SAE model for hydraulic pump fault diagnosis that used frequency features generated by Fourier

transform [11]. Liu et al. used the normalized spectrum generated by Short-time Fourier trans-

form (STFT) of sound signals as the input of a SAE model consisting of two layers. Moreover,

multi-domain statistical features including time domain features, frequency domain features and

time-frequency domain features were fed into the SAE model as a way of feature fusion [12, 13].

There are also some researchers focusing on deep belief network (DBN) [14, 15, 16]. Convolu-

tional neural networks (CNN) [17, 18] as one of the most popular deep learning networks, which

have been successfully used in image recognition, is also used to realize fault diagnosis of me-

chanical parts. Many CNN architectures were proposed, such as VGGNet [19], ResNet [20] and

Inception-v4 [21], for 2-D image recognition. Also, CNN models for 1-D vibration signal were

proposed. For example, 1D raw time vibration signals were used as the inputs of the CNN model

for motor fault detection in [22], which successfully avoided the time-consuming feature extrac-

tion process. Guo et al. [23] proposed a hierarchical CNN consisting of two functional layers,

where the first part is responsible for fault-type recognition and the other part is responsible for

fault-size evaluation.

Most of the above proposed methods are only applicable to the situation that the data used

to train classifier and the data for testing are under the same working condition, which means

that these proposed methods work well only under a common assumption: the labeled train-

ing data (source domain) and unlabeled testing data (target domain) are drawn from the same

distribution. However, many real recognitions of bearing faults show this assumption does not

hold, especially when the working condition varies. In this case, the labeled data obtained in one

working condition may not follow the same distribution in another di

fferent working condition in

real applications. When the distribution changes, most fault diagnosis models need to be rebuilt

from scratch using newly recollected labeled training data. However, it is very expensive, if not

impossible, to annotate huge amount of training data in the target domain to rebuild such new

model. Meanwhile, large amounts of labeled training data in the source domain have not been

fully utilized yet, which apparently waste huge resources and e

ffort. As one of the important

research directions of transfer learning, domain adaptation (DA) typically aims at minimizing

the di

fferences between distributions of different domains in order to minimize the cross-domain

prediction error by taking full advantage of information coming from both source and target

domains. Recently, DA has been introduced into the field of bearings fault diagnosis, such as

[24, 25, 26, 27]. For instance, Zhang et al. [26] took 1-D raw time vibration signal as the input of

the CNN model, which realize fault diagnosis under di

fferent working loads. The domain adap-

tation capacity of this model originates from the method named Adaptive Batch Normalization

(AdaBN). Lu et al. [25] integrated the maximum mean discrepancy (MMD) as the regularization

term into the objective function of DNN to reduce the di

fferences between distributions cross

domains.

In general, the main problem existing in domain adaptation is the divergence of distribution

between the source domain and the target domain. We need to learn a new feature representa-

tion, which should be fault-discriminative and simultaneously be domain-invariant. The fault-

discriminative ability refers that the learned feature representation should minimize the label

classifier error, i.e., has a good ability to identify di

fferent faults. The domain-invariant ability

means that the learned feature representation should maximize the domain classification loss for

all domains. That is to say, instances sampled from the source and target domains have similar

distributions in the learned feature space. As a result, a domain classifier cant distinguish whether

data come from the source domain or from the target domain.

In 2014, Goodfellow et al. [28] proposed Generative Adversarial Nets (GAN). GAN simul-

2