13 results about "Differential operator" patented technology

The invention relates to a pipeline structure mechanics machine learning method based on a physical information neural network, and the method comprises the steps: building an equivalent variational differential equation according to pipeline structure mechanics, and carrying out the spatial discretization of a spatial domain related to the pipeline structure mechanics through a finite element method; aiming at a differential operator of the variable differential equation, based on a finite element method spatial discretization result, a local fitting method is adopted, and a convolution kernel field is obtained through conversion; coupling the convolution kernel field to a network architecture of a preset neural network, and collecting training data to train the neural network to obtain a trained physical information neural network; and based on the trained physical information neural network, performing calculation or simulation of pipeline structure mechanics.

The invention relates to the field of electric power, discloses a thermal power generating unit APS automatic start-stop full-process control method and system, and is used for solving the contradiction among safety, economy and rapidity of a traditional APS system. The method comprises the steps of establishing a differential algebraic equation system based on unit physical parameters to generate a unified model constraint set; generating a reference trajectory representing energy conversion efficiency and power in a differential flat space according to the start-stop target curve; predicting a thermal stress change rate through a fractional order differential operator based on the metal temperature to generate a safety margin instruction; generating an energy coordination correction instruction according to the Hamiltonian energy network balance point of the boiler heat storage and steam turbine kinetic energy solving port; and mapping the reference trajectory into a control instruction, integrating thermal stress constraint and energy coordination correction, and then distributing and executing. Safe and efficient start-stop control under full-process physical constraints is achieved, start-stop safety and economy are improved, and the service life of equipment is prolonged.

The invention relates to the technical field of simulation, and provides a pressure-bearing equipment structure cracking analysis method and system based on key-type near-field dynamics, and the method comprises the steps: geometric modeling, material parameter definition and initial parameter definition; discretizing the model; modeling a heat conduction process; modeling a deformation damage process; initial boundary condition configuration; the temperature field and the displacement field are solved in an explicit-implicit mixed mode; and calculating integral values of a plastic zone, damage distribution and a crack tip. According to the method provided by the invention, the high-precision advantage of a heat conduction model based on a near-field dynamic differential operator, the high-efficiency and high-precision characteristics of a key-type near-field dynamic thermoelastic-plastic model and the high-efficiency advantage of an explicit-implicit thermal staggered solution algorithm can be fully played; and a scientific method can be provided for accurate analysis of thermal elastic-plastic damage fracture of a typical pressure-bearing equipment structure.

Apparatuses, systems, methods, and computer program products are disclosed for hardware geometric regularization. A method includes receiving training data comprising labeled data points. A method includes selecting a class of self-adjoint differential operator equations. A method includes selecting a set of orthogonal polynomials as a spectral basis. A method includes iteratively optimizing parameters of the differential operator equations based on the training data using a gradient-based optimizer to minimize an objective function. A method includes solving the optimized differential operator equation using a spectral method with the selected orthogonal polynomials to generate a reproducing kernel represented by a kernel tensor. A method includes outputting a machine learning model comprising the reproducing kernel combined with support vectors derived from the training data, the model configured to infer labels for unseen data points by estimating similarity measures using the reproducing kernel.

This invention discloses a bearing fault diagnosis method and related device for new operating conditions with limited data, belonging to the field of bearing diagnosis technology. Addressing the challenges of scarce fault data and variable operating conditions in industrial settings, the proposed bearing fault diagnosis method employs a two-layer fractional-order differential enhancement mechanism: at the input layer, multi-order fractional-order differential operators are used to capture subtle temporal fluctuations in bearing vibration signals; at the feature layer, an adaptive distributed fractional-order feature extraction mechanism is designed, utilizing the nonlocal correlation of fractional-order calculus to characterize the dynamic evolution of deep features. The overall framework relies on a meta-learning paradigm, enabling the model to acquire efficient initialization priors through meta-training on a known set of operating conditions. This invention significantly improves diagnostic accuracy and robustness under conditions with very few samples, effectively solving the problem of rapid diagnostic deployment for rotating machinery under complex and variable operating conditions.

The application 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 power system chaos modeling. In order to solve the defects that the existing integer order modeling method still has the problems of insufficient modeling precision and difficult parameter solving in describing complex time-varying characteristics and nonlinear coupling behaviors, the technical scheme provided by the application is as follows: including: determining state variables of a preset model through a fractional order differential operator, and constructing a five-dimensional fractional order state differential equation; dimension reduction is performed on the five-dimensional equation by using a stator flux linkage orientation condition, and the five-dimensional fractional order state differential equation is simplified into a three-dimensional fractional order state differential equation; time fast and slow transformation factors are defined, and the preset model is run in a new time scale to optimize the parameter distribution of the state variables; the optimized state variables are converted through a scaling factor of affine transformation to optimize the coefficient distribution of the preset model. The application is suitable for application in the depiction work of the dynamic characteristics of the doubly-fed induction generator.

The invention discloses a central air-conditioning energy-saving optimization method based on deep learning, and the method specifically comprises the steps: 1, collecting the operation state data and environment state data of a central air-conditioning system, and carrying out the time index alignment, and forming time series data; 2, performing feature vectorization processing on the time sequence data to generate an input feature vector set; 3, inputting the input feature vector set into the fractional order neural network to generate a system operation state vector; 4, a Grunwald-Letnikov differential operator is introduced in the updating process of the system operation state vector, and a continuous spectrum fractional order state updating result vector is generated; 5, generating an energy consumption state vector based on a continuous spectrum fractional order state updating result; step 6, introducing a fractional order adjoint state layer, and generating an adjoint state vector representing a control parameter propagation relationship; and step 7, generating an operation control parameter set of the central air-conditioning system based on the adjoint state vector. According to the invention, energy-saving control is realized by introducing spectral fractional order modeling.

The invention discloses a low-complexity large-model long-sequence memory modeling method. The method comprises the following steps: firstly, constructing a fractional order state space model FOSSM by introducing a Capto fractional order derivative to replace an integer order differential operator; then, based on an asymptotic behavior of a Mittag-Leffler function, establishing a theoretical relationship between a power law attenuation property of an FOSSM memory kernel and a fractional order parameter; deducing the theoretical advantage boundary of the FOSSM in the aspect of power law data approximation compared with the standard SSM; and finally, the non-rational fractional order operator is converted into a rational transfer function through an Oustaloup rational approximation method, and efficient discretization of calculation complexity is realized. According to the method, power law long-range dependence can be modeled naturally, more matched mathematical representation is provided for a sequence with heavy-tailed time correlation, and the problem of path repetition caused by insufficient historical track memory in unmanned equipment navigation and the problem of poor interaction continuity caused by weak context keeping ability in man-machine interaction in a traditional method are solved.

A high-performance simulation method for heat conduction and thermal stress of embankment in non-homogeneous half-space. Based on the principle of geometric similarity transformation, the method constructs a scaling boundary modeling strategy, introduces a scaling line coordinate system, realizes the spatial mapping of Cartesian coordinates to scaling coordinates, and uses the Jacobian matrix to complete the coordinate transformation of differential operators, thereby accurately representing the non-uniform characteristics of the medium material. The Galerkin method is used to establish the control equation, and the semi-analytical solution technique is used to obtain the temperature field distribution; then the fourth-order Runge-Kutta algorithm is used for reverse iteration to further calculate the thermal stress field caused by the temperature field. The invention can effectively solve the problems of high calculation cost, complex boundary modeling and poor interface continuity of existing numerical methods in non-homogeneous media. It has high computational efficiency, excellent numerical stability and high precision characteristics, and is suitable for thermal-mechanical coupling analysis of complex engineering structures such as multi-layer foundation, embankment-water-foundation coupling system, etc.

Apparatuses, systems, methods, and computer program products are disclosed. A method includes receiving training data (106) comprising labeled data points. A method includes selecting a class of self-adjoint differential operator equations (108). A method includes selecting a set of orthogonal polynomials (110) as a spectral basis. A method includes iteratively optimizing parameters of the differential operator equations (108) based on the training data (106) using a gradient-based optimizer (112) to minimize an objective function. A method includes solving the optimized differential operator equation (108) using a spectral method with the selected orthogonal polynomials (110) to generate a reproducing kernel (114) represented by a kernel tensor. A method includes outputting a machine learning model (116) comprising the reproducing kernel (114) combined with support vectors derived from the training data (106), the model (116) configured to infer labels for unseen data points by estimating similarity measures using the reproducing kernel (114).

The invention discloses a high-performance simulation method for heat conduction and thermal stress of a non-uniform half-space dike. According to the method, on the basis of a geometric similarity transformation principle, a proportion boundary modeling strategy is constructed, a scaling line coordinate system is introduced, space mapping from Cartesian coordinates to proportion coordinates is achieved, coordinate transformation of a differential operator is completed through a Jacobian matrix, and therefore the non-uniform characteristic of the dielectric material is accurately represented. Establishing a control equation by adopting a Galerkin method, and obtaining temperature field distribution in combination with a semi-analytical solution technology; and then a fourth-order Runge-Kutta algorithm is utilized to carry out reverse iteration, and a thermal stress field caused by the temperature field is further calculated. According to the method, the problems of high calculation cost, complex boundary modeling, poor interface continuity and the like of the existing numerical method in the heterogeneous medium can be effectively solved. The method has the characteristics of high calculation efficiency, excellent numerical stability and high precision, and is suitable for heat-force coupling analysis of complex engineering structures such as a multi-layer foundation, a dike-water body-foundation coupling system and the like.

This invention discloses a method for performance evaluation and optimization of automatic differential operators. Under specified hardware and a deep learning framework, it evaluates multiple candidate automatic differential operators and constructs performance profiles. Combining the target scenario, it sets data batch anchor points, compares and analyzes to determine the optimal operator at each anchor point, and uses this operator to train a physical information neural network, gradually increasing the network complexity. It then obtains the maximum runnable network structure under hardware constraints and the upper bound of the data batch without memory overflow, generating corresponding recommended configurations. This invention achieves reproducible operator performance profiles under unified evaluation, quantitatively assesses computational efficiency and resource consumption under different data and network scales, and provides a quantifiable optimization basis for the training configuration of physical information neural networks.

This invention relates to a coherent calculation method for gradient structure tensors based on Gaussian differential operators. It includes: preprocessing a 3D seismic data volume; performing a Hilbert transform on the processed data volume and calculating the instantaneous phase, using the calculated instantaneous phase information as input data for constructing the structure tensor; using multi-scale Gaussian differential operators to calculate the gradients in the traverse, trace, and time directions to construct the gradient structure tensor; using Gaussian smoothing in the approximate fault and stratigraphic directions to enhance the lateral discontinuities in the gradient structure tensor corresponding to fault and stratigraphic features; performing matrix eigenvalue decomposition; and finally, performing different coherence solutions. This invention's gradient structure tensor coherent calculation method based on Hilbert transform and Gaussian smoothing can highlight narrow channels and small-impact faults; by utilizing the structure tensor, it reduces the sensitivity of coherence algorithms to noise, reduces signal clutter and strong noise interference at the intersections of channels and small-scale faults, and improves the accuracy of coherence identification.