6th International Forum on Advanced Technologies
March 9th-10 th, 2020, Tokushima, Japan

Time Series Classification of Vibration Data
Using Attractors Made from Multidimensional Spaceby Convolutional Neural Network
Tomoya Takata1, Yoko Uwate1, Hidekuni Takao2 and Yoshifumi Nishio1
𝑇𝑜𝑘𝑢𝑠ℎ𝑖𝑚𝑎 𝑈𝑛𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦, 2‐ 1 𝑀𝑖𝑛𝑎𝑚𝑖‐ 𝐽𝑜𝑠𝑎𝑛𝑗𝑖𝑚𝑎, 𝑇𝑜𝑘𝑢𝑠ℎ𝑖𝑚𝑎, 770‐ 8506, 𝐽𝑎𝑝𝑎𝑛1
𝐸‐ 𝑚𝑎𝑖𝑙: {𝑡𝑜𝑚𝑜𝑦𝑎, 𝑢𝑤𝑎𝑡𝑒, 𝑛𝑖𝑠ℎ𝑖𝑜}@𝑒𝑒. 𝑡𝑜𝑘𝑢𝑠ℎ𝑖𝑚𝑎‐ 𝑢. 𝑎𝑐. 𝑗𝑝1
𝐾𝑎𝑔𝑎𝑤𝑎 𝑈𝑛𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦, 1‐ 1 𝑆𝑎𝑖𝑤𝑎𝑖𝑐ℎ𝑜, 𝑇𝑎𝑘𝑎𝑚𝑎𝑡𝑠𝑢, 𝐾𝑎𝑔𝑎𝑤𝑎, 760‐ 0016, 𝐽𝑎𝑝𝑎𝑛2
𝐸‐ 𝑚𝑎𝑖𝑙: 𝑡𝑎𝑘𝑎𝑜@𝑒𝑛𝑔. 𝑘𝑎𝑔𝑎𝑤𝑎‐ 𝑢. 𝑎𝑐. 𝑗𝑝2

1. Introduction
The researches on time series data analysis have been actively conducted in recent years. This data hasvarious characteristics, such as oscillating regularly and irregularly. Chaos theory mainly handles irregularly
oscillating data. The theory deals with a phenomenon that appears in a part of a dynamical system. It shows acomplicated state that cannot be predicted due to numerical errors. Unpredictability is not random and follows
deterministic rules. However, because it cannot be obtained by the integration method, the methods forobserving other phenomena are required. One of them is the time delay coordinate system which is a kind ofchaos theory [1]. By using this method, 1-dimensional data (1d-data) can be converted into multidimensional
data such as 2-dimensional data (2d-data) and three-dimensional data. It is applied in various fields such as
cranial nerve system and engineering system.
In recent years, the researches on time series data analysis using Neural Networks (NN) such as
1-dimensional Convolutional Neural Network (1d-CNN) and Recurrent Neural Network (RNN) has been
actively performed [2]. The reason why NN attract attention is that NN can learn and recognize input
information by itself. However, even if these models are used, it is difficult to analyze time series data withvery irregular vibrations. It is impossible for NN to learn the numerical and time series characteristics of thedata. Therefore, it is necessary for NN to preprocess this data. In order to solve this problem, this study extends
the data to multidimensional data using the time delay coordinate system. The objective is to find regularitythat NN can easily learn from time series data with irregular vibrations.
2. Convolutional Neural NetworkCNN is one of the NN and is mainly used in image recognition [3]. It is established in 1956 as an academic
field, and it has received a lot of attention since winning the image recognition competition in 2012. Recently,
various networks such as VGGNet and ResNet have been devised, and the misrecognition rate has been greatly
improved [4], [5]. CNN is used in various fields such as medicine and automobiles, and its application range isexpanding. It already puts into practical use in automated driving, robots, surveillance cameras and so on.
Besides images such as object detection and segmentation, it has achieved tremendous performance in manytasks such as natural language processing and speech processing. CNN is inspired by the biological processes
and mimics the arrangement of the visual cortex of animals. It consists of an input layer, an output layer, and anumber of hidden layers between them. It is usually composed of the convolutional layers, the pooling layers,
and the fully connected layers. The convolution layers and the pooling layers are feature amount extraction
parts that read the image and create the feature map. In the convolution layer, some of the filters with different
resolutions are applied to each learning image, and the output of each convolution images is used as an input tothe next layer. The filter starts from the detection of very simple features such as brightness and edges, andextracts even complex features unique to the object. Furthermore, filters increase the level of complexity offeatures that uniquely define objects. The pooling layer reduces the size of the original image while leaving
important information as a feature. By performing this process, it is possible to prevent difficulty in learningand over learning due to an increase in the amount of data. Even if the image moves and rotates, the samevalue as the original image can be also output. In the last fully connected layer, the output is converted into a
1-dimensional array, and the probability of classification is calculated.

6th International Forum on Advanced Technologies
March 9th-10 th, 2020, Tokushima, Japan
3. Proposed Method
In this study, 1d-data is converted into multidimensional data using the time delay coordinate system. First,
let the value of data at a specific time be 𝑥(𝑛). Furthermore, if the time delay value is 𝜏, this system can be
expressed by Eq. (1).
(1)

𝑓(𝑥) = 𝑥(𝑛), 𝑥(𝑛 + 𝜏), 𝑥(𝑥 + 2𝜏), …

Thereupon, we propose to extract 2d-data as image made from the multidimensional space (Fig. 1). In thisstudy, the number of the dimensions is set to 5. The objective is to successfully extract the amount of
information in the multidimensional space as image features. Figure 2 shows the flow of this study. First,
1d-data is converted into multidimensional data using the time delay coordinate system. Next, 2d-data isextracted from the multidimensional data. Finally, CNN is used to extract image features and perform binaryclassification.

Fig.1

Method how to make image

Fig.2

Flowchart of this study

4. Simulation Method
The data used in this study are the surface shapes of two fabrics that change in 1 [𝑚𝑠] acquired by a tactile
nanosensor [6]. This surface shapes indicate the vibrations when any loads are applied to the fabrics. Table 1
shows the number of data for each fabric used in this study. Time series data of 2000 [𝑚𝑠] are used. There are
CNN are used for attractor images and 1d-CNN and RNN are used for original time series data.
Table 1 The number of the dataset

Figure 3 shows the structure of the CNN used in this study. CNN is the network that extracts features in theconvolutional layer and classifies inputs based on the features. Figure 4 shows the structure of the RNN usedin this study. RNN has recursion in which the output of a certain layer is input retrospectively.

Fig.3

CNN structure

Fig.4

RNN structure

6th International Forum on Advanced Technologies
March 9th-10 th, 2020, Tokushima, Japan
5. Simulation Result
We investigate the average of 10 times of train and test accuracies. Table 2 shows the accuracies when thenumber of dimensions is set to 5. For example, attractor 1-3 is generated in the first and third dimensions. The
test accuracy of the attractor 1-5 is the best. However, the test accuracies of most of the attractors are lower
than those of the RNN and 1D-CNN. It can be seen that a specific attractor is effective in the CNN feature.
Table 2 Train and test accuracies

6. Conclusion
In this study, we proposed a method that uses time delay coordinate system to expand time series data into
multidimensional space and converted the data into images. It was confirmed that how the accuracy of the timeseries classification changes using CNN by extending 1d-data to multidimensional data. As a result, some of
the test accuracies using the proposed method were superior to those using the conventional method.
However, most of the test accuracies of the proposed method were lower than those of RNN and 1D-CNN. In
the future, we will explore how to extract and utilize multidimensional features and clarify how to obtainsufficient classification accuracy. In order to clarify the characteristics of the time series data, it is also
examined which part of the image the NN focus on.
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[2] A. Sherstinsky, “Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory(LSTM) Network'', arXiv:1808.03314, Submitted on 9 August 2018 (v1), last revised 4 Nov 2018.
[3] M. Matsugu, K. Mori, Y. Mitari and Y. Kaneda, “Subject independent facial expression recognition withrobust face detection using a convolutional neural network”, Neural Networks 16., vol.5, pp.555-559,2003.
[4] K. Simonyan, A. Zisserman, “Very Deep Convolutional Networks for Large-Scale Image Recognition'',IEEE International Conference on Computer Vision, arXiv:1409.1556, 10 Apr 2015.
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