Algorithm 1. The proposed hierarchical sampling strategy under AL framework.

Input: a HC tree of $n$ unlabeled data samples; iteration step $n_s$ Process: 1:Repeat following steps until labeled samples are enough for high-quality soft sensing or all unlabeled samples are labeled. 2:Choose the node $v\in T$ with minimal value of probability $p_{v,c}^{LB}$, and replace node $v$ with its child nodes $v_p$ and $v_q$ if it satisfies ${\tilde{\epsilon }}_{v, c}>{\tilde{\epsilon }}_{v_p,c_p}+{\tilde{\epsilon }}_{v_q,c_q}$. 3:Choose one of the child nodes $z$ in the same way, until there are no child nodes, then an informative sample $x$ is selected. 4:Update $p_{u, c}^{LB}$ of all nodes $u\in T$. 5:Repeat step2 to step4 until $n_s$ unlabeled samples are selected. 6:Query the labels of $n_s$ selected data points, and then configure the selected dataset $x^s$. 7:Update the labeled dataset as $x_{new}^l\leftarrow [x^l+x^s]$, $y_{new}^l\leftarrow [y^l+y^s]$, the unlabeled dataset $x_{new}^u\leftarrow [x^u-x^s]$. Output: Newly labeled dataset $x_{new}^l\leftarrow [x^l+x^s]$, $y_{new}^l\leftarrow [y^l+y^s]$.