Domain Adaptation in Robot Fault Diagnostic Systems
Industrial robots play an important role in manufacturing process. Since robots are usually set up in parallel-serial settings, breakdown of a single robot has a negative effect on the entire manufacturing process in that it slows down the process. Therefore, fault diagnostic systems based on the internal signals of robots have gained a lot of attention as essential components of the services provided for industrial robots. The current work in fault diagnostic algorithms extract features from the internal signals of the robot while the robot is healthy in order to build a model representing the normal robot behavior. During the test, the extracted features are compared to the normal behavior for detecting any deviation. The main challenge with the existing fault diagnostic algorithms is that when the task of the robot changes, the extracted features differ from those of the normal behavior. As a result, the algorithm raises false alarm. To eliminate the false alarm, fault diagnostic algorithms require the model to be retrained with normal data of the new task. In this paper, domain adaptation, a.k.a transfer learning, is used to transfer the knowledge of the trained model from one task to another in order to prevent the need for retraining and to eliminate the false alarm. The results of the proposed algorithm on real dataset show the ability of the domain adaptation in distinguishing the operation change from the mechanical condition change.
keywords- Fault Diagnosis, Anomaly Detection, Predictive Maintenance, Transfer Learning, Domain Adaptation
Robots have revolutionized the manufacturing process by performing tasks in faster and more accurate ways. However, sudden breakdowns of robots still may affect the speed of the production, which leads to the decrease in the production quantity. In order to prevent unscheduled maintenance, fault diagnostic, a.k.a. predictive maintenance, systems have gained a lot of attention recently [1, 2]. Fault diagnostic can be performed on software and hardware levels. Software faults are communication problems, controller software malfunctioning, etc. Hardware issues are mostly related to broken sensors, broken gears, backlash, etc. The focus of this paper is to identify hardware issues through analyzing the internal signals of the robots. An accurate system capable of detecting hardware problems require extra sensor instalment. However, using extra sensors to perform fault diagnosis is not feasible in many situations because it increases the cost, complexity, system weights, and requires extra space . That is why fault diagnostic systems based on machine learning algorithms have gained popularity recently and it is the focus of this paper.
Several research have been done recently [1, 3]. In , data is mapped to positive and negative groups where positive data includes all area of data space accessed during normal use while negative data belongs to the unknown area of data space. In order to approximate the positive data space, radial basis function kernels are used. The anomaly is detected by training a support vector machine (SVM) on positive and negative data. In another work , it was proposed to use multimodal sensory data such as haptic, auditory, visual, and kinematic signals to train a hidden Markov model (HMM). Then, the trained HMM provides a probability of the test data belonging to the normal behavior, which can be used as a criterion for anomaly detection.
Generally, these approaches consist of data pre-processing, feature extraction, dimension reduction and a model-based classifier. A model is trained for each axis of the robot based on the training data collected while the robot is healthy and performing a specific task. Later, the health of the robot is evaluated by collecting data and comparing it with the trained model.
The problem with existing fault diagnostic algorithms is that they raise false alarm when the task during which test data is collected differs from the one used during the training. When the task changes, features such as frequency components extracted from data change as well. This change in the features fools the systems to raise an alarm for an abnormality whereas the robot is still healthy. In order to avoid the false alarm, current algorithms require the model to be retrained whenever the task of the robot changes.
In this paper, it is proposed to use domain adaptation, a.k.a. transfer learning and knowledge transfer, as an intermediate step in order to avoid retraining of the model every time the task of the robot changes. In the proposed method, the training data is collected while the robot is healthy and performing the task A. Then, the short-time Fourier transform (STFT) of the data and their combinations are calculated as the features. These features are in a subspace called source domain, , representing the healthy robot. The test data is collected while the robot is doing the task B. Test data is in the target domain, . The goal of the domain adaptation algorithm is to transfer the model learned in the source domain to the target domain . It is assumed that the labeled data of the healthy and the faulty robots is not available in the target domain. Therefore, the unsupervised methods are used to transfer the knowledge between the domains. The unsupervised method used in this paper is manifold alignment [5, 6]. Manifold alignment is a local-preserving algorithm which finds a common subspace of the source and the target domains.
Furthermore, since it is not convenient to ask the users of the robot to run the transfer learning algorithm each time the task of the robot changes, we assume that the test data might be from the target domain. Therefore, manifold alignment algorithm is constantly applied to the features extracted from the test data to make sure that the comparison between healthy data and the test data is performed in the same domain. The experiments on the real dataset obtained from two types of industrial robots show a significant performance improvement in handling change of the task of the robot as well as the ability of the algorithm to correctly identify the abnormalities.
The following section describes the dataset, preprocessing, feature extraction and detection methods. Section III explains the proposed fault diagnostic method based on the manifold alignment algorithm. Section IV is dedicated to the experimental results. The final section concludes the findings of this paper and the future work.
The dataset is collected from two robots. Robot is from a series of single arm robots with 6 axis. Their reach is up to 3.0m and their payload is around 100kg. Robot is also from a series of 6-axis single arm robots and reach of up to 4.0m and the payload of maximum 600kg. Three signals: ”position, speed and torque” are recorded from the controller of these robots. The sampling frequency of speed and torque signals are while the frequency sampling of the position signal is .
Since the sampling frequency of the position signal is lower than the other two signals, the missing values of the position signal are imputed by bicubic interpolation method.
Ii-C Feature Extraction
In order to identify any abnormality, a certain set of features is required to be extracted from three signals depending on the type of abnormality. Various types of features such as Fourier transform, wavelet coefficients, etc are available. However, finding the appropriate features for the robot fault diagnosis is not a focus of this paper. In this paper, short-time Fourier transform (STFT) of three signals and their combinations is calculated as the set of features.
The extracted features are used to train a model representing the healthy robot. Here, the features of the healthy robot is used to build a subspace. The training and test data are project onto this subspace. Their -norm distance is used as a criterion to identify whether the test data represents the faulty robot. If the robot is still healthy, the subspace should be able to represent the features of the test data and their distance to the training data in this subspace should be small. On the other hand, the large distance in this subspace is an indication of a faulty robot. Hypothesis testing is performed on the calculated -norm distances in order to find an appropriate threshold in order to decide when to raise an alarm.
Iii Domain Adaptation for Robot Anomaly Detection
The problem with existing method is that the subspace built from the features of the healthy data (training data) of one operation is not able to represent the healthy data (test data) of another operation. As a result, the -norm distance increases and the algorithm raises a false alarm. In this section, domain adaptation is used to find a common subspace of the training and test data. Then, the -norm distance is calculated in this common subspace.
Let represents the feature space in the source domain, and are features of training samples drawn from this space. Let be features of test samples collected while the robot is operating in the customers’ factories, drawn from the target feature space . Since the application of the robot during training and test are different, their corresponding feature spaces are different: . Therefore, there is a need for domain adaptation algorithm which reduces the difference between these two spaces while preserving the geometric properties of these spaces . This can be achieved through finding a common subspace between source and target spaces through minimizing a cost function. Manifold alignment is an unsupervised domain adaptation algorithm which provides a closed-form solution [5, 6]. The closed form solution allows the implementation to be computationally efficient for real time purposes. Manifold alignment algorithm finds the projection matrix to find the low-rank embeddings of and in a joint subspace.
The low rank embedding (LRE) of the source and target features, and , are calculated through minimizing the loss function:
where , and are Frobenius and spectral norms, respectively. In this equation, and are the low rank embeddings of and , respectively, and and are their reconstruction coefficient matrices.
Closed form solution to this problem  is as follows: matrices and are decomposed using singular value decomposition (SVD), and . The reconstruction coefficient matrices are calculated as follows: , , where is the singular values greater than one and is their corresponding right singular vectors. The block reconstruction coefficient matrix is formed as:
The inter-set correspondence between the samples of the training and test datasets is represented with , where is the identity matrix.
After finding LRE of source and target samples, the projection matrices from the source and the target space into the common subspace and the embedding of the source and target samples are calculated by minimizing the following cost function:
where determines the importance of the local geometry (first term) vs. the inter-set correspondence (second term). After some plug-in and simplification, the cost function simplifies  to:
where is the Laplacian matrix of . This cost function is minimized by replacing with smallest eigenvectors of Eq. 4. is the -dimensional embeddings of training and test features in the common subspace.
Since is assumed to be the training features which is collected when the robot is healthy, the dimensional embeddings of the test dataset is compared to that of the test dataset using Euclidean distance: . If is abnormal, its distance is larger than the normal behavior. In order to perform hypothesis testing on the test data, the metric is calculated for several normal dataset to build a probability distribution function. The empirical distribution of the metric is the positive half of Laplace distribution with , and any outside of the confidence interval is marked as abnormal.
Iv Experimental Results
In this section, the proposed algorithm is evaluated on two separate datasets from Robot and Robot . In order to show the importance of the proposed method in the robot fault diagnostic systems, principal component analysis (PCA) is also used to build the subspace of the features (STFT of signals and their combinations) of the healthy robot from the training data. The extracted features of the test dataset are projected to this subspace and compared with the training dataset.
The signals of the fourth axis of the robot were collected for 190 consecutive days. The dataset on each day is 3 seconds long. No break down or abnormality was reported for this axis of the robot, however, the task of the robot has changed three times during these 190 days. After preprocessing, the dataset on day 1 is used as the training data (healthy robot) and their STFT are calculated as the extracted features: . The datasets of the following days are used as the test datasets to form . is calculated for each day with respect to the first day to identify any changes with respect to the first day. The assumption is that the robot is in a great condition on the first day which can be the inspection time at the robot manufacturing facility. Fig. 1(a) shows . Apparent in this figure, none of the changes in the task of the robot is identified as an abnormal behavior. On the other hand, Fig. 1(b) shows s obtained using the PCA projection. All three changes in the task of the robot is obvious in this figure. This indicates that the use of the conventional methods such as PCA fails to distinguish the change in the mechanical condition of the robot from the change in its task. The other observation from comparing these two figures is the magnitude of . The values in Fig. 1(b) are larger than those of Fig. 1(a). This also proves that s are not in the same subspace of , which is why their distances are large. On the other hand, the small values of in Fig. 1(a) indicate that their projection onto the common subspace make them comparable.
In the second experiment, three signals of the fifth axis of the robot are collected for 148 days. The signals on each day lasts 3 seconds. The axis of the robot broke down on 149th day. However, the task of the robot did not change during 148 days. The proposed algorithm is applied to this dataset in the similar manner. The first day is considered as the training data and the features are extracted from this dataset as . The extracted features of other days form . s are compared to using -norm distance to form s. Fig. 2(a) shows s of the proposed algorithm. Similarly, PCA is used to build the subspace of the healthy robot for comparing the training and test dataset and the outcome is presented in Fig. 2(b). According to two plots in Fig. 2, both method performs equally well in identifying the trend of leading to the breakdown of the axis on the th day. However, comparing the values of both plots demonstrates the training and test data are being compared in the same subspace in the proposed algorithm in contrast to PCA-based method in Fig. 2(b).
Fault diagnostic systems have been of interests of many apparatus manufacturers such as drives and robots. The goal of such systems is to build a healthy model of the device and constantly compare the device with the healthy model to identify any possible malfunctioning. However, the challenge with the application of fault diagnostic systems in robotics is that the healthy model requires to be retrained every time the task of the robot changes. In this paper, it was proposed to use domain adaptation algorithms to generalize the trained model for various tasks the robot can perform. The manifold alignment, an unsupervised domain adaptation algorithm, was applied to the features extracted from the training and test data to project them onto a common subspace. The test data was compared to the healthy data in the common subspace to identify any abnormality. The experimental results on the real dataset showed the great performance of the proposed algorithm in the face of changes in the task of the robot vs changes in the mechanical conditions of the robot.
- footnotetext: * Parts of this paper are patent pending.
- footnotetext: ©2018 Arash Mahyari
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