Algorithm 1 General Procedure of the Proposed Method

Input: Given the bearing dataset composed of vibration signal samples, the architecture and hyper-parameters of the proposed CNN and the RF classifier Output: The diagnostic results, and the testing accuracy and efficiency Step 1: Generate the training dataset and the test dataset 1.1: Obtain the spectrums of $n$ vibration signal samples for training and $m$ samples for testing using the signal-to-image conversion method. 1.2: Use the spectrums to generate the training dataset $X_s$ and the test dataset $X_t$. Step 2: Construct and train the CNN for multi-level features extraction 2.1 Construct the CNN and initialize the parameters $\theta \left\{W,b\right\}$ (weight vectors and bias) of the CNN randomly. 2.2 Train the CNN on the training dataset $X_s$, calculate the outputs of layers in the CNN using Equations (1)–(4). 2.3 Calculate the outputs of the output layer and the loss function of softmax classifier using Equations (9) and (10). 2.4 Optimize the parameters $\theta \left\{W,b\right\}$ through minimizing the Equation (10) using the mini-batch stochastic gradient descent method. 2.5 Repeat (2.2)–(2.4) until meeting the training requirements, and finish the training process of the CNN. 2.6 Extract the features $x^2$, $x^4$, $x^5$ in layer S2, S4 and FC5 from the trained CNN, and $x^j$ donates the output feature map of $j$th level. Step 3: Use multi-level features to train multiple RF classifiers 3.1 Use the extracted features $x^2$, $x^4$, $x^5$ to train the classifiers RF1, RF2, RF3, respectively. 3.2 Output the diagnostic results of three RF classifiers separately. Step 4: Output the final result using the ensemble method Aggregate the outputs of three RF classifiers with the winner-take-all ensemble strategy to output the final diagnostic result. Step 5: Validate the performance of the proposed method Validate the performance of the proposed method on test dataset $X_t$ and output the testing accuracy and efficiency of the proposed method