。同时提出了一种新的粒子交换机制，以实现有效的粒子互流。同时，随机响应面用于将结构参数与响应相关联，以进行快速响应计算。此外，似然计算被模拟和测量样本之间的距离测量所取代。最后，所提出的推理策略已经针对具有不同损伤场景的数值和实验梁进行了验证。通过灰度区间和内核的变化成功地识别出损伤位置和严重程度。似然计算被模拟和测量样本之间的距离测量所取代。最后，所提出的推理策略已经针对具有不同损伤场景的数值和实验梁进行了验证。通过灰度区间和内核的变化成功地识别出损伤位置和严重程度。似然计算被模拟和测量样本之间的距离测量所取代。最后，所提出的推理策略已经针对具有不同损伤场景的数值和实验梁进行了验证。通过灰度区间和内核的变化成功地识别出损伤位置和严重程度。