Rolling element bearings are important components in the modern rotating machineries [1] . The real-time knowledge about the health status of rotating machines and their components, can help avoid accidents and offer obvious economic benefits to manufacturers [2] . Therefore, fault detection and diagnosis of rolling element bearings is a significant task and of considerable interest in the industry [3] [4] . Majority of the research in the last decade has focused on developing machine learning algorithms for intelligent fault diagnosis [5] . Despite their achievements, the practical industrial implementation of these algorithms has been limited [6] [7] as their performance is influenced by the availability of massive labelled data.
In practice, the rotating machines operate in varying conditions of load and speed. Therefore, the machine learning algorithms trained on data sets from one working condition, i.e. the source domain, may not generalize well on the data sets collected from a different set of working conditions, i.e. the target domain, even for the exact same machine. This happens due to the shift in data distributions of source and target domain and is commonly referred to as domain shift phenomenon [8] . One intuitive solution to this problem is the collection of data from many possible working conditions. However, this is not feasible because, (1) in general, bearings operate in healthy working conditions and capturing data from fault occurrences is difficult in industrial environments; (2) the type of faults that occur are usually unknown during operation. Also, it must be realized that, it is impractical to stop machines frequently in manufacturing environments for health inspection or data collection purposes. Thus, most of the collected data is unlabelled, and it is therefore challenging to train a reliable intelligent model for fault diagnosis.
Rolling element bearings are important components in the modern rotating machineries [1] . The real-time knowledge about the health status of rotating machines and their components, can help avoid accidents and offer obvious economic benefits to manufacturers [2] . Therefore, fault detection and diagnosis of rolling element bearings is a significant task and of considerable interest in the industry [3] [4] . Majority of the research in the last decade has focused on developing machine learning algorithms for intelligent fault diagnosis [5] . Despite their achievements, the practical industrial implementation of these algorithms has been limited [6] [7] as their performance is influenced by the availability of massive labelled data.
In practice, the rotating machines operate in varying conditions of load and speed. Therefore, the machine learning algorithms trained on data sets from one working condition, i.e. the source domain, may not generalize well on the data sets collected from a different set of working conditions, i.e. the target domain, even for the exact same machine. This happens due to the shift in data distributions of source and target domain and is commonly referred to as domain shift phenomenon [8] . One intuitive solution to this problem is the collection of data from many possible working conditions. However, this is not feasible because, (1) in general, bearings operate in healthy working conditions and capturing data from fault occurrences is difficult in industrial environments; (2) the type of faults that occur are usually unknown during operation. Also, it must be realized that, it is impractical to stop machines frequently in manufacturing environments for health inspection or data collection purposes. Thus, most of the collected data is unlabelled, and it is therefore challenging to train a reliable intelligent model for fault diagnosis. 
Rolling element bearings are important components in the modern rotating machineries [1] . The real-time knowledge about the health status of rotating machines and their components, can help avoid accidents and offer obvious economic benefits to manufacturers [2] . Therefore, fault detection and diagnosis of rolling element bearings is a significant task and of considerable interest in the industry [3] [4] . Majority of the research in the last decade has focused on developing machine learning algorithms for intelligent fault diagnosis [5] . Despite their achievements, the practical industrial implementation of these algorithms has been limited [6] [7] as their performance is influenced by the availability of massive labelled data.
In practice, the rotating machines operate in varying conditions of load and speed. Therefore, the machine learning algorithms trained on data sets from one working condition, i.e. the source domain, may not generalize well on the data sets collected from a different set of working conditions, i.e. the target domain, even for the exact same machine. This happens due to the shift in data distributions of source and target domain and is commonly referred to as domain shift phenomenon [8] . One intuitive solution to this problem is the collection of data from many possible working conditions. However, this is not feasible because, (1) in general, bearings operate in healthy working conditions and capturing data from fault occurrences is difficult in industrial environments; (2) the type of faults that occur are usually unknown during operation. Also, it must be realized that, it is impractical to stop machines frequently in manufacturing environments for health inspection or data collection purposes. Thus, most of the collected data is unlabelled, and it is therefore challenging to train a reliable intelligent model for fault diagnosis. 
In the recent years, the intelligent data-driven fault diagnosis methods on the rotating machines have been popularly developed. Especially, deep learning algorithms have been adopted in several studies and promising results have been obtained. However, the cross-domain fault diagnostic problem still remains a challenging issue, where the training and testing data are collected from different operating conditions of the machine. To bridge the domain gap in the training and testing data and increase the model generalization ability, a domain adaptation approach is proposed in this paper within the deep learning framework. Multiple convolutional operations are employed for automatic feature extraction. The maximum mean discrepancy is used to optimize the distributions of the learned features for accurate diagnosis. To further enhance the model generalization ability, the health condition labels of the data are injected with additional noise during model training. Experiments on a bearing fault diagnosis dataset are carried out for validation. The results show that, compared with the popular transfer learning algorithms, the proposed method with noisy health labels can successfully improve the cross-domain diagnosis performance on rotating machines.
Rolling element bearings are important components in the modern rotating machineries [1] . The real-time knowledge about the health status of rotating machines and their components, can help avoid accidents and offer obvious economic benefits to manufacturers [2] . Therefore, fault detection and diagnosis of rolling element bearings is a significant task and of considerable interest in the industry [3] [4] . Majority of the research in the last decade has focused on developing machine learning algorithms for intelligent fault diagnosis [5] . Despite their achievements, the practical industrial implementation of these algorithms has been limited [6] [7] as their performance is influenced by the availability of massive labelled data.
In practice, the rotating machines operate in varying conditions of load and speed. Therefore, the machine learning algorithms trained on data sets from one working condition, i.e. the source domain, may not generalize well on the data sets collected from a different set of working conditions, i.e. the target domain, even for the exact same machine. This happens due to the shift in data distributions of source and target domain and is commonly referred to as domain shift phenomenon [8] .
One intuitive solution to this problem is the collection of data from many possible working conditions. However, this is not feasible because, (1) in general, bearings operate in healthy working conditions and capturing data from fault occurrences is difficult in industrial environments; (2) the type of faults that occur are usually unknown during operation. Also, it must be realized that, it is impractical to stop machines frequently in manufacturing environments for health inspection or data collection purposes. Thus, most of the collected data is unlabelled, and it is therefore challenging to train a reliable intelligent model for fault diagnosis.
48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to COVID- 19) In the recent years, research attention has shifted to the development of deep learning-based cross domain adaptation methods, which offer a promising solution to address the domain shift problem. Basically, the target domain data is related to the source domain data in terms of knowledge/characteristics but differs in terms of the domain shift in the distribution. Therefore, the fundamental idea in these methods is to draw the source and target domain distributions close to each other using a distribution discrepancy measure. The concept of the domain adaptation method is presented in Fig. 1 ., where the shared features are expected to be learned from different domains, to perform accurate diagnosis. In this way, the learned knowledge from the source domain can be generalized to the target domain. [10] proposed to simultaneously minimize the distance of intra-class variations and maximize the distance of inter-class variations, through the learned representations of multiple hidden layers of a CNN, for bearing fault diagnosis. Kim et al. [11] implemented the concept of selective parameter freezing, wherein only a portion of model parameters are frozen, and remaining parameters within a layer are fine tuned to avoid overfitting to a small number of target data samples. Yang et. al. [12] proposed a feature-based transfer neural network, to extract transferable features of raw vibration data, and then reduced the distribution discrepancy between class distance of the learned transferable features.
While many studies have been carried out in the cross-domain fault diagnosis topic, this problem remains challenging due to the significant distribution discrepancy between training and testing data in the practical cases. Therefore, in order to further enhance the model generalization ability in different operating conditions of the rotating machines, a novel algorithm is proposed in the deep learning-based fault diagnosis framework. The machine health condition labels are injected with additional noise during model training, rather than using the popular one-hot vectors, as found in most existing studies. Experiments on a real-world machine fault diagnosis dataset are carried out for validation. The results indicate that the proposed method is well suited for the crossdomain fault diagnosis task, and improvements in the testing accuracy can be achieved with the proposed noisy label algorithm. The remainder of this paper starts with the proposed methodology in Section 2. The details related to the experimental data set are provided in Section 3. The experimental results and benchmarking with other methods, are presented in Section 4. We close this paper with conclusions in Section 5.
In recent years, neural networks have been gaining increasing attention for machinery health assessment and fault diagnosis [17] . Convolutional neural networks (CNN) have achieved remarkable merits in various domains, mainly due to their distinguishing characteristics, such as shared network weights and spatial subsampling. The architectural framework of CNN used in this study is depicted in Fig. 2 . In general, the architecture mainly consists of three layers: 1) convolutional layer; 2) pooling layer and 3) fully connected (FC) layer. The convolutional layer contains a number of filters which are convolved with the raw data. The idea behind using a number of filters is that, different filters would detect/identify a different set of features when convolved with the input data.
In this study, a 1D-CNN architecture is used for fault diagnosis. Initially, all the raw input training data is arranged in a two-dimensional (2D) format, with its dimension in the form of Ns x Ndim, where Ns is the number of samples and Ndim is the sample dimension. With respect to each sample, the data dimension is, thus, Ndim. There are three stacked 1-D convolutional layers in the network, for feature extraction purpose, that have the same configuration, which involves NF filters with size LF. As the number and size of each filter in each layer of the network significantly affects the network performance, the filter number is kept as 50 and the filter length is also selected as 50 in this research work. These hyperparameters gave the most optimum results after running multiple experiments, while fine-tuning the network. During convolution, zero-padding operation is used to prevent changes At the end, a softmax classifier with ten neurons, representing the ten health classes respectively, is used, to predict the fault condition class. The leaky ReLU (rectified linear units) [18] is used as the activation function in the network, as it does not undergo gradient diffusion or vanishing during network training process and provides better performance in deep architectures. In each layer, the Xavier kernel initializer is used for initialization of weights and biases [19] and Adam algorithm [20] is adopted for network optimization. The parameters defining each layer in the proposed network architecture have been presented in Table 1 . It should be pointed out that, the network model automatically learns useful features for fault diagnosis, instead of manually designing features as the conventional signal processing methods. 
In domain adaptation tasks, the most important concern is to minimize the difference between source and target domain distributions using a reliable discrepancy measure. In this paper, maximum mean discrepancy (MMD) is used to evaluate the domain discrepancy between labelled source domain samples and unlabelled target domain samples [21] . Specifically, MMD is the squared value of distance between kernel embeddings of marginal probability distributions in the reproducing kernel Hilbert space (RKHS) [22] . As shown in Equation (1), it can be mathematically expressed as follows:
where S and T denote the data distributions of source and target domains respectively, and ℋ represents the reproducing kernel Hilbert space. The choice of kernel significantly influences the process of MMD computation as stated in [23] . Hence, in order to utilize the power of multiple kernels and design a principled approach for efficient kernel selection, a mixture of 5 radial basis function (RBF) kernels is used in this study, whose bandwidth parameters are 1, 2, 4, 8 and 16.
In this study, a novel algorithm is proposed to further enhance the model generalization ability in the proposed deep domain adaptation framework. Specifically, the machinery health condition labels are injected with additional noise to serve as regularizations.
Usually, the one-hot vector is used as the class labels in the deep learning-based classification studies. In each training epoch, with respect to each labelled training sample, a random noise number ny is generated, which is uniformly selected from [0, nrange]. nrange denotes the noise level used in the experiments, which is a pre-determined value. Afterwards, the one-hot class label of the sample is injected with additional noise of ny. The true class element is subtracted by ny, and the other elements increase correspondingly to make sure the sum is still one.
For example, let [0, 1, 0, 0, …, 0] be the one-hot label of the sample, where Nc classes are considered. After injection of noise ny, the noisy label is thus [ny/(Nc -1), 1-ny, ny/(Nc -1), ny/(Nc -1), …, ny/(Nc -1)]. Therefore, the noisy label is still represented in a similar way as the traditional one-hot vector labels for the softmax function. A schematic illustration of this concept is shown in Fig. 3 . 
This study follows the basic assumptions as stated below: • The number and type of health labels are same in both the source domain and target domain. • In the model training phase, labeled samples are available from source domain, however only unlabeled samples are available from target domain. The basic expectation of a CNN architecture is to ensure precise classification. Hence, it uses an objective function to minimize the classification error on the source domain labelled data during the training phase. For achieving this objective, the cross-entropy loss function ℒc is adopted in this case [24] .
In addition, for decreasing the distribution discrepancy between the source and target domain, single-layer maximum mean discrepancy (MMD) between output of the fully connected layer for source and target samples, is considered as an optimization objective [14] . The multi-kernel MMD loss function, can be mathematically represented using Equation (2) as:
where, S f and T f , denote the source and target domain representations in the last fully connected layer of the network, K denotes the set of kernel filters 'k' used, and MMDk (S f ,T f ) is the MMD loss computed between the learned feature representation of the two domains. Hence, the overall objective function by combining the cross-entropy loss with the MMD loss mentioned above, is represented using Equation (3) as:
where β represents penalty co-efficient, whose value is set to 1 in this study for simplicity.
To validate the proposed methodology, vibration data from the Bearing Data Centre of Case Western Reserve University (CWRU) has been considered for this study. The test rig is shown in Fig. 4 . The vibration data recorded from two motor loads of 0 and 3 HP, corresponding to motor speeds of 1797 and 1730 RPM, is considered respectively. Three kinds of machine faults are implemented, i.e. inner race fault (IRF), ball fault (BF) and outer race fault (ORF). The faults ranging in diameter of 0.007, 0.014 and 0.021 inch, were seeded on the drive-end (DE) bearings (SKF deep-groove ball bearings: 6205-2RS JEM) of the motor at different locations. Therefore, a total number of 10 health conditions are considered in this paper. For the ease of classification, these 10 health classes with different locations of faults (IRF, BF and ORF) and different fault severities (0.007", 0.014" and 0.021") are set as class labels 1 to 10 respectively. Table 2 represents the details of the transfer tasks considered for analysis in this study. Nsource and Ntarget represent the respective source and target domain samples for each health condition under one speed. For simplicity, Nsource is kept equal to Ntarget in this study. The dimension of the prepared samples with sequential acceleration data is denoted using Ndim. Each transfer task consists of 10 health conditions (1 healthy and 9 faulty). Since the CWRU data is relatively clean with less noise, it is easy to perform fault diagnosis on this dataset, as shown in the literature. To evaluate the model performance in noisy environments, additional noise is added to the raw vibration data to simulate the noisy environments. Specifically, the signal-to-noise ratio (SNR), is adopted in this study as shown in Table 2 . The default parameters used in this paper are presented in Table 3 , which are determined based on the performance on the same-domain validation set. The selected parameters such as filter number equal to 50, achieve the optimal accuracies on the fault diagnosis problem. Therefore, they are used as the default values. All the experiments on the network are implemented in Python using TensorFlow, on a CPU-based device. Nsource 100
Ntarget 100
Ndim 500
To validate the reliability, effectiveness and robustness of the proposed method, a comparison with different approaches is conducted with the following methods:
Traditional machine learning algorithms: k-nearest neighbor (k-NN) and Support vector machines (SVM) methods are popularly used for unsupervised learning. The labels of the nearest neighbors of the testing sample are adopted for predicting the health condition in k-NN algorithm. Structural risk minimization criteria in the statistical learning theory is employed for the SVM model establishment.
TCA: Transfer component analysis (TCA) is a popular method for finding a feature subspace in the domain adaptation approach, which assumes the source and target data distributions are similar. For the obtained subspace, an SVM model is developed with the source data, and then the built model is used for testing.
The basic deep convolutional neural network-based method is implemented for comparison, where CNN based feature extraction without cross domain adaptation is considered. The model trained on source domain data is directly used for testing.
CNN -With DA: This is the proposed method which implements domain adaptation in the deep learning framework.
Moreover, to evaluate the influence of the proposed noisy label algorithm, the deep learning-based methods are implemented both with and without the noisy labels of the data. In the reported results, the notations "with NL" denote the methods with the noisy labels, and the notations "without NL" denote those without the noisy labels, i.e. the conventional supervised learning paradigm.
The results from all 8 transfer tasks, i.e. T1, T2, …T8 are presented in Fig. 5 . As seen in the figure, the results clearly indicate that, the proposed noisy label CNN-based cross domain adaptation methodology achieves the highest testing diagnosis performance among all techniques in different tasks. The traditional machine learning models (SVM and k-NN) lead to poor generalization when source domain data is applied directly to the target domain data. In contrast, TCA (domain adaptation technique) performs significantly better than the traditional machine learning algorithms. Furthermore, CNNwith domain adaptation and without the use of noisy labels provides higher diagnosis performance relative to CNNwithout domain adaptation results (for both, with and without the use of noisy labels). However, incorporation of noisy labels in the source domain data improves the performance of CNN model with domain adaptation methodology and confirms the effectiveness of the proposed approach. In order to better evaluate the proposed noisy label algorithm, different tests were conducted by varying the level of injected noise, in small increments, and observing the corresponding changes in testing accuracy. The results of these tests are summarized in Fig. 6 . It can be observed that smaller additional noise in the labels, generally leads to noticeable improvement in the testing accuracies. However, when strong noise is introduced, the performance deteriorates. For instance, the testing accuracy suddenly drops by almost 3%, when the noise level crosses 0.25. Hence, based on these results, an optimal noise level of nrange = 0.25 is selected, and a random noise number in the range of [0, 0.25] is generated during each training epoch, to form the required noisy labels in this study. The reason for the performance improvement after using noisy labels, mostly lies in the strong regularization introduced by the algorithm. Data diversity is much enhanced, and model randomness is increased, that significantly results in better generalization ability. On one hand, the noisy label can be 89 It should be pointed out that in this study, the integration of the domain adaptation and noisy label techniques is proposed to address the challenging cross-domain fault diagnosis problem. Using the noisy label alone, without domain adaptation, will inevitably introduce additional noise, which deteriorates the performance of the model. Domain adaptation provides the basic ability to extract generalized features across different domains, and noisy label offers additional improvements in generalization ability of the model.
In general, the fully connected layer captures the most important fault features and thus visualization of highdimensional features in the fully connected layer is presented in this section. The t-SNE algorithm was used for visualizing the high-dimensional data representations. Fig. 7 depicts the 2D plots of the learned features obtained using 'CNN-with DA' approach (with and without NL) and 'CNN-without DA' approach (with and without NL), for transfer task T1.
For the without-DA method, the learned feature representations with the same health conditions cluster together independently in source and target domains and the respective health labels of both domains are projected into far-off regions. Consequently, the learned health identification knowledge from the source domain cannot be well applied in the target domain. This scenario necessitates the proposed idea of domain adaptation. In contrast, the learned feature representation after cross domain adaptation with the same health conditions practically overlap each other, which indicates that the domaininvariant features are extracted. The effects of the proposed noisy label algorithm are also shown in Fig. 7 . Clear clusters of the 10 health conditions are obtained using the proposed method. Therefore, the effectiveness of the domain adaptation method is quantitatively validated in this section. 
In this study, a deep learning-based domain adaptation method is proposed for the rotating machine fault diagnosis problems. To enhance the model generalization ability, a novel algorithm is introduced where the machinery health condition labels are injected with additional noise, rather than directly using the popular one-hot vectors. Experiments on a real-world dataset have been carried out to validate the effectiveness of the proposed method. The results show that the proposed algorithm can further improve the cross-domain diagnosis performance in most cases.
However, it should be noted that, while promising results have been obtained, sufficient training data is generally required by the proposed method. Since data collection is usually difficult, further research will be focused on developing effective diagnosis methods, that use limited training data.