188 results about "Basis function" patented technology

The invention relates to a thermal coupling over-reduced order prediction method and system for a multi-component assembled nonlinear system. The method comprises the following steps: collecting multi-scale physical field data; constructing an intrinsic orthogonal decomposition basis function space of a temperature field and a stress field, and establishing a double-field coupling constraint equation; constructing contact thermal resistance parameterized proxy models of a cylinder contact area, a bolt area and a free deformation area by adopting a domain discrete empirical interpolation method; constructing a parametric intrinsic mode tensor network to obtain a decline model which is used for realizing real-time reconstruction of a mode basis function through acquired tensor slices in an online stage; performing dynamic inversion based on a modal basis function reconstruction result, and outputting a predicted transient displacement field, a predicted temperature gradient field and a predicted contact stress field; and obtaining real-time parameters, and calculating a residual error with a corresponding prediction result so as to dynamically update the primary function and interpolation point distribution. Compared with the prior art, the real-time prediction of the transient thermal coupling of the multi-component contact system is realized on the premise of ensuring the precision.

The invention relates to the field of remote sensing image processing, and provides a remote sensing image terrain radiation correction method, device and equipment, and the method comprises the steps: obtaining a to-be-corrected remote sensing image, calculating the terrain parameter of each pixel, dividing the to-be-corrected remote sensing image into a shadow region and a non-shadow region, and determining the direction weighting function of each pixel; calculating a topographic modulation spherical harmonic primary function corresponding to each pixel; training samples are selected in the shadow area and the non-shadow area respectively, a linear model is constructed, and spherical harmonic illumination coefficients representing overall three-dimensional illumination distribution of the shadow area and the non-shadow area are solved; and based on the topographic modulation spherical harmonic primary function, combining the spherical harmonic illumination coefficient corresponding to the area to which each pixel belongs, reconstructing the average incident radiance of each pixel, and then performing inversion to obtain the real reflectivity of the earth surface. According to the method, the problem of inaccurate radiation distortion correction of the remote sensing image under the complex terrain in the prior art is solved, and accurate inversion of the real reflectivity of the earth surface is realized.

The invention relates to the field of rotating machinery fault diagnosis, and discloses a bearing fault diagnosis method based on a physical perception KAM network, and the method comprises the steps: carrying out the discretization of a bearing vibration signal through a Gabor filter group based on physical prior initialization, and generating modal feature lexical elements with physical frequency band meanings; and inputting the lexical elements into a PC-KAM backbone network, calculating a hidden state vector by using a state space model branch, and dynamically adjusting the position of a primary function node of a Kolmogov-Arnod network branch to realize collaborative dynamic feature extraction. In the training stage, an orthogonal subspace constraint and physical perception low-rank adaptation fine tuning mechanism is introduced. And finally, searching a historical fault case, performing multi-modal fusion on the historical fault case and the deep feature sequence, mapping a fusion representation into a soft prompt, and inputting the soft prompt into a large language model to generate a diagnosis report. According to the method, the problems of poor physical interpretability of characteristics and few-sample diagnosis under variable working conditions are effectively solved, and the generalization and decision-making ability of a diagnosis system are improved.

The invention belongs to the field of automatic control, and particularly relates to a nonlinear system dynamic gain global trajectory tracking control method based on a self-adaptive neural network observer, which comprises the following steps: converting an uncertain nonlinear system model with unknown interference according to the requirement of output feedback control to obtain a first nonlinear system model; enabling an unknown nonlinear continuous function in the first nonlinear system model to be expressed as a function only containing an output signal and other system state estimation values; performing approximate approximation on an unknown nonlinear continuous function in the first nonlinear system model by using the first radial basis function neural network vector to obtain a second nonlinear system model; designing a second radial basis function neural network vector to construct a dynamic gain state observer of the second nonlinear system model, and obtaining an estimated value of a system state and an estimated value of an unknown nonlinear continuous function in the model; according to an inversion control method, defining a dynamic system tracking error index containing an intermediate virtual control signal, designing a Lyapunov function, and obtaining a change rate of a dynamic gain, a weight adaptive update rate of a second radial basis function neural network vector, and a control rate of the intermediate virtual control signal and a system input signal; different from most existing nonlinear system control methods, the method combines a novel dynamic gain neural network observer with an inversion controller with dynamic gain, and provides a robust global trajectory tracking control solution for a dynamic system operating under uncertain conditions.

The invention discloses a fracture pressure prediction and internal friction angle joint inversion method for a heterogeneous stratum. The invention belongs to the technical field of petroleum engineering and artificial intelligence cross application, well depth is used as an independent variable, the minimum / maximum horizontal stress, pore pressure and cohesion are combined to construct well depth mixed input, only multi-scale periodic basis function transformation is carried out on the well depth, and a linear well depth channel is reserved; establishing a rupture pressure depth mapping model, introducing an augmented Lagrange physical constraint containing dual variables and a dynamic threshold, adaptively adjusting a physical weight according to a physical residual error and a threshold difference value, realizing dynamic balance of a rupture criterion and data fitting, and searching and optimizing a model topology by using a multi-target network structure; under a limited sample, a fracture pressure profile and a physically reasonable internal friction angle can be obtained at the same time, and the prediction precision and the physical consistency are improved.

The invention discloses a split type three-box girder nonlinear vortex vibration steady-state amplitude intelligent prediction method, belongs to the field of bridge vortex-induced vibration control, and aims to solve the problem of low accuracy of three-box girder vortex vibration nonlinear modeling and amplitude prediction. The method comprises the following steps: acquiring displacement time sequence data through a reduced scale model wind tunnel test, preprocessing to obtain displacement, speed and acceleration dimensionless data, and dividing a data set; constructing a candidate function library containing high-order polynomial terms of the primary function; performing nonlinear system sparse recognition by taking acceleration data as a target item and combining an improved algorithm to obtain a preliminary feature set; a final feature set is obtained through energy-statistics-self-adaption three-stage screening; and finally, constructing a control equation to predict the steady-state amplitude. The method can accurately predict amplitude, coincide test and real bridge observation results, and is less in computing resource occupation and high in numerical value precision.

The invention provides a frequency dispersion curve calculation method based on a decoupling type Legendre-Gauss-Labatto spectral element method, and belongs to the technical field of discrete solution of guided wave propagation in a thin plate, and the method comprises the following steps: S1, constructing a wave equation which comprises a Cartesian space coordinate system based on an orthotropic plate, and combining a constitutive equation, a geometrical relationship under the coordinate system and guided wave displacement to obtain a wave dispersion curve; substituting into a control equation when the volume force is zero to obtain an improved three-dimensional elastic wave equation; s2, a differential matrix is constructed, wherein discretization and decoupling are carried out on a wave equation on the basis of a Lagrange interpolation basis function of a Legendre-Gauss-Labatto node; s3, explicitly embedding the stress free boundary condition into the solving process through matrix line transformation, and solving to obtain a frequency dispersion curve, the derivation process is simplified, the boundary and the interior of the material are decoupled, and the physical significance is clearer. And meanwhile, the high-precision advantage of the spectrum method is maintained, and the calculation rate is remarkably improved.

Various embodiments of this disclosure relate to generation and reception of signals comprising cyclically shifted basis functions. A device may obtain a set of modulation symbols and modulate a plurality of basis functions based on the set of modulation symbols to generate a signal. The plurality of basis functions may comprise cyclically shifted versions of a basis function and a periodic autocorrelation function of the basis function may comprise an ideal (e.g., perfect) periodic autocorrelation function.

The invention belongs to the technical field of hydraulic engineering digital twinning, and provides an arch dam static response rapid calculation method which comprises the following steps: sampling and simulating based on a finite element model in an offline stage to obtain a displacement field snapshot matrix, extracting a dominant mode through intrinsic orthogonal decomposition to construct a reduced-order subspace, and calculating a mode coefficient; and training a radial basis function neural network to establish a nonlinear mapping relation by taking the working condition parameters as input and the modal coefficient as output, and finally, inputting the target working condition parameters into the trained network to predict the modal coefficient in an online stage, and quickly reconstructing a complete displacement field response through linear combination with the POD modal. The method achieves the quick and accurate prediction of the static physical field of the arch dam, and remarkably improves the calculation efficiency of the displacement field of the arch dam.

The invention discloses a method and device for compensating the dispensing height through curved surface fitting. The method comprises the steps that three-dimensional coordinate point information of a plurality of discrete sampling points on the surface of a to-be-dispensed target is collected; building a polynomial of a curved surface model for compensating dispensing according to the number of the sampling points; constructing a matrix, and constructing a linear equation set based on the primary function; and the weight coefficient of the linear equation set is solved through a Gaussian elimination method, a fitted quadric surface equation after interpolation calculation is obtained, and the dispensing height is compensated based on the quadric surface equation. According to the method, the polynomial is fitted through the three-dimensional coordinate point information, the linear equation set is constructed, the predicted compensation value is obtained after interpolation calculation is carried out according to the fitting result so as to compensate the dispensing height, the high-precision continuous curved surface model can be constructed by collecting discrete sampling points, real-time interpolation calculation of any coordinate is supported, and the precision of the dispensing height is improved. The method can solve the problem of insufficient fitting precision of dispensing height compensation based on a single plane.

The invention discloses a front subframe structure MaOP method and device based on TPT, a medium and a program product, and the method comprises the steps: (1) constructing a MaOP design model capable of optimizing the weight, modal, strength and rigidity at the same time based on front subframe longitudinal beam and load analysis; (2) generating an elite population based on a diversity criterion and Latin hypercube, obtaining target values of the elite population, establishing a data set, and constructing a radial basis function model; (3) designing co-evolution operation driven by TPT to generate a candidate frame set; (4) an individual potential evaluation criterion is constructed based on the advantage and disadvantage target sets, and an optimal candidate frame is screened; and (5) obtaining each target value of the optimal candidate frame, updating the data set and the radial basis function model, returning to the step (3) until all optimization targets meet requirements, and outputting an optimal parameter value. According to the method, a TPT-driven coevolution mechanism is adopted, radial basis function model prediction is combined, and the multi-performance index optimization process for the front auxiliary frame can be effectively balanced.

The invention belongs to the field of real-time monitoring, particularly relates to a chemical process real-time monitoring method and system based on digital twinning, and aims to solve the technical problem that an existing method lacks an online model correction and updating mechanism. The monitoring method comprises the following steps: S1, constructing a state snapshot data set, and synchronously collecting real-time measurement data; s2, identifying a process fluctuation interval, and selecting to-be-selected state snapshots to form an optimal snapshot matrix; s3, calculating a reduced-order truncation error energy ratio, and constructing a reduced-order model based on a reduced-order basis function; s4, in the real-time monitoring stage, if the norm of the prediction residual error is smaller than a monitoring threshold value, a Kalman filtering algorithm is adopted to correct the state coefficient of the reduced-order model; otherwise, calculating the projection error of the prediction residual on each primary function in the standby primary function library; and outputting a full-order state vector reconstructed based on the corrected or updated reduced-order model. The monitoring method provided by the invention ensures the continuous effectiveness and accuracy of monitoring when the chemical process changes.

The invention belongs to the technical field of space geodetic survey observation data inversion regional land water reserve change, and provides a method and related equipment for inversion of land water reserves based on a Slepian basis function combined with GNSS three-dimensional deformation, and the method comprises the steps: obtaining vertical and horizontal deformation observation values of GNSS through simulation; determining a Slepian primary function of the target area according to the boundary data and a preset maximum expansion order, and further determining a function relationship between a Slepian coefficient of GNSS three-dimensional deformation and a Slepian coefficient driven by mass load change; determining an observation equation according to the function relationship, and resolving the observation equation by adopting least square joint adjustment; and according to the Slepian coefficient driven by the mass load change, carrying out inversion on the regional land water reserves of the target region to obtain a regional land water reserve change result. The method has the beneficial effect that the precision and efficiency of regional land water reserve inversion are improved.

The invention discloses a load curve decomposition method and system based on a curvature equipartition rational B-spline basis function, and the method comprises the steps: calculating the curvature of a historical load sequence, generating a continuous curvature function, determining a group of B-spline node sequences meeting the cumulative absolute curvature equipartition condition, and enabling the node distribution to be adaptive to the load fluctuation intensity; a B-spline primary function is generated based on the node sequence, and a rational B-spline primary function is constructed through weight optimization so as to finely describe a continuous time fluctuation mode; a fitting model is established in combination with time period virtual variables, and a load curve is decomposed into two parts, namely a time period characteristic load level representing different time period reference power consumption intensity and a time characteristic load curve representing a continuous change fluctuation form. The defect that a traditional uniform spline is poor in adaptability to a non-uniform load form is overcome, self-adaptive decomposition with definite physical significance is achieved, and a better-quality data basis is provided for load analysis and prediction.

The present application belongs to the technical field of structure optimization design, and discloses a macro-micro double-scale structure topology optimization method and equipment capable of controlling the minimum size of microstructure, comprising the following steps: (1) interpolating the elastic matrix and the corresponding density of the actual microstructure in the offline database by using radial basis function interpolation, and then constructing a mapping model; (2) constructing a compliance minimization optimization model, wherein the design variables of the optimization model are the cutting height of two virtual microstructures in each unit and the topology variable, and the constraint functions are the volume fraction of the overall structure and the topology variable constraint; (3) calculating the sensitivity of the objective function and the constraint function to the design variable, and then updating the design variable; (4) when the compliance error of the updated double-scale structure meets the optimization termination condition, the optimization is completed and the double-scale structure meeting the requirements is obtained; otherwise, go to step (3). The present application solves the problems of low calculation efficiency and poor connectivity.

The invention discloses a rapid prediction method for a particle thermal-mechanical coupling process, and the method comprises the steps: scanning energy carrier particles based on a microfocus computed tomography technology, and generating a three-dimensional digital model; importing the three-dimensional digital model into a multi-physics field simulation platform, and establishing a transient full-order model; based on the transient full-order model, generating a training data set and a test data set under different working conditions and corresponding temperature fields and stress fields; performing decomposition calculation on the training data set by using an intrinsic orthogonal decomposition POD reduced-order model to obtain a POD primary function and a spectral coefficient; establishing a mapping model from an input working condition to an output spectral coefficient based on a BP neural network; inputting the target working condition into the mapping model, and outputting a POD spectral coefficient; and on the basis of the calculation result and the POD spectral coefficient, reconstructing full-field physical quantity distribution at any moment under the target working condition through linear combination. The method solves the problems that traditional numerical simulation is low in calculation efficiency and large in resource consumption.

The invention provides a numerical feature embedding method based on a scale perception radial basis function and a situation awareness method for the health degree of power equipment, and the method comprises the steps: obtaining a logarithm of to-be-coded numerical data x, and obtaining a base number D and an index L; performing RBF (Radial Basis Function) expansion on the base number D to obtain the expression of the base number D; carrying out soft sub-bucket distribution on the index L to obtain a distance from the index L to each soft sub-bucket, taking the distance as a coefficient of the soft sub-bucket, and weighting each soft sub-bucket according to the coefficient of the soft sub-bucket to obtain representation of the index L; and converting the representation of the index L into two numbers by adopting a gated linear layer network, and scaling the representation of the base number D to obtain the coded representation of the numerical data x.

This invention discloses a method and system for fitting safety monitoring data based on adaptive hybrid basis functions, belonging to the field of computer-aided data analysis technology. The method achieves fully automatic high-precision curve fitting through a six-layer adaptive architecture: it automatically analyzes the trend complexity, periodicity, noise level, and nonlinearity of the data using multi-dimensional feature recognition technology; it calculates the data complexity score based on the feature analysis results and intelligently selects basis function combinations from an extended basis function library containing 32 sub-functions across 8 categories; it constructs a dynamic weighted hybrid basis function model, achieving adaptive adjustment of model parameters through time-varying weight functions and coupling correction terms; and it employs a multi-model dynamic fusion mechanism, integrating multiple candidate models based on six-dimensional confidence evaluation. This invention innovatively introduces adaptive regularization technology and a hierarchical optimization strategy, effectively balancing fitting accuracy and generalization ability, and possesses advantages such as full automation, strong robustness, and complete uncertainty quantification.

The present application relates to the field of electromagnetic numerical calculation, and discloses a kind of method for solving electromagnetic scattering based on adaptive block Krylov subspace base function, method includes the following steps: step one: target region is carried out adaptive region decomposition, and target subdomain is obtained;Step two: target subdomain is expanded, and extended subdomain is formed;Step three: using optimized extended subdomain, the solving calculation of electromagnetic scattering is carried out.The main advantage of the present application is that the efficiency of constructing Krylov subspace base function is higher by using adaptive block technology, which significantly reduces the generation time of Krylov subspace base function based on block, optimizes the block expansion of subdomain, improves the solving calculation time, uses clustering algorithm to carry out region decomposition on the calculation target, and uses the average distance of clustering data points to cluster center to expand each subdomain to ensure the continuity of current, which not only ensures the calculation accuracy, but also improves the construction efficiency of base function, significantly reduces the generation time of Krylov subspace base function based on block.

The invention relates to the technical field of high-current particle beam diagnosis, in particular to a high-energy ion beam three-dimensional reconstruction method and system based on secondary electron emission signals. According to the technical scheme, the method comprises the steps of data preprocessing and conversion, geometric space up-sampling, point assignment generation and model boundary division and output. According to the method, the spatial sparsity of original data is overcome through geometric upsampling, the fidelity of physical attribute reconstruction is remarkably improved by utilizing a topological structure based on a minimum spanning tree and a primary function frequency superposition model, automatic and accurate division of beam boundaries is realized according to a physical threshold value, an end-to-end automatic processing flow is formed, and the method has the advantages that the method is simple and convenient to operate and high in practicability. And outputting a visual three-dimensional model supporting interactive analysis, systematically solving the problems of data sparsity, interpolation distortion and boundary fuzziness in the prior art, and realizing high-precision and high-efficiency reconstruction and visual analysis of the three-dimensional form of the high-energy ion beam.

The invention discloses a meshless Galerkin-Newmark method for calculating a transient wave propagation problem. The meshless Galerkin-Newmark method comprises the following steps: dispersing a transient wave propagation problem domain into nodes; selecting an interpolation primary function and a weight function; constructing a node interpolation primary function and a global interpolation format by adopting a moving least square method based on the selected function; based on a global interpolation format, combining a partial differential control equation and a Galerkin weighted residual value method to obtain a transient wave propagation problem system matrix equation; performing time domain discretization through a Newmark time integration method to obtain a discrete time equation; solving the discrete time equation to obtain a numerical calculation result; and analyzing a result and comparing the result with a common method to finish solving and analyzing a transient wave propagation problem. The meshless Galerkin-Newmark method for calculating the transient wave propagation problem has a monotonous consistent convergence characteristic in the numerical calculation of the transient wave propagation problem, and the calculation precision can be continuously improved along with the reduction of the time integral step length.

This invention belongs to the field of artificial intelligence and system response calculation technology, and provides a method and system for calculating system response based on a generalizable physical information neural network. The technical solution involves establishing a family of differential equations consisting of multiple governing equations based on the physical characteristics of the system to be analyzed, and obtaining the corresponding dataset; constructing a neural network model consisting of a main network and multiple channel networks, where the main network learns the basis functions representing the system response and shares them with all channel networks; each channel network processes a specific differential equation task within the task family and learns the basis function coefficients corresponding to that task; inputting the dataset into the neural network model, training the model by minimizing a loss function containing multiple constraints, and obtaining the optimal solution for the system response under different stimuli based on the trained model. This method can solve complex differential equations more accurately and improve the model's generalization performance on unseen tasks.

The invention discloses a key area restoration parameter mapping method based on dynamic grid local re-subdivision, and belongs to the technical field of engineering simulation. The method comprises the following steps that octree and quadtree partitions of an old grid are searched for units of a re-subdivision area on a new grid; searching an old grid unit where the degree-of-freedom coordinate point is located in the unit array of the partition, and then interpolating the physical field through a primary function; and calculating the value of the freedom degree coordinate point of the new grid. Mapping operation is carried out in a key area near the moving part in a concentrated mode; performing a moving restoration operation on a re-subdivision area near the boundary of the moving part, and then performing search mapping; and a simplified treatment mode is adopted for the air domain. According to the method, the unit search range and the calculation overhead in the physical field parameter mapping process are reduced, the dynamic grid physical field mapping efficiency is improved, the accuracy and the consistency of physical field transmission in a key area are guaranteed, and efficient and accurate physical field mapping and comprehensive improvement of engineering simulation efficiency are achieved.

The invention discloses a method for analyzing time-frequency characteristics of collision vibration by using a segmented B-spline wavelet collocation method, which comprises the following steps of: (1) establishing a dynamic equation for wavelet discretization, discretizing a dynamic control equation of a collision-vibrator system by using a 4-order B-spline wavelet basis function, and establishing a nonlinear algebraic equation set about a wavelet coefficient; (2) carrying out segmented iterative solution on the time domain, dividing the whole time domain into a plurality of sub-time periods which are connected in sequence, and carrying out iterative solution on the nonlinear algebraic equation set in each sub-time period to obtain a global wavelet coefficient; and (3) analyzing the time-frequency characteristics, and directly calculating energy distribution based on the wavelet coefficient to realize time-frequency joint characterization. The invention aims to provide a method which can fuse solution of system response and extraction of time-frequency characteristics in a unified mathematical framework, and realizes high-precision time-frequency joint characterization by directly solving wavelet coefficients, thereby overcoming inherent defects of an existing two-step method.

The invention provides a continuous intervention effect prediction method and device, a training method and device, equipment and a medium, and relates to the technical field of computers, in particular to artificial intelligence, big data and deep learning technologies. Comprising the following steps: performing multi-head self-attention interaction on covariables to obtain covariable embedding; embedding the covariable and inputting the processing variable into a countercurrent network, wherein the countercurrent network is used for estimating conditional distribution of the processing variable under the covariable condition; mapping the processing variables into processing vectors through a smooth basis function, and generating network parameters of each layer in the main network according to different processing variables in the processing vectors; the covariable embedding and processing vector is input into the main network, and the main network is used for calculating fusion features based on the network parameters of each layer according to the covariable embedding and processing vector and outputting an initial prediction result according to the fusion features; and performing weighted calculation on the initial prediction result by using conditional distribution to obtain a target prediction result of the dependent variable under continuous intervention of the covariable and the processing variable.

The invention provides an interference fit-oriented cylinder surface system error separation and morphology modeling method, which comprises the following steps of: 1, measuring point cloud data of shaft and hole cylindrical surfaces, measuring the point cloud data of the shaft and hole assembling cylindrical surfaces of to-be-measured interference fit shaft and hole parts by adopting a three-coordinate measuring instrument, and measuring the point cloud data of the shaft and hole assembling cylindrical surfaces by adopting a three-coordinate measuring instrument; decoupling separation of the system error and the random error is realized in the cylinder surface global range, a first-order eccentric component is eliminated through axis iteration positioning, and a significant Fourier component is screened through partial F test, so that decoupling separation of the system error and the random error in the cylinder surface global range is realized; the system error traceability accuracy is greatly improved; meanwhile, a Fourier basis function and radial basis function mixed model is provided, multi-scale morphology high-fidelity reconstruction is achieved, local random concave-convex errors, periodic textures and the overall trend are restored in a high-precision mode, and compared with an existing single model, the morphology restoration degree is greatly improved.

A method for maintaining physical assets based on recommendations generated from operational data analysis and a composite model representing multiple models of the physical assets includes: constructing the composite model by a computing device using a port-reduced static condensed reduction primitive approximation with respect to at least a portion of a partial differential equation; the computing device analyzing error indices associated with at least one model within the composite model to determine if the error indices exceed a tolerance level, and accordingly increasing the number of basis functions in the port-reduced static condensed reduction primitive approximation; the computing device receiving first operational data associated with at least one region of the physical asset and updating the composite model; and the computing device providing recommendations for maintaining the physical asset based on the updated composite model.

A model representing a physical object in a shape optimization according to a design objective, and a control point for altering a shape of the physical object are received. The shape is defined by a set of nodes in the model. Sibling models are generated from the model according to a perturbation scheme. The control point is perturbed with respective perturbed values for the sibling models. Each sibling model contains nodal location changes for the nodes. The nodal location changes are determined based on a respective shape function formulated according to a respective perturbed value at the control point and one or more simulated physical behaviors of the model. The model is updated to have an optimal value for the control point. The optimal value is identified from a relationship according to the design objective. The relationship correlates a physical characteristic of the sibling models to the respective perturbed values.

This invention relates to the field of pet food spectral detection technology, and discloses a pet food spectral detection device and method. The method involves sampling at equal intervals within a preset wavelength range, eliminating noise interference through dark current and standard white plate calibration; taking the natural logarithm of reflectance to balance the dynamic range; constructing a linear spline basis at equal intervals, and adaptively calculating the regularization coefficient based on the energy ratio of the signal and basis functions; constructing an augmented matrix based on the inner product of the basis functions and the signal, and solving for the spline coefficients using Gaussian elimination; reconstructing the spectrum using the coefficients and quantifying the residuals; establishing a reference model based on the mean and standard deviation of multiple qualified sample coefficients; comparing the Euclidean distance between the coefficients of the sample to be tested and the model mean with a threshold, and generating residuals, distances, thresholds, and a judgment report; the entire process requires no empirical parameters or manual tuning, enabling batch online adaptive detection, achieving rapid and accurate detection with noise correction, feature enhancement, overfitting suppression, and traceability.

The application discloses a multi-constraint geometric nonlinear level set topology optimization method, device and medium, and aims to solve the problem that the current linear condition level set method is difficult to well optimize the large deformation of a to-be-optimized component. The method divides a design domain corresponding to the to-be-optimized component into a plurality of finite element units, and establishes corresponding level set radial basis functions based on volume constraints; according to the relationship between the element strain increment and the node displacement increment of the finite element unit, displacement constraint terms and frequency constraint terms are introduced to extend the Lagrange function; according to the nonlinear element unbalanced force, the element thermal load and the overall thermal load are calculated; based on the extended Lagrange function and the overall thermal load of the to-be-optimized component under the set temperature, the design domain is topologically optimized. The application considers the displacement constraint and the frequency constraint under the nonlinearity, is suitable for the to-be-optimized component under the large deformation condition, and can achieve an optimal topology result.