3 results about "Lie derivative" patented technology

The invention relates to the field of nonlinear system modeling, and particularly provides a global linear modeling method and system for a nonlinear system based on Lie derivative and sparse recognition, a terminal and a medium, and the method comprises the steps: obtaining an explicit nonlinear kinetic equation of a target system, calculating the Lie derivative of a state variable or an output variable of the system based on the kinetic equation, constructing a candidate observation function library directly associated with the physical mechanism of the system; performing screening and dimension reduction on the candidate observation function library by adopting a sparse recognition method to obtain a low-dimensional observation function set; and on the basis of the screened observation function and system operation data, a finite-dimensional global linear model of the target system in the dimension raising observation space is obtained through identification by using a data driving algorithm. According to the method, the online solving efficiency and the control real-time performance are improved, and efficient and reliable multi-target collaborative optimization control of systems such as a wind driven generator is realized.

The invention provides a building electrical system fault diagnosis method and system, belongs to the field of building electrical system monitoring and fault diagnosis, and is used for solving the problems that the diagnosis dimension is single, a fault dynamic propagation and causal mechanism is difficult to model, and the model self-adaption and generalization ability is insufficient in the related technology. According to the method, multi-modal time sequence data is mapped to Riemannian manifold, a unified manifold control differential equation model is utilized, node state evolution dynamics and geometric causal interaction between nodes are modeled internally and synchronously, and accurate fault detection and positioning are realized based on Lie derivative difference and geometric divergence difference. The system correspondingly comprises a data acquisition module, a unified model module and a fault judgment module. Through combination of meta-learning rapid adaptation, antagonistic robust training and geometric federated learning, the scheme realizes high-precision and explainable diagnosis of the composite fault, and has strong adaptive ability and coevolution potential.

This invention discloses a GNSS noise identification method and system based on Riemannian manifold evolution and neural operators, belonging to the field of high-precision data processing for satellite navigation. The method first reconstructs the phase space of the GNSS coordinate sequence, using a manifold encoder to map it to the latent space of the Riemannian manifold to obtain the metric tensor. Second, it constructs a continuously evolving vector field controlled by a neural constant differential operator, and generates the eigenphysical evolution ideal trajectory through spatiotemporal integration. Subsequently, it introduces the Lie derivative operator to calculate the geometric deviation rate of the observation field along the ideal field evolution to strip away the physical signal, outputting a high-purity random noise manifold. Finally, it uses a Fourier neural operator to extract frequency domain features, fits the power spectral density, inputs a fully parameterized characteristic equation to calculate the significance coefficients, and dynamically outputs the optimal combined noise model. This invention overcomes the shortcomings of traditional methods that are sensitive to discrete sampling and missing data, achieving high-precision geometric decoupling of physical signals and random noise, and adaptive identification of complex noise.