32 results about "Signomial" patented technology

The invention discloses a Bernstein polynomial-based multi-region frequency safety unit scheduling method and device, and the method comprises the steps: constructing a multi-region frequency response model based on the dynamic primary frequency modulation response of a synchronous generator, and the optimal distribution of a speed regulator dead zone and frequency modulation reserve; carrying out approximation on an integral-differential algebraic equation of the multi-region frequency response model through a Bernstein polynomial to obtain a dynamic algebraic expression of the multi-region frequency, and constructing a multi-region frequency security constraint according to the dynamic algebraic expression of the multi-region frequency; embedding the multi-region frequency security constraint into a unit commitment problem, and constructing a multi-region frequency security constraint unit commitment model; decomposing a mixed integer programming problem of the multi-region frequency security constraint unit commitment model into a main problem and a sub-problem through an adaptive double-layer decomposition algorithm; and solving to obtain a multi-region frequency safety unit scheduling scheme. According to the method, the frequency dynamic difference between the regions is accurately captured, and the frequency safety of the high-proportion new energy power system is improved.

An on-loop efficient multiplication optimization method based on a sparse ternary polynomial and precomputation belongs to the field of cryptography and comprises the following steps: compressing a cyclic matrix of a prime order domain loop into a single row to obtain a generation operator matrix temp; storing the second column of elements in the temp in an inverted sequence; according to the sparse property of a ternary polynomial and the algebraic structure characteristic of a finite ring (Z / q) [x] / (xp-x-1), through sparse coefficient traversal, table look-up operation is carried out on non-zero coefficients of the ternary polynomial. According to the method, traditional NTT multiplication is replaced by addition and subtraction, the sparse small polynomial characteristics are combined, the theoretical complexity of polynomial multiplication is reduced to be close to O (p) from O (p2), and the operation efficiency is remarkably improved; a compression type precomputation cyclic matrix and a reverse storage strategy are adopted, memory occupation is reduced, the resource utilization rate is improved, the application scene is expanded, and flexibility and practicability are remarkably improved.

The invention discloses a rapid dynamic collision detection method for the motion trail of a positioner, and the method comprises the steps: firstly constructing a forward kinematics equation of the positioner through forward kinematics analysis, representing the position of a point on a vertical column of the positioner as a polynomial function of a joint parameter, and providing an accurate mathematical model for collision detection; thirdly, defining a tangent configuration space of the positioner, re-parameterizing the forward kinematics through self-defined parameters, and constructing a mathematical space for describing all possible postures of the positioner; on the basis, the positioner and the obstacle are abstracted as convex bodies in a topological linear space, a series of hyperplanes for segmenting the positioner and the obstacle are searched by using a polynomial convex optimization method, and the hyperplanes are used as collision-free proof, so that potential collision risks can be detected in the planned movement track of the positioner. According to the technical scheme provided by the invention, the problems of low collision detection efficiency and insufficient accuracy in the prior art are solved.

The invention provides a double-layer safe trainable quantum machine learning method based on polynomial dynamics Lie algebra, and the method comprises the following steps: 1, constructing core variation simulation meeting the constraint of the polynomial dynamics Lie algebra, and guaranteeing the trainability of a model; 2, performing truncated Chebyshev graph coding at an input end, and constructing a rugged loss function landscape by using graph state entanglement and a Chebyshev tower strategy to prevent a snapshot inversion attack; 3, executing dynamic local scrambling at an output end, applying time-varying random local unitary transformation before measurement, and confusing a linear relation between gradient and a snapshot to prevent recovery attack of the snapshot; and 4, measuring and calculating a loss function, and updating parameters. According to the method, an orthogonal decoupling strategy is adopted, a privacy protection mechanism is externally arranged on an input / output interface, and trainability is anchored to core configuration, so that the capability of resisting algebraic attacks is remarkably improved while model convergence is ensured.

This invention discloses a method for solving the job shop scheduling problem based on the red deer algorithm, belonging to the field of shop scheduling. The method decodes the job shop schedule using a random key, explores and utilizes a balancing algorithm of roaring, fighting, and pairing operations, and uses the Euclidean distance to measure the distance between male and female deer to solve the job shop scheduling problem. This invention is the first to attempt to apply the red deer algorithm to the job shop scheduling problem. Compared with traditional mathematical programming methods, this method can obtain satisfactory scheduling solutions for large-scale scheduling problems in polynomial time, while maintaining low computational complexity and high robustness.

The invention discloses a distributed photovoltaic aggregation frequency modulation standby optimal configuration method considering node frequency security constraints under transmission and distribution cooperation. The method comprises the following steps: describing uncertainty of photovoltaic aggregation frequency modulation capability by using a Gaussian mixture model, and establishing a power transmission network node frequency response model containing frequency space distribution characteristics; taking minimization of system power generation and frequency modulation reserve cost as a target, and combining opportunity constraint planning to construct an optimal configuration model; a response model is reduced based on a frequency divider theory, a Bernstein polynomial approximates frequency dynamics, and a differential algebraic equation is converted into an algebraic equation; then, binary expansion and Gaussian mixture model linear invariance are utilized to convert the model into a mixed integer linear programming model, and Bernstein polynomial convex hull property tightening constraint is combined; and finally, solving the model to obtain the optimal photovoltaic aggregation frequency modulation reserve capacity and control parameters. The frequency space distribution is accurately described, the problem of insufficient frequency safety risk identification is solved, and the frequency safety level of a power system is improved.

The present invention provides an improved method and system for variational quantum algorithms (VQA). These include receiving a quantum circuit for implementing the VQA, the quantum circuit being par

The application discloses a multi-region frequency safety unit scheduling method and device based on Bernstein polynomials, and the method is based on the optimal distribution of the dynamic primary frequency modulation response of a synchronous generator, a speed governor dead zone and a frequency modulation backup, and a multi-region frequency response model is constructed; the integral-differential algebraic equation of the multi-region frequency response model is approximated through Bernstein polynomials to obtain an algebraic expression of the multi-region frequency dynamics, and a multi-region frequency safety constraint is constructed according to the algebraic expression; the multi-region frequency safety constraint is embedded into a unit combination problem to construct a multi-region frequency safety constraint unit combination model; through a self-adaptive double-layer decomposition algorithm, a mixed integer programming problem of the multi-region frequency safety constraint unit combination model is decomposed into a main problem and a sub-problem; and through solving, a multi-region frequency safety unit scheduling scheme is obtained. The application accurately captures the frequency dynamic difference between regions and improves the frequency safety of a high-proportion new energy power system.

The present invention proposes an optimization method for two-shift multi-task scheduling considering switching time, taking two-shift multi-task processing as the research object and considering the actual problem of the impact of workpiece switching between different shifts on production objectives. By establishing a workpiece switching model, analyzing the relationship between the switching time of workpiece switching and shifts, designing a pseudo-polynomial time dynamic programming algorithm, a multi-task scheduling decision scheme is obtained. The present invention is oriented to production practice, aiming to provide a theoretical basis for enterprises to coordinate the optimization decision of multi-task scheduling under the two-shift working system, and also provide a research model for reference for working modes such as three-shift.

The invention relates to a double-engine propeller noise prediction and optimization method based on an analytical method, and belongs to the field of aviation acoustics. The method disclosed by the invention comprises a noise prediction method and a noise optimization method, the noise prediction method establishes a noise prediction model based on an improved propeller characteristic theory, and the noise optimization method comprises the following steps: S1, establishing a noise objective function based on the noise prediction model, solving a first-order partial derivative and a Hessian matrix of the noise objective function, and obtaining a first-order partial derivative of the noise objective function; the method comprises the steps of S1, providing a noise target function, S2, providing a new Euler formula transformation method, and converting a triangular polynomial corresponding to a first-order partial derivative of the noise target function into a zero-equivalent algebraic polynomial, S3, analyzing and solving the zero point of the algebraic polynomial by using a Fourier-Frobenius matrix method, and S4, realizing synchronous maximum noise reduction control. According to the method, an improved propeller characteristic value theory and a Hessian + Fourier-Frobenius matrix method are used for rapidly and accurately solving an analytical solution of the minimum noise, and the method is combined with synchronous control, so that the limitation on the time and precision of predicting the minimum noise is overcome.

The invention provides a method and system for inverting a material shear constitutive relation based on solid round rod torsion, and relates to the technical field of constitutive relation inversion, and the method comprises the steps: obtaining torque-torsion angle curve data of a solid round rod test piece in a pure torsion experiment, and the length and radius of the solid round rod test piece; establishing a shear stress-shear strain and torque-torsion angle bipolynomial model, and forming a mathematical model based on a polynomial form; then deriving a conversion relation between polynomial coefficients based on a round rod torsion theory, and fitting experimental data through an optimization algorithm to solve a torque polynomial coefficient; and finally, obtaining a constitutive relation coefficient by utilizing mathematical conversion, and generating the shear constitutive relation of the material. The method does not need to preset a constitutive form, is suitable for various materials such as metals and macromolecules, and has the advantages of simple model, efficient inversion, low experiment cost and the like.

The invention relates to the technical field of scientific simulation, in particular to a finite element model parameter optimization method and system based on an intelligent algorithm, equipment and a medium, a traditional manual iterative optimization process is converted into an automatic process through parametric modeling and automatic generation of a Python macro command, the manual operation time is remarkably shortened, and the efficiency is improved. And meanwhile, seamless connection from parameterized modeling of the finite element model to optimization result output is realized, so that the dependence on a user algorithm and programming capability is reduced, and full-process automation is realized. Secondly, multi-objective optimization and nonlinear constraint are supported, common non-convex and high-dimensional optimization problems in engineering can be flexibly processed, and the limitation of a traditional gradient algorithm on the continuity of an objective function is broken through; the response surface agent model replaces high-time-consuming finite element calculation through chaos polynomial expansion, a black box problem is converted into an explicit mathematical relationship, the dependence of an optimization algorithm on actual simulation is reduced, and the iteration efficiency is improved.

The invention discloses an invisible shipboard aircraft re-flight trajectory optimization method and device based on a pseudo-spectral method, a medium and a product, and relates to the technical field of automatic control, and the method comprises the steps: constructing a re-flight dynamics model according to dynamics and kinematics equations of an invisible shipboard aircraft, and determining a target function and constraint conditions; determining a plurality of collocation points through a zero point of a Legendre polynomial, respectively converting a state variable and a control variable into discrete variables at each collocation point, and then converting a target function and a constraint condition into algebraic constraints to obtain a nonlinear programming equation set; solving an optimal solution of the nonlinear programming equation set at each collocation point by using a sequential quadratic programming algorithm; and finally, carrying out serialization by utilizing a Lagrange interpolation polynomial to obtain a camouflage shipboard aircraft re-flight trajectory optimization result. According to the method, the capacity of an execution mechanism of the stealth shipboard aircraft is fully considered, the optimal re-flight track of the stealth shipboard aircraft is obtained, and the problem that the flight capacity in a traditional re-flight strategy is not fully utilized is solved.

The invention discloses an electric power system scheduling method and device based on multi-dimensional full-pure embedding approximate dynamic programming, terminal equipment and a storage medium, and belongs to the field of electric power systems.The method comprises the steps that optimization constraints are constructed, and an optimization model represented by a plurality of decoupled value functions is constructed; converting each decoupled value function into a corresponding Lagrange function, and then solving a gradient to obtain a plurality of KKT conditions; embedding preset complex parameters into each KKT condition to obtain a plurality of polynomial equation sets; calculating a zero-order coefficient of each polynomial equation set, and performing recursive calculation on a non-zero-order coefficient of each polynomial equation set; and obtaining an approximate expression of a value function corresponding to each polynomial equation set according to the obtained coefficient solution of each order, obtaining a solution of an optimization model according to the approximate expression, and scheduling the power system. By implementing the method and the device, the defects of low efficiency and poor effect in solving the scheduling problem of the power system in the prior art can be solved.

The present invention relates to a multi-scale optimization intelligent design method for special-shaped structures, belonging to the field of additive manufacturing of spacecraft structures and mechanisms. It includes: constructing a special-shaped lattice structure using a level set function and performing interpolation and correction; setting relative density sample points and performing polynomial interpolation to establish a geometric surrogate model; obtaining a constitutive matrix through numerical homogenization and establishing a constitutive surrogate model; based on the constitutive surrogate model and the isogeometric topology optimization method, iteratively solving with the goal of minimizing the compliance of the special-shaped sandwich structure to obtain the optimal density distribution; substituting the optimal density distribution into the geometric surrogate model to output interpolation coefficients, and generating an implicit model of the special-shaped sandwich structure by gradient lattice filling. This method solves the problem of the lack of a multi-scale optimization design method for special-shaped sandwich structures filled with gradient lattices by constructing an implicit model of a special-shaped sandwich structure filled with a conforming continuous gradient special-shaped lattice structure and generating a special-shaped sandwich structure by additive manufacturing based on the implicit model.

The present application belongs to the technical field of multi-agent cooperative control and path planning, and particularly relates to a multi-agent collision-free prediction optimization method based on smooth potential field and parallel ADMM. The method is based on the parallel ADMM architecture, and decouples the optimization problem into two sub-problems of individual dynamics and cooperative collision avoidance. At the individual level, the dual decomposition technique is used to convert the constrained optimization into a parallel solution of dual quadratic programming; at the cooperative level, a second-order differentiable smooth potential energy function is used to replace the mixed integer programming to handle the collision avoidance constraint. The present application reduces the computational complexity from exponential to polynomial, and significantly improves the real-time planning capability and robustness of large-scale multi-agent clusters in complex environments.

The present invention relates to a robust optimal guidance method for powered descent of a probe based on uncertainty quantification. The method comprises: constructing a robust fuel optimal guidance model for powered descent that accounts for the uncertainties of the initial state and model environment; transforming the optimal guidance model into a deterministic problem using an uncertainty quantification method based on chaotic polynomial expansion; and solving the deterministic optimization problem using a sequential convex optimization method to obtain a robust optimal landing trajectory and corresponding feedback guidance law. This method transforms complex nonlinear optimal control problems involving randomness into easily solvable convex optimization problems, improving solution efficiency while ensuring a high solution success rate. The designed optimal trajectory can satisfy various constraints even under uncertainty, and the corresponding feedback guidance law can be directly applied online.

The embodiment of the invention provides a method and a device for jointly carrying out service data processing, which are characterized in that in a service processing process executed by a plurality of participants based on security computing, a simple algebraic polynomial and a trigonometric polynomial are used for adding a processing result of data r to replace a processing result of a complex function to the data r; therefore, related business processing is carried out through relatively simple safe multiplication and safe addition calculation. According to the embodiment, the service processing precision can be improved on the basis of reducing the calculation overhead.

The invention discloses a parameter identification method for a magneto-rheological damper mechanical model. The parameter identification method comprises the following steps: step 1, testing and obtaining an output curve of a magneto-rheological damper; step 2, a Bouc-wen model is built in MATLAB (matrix laboratory) / SIMULINK (single matrix laboratory); step 3, performing parameter optimization processing by using a particle swarm optimization algorithm as an optimization tool, including: determining a target function as # imgabs0 #; step 4, judging the recognition precision of the optimization algorithm; 5, performing polynomial fitting; 6, evaluating the output condition of the model; according to the method, the problem of complex nonlinear output and mathematical model parameter identification of the magneto-rheological damper can be converted into a process parameter identification process, the process is simple, the requirement for priori knowledge of engineers is not high, and the method has important guiding significance for practical engineering.

The invention discloses a generator set coal consumption curve fitting method and system based on an APSO algorithm. The method comprises the steps of data acquisition and time sequence construction; preprocessing the data; calculating a target variable according to the acquisition quantity, and completing normalization and boundary constraint; a quadratic polynomial model and a piecewise linear model are constructed in parallel, weighted fusion is carried out through learnable weights, and mixed expression of a coal consumption curve is obtained; performing adaptive particle swarm optimization: performing global optimization on the quadratic polynomial and piecewise linear model parameters; the inertia weight and the learning factor are adaptively adjusted along with iteration, and disturbance is applied to partial particle velocity when a plurality of generations are not improved so as to avoid local optimum; the fitness function is the error measure of the predicted coal consumption rate and the measured value; outputting and issuing a result: outputting an optimal parameter and a residual error index; and performing first-order derivation on the fitted curve to obtain an economic load area, performing highlight display on an HMI interface, and writing the curve, the interval and the index into a real-time database to be called by a scheduling / energy efficiency system.

The invention discloses an interval power flow calculation method and system for an AC-DC hybrid system, and belongs to the technical field of power system analysis and calculation, and the method comprises the steps: obtaining system basic parameters and an uncertainty range, building a nonlinear power flow model containing a synchronous generator, an LCC-HVDC, and a ZIP load, and formalizing the nonlinear power flow model into a polynomial optimization problem; a sparse moment relaxation technology is adopted to convert the model into a semi-definite programming model; decomposing and solving the sub-problems through a maximum clique decomposition strategy; and introducing McCormick constraint and an optimality boundary tightening technology to iteratively optimize a variable domain, and finally outputting upper and lower bounds of a power flow solution. The system comprises a parameter module, a conversion module, a decomposition module, a solving module and an output module. According to the method, the uncertainty power flow problem in the alternating-current and direct-current hybrid system can be efficiently and accurately solved, and the method is suitable for power grid safety assessment and optimal scheduling.

The invention relates to the technical field of hydrological simulation, and particularly discloses an extra-small watershed layered three-dimensional hydrological-hydrodynamic full-coupling simulation method, which comprises the following steps: collecting multi-source data to construct a three-dimensional space discrete grid and dividing initial time units; the control equation set is converted into an algebraic system based on a Legendre polynomial and a Gaussian-Loabar node; adaptively adjusting a time unit length and a spectral basis function order according to the local time gradient change rate; a convergence spectral coefficient is obtained through spectral delay correction iteration solution; and finally, forcibly executing mass conservation constraint, controlling step recalculation according to a local time error, and gradually outputting a flow hydrograph and water depth and infiltration rate distribution according to time unit endpoints. According to the method, the dual self-adaption of the time step length and the polynomial order is realized, the numerical oscillation of the infiltration rate caused by the sudden change of the ponding depth can be effectively inhibited, the mass conservation is ensured, and the stability and the efficiency of the rainstorm flood simulation of the extra-small watershed are improved.

The present invention discloses a forward solution algorithm for a parallel mechanical platform based on polynomial regression, comprising the following steps: Step 1: constructing a six-variable cubic polynomial as follows: #imgabs0# wherein: is the parameter to be solved, A is the cubic coupling term parameter of 1, B is the quadratic coupling term parameter of 1, C is the linear term parameter of 1, and D is a constant parameter; Step 2: kinematically inversely solving the known posture parameters to obtain the corresponding robotic arm length, and then eliminating the remaining unknowns except for the parameters A, B, C, and D in the above formula; Step 3: establishing a set of 259 linear equations for solving A, B, C, and D, solving the linear equations, and obtaining the values of A, B, C, and D. The present invention solves the problems of non-globality and poor real-time performance of Newton iteration in kinematic forward solution problems, and can be used in a multivariate polynomial regression forward solution algorithm for a parallel mechanical platform. The polynomial regression method can converge globally and has stronger real-time performance.

The invention discloses a linear trajectory planning method for a space manipulator load operation task, and relates to the technical field of space manipulator trajectory planning. Designing a multi-objective optimization model, wherein optimization objectives comprise straightness vector optimization, obstacle avoidance optimization and jerk optimization; a trajectory planner is designed, a searched individual is an intermediate node configuration of a quintic polynomial trajectory, a quantum state encoding mode is adopted to encode a mechanical arm configuration, a QBSO algorithm is provided, a complete trajectory of the mechanical arm is formed by connecting a plurality of intermediate node configurations in sequence, a next node configuration is searched according to a current configuration position and a target trajectory every time, and the next node configuration is searched for a target trajectory. And finally forming a joint track which is formed by n intermediate nodes and is connected according to a quintic polynomial equation. By designing a mathematical coding mode of a quintic polynomial trajectory, designing a linear trajectory planner framework based on a sampling algorithm and designing a straightness vector constraint model, an optimal trajectory meeting constraint requirements can be generated.

The application discloses a special section stiffness accurate calculation method based on feature adaptive sampling and a general analytic operator, and comprises the following steps: feature adaptive sampling and data semanticization; solving of an explicit spline equation based on topological decoupling; normalized parameter mapping and coefficient vector construction; general analytic calculation based on polynomial algebra; global assembly and stiffness matrix generation; the method retains topological sharp points through feature semantic sampling, unifies an integral domain through a normalized parameter equation, and converts a calculus problem into a linear algebra problem through polynomial algebra operation, so that fast and accurate solving of special section stiffness characteristics is realized.

The invention relates to the technical field of ejector structure optimization, in particular to an ejector structure optimization method based on a polynomial function, and the method comprises the steps: obtaining a preset geometric boundary condition of a nozzle diffusion section; generating candidate nozzle contours; obtaining a nozzle injection ratio and a nozzle total entropy product corresponding to the candidate nozzle contour; determining an optimal nozzle contour; a preset pump body starting half angle and a preset pump body ending half angle of the pump body are obtained; acquiring a preset curve starting point coordinate and a preset curve ending point coordinate of the pump body; constructing a pump body contour curve function; generating a candidate pump body contour; constructing a complete ejector model; the model injection ratio of the complete ejector model, the model total entropy production of the complete ejector model and the model maximum allowable backpressure of the complete ejector model are obtained; obtaining a preset engineering application requirement; determining and outputting a final optimization scheme; according to the invention, a break angle caused by geometric mutation is eliminated, and a flow channel is continuous and smooth, so that the generation of shock wave and flow separation is inhibited.

The invention relates to a tough power grid, in particular to a convex hull solving method for tough looped network reconstruction, which is used for solving the problems that the solving efficiency of a reconstruction model of an existing annular structure power grid is low, and particularly, a mixed integer linear programming method for mainstream reconstruction is difficult to solve when facing a large-scale power distribution network reconstruction problem. According to the scheme, when the power grid of the annular structure is reconstructed, a completely equivalent convex hull solving method is deduced by adopting multiple rounds of mathematical changes and simplification of dynamic programming, bilevel programming and strong dual transformation, the method has polynomial complexity, repeated calculation is reduced, calculation performance is improved, and the calculation efficiency is improved. The reconstruction solving efficiency of the existing large-scale power distribution network is effectively improved, the result is ensured to be optimal, and technical support is provided for safe supply of a tough power grid.

The application discloses a method and system for expanding a vehicle stability domain estimated by a sum-of-squares programming algorithm, and belongs to the technical field of computers, and comprises the following steps: a rational polynomial-based whole vehicle polynomial model is constructed by combining a two-degree-of-freedom dynamics model of a vehicle and a rational polynomial nonlinear tire model; a vehicle stability region is estimated by a sum-of-squares programming algorithm based on the whole vehicle polynomial model, and a stability region boundary curve is obtained; the stability region boundary curve is subjected to discrete processing, and an initial point set is obtained; a convex hull of a stability domain expansion is obtained by trajectory inversion according to the stability region boundary curve and the initial point set; and the convex hull of the stability domain expansion is taken as an expanded stability region. The application can realize maximum estimation of a stability domain boundary, greatly improve the conservativeness of the stability domain, make the judgment of vehicle stability more accurate, and be favorable to improving the reliability of vehicle stability control.

The present invention provides a simple method for solving the stress and strain of an infinite flat plate with an opening of any shape. By using the conformal mapping method, the unit circular opening on the mapping plane is mapped into a non-circular opening on the physical plane; a series form of the complex variable stress function is ingeniously set on the mapping plane, and directly substituting it into the free boundary conditions, and using the polynomial identity, the coefficients of the series expressions of the two complex variable stress functions can be determined by solving algebraic equations. The present invention avoids complex Cauchy integral operations, has simple operations, and clear mathematical and physical concepts.