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the precision and recall of A2CNNS are also very similar to A2CNN7. This can be interpreted

as that there is little di

ﬀerence in the distribution between domain A and domain B.

Then, for the domain adaptation from A to C and from C to B, we only need to untie the

last two fully-connected hidden layers (i.e. A2CNN2) to achieve the same highest accuracy

as A2CNN7. However, the distribution di

ﬀerences between domains are not symmetrical. By

contrast, for the domain adaptation from C to A and from B to C, we have to respectively untie

the last six (i.e. A2CNN6) and four (i.e. A2CNN4) layers to achieve the almost best results.

85.00%

87.00%

89.00%

91.00%

93.00%

95.00%

97.00%

99.00%

A2CNNs

A2CNN1

A2CNN2

A2CNN3

A2CNN4

A2CNN5

A2CNN6

A2CNN7

A->B

A->C

B->A

B->C

C->A

C->B

Figure 3: The Parameter inﬂuence of the number of untied layers l on A2CNN.

4.6. Networks visualizations

Generally, deep learning is an empirical success rather than a mathematical solution to the

learning problem. In order to explain why the proposed A2CNN model can achieve such a great

performance in bearing fault diagnosis under varying working conditions vividly, the features

extracted by the MS and MT are visualized in this subsection.

t-Distributed Stochastic Neighbor Embedding

(t-SNE) is a technique for dimensionality re-

duction that is wildly used for the visualization of deep neural networks. The goal of t-SNE is to

take a set of points in a high-dimensional space and ﬁnd a faithful representation of those points

in a lower-dimensional space, typically the 2D plane. In this paper, t-SNE is used to visualize the

features extracted by A2CNN. For more details about t-SNE one can refer to Ref.[43].

Take the domain adaption task B → C as an example, t-SNE is used to visualize the high-

dimensional features extracted by the source feature extractor MS and the target feature extractor

MT . The result is shown in Figure4. In all subgraphs of Figure 4, features of the source sample

{xi

=1 are extracted by MS , i.e., MS (x

S )

=1. For the target sample, features extracted by MS

(i.e., MS (x

T )

=1) are shown in (a) and features extracted by the ﬁne-tuning MT after 1000 and

2000 iterations are shown in (b) and (c). For convenience, these features are denoted by MS (xS ),

MS (xT ) and M

T (xT ), where the number of iterations it is selected from

{1000, 2000}.

There are some interesting observations as follows.

1. MS (xS ), MS (xT ) and M

T (xT ) are classiﬁable when they are diagnosed separately.

This

illustrates that 1-D CNN used for MS and MT has a very strong ability to distinguish

various rolling bearing faults and explains the reason why A2CNNS can even achieve such

a good classiﬁcation accuracy.

2. In Figure4(a), the distribution of fault ’0.007

/IF’ is completely diﬀerent between domains.

This explains why A2CNNS has the very low recall of 1.13% when adapting from domain

B to C.

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