4 results about "Fractional differential" patented technology

The application discloses an RGB-D surface normal vector estimation method based on fractional differential. The method firstly performs coordinate system conversion on pixel points of an image, then performs neighborhood point screening on each point in the image, removes hollow points and points with relatively large errors, then solves an algebraic expression of a normal vector by using the property that the normal vector is perpendicular to a plane where the pixel point is located, and finally solves fractional differential optimization gradient to improve the calculation precision of the surface normal vector.

The invention relates to the technical field of pipeline safety monitoring and integrity evaluation, and discloses an environmental corrosion evaluation and pressure pipeline failure analysis method based on an AI database, and the method comprises the steps: firstly constructing a high-dimensional phase space point cloud of monitoring data through a sliding time window, and generating a topological persistent landscape representing environmental steady state features through topological data analysis; constructing a Riemannian manifold dynamics database, and searching an optimal evolution path conforming to physical smoothness in a manifold space based on a Hessian energy minimization principle; and calculating a real-time topological entropy, dynamically driving the order of the variable-order fractional order differential equation by using the real-time topological entropy, and solving the equation in combination with an evolution path parameter to deduce the wall thickness attenuation process. Through fusion of algebraic topology and manifold geometry, deep coupling of data geometric features and a physical mechanism model is realized, the problems that a traditional model lacks interpretation and cannot adaptively describe a corrosion historical memory effect are solved, and the physical reliability of failure analysis is remarkably improved.

The invention discloses an image edge enhancement method based on adaptive fractional differential, and relates to the technical field of digital image processing. Comprising the following steps: inputting a to-be-processed original grayscale image; the original grayscale image is preprocessed, and a local feature map of the image is calculated; constructing an adaptive fractional order mapping function v (x, y); constructing x-direction and y-direction fractional order differential masks; performing adaptive fractional order differential convolution on each pixel point in the preprocessed gray level image to obtain adaptive fractional order differential values of the pixel point in x and y directions; calculating a gradient magnitude graph; and fusing the original grayscale image and the gradient magnitude image to obtain a final edge-enhanced image. According to the method, the optimal fractional differential order can be dynamically and adaptively determined according to the gradient, texture complexity and other characteristics of the local region of the image, noise is effectively suppressed and more detail information is reserved while the edge is enhanced, and a more accurate and robust edge enhancement effect is achieved.

A parameter identification method for fractional-order time-delay systems based on the Gegenbauer wavelet operation matrix is ​​presented, addressing the problem that existing parameter identification methods cannot identify fractional-order systems with time delays. This method constructs a Gegenbauer wavelet operation matrix for both fractional-order integral operators and time-delay operators. Then, the original fractional-order time-delay differential equation is transformed into a system of algebraic equations, thus avoiding direct numerical approximation of fractional-order differential terms. Furthermore, a nonlinear least squares method is used to jointly estimate the fractional-order order, time-delay parameters, and system parameters. Finally, the optimal fractional-order order and model parameters are determined based on minimizing the error between the model output and the actual output. This method effectively reduces solution complexity and improves the numerical stability and accuracy of parameter identification. It provides an effective tool for high-precision modeling and analysis of fractional-order time-delay systems.