A C0C^0 Linear Finite Element Method for a Second Order Elliptic Equation in Non-Divergence Form with Cordes Coefficients

In this paper, we develop a gradient recovery based linear (GRBL) finite element method (FEM) and a Hessian recovery based linear (HRBL) FEM for second order elliptic equations in non-divergence form. The elliptic equation is casted into a symmetric non-divergence weak formulation, in which second order derivatives of the unknown function are involved. We use gradient and Hessian recovery operators to calculate the second order derivatives of linear finite element approximations. Although, thanks to low degrees of freedom (DOF) of linear elements, the implementation of the proposed schemes is easy and straightforward, the performances of the methods are competitive. The unique solvability and the $H^2$ seminorm error estimate of the GRBL scheme are rigorously proved. Optimal error estimates in both the $L^2$ norm and the $H^1$ seminorm have been proved when the coefficient is diagonal, which have been confirmed by numerical experiments. Superconvergence in errors has also been observed. Moreover, our methods can handle computational domains with curved boundaries without loss of accuracy from approximation of boundaries. Finally, the proposed numerical methods have been successfully applied to solve fully nonlinear Monge-Amp\`{e}re equations

Bearing fault diagnosis based on adaptive mutiscale fuzzy entropy and support vector machine

This paper proposes a new rolling bearing fault diagnosis method based on adaptive multiscale fuzzy entropy (AMFE) and support vector machine (SVM). Unlike existing multiscale Fuzzy entropy (MFE) algorithms, the scales of AMFE method are adaptively determined by using the robust Hermite-local mean decomposition (HLMD) method. AMFE method can be achieved by calculating the Fuzzy Entropy (FuzzyEn) of residual sums of the product functions (PFs) through consecutive removal of high-frequency components. Subsequently, the obtained fault features are fed into the multi-fault classifier SVM to automatically fulfill the fault patterns recognition. The experimental results show that the proposed method outperforms the traditional MFE method for the nonlinear and non-stationary signal analysis, which can be applied to recognize the different categories of rolling bearings

Diagnostics of reciprocating compressor fault based on a new envelope algorithm of empirical mode decomposition

Empirical mode decomposition (EMD), a self-adaptive time-frequency analysis methodology, is particularly suitable for processing the nonlinear and non-stationary time series, which can decompose a complicated signal into a series of intrinsic mode functions. Although it has the attractive features, the approach to construct the envelop-line in EMD has obvious shortcomings. A suggested improvement to EMD by adopting the optimized rational Hermite interpolation is proposed in this paper. In the proposed method, it adopts rational Hermite interpolation to compute the envelope-line, which has a shape controlling parameter compared with the cubic Hermite interpolation. In the meantime, one parameter determining criterion is introduced to guarantee the shape controlling parameter selection performs optimally. Besides the empirical envelope demodulation (EED) is introduced and utilized to analyze the IMFs derived from the improved EMD method. Hence, a new time-frequency method based on the optimized rational Hermite-based EMD combined with EED is proposed and the effectiveness was validated by the numerical simulations and an application to the reciprocating compressor fault diagnosis. The contributions of this paper are three aspects: Firstly, the definition of the best envelope is non-existent, some light is given about which envelope maybe better in this paper. Secondly, the optimal shape controlling parameter selection combined with rational Hermite interpolation is developed, leading to the significant performance enhancement. Thirdly, little research has been carried out on the fault diagnosis of the reciprocating compressor using EMD, the proposed method is a good start

Two types of spectral volume methods for 1-D linear hyperbolic equations with degenerate variable coefficients

In this paper, we analyze two classes of spectral volume (SV) methods for one-dimensional hyperbolic equations with degenerate variable coefficients. The two classes of SV methods are constructed by letting a piecewise $k$-th order ($k\ge 1$ is an arbitrary integer) polynomial function satisfy the local conservation law in each {\it control volume} obtained by dividing the interval element of the underlying mesh with $k$ Gauss-Legendre points (LSV) or Radaus points (RSV). The $L^2$-norm stability and optimal order convergence properties for both methods are rigorously proved for general non-uniform meshes. The superconvergence behaviors of the two SV schemes have been also investigated: it is proved that under the $L^2$ norm, the SV flux function approximates the exact flux with $(k+2)$-th order and the SV solution approximates the exact solution with $(k+\frac32)$-th order; some superconvergence behaviors at certain special points and for element averages have been also discovered and proved. Our theoretical findings are verified by several numerical experiments

Simultaneous state and actuator fault estimation for satellite attitude control systems

AbstractIn this paper, a new nonlinear augmented observer is proposed and applied to satellite attitude control systems. The observer can estimate system state and actuator fault simultaneously. It can enhance the performances of rapidly-varying faults estimation. Only original system matrices are adopted in the parameter design. The considered faults can be unbounded, and the proposed augmented observer can estimate a large class of faults. Systems without disturbances and the fault whose finite times derivatives are zero piecewise are initially considered, followed by a discussion of a general situation where the system is subject to disturbances and the finite times derivatives of the faults are not null but bounded. For the considered nonlinear system, convergence conditions of the observer are provided and the stability analysis is performed using Lyapunov direct method. Then a feasible algorithm is explored to compute the observer parameters using linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed approach is illustrated by considering an example of a closed-loop satellite attitude control system. The simulation results show satisfactory performance in estimating states and actuator faults. It also shows that multiple faults can be estimated successfully

Coal Mine Gas Emission Gray Dynamic Prediction

AbstractThis paper introduces three kinds of mathematical prediction models: grey prediction, new information, and metabolism. The three prediction models were verified and analyzed by the example of the mine in Hegang, as a result, it is showed that the new information model predictions’ result was more accurate, the information model combines with the monitoring system can realize the dynamics of coal mine gas emission projections

The SpeakIn System Description for CNSRC2022

This report describes our speaker verification systems for the tasks of the CN-Celeb Speaker Recognition Challenge 2022 (CNSRC 2022). This challenge includes two tasks, namely speaker verification(SV) and speaker retrieval(SR). The SV task involves two tracks: fixed track and open track. In the fixed track, we only used CN-Celeb.T as the training set. For the open track of the SV task and SR task, we added our open-source audio data. The ResNet-based, RepVGG-based, and TDNN-based architectures were developed for this challenge. Global statistic pooling structure and MQMHA pooling structure were used to aggregate the frame-level features across time to obtain utterance-level representation. We adopted AM-Softmax and AAM-Softmax combined with the Sub-Center method to classify the resulting embeddings. We also used the Large-Margin Fine-Tuning strategy to further improve the model performance. In the backend, Sub-Mean and AS-Norm were used. In the SV task fixed track, our system was a fusion of five models, and two models were fused in the SV task open track. And we used a single system in the SR task. Our approach leads to superior performance and comes the 1st place in the open track of the SV task, the 2nd place in the fixed track of the SV task, and the 3rd place in the SR task.Comment: 4 page

SAMRS: Scaling-up Remote Sensing Segmentation Dataset with Segment Anything Model

The success of the Segment Anything Model (SAM) demonstrates the significance of data-centric machine learning. However, due to the difficulties and high costs associated with annotating Remote Sensing (RS) images, a large amount of valuable RS data remains unlabeled, particularly at the pixel level. In this study, we leverage SAM and existing RS object detection datasets to develop an efficient pipeline for generating a large-scale RS segmentation dataset, dubbed SAMRS. SAMRS totally possesses 105,090 images and 1,668,241 instances, surpassing existing high-resolution RS segmentation datasets in size by several orders of magnitude. It provides object category, location, and instance information that can be used for semantic segmentation, instance segmentation, and object detection, either individually or in combination. We also provide a comprehensive analysis of SAMRS from various aspects. Moreover, preliminary experiments highlight the importance of conducting segmentation pre-training with SAMRS to address task discrepancies and alleviate the limitations posed by limited training data during fine-tuning. The code and dataset will be available at https://github.com/ViTAE-Transformer/SAMRS.Comment: Accepted by NeurIPS 2023 Datasets and Benchmarks Trac

Bearing fault diagnosis based on adaptive mutiscale fuzzy entropy and support vector machine

This paper proposes a new rolling bearing fault diagnosis method based on adaptive multiscale fuzzy entropy (AMFE) and support vector machine (SVM). Unlike existing multiscale Fuzzy entropy (MFE) algorithms, the scales of AMFE method are adaptively determined by using the robust Hermite-local mean decomposition (HLMD) method. AMFE method can be achieved by calculating the Fuzzy Entropy (FuzzyEn) of residual sums of the product functions (PFs) through consecutive removal of high-frequency components. Subsequently, the obtained fault features are fed into the multi-fault classifier SVM to automatically fulfill the fault patterns recognition. The experimental results show that the proposed method outperforms the traditional MFE method for the nonlinear and non-stationary signal analysis, which can be applied to recognize the different categories of rolling bearings