Inferring unknown unknowns: Regularized bias-aware ensemble Kalman filter
Inferring unknown unknowns: Regularized bias-aware ensemble Kalman filter
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DOI：
10.1016/j.cma.2023.116502
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发表时间：
2023-06
影响因子：
7.2
通讯作者：
Andrea N'ovoa;A. Racca;L. Magri
中科院分区：
文献类型：
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作者：
Andrea N'ovoa;A. Racca;L. Magri
由于物理假设和数值近似，低阶模型会受到状态和参数的不确定性以及模型偏差的影响。模型偏差，也称为模型误差或系统误差，很难推断，因为它们是“未知的未知数”，即我们不一定知道它们的先验函数形式。对于有偏差的模型，数据同化方法可能是不适定的，因为（i）它们是“偏差无意识的”，因为估计量被假设为无偏差，（ii）它们依赖于偏差的先验参数模型，或者（iii）它们可以推断出对于相同模型和数据来说不是唯一的模型偏差。首先，我们设计一个数据同化框架来执行组合状态、参数和偏差估计。其次，我们提出了一种采用顺序方法的数学解决方案，即正则化偏差感知集成卡尔曼滤波器（r-EnKF），它需要偏差及其梯度（即雅可比行列式）的模型。第三，我们提出一个回声状态网络作为模型偏差估计器。我们推导了网络的雅可比行列式，并设计了具有数据增强的鲁棒训练策略，以准确推断不同场景中的偏差。第四，我们将 r-EnKF 应用于受不同形式偏置影响的非线性耦合振荡器（有或没有时滞）。 r-EnKF 推断实时参数和状态，以及独特的偏差。我们展示的应用与声学、热声学和振动相关；然而，r-EnKF 为非线性系统中实时和动态预测的组合状态、参数和偏差估计开辟了新的机会。
Because of physical assumptions and numerical approximations, low-order models are affected by uncertainties in the state and parameters, and by model biases. Model biases, also known as model errors or systematic errors, are difficult to infer because they are ‘unknown unknowns’, i.e., we do not necessarily know their functional forma priori. With biased models, data assimilation methods may be ill-posed because either (i) they are ‘bias-unaware’ because the estimators are assumed unbiased, (ii) they rely on ana prioriparametric model for the bias, or (iii) they can infer model biases that are not unique for the same model and data. First, we design a data assimilation framework to perform combined state, parameter, and bias estimation. Second, we propose a mathematical solution with a sequential method, i.e., theregularized bias-aware ensemble Kalman Filter(r-EnKF), which requires a model of the bias and its gradient (i.e., the Jacobian). Third, we propose an echo state network as the model bias estimator. We derive the Jacobian of the network, and design a robust training strategy with data augmentation to accurately infer the bias in different scenarios. Fourth, we apply the r-EnKF to nonlinearly coupled oscillators (with and without time-delay) affected by different forms of bias. The r-EnKF infers in real-time parameters and states, and a unique bias. The applications that we showcase are relevant to acoustics, thermoacoustics, and vibrations; however, the r-EnKF opens new opportunities for combined state, parameter and bias estimation for real-time and on-the-fly prediction in nonlinear systems.