The manipulator workspace mapping is an important problem in robotics and has attracted significant attention in the community. However, most of the pre-existing algorithms have expensive time complexity due to the reliance on sophisticated kinematic equations. To solve this problem, this paper introduces subspace learning (SL), a variant of subspace embedding, where a set of robot and scope parameters is mapped to the corresponding workspace by a deep neural network (DNN). Trained on a large dataset of around 6 × 104 samples obtained from a MATLAB®implementation of a classical method and sampling of designed uniform distributions, the experiments demonstrate that the embedding significantly reduces run-time from 5.23 × 103 s of traditional discretization method to 0.224 s, with high accuracies (average F-measure is 0.9665 with batch gradient descent and resilient backpropagation).1MATLAB® Scripts are available at https: github.com liaopeiyuan Subspace-Learning
In the literature, the development of a neural network for workspace generation has been already tested on both serial-link and parallel mechanisms, utilizing several model architectures and optimization methods @cite_20 @cite_24 . The feasibility of using an artificial neural network for workspace analysis is first proposed and investigated by @cite_19 , where a two-layer perceptron learns to generate the orientation workspace of a 6-3 SPM parallel mechanism based on a 3-tuple input. In a similar approach, @cite_21 constructs a three-layer deep network that takes the input joint angles of a 2-DOF parallel manipulator and gives the workspace of the mechanism in a particular Cartesian plane. Levenberg-Marquardt method is used for optimization, and the lowest mean squared error obtained by the algorithm is 0.026.
@cite_24 @cite_19 @cite_21 @cite_20
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Purpose – This paper aims to combine and further develop different mathematical models of the workspace representation of 6 degrees of freedom parallel mechanisms and to bring a new point of view to existing workspace analysis methods through using neural networks (NN).Design methodology approach – For the orientation workspace of the 6‐3 SPM, discretization method is used which is based on Euler angles and the NN algorithm is applied.Findings – The workspace analysis is carried out in the direction perpendicular to the moving platform which is the most workable direction of 6‐3 Stewart platform mechanisms and NN algorithm has decreased processing time.Originality value – The determination of the point, on that direction, at which the workspace is maximum, is outlined. It is the first time that the NN is used for classification of workspace of a parallel manipulator. The main purpose of the paper is to develop a neural network application destined to the workspace generation of a parallel mechanism, as an performant alternative to the workspace representation based on inverse kinematic model. The paper describes both algorithms. The initial testing was made for a parallel mechanism with two degrees of freedom that could be applied for the orientation of different systems like a TV satellite dish antennas, sun trackers, telescopes, cameras, radars etc. This paper aims at verifying the accuracy of Artificial Neural Networks (ANN) in assessing the transient stability of a single machine infinite bus system. The fault critical clearing time obtained through ANN is compared to the results of the conventional equal area criterion method. The multilayer feedforward artificial neural network concept is applied to the system. The training of the ANN is achieved through the supervised learning; and the back propagation technique is used as a learning method in order to minimize the training error. The training data set is generated using two steps process. First, the equal area criterion is used to determine the critical angle. After that the swing equation is solved using the point-to-point method up to the critical angle to determine the critical clearing time. Then the stability of the system is verified. As a result we find that the critical clearing time is predicted with slightly less accuracy using ANN compared to the conventional methods for the same input data sets unless the ANN is well trained. Machine learning algorithms based on deep neural networks have achieved remarkable results and are being extensively used in different domains. However, the machine learning algorithms requires access to raw data which is often privacy sensitive. To address this issue, we develop new techniques to provide solutions for running deep neural networks over encrypted data. In this paper, we develop new techniques to adopt deep neural networks within the practical limitation of current homomorphic encryption schemes. More specifically, we focus on classification of the well-known convolutional neural networks (CNN). First, we design methods for approximation of the activation functions commonly used in CNNs (i.e. ReLU, Sigmoid, and Tanh) with low degree polynomials which is essential for efficient homomorphic encryption schemes. Then, we train convolutional neural networks with the approximation polynomials instead of original activation functions and analyze the performance of the models. Finally, we implement convolutional neural networks over encrypted data and measure performance of the models. Our experimental results validate the soundness of our approach with several convolutional neural networks with varying number of layers and structures. When applied to the MNIST optical character recognition tasks, our approach achieves 99.52 accuracy which significantly outperforms the state-of-the-art solutions and is very close to the accuracy of the best non-private version, 99.77 . Also, it can make close to 164000 predictions per hour. We also applied our approach to CIFAR-10, which is much more complex compared to MNIST, and were able to achieve 91.5 accuracy with approximation polynomials used as activation functions. These results show that CryptoDL provides efficient, accurate and scalable privacy-preserving predictions.