Algorithm 1: AL-DNN

Input: Labeled sensor dataset: $L=\{x_1,x_2,\mathrm{...},x_n\}$ Unlabeled sensor dataset: $U=\{x_{n+1},x_{n+2},\mathrm{...},x_{n+m}\}$ Parameters of DNN: the number of hidden layer n; learning rate $\lambda$ Iterations: ITER Number of chosen samples at the each iteration: k Output: The result of fault diagnosis Main step: Data preprocessing: data normalization by (Equation (6)) Pre-training (unsupervised): Use all samples in U to train a SDAE layer-by-layer, compute the weights of SDAE by minimizing the cost Function (Equation (10)): $W_{all}$, $b_{all}$ Use $W_{all}$ and $b_{all}$ to initialize DNN, Use labeled sensor dataset L to fine-tune DNN Obtain the overall parameters of trained DNN: ${\theta }^{*}$ Classify all unlabeled samples in U using the constructed DNN: $f(U)=Test(C,U)$ Initialization: $D_{test}$ = ∅ Active learning stage: For iteration = 1: ITER Compute the posterior probabilities of all unlabeled samples in U: post Select the samples having the lowest difference between the two highest values in post by (Equation (15)): $$x_{BvSB}=select\_BvSB(U)$$ Select the samples that will most probably show the false positive using (Equation (16)): $$x_{LFP}=select\_LFP(U)$$ Obtain k chosen samples $X_k=\{x_{s1},x_{s2}\mathrm{...}{x}_{sk}\}$ from U by the combination of two criteria: $$X_k=x_{BvSB}\cup x_{LFP}$$ Ask an expert to label the sensor dataset $X_{\mathrm{k}}$: $label(X_k)$ Update the unlabeled sensor dataset: $U\leftarrow U-X_k$ Augment the active training set: $D_{test}\leftarrow D_{test}\cup X_k$ Update the weights of DNN by fine-tuning using $D_{test}$ End