In many engineering applications, missing data during system identification can hinder the performance of the identified model. In this paper, a novel two-stage nonparametric framework is proposed for missing data imputation, uncertainty quantification, and its integration in system identification with reduced computational complexity. The framework does not require functional forms for both the imputation model and the identified mathematical model. Moreover, through the construction of a single imputation model, analytical expressions of predictive distributions can be given for missing entries across all missingness patterns. Furthermore, analytical expressions of the expectation and variance of distribution are provided to impute missing values and quantify uncertainty, respectively. This uncertainty is incorporated into a single mathematical model by mitigating the influence of samples with imputations during training and testing. The framework is applied to three applications, including a simulated example and two real applications on structural health monitoring and seismic attenuation modeling. Results reveal a minimum reduction of 21% in root mean squared error values, compared to those achieved by directly removing incomplete samples.

中文翻译：

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用于缺失数据插补、不确定性量化和纳入系统识别的两阶段非参数框架


在许多工程应用中，系统识别过程中丢失数据可能会影响所识别模型的性能。本文提出了一种新颖的两阶段非参数框架，用于缺失数据插补、不确定性量化及其在系统识别中的集成，同时降低了计算复杂性。该框架不需要插补模型和已识别的数学模型的函数形式。此外，通过构建单个插补模型，可以针对所有缺失模式中的缺失条目给出预测分布的分析表达式。此外，提供了分布的期望和方差的解析表达式，以分别估算缺失值和量化不确定性。通过在训练和测试期间减轻样本的影响，将这种不确定性纳入单个数学模型中。该框架应用于三个应用，包括一个模拟示例和两个结构健康监测和地震衰减建模的实际应用。结果显示，与直接删除不完整样本相比，均方根误差值至少减少了 21%。