Gaussian Domain Research Articles

Dynamic simulation-assisted Gaussian mixture alignment approach for fault diagnosis of rotation machinery under small samples

Abstract Obtaining a substantial number of actual samples for rotating machinery in an industrial setting can be challenging, particularly when faulty samples are acquired under hazardous working conditions. The issue of insufficient samples hinders the effective training of reliable fault diagnosis models, impeding the industrial implementation of advanced intelligent methods. This study proposes an innovative dynamic simulation-assisted Gaussian mixture alignment model (DSGMA) to address the challenge of applying fault diagnosis technologies, with its performance mined by advanced transfer algorithms. Specifically, we establish a fault dynamics model for rotating machinery and acquire a substantial amount of simulated data as the source domain to facilitate the training of the deep neural network model. Subsequently, we propose a Gaussian mixture-guided domain alignment approach that assigns a domain-independent Gaussian distribution to each category as prior knowledge, with the parameters calculated using limited actual samples. Diagnostic knowledge is transferred from the source domain to the target domain by minimizing the Kullback–Leibler divergence between the features of the simulated samples and the Gaussian mixture priors. Furthermore, the DSGMA model incorporates Gaussian clustering loss to augment the clustering capability of samples belonging to the same category from real devices and enhances the computational stability of the parameters in the Gaussian mixture model. The efficacy of the DSGMA method is validated using three publicly available datasets and compared against five widely adopted methods. The experimental findings illustrate that DSGMA exhibits superior diagnostic and robust capabilities, facilitating efficient fault diagnosis under scenarios of small samples.

CSF-GTNet: A Novel Multi-Dimensional Feature Fusion Network Based on Convnext-GeLU- BiLSTM for EEG-Signals-Enabled Fatigue Driving Detection.

Electroencephalography (EEG) signal has been recognized as an effective fatigue detection method, which can intuitively reflect the drivers' mental state. However, the research on multi-dimensional features in existing work could be much better. The instability and complexity of EEG signals will increase the difficulty of extracting data features. More importantly, most current work only treats deep learning models as classifiers. They ignored the features of different subjects learned by the model. Aiming at the above problems, this paper proposes a novel multi-dimensional feature fusion network, CSF-GTNet, based on time and space-frequency domains for fatigue detection. Specifically, it comprises Gaussian Time Domain Network (GTNet) and Pure Convolutional Spatial Frequency Domain Network (CSFNet). The experimental results show that the proposed method effectively distinguishes between alert and fatigue states. The accuracy rates are 85.16% and 81.48% on the self-made and SEED-VIG datasets, respectively, which are higher than the state-of-the-art methods. Moreover, we analyze the contribution of each brain region for fatigue detection through the brain topology map. In addition, we explore the changing trend of each frequency band and the significance between different subjects in the alert state and fatigue state through the heat map. Our research can provide new ideas in brain fatigue research and play a specific role in promoting the development of this field.

Domain-knowledge Inspired Pseudo Supervision (DIPS) for unsupervised image-to-image translation models to support cross-domain classification

The ability to classify images is dependent on having access to large labeled datasets and testing on data from the same domain of which the model was trained on. Classification becomes more challenging when dealing with new data from a different domain, where gathering and especially labeling a larger image dataset for retraining a classification model requires a labor-intensive human effort. Cross-domain classification frameworks were developed to handle this data domain shift problem by utilizing unsupervised image-to-image translation models to translate an input image from the unlabeled domain to the labeled domain. The problem with these unsupervised models lies in their unsupervised nature. For lack of annotations, it is not possible to use the traditional supervised metrics to evaluate these translation models to pick the best-saved checkpoint model. This paper introduces a new method called Domain-knowledge Inspired Pseudo Supervision (DIPS) which utilizes Gaussian Mixture Models and domain knowledge to generate pseudo annotations to enable the use of traditional supervised metrics. This method was designed specifically to support cross-domain classification applications contrary to other typically used metrics such as the Fréchet Inception Distance (FID) which were designed to evaluate the model in terms of the quality of the generated image from a human-eye perspective. DIPS outperforms state-of-the-art GAN evaluation metrics when selecting the optimal saved checkpoint. Furthermore, DIPS showcases its robustness and interpretability by demonstrating a strong correlation with truly supervised metrics, highlighting its superiority over existing state-of-the-art alternatives The boiling crisis problem has been approached as a case study. The code and data to replicate the results can be found on the official GitHub-repository11https://github.com/Hindawi91/DIPS..

Computer Vision Based Planogram Compliance Evaluation

Arranging products in stores according to planograms, optimized product arrangement maps, is an important sales enabler and necessary for keeping up with the highly competitive modern retail market. Key benefits of planograms include increased efficiency, maximized retail store space, increased customer satisfaction, visual appeal, and increased revenue. The planograms are realized into product arrangements by humans, a process that is prone to mistakes. Therefore, for optimal merchandising performance, the planogram compliance of the arrangements needs to be evaluated from time to time. We investigate utilizing a computer vision problem setting—retail product detection—to automate planogram compliance evaluation. Retail product detection comprises product detection and classification. The detected and classified products can be compared to the planogram in order to evaluate compliance. In this paper, we propose a novel retail product detection pipeline combining a Gaussian layer network product proposal generator and domain invariant hierarchical embedding (DIHE) classifier. We utilize the detection pipeline with RANSAC pose estimation for planogram compliance evaluation. As the existing metrics for evaluating the planogram compliance evaluation performance assume unrealistically that the test image matches the planogram, we propose a novel metric, called normalized planogram compliance error (EPC), for benchmarking real-world setups. We evaluate the performance of our method with two datasets: the only open-source dataset with planogram evaluation data, GP-180, and our own dataset collected from a large Nordic retailer. Based on the evaluation, our method provides an improved planogram compliance evaluation pipeline, with accurate product location estimation when using real-life images that include entire shelves, unlike previous research that has only used images with few products. Our analysis also demonstrates that our method requires less processing time than the state-of-the-art compliance evaluation methods.

Optimal coefficient selection in Compute and Forward relaying using improved Schnorr–Euchner search algorithm

Physical layer Network Coding with Compute and Forward relaying (CF) is a promising transmission strategy that effectively exploits the natural linear computation of the multiuser wireless channel. In CF relaying, the relay nodes receive a linear combination of transmitted signals with additive noise and each relay node computes an integer linear combination of transmitted codewords which are then forwarded to the destination. After receiving enough independent equations from multiple relay nodes, the destination could decode individual source nodes’ messages. The source nodes use nested lattice codes which have the property that an integer linear combination of codewords is a valid codeword in the codeset. The simulation set up includes a K×K×1 network model with K source nodes, K relay nodes and 1 destination node. Relay nodes are assumed to have perfect channel state information, which is used in computing the linear equation. The success of CF relaying lies in choosing the optimal coefficient in computing the independent linear equation at each relay node. Optimal coefficient selection aims to maximize the computation rate which can be achieved when the equation coefficients are matched with complex-valued channel gains. This paper proposes an iterative algorithm for finding the optimal coefficient vector in the Gaussian integer domain using an improved Schnorr–Euchner search strategy. The performance of the proposed coefficient search algorithm in terms of computation complexity and the achievable rate is compared with other existing algorithms through MATLAB simulation. Simulation is performed for networks with 2, 4, 8 and 16 numbers of source and relay nodes. The proposed coefficient selection algorithm is validated for varying Signal to Noise Power under Rayleigh fading channel environment.

Gaussian mixture continuously adaptive regression for multimode processes soft sensing under time-varying virtual drift

Due to time-varying virtual drift in multimode processes, the performance of soft sensors will degrade after online deployment. Traditional adaptive mechanisms have been developed to address this issue, but all have limitations in the real-world scenario. Therefore, this paper explores domain adaptation as a new adaptive mechanism for its unsupervised knowledge calibration effect, and a Gaussian mixture continuously adaptive regression (GMCAR) is proposed for soft sensor modeling. First, we extend Gaussian domain adaptation to Gaussian mixture domain adaptation, in which the target domain could transfer knowledge from multiple Gaussian source domains with different posterior probabilities. Furthermore, a new sensitivity-based continuous domain adaptation is presented to efficiently and naturally update the Gaussian mixture domain adaptation by exploring existing knowledge and using the continuity of data streams. As well, an adaptive Gaussian mixture regression is designed to continuously update the soft sensing model according to the current process state. Finally, experimental results on the TE benchmark process and a real air separation process demonstrate that the proposed GMCAR-based soft sensor achieves state-of-the-art performance under time-varying virtual drift.

Blind-noise image denoising with block-matching domain transformation filtering and improved guided filtering

The adaptive block size processing method in different image areas makes block-matching and 3D-filtering (BM3D) have a very good image denoising effect. Based on these observation, in this paper, we improve BM3D in three aspects: adaptive noise variance estimation, domain transformation filtering and nonlinear filtering. First, we improve the noise-variance estimation method of principle component analysis using multilayer wavelet decomposition. Second, we propose compressive sensing based Gaussian sequence Hartley domain transform filtering to reduce noise. Finally, we perform edge-preserving smoothing on the preprocessed image using the guided filtering based on total variation. Experimental results show that the proposed denoising method can be competitive with many representative denoising methods on the evaluation criteria of PSNR. However, it is worth further research on the visual quality of denoised images.

Domain Adaptation Mixture of Gaussian Processes for Online Soft Sensor Modeling of Multimode Processes When Sensor Degradation Occurs

Sensor degradation seriously hinders the practical application of soft sensors. To reduce the negative effect of sensor degradation, in this article, we propose a robust domain adaptation mixture of Gaussian processes (DA-MGP) for online soft sensor modeling of multimode processes. Based on the decomposition of industrial data into a group of Gaussian domains, Gaussian domain discrepancy (GDD) is designed for domain adaptation and process mode recognition. After recognizing the process mode based on GDD, a Gaussian domain adaptation is presented to correct the drifted online input data by domain mapping, which can significantly improve the robustness of the soft sensor against sensor degradation. Furthermore, the domain mapping matrix is utilized as a transferred basis function for a local transferred Gaussian process component, which is used for robust soft sensor modeling. Additionally, an online block processing framework is adopted when the DA-MGP-based soft sensor is applied in online quality prediction. Finally, the TE benchmark process and a real industrial polypropylene process are employed to verify the effectiveness of the proposed method. In the designed five cases of sensor degradation, the DA-MGP-based soft sensor shows its strong robustness against sensor degradation.

Few-Shot Wideband Tympanometry Classification in Otosclerosis via Domain Adaptation with Gaussian Processes

Otosclerosis is a common middle ear disease that requires a combination of examinations for its diagnosis in routine. In a previous study, we showed that this disease could be potentially diagnosed by wideband tympanometry (WBT) coupled with a convolutional neural network (CNN) in a rapid and non-invasive manner. We showed that deep transfer learning with data augmentation could be applied successfully on such a task. However, the involved synthetic and realistic data have a significant discrepancy that impedes the performance of transfer learning. To address this issue, a Gaussian processes-guided domain adaptation (GPGDA) algorithm was developed. It leveraged both the loss about the distribution distance calculated by the Gaussian processes and the loss of conventional cross entropy during the transferring. On a WBT dataset including 80 otosclerosis and 55 control samples, it achieved an area-under-the-curve of 97.9±1.1 percent after receiver operating characteristic analysis and an F1-score of 95.7±0.9 percent that were superior to the baseline methods (r=10, p<0.05, ANOVA). To understand the algorithm’s behavior, the role of each component in the GPGDA was experimentally explored on the dataset. In conclusion, our GPGDA algorithm appears to be an effective tool to enhance CNN-based WBT classification in otosclerosis using just a limited number of realistic data samples.

Efron’s asymptotic monotonicity property in the Gaussian stable domain of attraction

In Efron (1965), Efron studied the stochastic increasingness of the vector of independent random variables entering a sum, given the value of the sum. Precisely, he proved that log-concavity for the distributions of the random variables ensures that the vector becomes larger (in the sense of the usual multivariate stochastic order) when the sum is known to increase. This result is known as Efron’s “monotonicity property”. Under the condition that the random variables entering in the sum have density functions with bounded second derivatives, we investigate whether Efron’s monotonicity property generalizes when sums involve a large number of terms to which a central-limit theorem applies.

Inductive Gaussian representation of user-specific information for personalized stress-level prediction

The accurate prediction of stress in a person’s life has a significant effect on improving personal health and the national economy. Since individuals have different historical circumstances and personality traits, stress symptoms and levels may vary from person to person. Thus, most studies on stress prediction pay attention to personalized models, which determine the personal stress level using user-specific information and heterogeneous stress-related data. However, these models cannot elaborately handle the uncertainty caused by the sparsity, data imbalance, irregularity, and high-dimensionality of user-specific information. In particular, out-of-sample users increase uncertainty. To cope with the problem, we propose a personalized stress-level prediction model with inductive Gaussian representation (PSP-IGR), which exploits heterogeneous inputs with a unified end-to-end approach. PSP-IGR extracts feature vectors from the heterogeneous inputs via Gaussian sampling, domain rules, and deep learning, depending on the characteristics of each input. Especially, PSP-IGR inductively generates a Gaussian feature vector called IGR by Gaussian sampling from the shared contents of user-specific information. Thus, PSP-IGR not only generalizes to both in-sample and out-of-sample users effectively but also deals with the uncertainty problem caused by limitations of healthcare datasets. Also, since we fuse the extracted feature vectors considering their characteristics (Gaussian and point vectors), we can preserve the expressiveness of each feature vector. Experiments on a real-world dataset, including survey results, wearable sensor signals, and contexts, demonstrate that PSP-IGR shows higher accuracy in predicting individual stress-level than previous models.

An improved Gaussian frequency domain sparse inversion method based on compressed sensing

The traditional compressed sensing method for improving resolution is realized in the frequency domain. This method is affected by noise, which limits the signal-to-noise ratio and resolution, resulting in poor inversion. To solve this problem, we improved the objective function that extends the frequency domain to the Gaussian frequency domain having denoising and smoothing characteristics. Moreover, the reconstruction of the sparse reflection coefficient is implemented by the mixed L1_L2 norm algorithm, which converts the L0 norm problem into an L1 norm problem. Additionally, a fast threshold iterative algorithm is introduced to speed up convergence and the conjugate gradient algorithm is used to achieve debiasing for eliminating the threshold constraint and amplitude error. The model test indicates that the proposed method is superior to the conventional OMP and BPDN methods. It not only has better denoising and smoothing effects but also improves the recognition accuracy of thin interbeds. The actual data application also shows that the new method can effectively expand the seismic frequency band and improve seismic data resolution, so the method is conducive to the identification of thin interbeds for beach-bar sand reservoirs.

High-Resolution Chest X-Ray Bone Suppression Using Unpaired CT Structural Priors.

There is clinical evidence that suppressing the bone structures in Chest X-rays (CXRs) improves diagnostic value, either for radiologists or computer-aided diagnosis. However, bone-free CXRs are not always accessible. We hereby propose a coarse-to-fine CXR bone suppression approach by using structural priors derived from unpaired computed tomography (CT) images. In the low-resolution stage, we use the digitally reconstructed radiograph (DRR) image that is computed from CT as a bridge to connect CT and CXR. We then perform CXR bone decomposition by leveraging the DRR bone decomposition model learned from unpaired CTs and domain adaptation between CXR and DRR. To further mitigate the domain differences between CXRs and DRRs and speed up the learning convergence, we perform all the aboved operations in Laplacian of Gaussian (LoG) domain. After obtaining the bone decomposition result in DRR, we upsample it to a high resolution, based on which the bone region in the original high-resolution CXR is cropped and processed to produce a high-resolution bone decomposition result. Finally, such a produced bone image is subtracted from the original high-resolution CXR to obtain the bone suppression result. We conduct experiments and clinical evaluations based on two benchmarking CXR databases to show that (i) the proposed method outperforms the state-of-the-art unsupervised CXR bone suppression approaches; (ii) the CXRs with bone suppression are instrumental to radiologists for reducing their false-negative rate of lung diseases from 15% to 8%; and (iii) state-of-the-art disease classification performances are achieved by learning a deep network that takes the original CXR and its bone-suppressed image as inputs.

Optimized OpenCL™ kernels for frequency domain image high-boost filters using image vectorization technique

Image high boost filtering uses high-boost filters to enhance the quality of an image, which has also seen in remote sensing, satellite broadcasting, classroom monitoring, and many more real-time video processing applications and requires its faster implementation. OpenCL is a widely adapted parallel programming framework that provides core level data parallelism, and dedicated for heterogeneous parallel devices like from low cost DSP to high-end CPU, GPU and FPGA. In this article, we have considered mostly used Ideal, Gaussian, Butterworth, and Laplacian of Gaussian frequency domain high-boost filters and implemented channelized OpenCL kernels for their rapid execution. In addition to that, these kernels are modified using image vectorization technique to optimize their time utilization by reducing the execution time of these OpenCL kernels to half. At last, performance analysis is carried out for these two types of OpenCL kernel implementations to determine their effectiveness with regard to time consumption and accuracy. Here, different image performance evaluation metrics like entropy, standard deviation, mean absolute error, percentage fit error, SSIM, correlation, and peak signal to noise ratio are applied to measure rightness of the above high-boost filters. From the results, we have concluded that a vectorized Butterworth high-boost filter kernel is the suitable one to provide better results among those filters, which might be highly adaptable in time bound real-time applications using various embedded devices.

Multi-Scale Gradient Image Super-Resolution for Preserving SIFT Key Points in Low-Resolution Images

Low-resolution images present challenges to a variety of object recognition problems in a variety of surveillance and navigation applications. In recent years, deep learning has advanced the state of the art in image super-resolution (SR) in terms of pixel domain peak signal to noise ratio (PSNR)/ mean square error (MSE). Inspired by the recent advances of deep convolutional neural networks in general image SR tasks, we develop a computer vision task-driven image SR solution by learning super-resolved gradient images using multiple convolutional neural networks for different scales. Recovering super-resolved gradient images at multiple scales, enables the system to recover more information useful for high level vision tasks than simply SR in the pixel domain. In particular, we propose a residual learning framework to perform image SR in the Difference of Gaussian (DOG) domain. The trained residual network models are then adapted to drive a widely adopted key point algorithm for image recognition, i.e. the SIFT detection and matching. Experimental results show that the proposed approach can significantly improve the SIFT keypoints repeatability compared to the state of the art in pixel domain image SR solutions.

Hyperspectral anomaly detection using differential image

A hyperspectral anomaly detector, which uses the benefits of a proposed background feature extraction method and the kernel trick, is introduced in this study. The proposed method is differential image based detector (DID). The DID method uses the differential image to estimate the variations of background in the feature extraction phase. The proposed feature extraction method slows the variations of background. So, it suppresses the background signal and highlights the anomalous signal. The separation between anomalous targets and background clutter is increased in the projected feature space. Before feeding the transformed data into the Reed-Xiaoli (RX) detector, the kernel learning method is applied. The kernel technique transforms the projected data with a linear non-Gaussian model to a potentially high-dimensional feature space with the non-linear Gaussian domain. Experiments are conducted on two real hyperspectral images. The experimental results indicate that the proposed DID method outperforms RX and some state-of-the-art anomaly detection approaches.

Correction formula approach to evaluate fatigue damage induced by non-Gaussian stress state

In the present paper the authors define an original analytical expression of a corrective coefficient to evaluate fatigue damage induced by a non-Gaussian stress state affected by high Kurtosis (values higher than 5) and by zero Skewness.This approach starts from a previous activity in which the authors solved an analogous problem but for light non-Gaussian stress states (Kurtosis value less than 5).The proposed procedure assumes to know the fatigue damage induced by Gaussian equivalent stress state time domain process. This characteristic allows the proposed procedure to be easily adopted inside the so-called Frequency Domain Fatigue Methods but in parallel with the statistical analysis of the system time domain response (Kurtosis and Skewness evaluation).Interesting considerations about its applicability will be proposed as concerns the non-Gaussianity and non-Stationarity of the inputs when the system is a flexible component excited in its frequency range.

Lévy-Khintchine random matrices and the Poisson weighted infinite skeleton tree

We study a class of Hermitian random matrices which includes Wigner matrices, heavy-tailed random matrices, and sparse random matrices such as adjacency matrices of Erdős-Rényi random graphs with p n ∼ 1 n p_n\sim \frac 1 n . Our n × n n\times n random matrices have real entries which are i.i.d. up to symmetry. The distribution of entries depends on n n , and we require row sums to converge in distribution. It is then well-known that the limit distribution must be infinitely divisible. We show that a limiting empirical spectral distribution (LSD) exists and, via local weak convergence of associated graphs, that the LSD corresponds to the spectral measure associated to the root of a graph which is formed by connecting infinitely many Poisson weighted infinite trees using a backbone structure of special edges called “cords to infinity”. One example covered by the results are matrices with i.i.d. entries having infinite second moments but normalized to be in the Gaussian domain of attraction. In this case, the limiting graph is N \mathbb {N} rooted at 1 1 , so the LSD is the semicircle law.

Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels

We present a framework for studying bosonic non-Gaussian channels of continuous-variable systems. Our emphasis is on a class of channels that we call photon-added Gaussian channels, which are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian domain for numerous tasks in continuous-variable quantum information processing such as entanglement distillation from Gaussian states and universal quantum computation. The single-mode photon-added channels we consider are obtained by using two-mode beam splitters and squeezing operators with photon addition applied to the ancilla ports giving rise to families of non-Gaussian channels. For each such channel, we derive its operator-sum representation, indispensable in the present context. We observe that these channels are Fock preserving (coherence nongenerating). We then report two examples of activation using our scheme of photon addition, that of quantum-optical nonclassicality at outputs of channels that would otherwise output only classical states and of both the quantum and private communication capacities, hinting at far-reaching applications for quantum-optical communication. Further, we see that noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels. We also present other physical and information-theoretic properties of these channels.

Быстрое L1-преобразование Гаусса для сглаживания изображений с сохранением границ

Gaussian convolution and its discrete analogue, Gauss transform, have many science and engineering applications, such as mathematical statistics, thermodynamics and machine learning, and are widely applied to computer vision and image processing tasks. Due to its computational expense (quadratic and exponential complexities with respect to the number of points and dimensionality, respectively) and rapid spreading of high quality data (bit depth/dynamic range), accurate approximation has become important in practice compared with conventional fast methods, such as recursive or box kernel methods. In this paper, we propose a novel approximation method for fast Gaussian convolution of two-dimensional uniform point sets, such as 2D images. Our method employs L1 distance metric for Gaussian function and domain splitting approach to achieve fast computation (linear computational complexity) while preserving high accuracy. Our numerical experiments show the advantages over conventional methods in terms of speed and precision. We also introduce a novel and effective joint image filtering approach based on the proposed method, and demonstrate its capability on edge-aware smoothing and detail enhancement. The experiments show that filters based on the proposed L1 Gauss transform give higher quality of the result and are faster than the original filters that use box kernel for Gaussian convolution approximation.