8 results about "Fractional differential" patented technology

The invention discloses a modeling method and device for a fractional order chaotic system of a doubly-fed induction generator, and relates to the technical field of chaotic modeling of a power system. In order to solve the defects that in the prior art, an existing integer order modeling method still has the problems of insufficient modeling precision and difficult parameter solving when describing complex time-varying characteristics and nonlinear coupling behaviors, the technical scheme provided by the invention is as follows: the method comprises the following steps: determining a state variable of a preset model through a fractional order differential operator; constructing a five-dimensional fractional order state differential equation; performing dimension reduction on the five-dimensional equation by using a stator flux linkage orientation condition, and simplifying the five-dimensional equation into a three-dimensional fractional order state differential equation; defining a time fast and slow transformation factor, operating the preset model under a new time scale, and optimizing parameter distribution of state variables; and converting the optimized state variable through a telescopic factor of affine transformation, and optimizing coefficient distribution of the preset model. The method is suitable for depicting the dynamic characteristics of the doubly-fed induction generator.

The invention discloses a fractional order sliding mode prediction control method for a V2G vehicle-mounted converter, and relates to the technical field of vehicle-mounted bidirectional converter control. According to the method, firstly, a fractional order mathematical model of a V2G (Vehicle-to-Grid) vehicle-mounted converter is established on the basis of a fractional order calculus theory; the method comprises the following steps: firstly, constructing a fractional order state space model of a system by introducing a fractional order differential operator, and deriving a fractional order state space equation of a vehicle-mounted bidirectional transducer; the invention provides a V2G vehicle-mounted converter control strategy combining a fractional order mathematical model, a sliding mode controller and a model prediction control method, and realizes accurate control of a front-stage totem-pole bridgeless PFC and a rear-stage CLLC resonant converter of the V2G vehicle-mounted converter. Through the control strategy, the limitation of modeling precision of traditional integer order modeling in V2G vehicle-mounted converter control is effectively solved, and the control precision and the dynamic response performance of the system are remarkably improved.

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.

The invention discloses a fractional order active disturbance rejection control method for a fractional order chaotic system, and the method comprises the following steps: constructing a mathematical model of a fractional order Lorenz chaotic system according to a fractional order calculus theory; designing a fractional order tracking differentiator in order to accurately extract fractional order differential information of a system state variable; designing a fractional order expansion state observer for observing the total disturbance of the fractional order chaotic system; comparing the output of the fractional order expansion state observer with the output of the fractional order tracking differentiator to obtain an error signal, and designing a fractional order PID controller; and designing a fractional order active disturbance rejection controller to realize stable control of the fractional order Lorenz system. The fractional order active-disturbance-rejection control method for the fractional order chaotic system effectively makes up for the defects of the existing control technology, and remarkably improves the control precision, the anti-interference capability and the chaos phenomenon suppression capability of the fractional order chaotic system.

The invention discloses a circuit and a method for solving a Grunwald-Letnikov fractional order differential equation set of a pipeline structure. The solving circuit comprises a pipelined continuous multiply accumulation module, a pipelined differential equation right side function operation module, a pre-estimation correction module and a recursion module. The solving method comprises the steps that the successive multiplication and accumulation module and the recursion module work in parallel and cooperatively, and the recursion algorithm for solving the numerical value of the Grunwald-Letnikov fractional order differential equation set is achieved; the differential equation right function calculation module adopts a pipeline structure; and the pre-estimation and correction module is used for solving the problem of output hysteresis of the differential equation right side function operation module introduced by the pipeline structure. According to the scheme, the defects that an existing circuit implementation scheme cannot respond to input excitation signals in real time, and the data processing speed is limited due to high combinational logic time delay are overcome; a circuit design of a pipeline structure is adopted, and the method is characterized in that an externally input excitation signal can be responded in real time, a solution of a fractional order differential equation set at a time point can be calculated in a single clock period at a high throughput rate, and the calculation speed of hardware solution is improved.

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.