50 results about "Positive-definite matrix" patented technology

The invention discloses a construction scene dynamic obstacle avoidance method and system based on multi-source image fusion, and belongs to the technical field of computer vision and image processing, and the method comprises the steps: mapping multi-source image data to a symmetric positive definite matrix manifold space, carrying out the high-precision registration based on Riemannian geometric measurement, achieving the self-adaptive feature fusion through geometric flow optimization, and achieving the dynamic obstacle avoidance of a construction scene. According to the method, spatial topological features of obstacles are extracted through topological data analysis, and probability trajectory prediction is carried out through a variational inference method. Compared with the prior art, the method has the advantages that the obstacle avoidance success rate is increased by 35%-50%, the false alarm rate is reduced by 40%-60%, the similarity of the technical scheme is lower than 20%, and the method has the advantages that the method is suitable for large-scale popularization and application. And the accuracy, the reliability and the self-adaptive capability of dynamic obstacle avoidance in the construction scene are remarkably improved.

The invention discloses an interval type parameter uncertainty model correction method based on a Riemannian manifold and Gaussian process model, and belongs to the technical field of engineering parameter uncertainty quantification and model correction. According to the method, aiming at the defect that traditional interval analysis cannot represent parameter correlation, a convexly optimized minimum volume ellipsoid model is constructed, and a coupling relation between parameters is captured through a geometric learning framework; designing a Gaussian process regression agent model based on a logarithm Euclidean metric kernel function, and keeping symmetric positive definite matrix constraints by using a manifold kernel function; and providing a Riemann gradient optimization algorithm, and realizing parameter space unconstrained optimization through matrix logarithm mapping. The technical scheme comprises three core modules: an ellipsoid convex model parameterization module for realizing and explicit representation of parameter correlation, a manifold embedding agent model module for guaranteeing mathematical consistency of physical constraints, and a manifold gradient optimization module for improving high-dimensional parameter correction efficiency. According to the method, the problems that a traditional method depends on heuristic projection, the calculation efficiency is low, and constraint keeping is difficult are effectively solved, and a high-precision and interpretable uncertainty parameter correction tool is provided for a numerical model in engineering.

The invention discloses a Riemannian manifold-based space-time joint anti-interference direct positioning method. The method comprises the following steps of: acquiring signals emitted by an interference source and a radiation source by using a plurality of distributed antenna arrays; segmenting a received signal, constructing a sample covariance sequence, and establishing a model covariance matrix at each frequency; determining a Riemannian distance expression between the sample covariance sequences by constructing a Riemannian manifold on the basis of the characteristic that the sample covariance sequences are located on an Ermitt positive definite matrix manifold, and solving a Riemannian mean value of the sample covariance sequences; utilizing Riemannian geometric characteristics of a sample covariance matrix, and taking a Riemannian distance on an HPD matrix manifold as a judgment criterion of fitting accuracy; replacing an Euclidean distance with a Riemannian distance, performing approximate processing on the Riemannian distance by using a logarithm Euclidean distance, and constructing a direct positioning cost function based on the logarithm Euclidean distance; and two-step spectrum peak searching is carried out through the direct positioning power spectrum, and a direct positioning result of the direct positioning cost function is determined.

This application discloses a method and system for estimating the direction of arrival (DOA) of weak targets based on Riemannian manifold background suppression and adaptive sparse Bayesian learning. The method includes: acquiring time-series signals using a sensor array to construct a series of sample covariance matrices, mapping them to a point sequence on a Hermitian positive definite matrix manifold space; iteratively calculating the background interference covariance matrix using the non-Euclidean geometric properties and logarithmic shielding effect of the Riemannian metric; mapping the background interference covariance matrix back to Euclidean space, adaptively performing background subtraction based on an energy decision mechanism to reconstruct a positive definite covariance matrix to be measured; inputting the covariance matrix to be measured into a sparse Bayesian learning framework, first iteratively recovering the signal power through adaptive mesh refinement sparse Bayesian learning, then performing a closed-loop iteration of subspace noise cleaning while keeping the mesh fixed to recover the sparse spatial spectrum of the target signal; and finally, using local analytical interpolation techniques to eliminate mesh quantization errors and calculate the precise DOA of the target.

The application provides a Riemannian manifold-based task degree-of-freedom robot joint motion planning method, which comprises the following steps: determining a plurality of position points and a plurality of poses corresponding to each position point according to an initial task path of a robot and unconstrained degrees of freedom; determining a configuration corresponding to at least one target pose of each position point according to the plurality of poses corresponding to each position point, an inverse kinematics formula and a threshold range of each joint; determining at least one symmetric positive definite matrix corresponding to each position point according to each configuration and a robot speed formula; determining a plurality of groups of to-be-optimized connecting lines based on the at least one symmetric positive definite matrix corresponding to each position point; iteratively optimizing the plurality of groups of to-be-optimized connecting lines to determine a target connecting line, and combining the position points corresponding to each target symmetric positive definite matrix in the target connecting line and the configurations in the corresponding configurations into a joint motion trajectory of the robot. The stability of the speed change in the robot motion process is improved, and the accuracy of the robot when performing a task is ensured.

The present application relates to a kind of facing polynomial fuzzy control system cost control stability judging method, comprising the following steps: establishing polynomial fuzzy model;According to the first SOS condition based on Lyapunov function, try to solve the first polynomial matrix and the second polynomial matrix, omit non-convex term in solving process, judge whether it is successful, if yes, based on the first polynomial matrix and the second polynomial matrix, obtain feedback gain;Based on feedback gain, according to the second SOS condition, try to solve positive definite matrix, judge whether it is successful, if yes, based on positive definite matrix, construct polynomial Lyapunov function, realize cost control analysis based on polynomial Lyapunov function.Compared with prior art, the present application solves the non-convex optimization problem in cost control in two steps, avoids the influence of the constraint existing in input matrix itself on the flexibility of fuzzy control system design, and improves the performance of control system by obtaining the numerical value of cost J.

The invention provides a data compression method and device, electronic equipment and a chip system, and the method comprises the steps: carrying out the diagonalization matrix transformation of original conjugate symmetric positive definite matrix data, and determining the transformed target matrix data; the diagonal element data in the target matrix data are stored by adopting a first bit width, the non-diagonal element data in the target matrix data are stored by adopting a second bit width, and the first bit width is larger than the second bit width. According to the method, most information in matrix data is concentrated on diagonal elements through low-complexity matrix transformation, and secondary information is reserved on non-diagonal elements. And in combination with differential bit width quantization storage, diagonal elements in the target matrix data are subjected to high bit width quantization storage, and non-diagonal elements in the target matrix data are subjected to low bit width quantization storage. Therefore, on the premise of ensuring low precision loss and low complexity, the conjugate symmetric positive definite matrix data can be effectively compressed, so that the hardware storage overhead is reduced.

The invention discloses a vehicle interaction decision-making method based on an unprotected intersection and a related device, and the method comprises the steps: obtaining a system state matrix, an own vehicle control matrix and an other vehicle control matrix in linear system state equations of an own vehicle and an other vehicle, first to fourth positive semi-definite matrixes and first and second positive definite matrixes are arranged in the optimization target of the linear quadratic differential game problem of the own vehicle and the other vehicle; taking the first positive semidefinite matrix and the third positive semidefinite matrix as a first intermediate matrix and a second intermediate matrix at the Nth moment respectively; according to the first intermediate matrix, the second intermediate matrix, the first positive definite matrix, the second positive definite matrix, the system state matrix, the self-vehicle control matrix, the other-vehicle control matrix, the second positive definite matrix and the fourth positive definite matrix at the Nth moment, reverse recursion is carried out on an optimal control gain matrix equation set of the two vehicles and a coupling Riccati equation of the first intermediate matrix and the second intermediate matrix at the kth moment; and obtaining an optimal control gain matrix sequence of the vehicle, and controlling the vehicle according to a control quantity sequence determined based on the optimal control gain matrix sequence.

The application provides a negative virtualization method for a high resonance mode flexible system, first, a flexible system model is established, a dynamic feedforward compensator is introduced, and a system state space equation after feedforward compensation is given; second, a set of positive definite matrices is selected for the compensated system, and a set of matrix inequality conditions are derived, so that the compensated system has a negative virtual property, and further solving the matrix inequality conditions can obtain the parameters of the feedforward compensator; finally, an improved negative virtual controller is designed for the system after negative virtualization to ensure the stability of the closed-loop system. The method of the application ensures that the high resonance mode flexible system with non-negative virtual property can use the negative virtual theory to design the controller, and expands the application range of the negative virtual theory in the flexible system. Through the satellite model simulation experiment, it is shown that under the condition of parameter perturbation or unmodeled dynamics, the designed system can simultaneously consider the response characteristics and robustness.

The method comprises the following steps of: decomposing a measurement matrix of each strapdown triaxial magnetometer into a unit orthogonal matrix and a symmetric positive definite matrix by utilizing the characteristic that a magnetic field modulus is independent of the unit orthogonal matrix and adopting a polar decomposition technology, and obtaining an equivalent zero offset and the symmetric positive definite matrix of each strapdown triaxial magnetometer by adopting ellipsoid equation iteration linear least square fitting; a virtual coordinate system is introduced, a vector modulus value correction value of measurement data of each strapdown triaxial magnetometer is calculated, a correction value of a magnetic field horizontal modulus gradient is further obtained, and calibration of the strapdown triaxial cross magnetic array is completed. According to the method, the ellipsoid equation is solved with high precision by adopting the iterative linear least square method, the strapdown three-axis cross magnetic array does not need to be accurately rotated, high-precision calibration can be carried out under the condition of providing the geomagnetic field modulus, and the operation is simple and convenient; the iterative linear least square algorithm is simple, the calculation amount is small, and engineering implementation is easy.

The invention provides a PSR-JBLND-based DOA estimation method, apparatus and device, and a medium. The method comprises the steps of constructing a sensor array receiving signal model according to a guide vector of an information source; on a preset time sequence dimension, a coordinate delay reconstruction method is adopted, a sequence in the sensor array receiving signal model is mapped in a phase space of a preset embedding dimension, and a reconstruction track matrix is obtained; obtaining the optimal time delay during phase-space reconstruction through an average mutual information method, eliminating the time delay of a reconstruction track matrix based on the optimal time delay, and then carrying out augmented matrix construction to obtain an optimized sensor array receiving signal model matrix; matrix information geometry is introduced, Jensen-Bregman LogNorm divergence is constructed, and based on the Jensen-Bregman LogNorm divergence, two Hermitian positive definite matrixes are constructed on an optimized sensor array receiving signal model matrix manifold; and obtaining a DOA estimation result based on the divergence measurement corresponding to the two Hermitian positive definite matrixes at different angles.

The invention discloses a radiation source direct positioning method for suppressing intermittent interference. The method comprises the following steps: acquiring receiving signals of a distributed antenna array for an interference source and a radiation source in the presence of an intermittent interference source; segmenting a received signal, and determining a corresponding sample covariance matrix based on sampling and Fourier transform so as to construct a sample covariance matrix sequence; determining a Riemannian distance expression between the sample covariance matrixes by constructing a Riemannian manifold on the basis of the characteristic that the sample covariance matrixes are located on an Ermitt positive definite matrix manifold, and solving a Riemannian mean value of a sample covariance matrix sequence; based on an MVDR criterion, constructing a cost function corresponding to each grid position in the to-be-solved region; replacing a sample covariance in the cost function with a Riemannian mean value, and solving the cost function by adopting an optimization method to obtain a direct positioning power spectrum based on the Riemannian mean value; and performing two-step spectrum peak search on the direct positioning power spectrum, and determining a position estimation value result of the radiation source.

The invention belongs to the technical field of medical image processing, provides a medical image-based computer-aided diagnosis method and system, and solves the problem of insufficient computer-aided diagnosis. The method comprises the following steps: collecting a brain diffusion tensor image of a target object and a surface electromyogram signal of an associated muscle group; converting the image into Riemannian manifold data through tensor resolving and symmetric positive definite matrix mapping; extracting a Hurst index of the electromyographic signal based on remarking range analysis, and generating a motion feature vector; using Riemannian logarithm mapping and canonical correlation analysis to project manifold data and motion features to a correlation space, and extracting a maximum correlation component to generate a coupling feature vector; determining a reconstruction site through Riemannian index mapping, and calculating a geodesic line length between the reconstruction site and the reference state point to obtain a deviation value; and quantitatively judging the nerve remodeling degree and the motor function level of the stroke patient according to the deviation value. According to the application, accurate quantitative evaluation of the stroke nerve remodeling and motion recovery state is realized.

This method uses magnetic resonance (MR) data to estimate a diffusion tensor distribution (DTD). The method includes inverting a Fredholm integral of the first kind, specifically performing an nD Inverse Laplace Transform subject to several constraints. First, a positive definiteness constraint is used, which zeros out a subset of diffusion tensor components that do not lie on a manifold of symmetric positive definite matrices. Second, marginal distribution constraints are used, which further partition the manifold of symmetric positive definite matrices into even smaller domains to improve DTD estimates in each MR voxel.

This invention discloses a data privacy protection method and related equipment based on Gaussian process regression, including: acquiring training data and test data; calculating the covariance matrix and training Gaussian process regression based on the training data; generating exponential random numbers and performing exponential calculation on a Gaussian integer ring using a secret sharing technique; decomposing the positive definite matrix in the Gaussian process regression according to the Joliski decomposition method, and inverting the decomposed positive definite matrix on a Gaussian integer ring using a secret sharing technique to construct a Gaussian process regression model; and predicting test data based on the Gaussian process regression model. This method can improve the efficiency of exponential calculation and achieve secure inversion without revealing the privacy of the input matrix.

The present invention proposes a Cholesky decomposition heterogeneous parallel optimization method and system based on the Shenwei architecture, which relates to the field of high-performance computing technology. The method comprises: dividing a symmetric positive definite matrix into sub-blocks based on a distributed parallel allocation scheme and iteratively completing the matrix decomposition; allocating each sub-block to a different process through the MPI programming model, exchanging data between processes through asynchronous communication, and performing coarse-grained task-level parallel acceleration; utilizing the master-slave core acceleration parallel characteristics of the Shenwei architecture to perform two-level parallel acceleration on the four operations in the Cholesky decomposition; wherein, for GEMM and SYRK operations, the column vectors of the matrix are mapped to the slave core array, and the columns are divided according to the number of slave cores; the calculation process is optimized through a double buffering mechanism, vectorized operations and loop unrolling technology to improve parallel efficiency; for the TRSM operation, it is decomposed into multiple TRSV operations, which are allocated to the slave cores for parallel execution, and the data dependency is reduced by loop reading and data broadcasting to achieve efficient parallel computing.

The invention provides a parallel solving method of a chip dynamic power consumption model based on Cholesky decomposition, and the method specifically comprises the following steps: S1, receiving sparse symmetric positive definite matrixes, carrying out the matrix sorting, and constructing a chip power consumption model matrix; s2, rearranging sub-matrixes of the chip power consumption model matrix and constructing an elimination tree; s3, performing hierarchical cutting and sub-tree recursive splitting on the eliminated tree; s4, traversing the sub-tree set after recursive splitting, merging the sub-trees with the node number lower than a preset minimum threshold value, and generating a multi-diagonal-block matrix; s5, performing Cholesky decomposition on the multiple diagonal block matrixes in parallel to obtain a lower triangular matrix; s6, the diagonal blocks and the non-diagonal coupling blocks of the lower triangular matrix are recombined into an extended sub-matrix, an inverse matrix is solved step by step through a recursion method, and parallel solving of the diagonal block inverse matrix in the multi-diagonal-block matrix is achieved; s7, solving an inverse matrix of the multi-diagonal block matrix; and S8, carrying out parallel calculation on the Schur complement based on the inverse matrix of the multi-diagonal block matrix so as to realize the parallel solution of the chip power consumption model.

The invention provides a Riemannian manifold-based task freedom degree robot joint motion planning method, which comprises the following steps of: determining a plurality of position points and a plurality of poses corresponding to the position points according to an initial task path and an unconstrained freedom degree of a robot; determining a configuration corresponding to at least one target pose of each position point according to the plurality of poses corresponding to each position point, an inverse kinematics formula and each joint threshold range; determining at least one symmetric positive definite matrix corresponding to each position point according to each configuration and a robot speedology formula; determining a plurality of groups of to-be-optimized connecting lines based on the at least one symmetric positive definite matrix corresponding to each position point; and iterative optimization is conducted on the multiple sets of connection lines to be optimized, target connection lines are determined, and the position points corresponding to the target symmetric positive definite matrixes in the target connection lines and the configurations in the corresponding configurations are combined into the joint movement track of the robot. The stability of speed change in the movement process of the robot is improved, and the precision of task execution of the robot is guaranteed.

The invention provides a non-Gaussian non-stationary signal detection method based on Riemannian manifold analysis, which belongs to the field of signal detection, and comprises the following steps: receiving a signal to be detected and a reference noise signal by a receiver, and preprocessing the signal into a covariance matrix sequence by using a Gaussian window function; a Hermitian positive definite matrix HPD manifold is constructed, Rao-Fisher measurement is selected on the HPD manifold, and the property of the HPD manifold is obtained according to the Rao-Fisher measurement; adopting a parameter estimation method on the HPD manifold to obtain the characteristics of Riemannian Gaussian distribution RGD; based on RGD characteristics on an HPD manifold, a generalized likelihood ratio detector based on RGD is constructed, the detector is applied to a covariance matrix sequence after received signal preprocessing to obtain a detection statistic, the detection statistic is compared with a detection threshold, and a detection judgment is made. The invention provides an efficient detection algorithm based on Riemannian manifold analysis aiming at the problems that weak target detection is difficult under a non-Gaussian non-stationary signal background and the performance loss of a traditional detection algorithm is large.

This application relates to a method and system for solving conjugate gradient finite element models based on sparse convolution preprocessing. The method includes establishing a structural finite element model, generating a structural stiffness matrix A and a load vector b, and constructing a linear equation system Ax=b, where A is a sparse symmetric positive definite matrix. A preprocessing sub-generator is constructed by training different structures using a sparse convolutional neural network. The stiffness matrix A is input into the preprocessing sub-generator to obtain a preprocessing factor. A symmetric positive definite preprocessor is constructed based on the preprocessing factor. The linear equation system Ax=b is solved using the preprocessed conjugate gradient method to obtain the displacement response vector x. This application optimizes the condition number of the preprocessed matrix to improve convergence speed and reduce solution time. It adapts the sparse convolutional U-net structure to large-scale sparse matrices, improving training efficiency and forming a unified and scalable preprocessing framework for structural engineering, providing a general and efficient preprocessing strategy for large-scale finite element model analysis.

This application discloses a real-time decision-making method, system, and medium for intelligent agents based on Riemannian manifolds, relating to the field of artificial intelligence technology. The method, executed by an intelligent decision-making system, includes: constructing a behavior transition graph based on a historical trajectory dataset; mapping the attention matrix generated by a large language model in the decision-making task to a symmetric positive definite matrix manifold for representation; embedding the behavior transition graph into a hyperbolic Riemannian space for representation; learning the geometric alignment mapping from the symmetric positive definite matrix manifold and hyperbolic Riemannian space to a common metric space by optimizing the objective loss function; in the inference phase, acquiring current environmental observation data and inputting it into the large language model to obtain the corresponding attention representation, which is then mapped to the common metric space to obtain a query vector; and using actions corresponding to action nodes with a geometric distance below a preset threshold as control commands. This significantly reduces the computational overhead of decision-making and improves cross-scenario generalization ability and decision interpretability.

The present invention belongs to the technical field of medical data processing and machine learning, and relates to an arrhythmia classification method based on statistical manifolds, including: heartbeat segmentation and subsequence division: performing R-wave peak detection, preprocessing, heartbeat extraction and subsequence division; constructing a Gaussian kernel matrix: calculating the DTW distance to provide a distance metric for the Gaussian kernel matrix, and constructing the Gaussian kernel matrix based on the DTW distance to capture the geometric structure relationship between subsequences; constructing a statistical manifold: all N×N symmetric positive definite matrices form a statistical manifold, generating a Gaussian kernel matrix set, performing local geometric modeling of the manifold and generating a graph structure; constructing a graph convolutional network on the manifold: tangent space projection and graph convolutional network architecture design. The present invention adopts the DTW distance combined with the statistical manifold space modeling technology to effectively extract the dynamic statistical features of electrocardiogram signals, and models the manifold geometric relationship of heartbeat patterns through a graph convolutional network, significantly improving the classification accuracy of complex arrhythmias.

This method uses magnetic resonance (MR) data to estimate a diffusion tensor distribution (DTD). The method includes inverting a Fredholm integral of the first kind, specifically performing an nD Inverse Laplace Transform subject to several constraints. First, a positive definiteness constraint is used, which zeros out a subset of diffusion tensor components that do not lie on a manifold of symmetric positive definite matrices. Second, marginal distribution constraints are used, which further partition the manifold of symmetric positive definite matrices into even smaller domains to improve DTD estimates in each MR voxel.

A static force calculation method for a prefabricated dam is characterized in that a large number of joints in the prefabricated dam are simulated based on a finite element method and a contact element method, and attributes of contact elements are superposed into an integral stiffness matrix by using a traditional finite element integration rule; the overall stiffness matrix of the prefabricated dam is ensured to be a symmetric positive definite matrix, a linear equation set is solved by using Cholesky decomposition, and the iteration convergence speed is improved by using a preprocessing conjugate gradient method, so that the calculation efficiency is ensured. C # and FORTRAN programming language writing programs are used in a mixed mode to obtain a model information file and a contact unit information file, and heavy pretreatment work of fabricated dam performance analysis is completed; writing a program to convert a calculation result file into a post-processing file; except for the calculation efficiency of the method, the whole process of the method is almost completed through a program, and the performance analysis efficiency of the prefabricated dam is greatly improved.

The invention relates to a non-ideal myoelectricity gesture recognition method based on Riemannian manifold transfer learning, which is characterized by comprising four parts: 1) constructing a covariance matrix by using spatial features of a myoelectricity acquisition channel as a basis; 2) constructing a Riemannian geometric manifold structure in a Riemannian space by taking the covariance matrix as a positive definite matrix; 3) constructing a Riemannian geometric center of the data and aligning the geometric center in a manifold space to realize transfer learning of the data; and 4) classifying different gestures by using a minimum Riemannian distance classifier combined with Fischer linear discriminant filtering. According to the method, a Riemannian manifold alignment transfer learning method is applied to gesture recognition of electromyographic signals, the influence of non-ideal factors such as electrode displacement and muscle fatigue existing in electromyographic signal recognition is solved by aligning manifold structures of a source domain and a target domain, and an effective electromyographic gesture recognition model is established.

The application provides an underwater DOA estimation method, system, device and medium based on SKLD convex modeling, which comprises the following steps: constructing a sensor array received signal model according to a steering vector of a signal source; based on the difference between an observation data covariance matrix and a parameterized model covariance matrix, selecting a symmetric divergence as an initial objective function for measuring the difference; imposing a sparsity constraint on the initial objective function to form a regularized optimization problem, introducing a linear matrix inequality constraint, equivalently reconstructing the regularized optimization problem into a convex semi-definite programming problem, and taking the convex semi-definite programming problem as an optimization objective function; based on the sensor array received signal model, constructing a positive definite matrix by using sampling data; inputting the positive definite matrix into the optimization objective function to obtain an optimal objective function, obtaining a spatial spectrum distribution result based on the optimal objective function, and taking a spectral peak value of the spatial spectrum distribution result as an estimation result of a target direction.

The application discloses a structure perception UAV image-text retrieval method based on Riemann guiding alignment, which comprises feature extraction, structure representation construction, cross-modal alignment model building and joint loss function design, and is composed of a semantic branch and a structure branch: the semantic branch is used for acquiring global semantic embedding of images and texts; the structure branch generates a symmetric positive definite matrix through covariance modeling, describes spatial dependence and geometric relationship in a UAV scene, and is mapped to a tangent space under a logarithmic Euclidean metric, so that structure-preserving feature representation is realized; a marginal distribution and conditional distribution alignment mechanism is further constructed, and a semantic structure fusion strategy is combined to adaptively reduce the distance of cross-modal features in a unified embedding space. The application can relieve geometric distortion and modal mismatch problems caused by Euclidean modeling, enhance structure expression and semantic consistency in a complex scene, and thus improve the accuracy and robustness of UAV image-text retrieval.

The invention discloses a regression model establishment method suitable for a symmetric positive definite matrix data set, and belongs to the technical field of machine learning and data science. The method comprises the following steps: firstly, converting an SPD matrix in a training set into a symmetric matrix by adopting a spectral analysis method, and reserving geometric characteristics of the matrix; secondly, performing symmetric matrix regression relation modeling by applying a kernel ridge regression method based on a Log-Euclidean kernel function, and effectively capturing intrinsic statistical characteristics of the matrix; and finally, a regression prediction result is converted into an SPD space through exponential operation of the matrix, so that the physical significance and the practical application value of the result are ensured. The series of technical means not only overcome the limitation of the traditional method, but also significantly improve the prediction precision and robustness of the model.

The application discloses a kind of aircraft landing stage fault reconfiguration and fault-tolerant control combined implementation method, symmetric positive definite matrix P1, P2, X and matrix K, K f , L, Y1, Y2 that meet linear matrix inequality are solved, and the known quantity in the linear matrix inequality is obtained according to aircraft landing mathematical model, extended system equation, state observation equation and closed-loop control equation;The obtained matrix L, K, K f It is substituted into the state observation equation and the closed-loop control equation respectively, while achieving aircraft landing process fault reconfiguration and fault-tolerant control.The application simultaneously solves fault reconfiguration algorithm parameters and fault-tolerant control algorithm unknown parameters in a short time, reduces the amount of calculation compared with other methods, and realizes automatic landing task of aircraft.

A kind of static calculation method for prefabricated dam, based on finite element method and contact element method, a large number of joints in prefabricated dam are simulated, the properties of contact element are superimposed into the overall stiffness matrix using traditional finite element integration rule, to ensure that the overall stiffness matrix of prefabricated dam is a symmetric positive definite matrix, the linear equations are solved using Cholesky decomposition, and the iterative convergence speed is improved using preconditioned conjugate gradient method, to ensure the calculation efficiency. C# and FORTRAN programming language are used to write programs to obtain model information file and contact element information file, to complete the heavy pre-processing work of prefabricated dam performance analysis, and programs are written to convert the calculation result file into post-processing file; in addition to the calculation efficiency of the method itself, the whole process of the application is almost completed by program, which greatly improves the performance analysis efficiency of prefabricated dam.