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The vibration signals for offshore wind-turbine high-speed bearings are often contaminated with noises due to complex environmental and structural loads, which increase the difficulty of fault detection and diagnosis. In view of this problem, we propose a fault-diagnosis strategy with good noise immunity in this paper by integrating the two-dimensional convolutional neural network (2DCNN) with random forest (RF), which is supposed to utilize both CNN's automatic feature-extraction capability and the robust discrimination performance of RF classifiers. More specifically, the raw 1D time-domain bearing-vibration signals are transformed into 2D grayscale images at first, which are then fed to the 2DCNN-RF model for fault diagnosis. At the same time, three procedures, including exponential linear unit (ELU), batch normalization (BN), and dropout, are introduced in the model to improve feature-extraction performance and the noise immune capability. In addition, when the 2DCNN feature extractor is trained, the obtained feature vectors are passed to the RF classifier to improve the classification accuracy and generalization ability of the model. The experimental results show that the diagnostic accuracy of the 2DCNN-RF model could achieve 99.548% on the CWRU high-speed bearing dataset, which outperforms the standard CNN and other standard machine-learning and deep-learning algorithms. Furthermore, when the vibration signals are polluted with noises, the 2DCNN-RF model, without retraining the model or any denoising process, still achieves satisfying performance with higher accuracy than the other methods. [ABSTRACT FROM AUTHOR]