613 research outputs found
Uniqueness and superposition of the distribution-dependent Zakai equations
The work concerns the Zakai equations from nonlinear filtering problems of
McKean-Vlasov stochastic differential equations with correlated noises. First,
we establish the Kushner-Stratonovich equations, the Zakai equations and the
distribution-dependent Zakai equations. And then, the pathwise uniqueness,
uniqueness in joint law and uniqueness in law of weak solutions for the
distribution-dependent Zakai equations are shown. Finally, we prove a
superposition principle between the distribution-dependent Zakai equations and
distribution-dependent Fokker-Planck equations. As a by-product, we give some
conditions under which distribution-dependent Fokker-Planck equations have
unique weak solutions.Comment: 19 page
Shift invariant sparse coding ensemble and its application in rolling bearing fault diagnosis
This paper proposes an automatic diagnostic scheme without manual feature extraction or signal pre-processing. It directly handles the original data from sensors and determines the condition of the rolling bearing. With proper application of the new technique of shift invariant sparse coding (SISC), it is much easier to recognize the fault. Yet, this SISC, though being a powerful machine learning algorithm to train and test the original signals, is quite demanding computationally. Therefore, this paper proposes a highly efficient SISC which has been proved by experiments to be capable of representing signals better and making converges faster. For better performance, the AdaBoost algorithm is also combined with SISC classifier. Validated by the fault diagnosis of bearings and compared with other methods, this algorithm has higher accuracy rate and is more robust to load as well as to certain variation of speed
Application of a Dense Fusion Attention Network in Fault Diagnosis of Centrifugal Fan
Although the deep learning recognition model has been widely used in the
condition monitoring of rotating machinery. However, it is still a challenge to
understand the correspondence between the structure and function of the model
and the diagnosis process. Therefore, this paper discusses embedding
distributed attention modules into dense connections instead of traditional
dense cascading operations. It not only decouples the influence of space and
channel on fault feature adaptive recalibration feature weights, but also forms
a fusion attention function. The proposed dense fusion focuses on the
visualization of the network diagnosis process, which increases the
interpretability of model diagnosis. How to continuously and effectively
integrate different functions to enhance the ability to extract fault features
and the ability to resist noise is answered. Centrifugal fan fault data is used
to verify this network. Experimental results show that the network has stronger
diagnostic performance than other advanced fault diagnostic models
Residual Denoising Diffusion Models
We propose residual denoising diffusion models (RDDM), a novel dual diffusion
process that decouples the traditional single denoising diffusion process into
residual diffusion and noise diffusion. This dual diffusion framework expands
the denoising-based diffusion models, initially uninterpretable for image
restoration, into a unified and interpretable model for both image generation
and restoration by introducing residuals. Specifically, our residual diffusion
represents directional diffusion from the target image to the degraded input
image and explicitly guides the reverse generation process for image
restoration, while noise diffusion represents random perturbations in the
diffusion process. The residual prioritizes certainty, while the noise
emphasizes diversity, enabling RDDM to effectively unify tasks with varying
certainty or diversity requirements, such as image generation and restoration.
We demonstrate that our sampling process is consistent with that of DDPM and
DDIM through coefficient transformation, and propose a partially
path-independent generation process to better understand the reverse process.
Notably, our RDDM enables a generic UNet, trained with only an loss
and a batch size of 1, to compete with state-of-the-art image restoration
methods. We provide code and pre-trained models to encourage further
exploration, application, and development of our innovative framework
(https://github.com/nachifur/RDDM)
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