208 results about "System of differential equations" patented technology

Methods and systems for finding optimal or near optimal solutions for generic optimization problems by an approach to minimizing functions over high-dimensional domains that mathematically model the optimization problems. Embodiments of the disclosed invention receive a mathematical description of a system, in symbolic form, that includes decision variables of various types, including real-number-valued, integer-valued, and Boolean-valued decision variables, and that may also include a variety of constraints on the values of the decision variables, including inequality and equality constraints. The objective function and constraints are incorporated into a global objective function. The global objective function is transformed into a system of differential equations in terms of continuous variables and parameters, so that polynomial-time methods for solving differential equations can be applied to calculate near-optimal solutions for the global objective function. Embodiments of the present invention also provide for distribution and decomposition of global-gradient-descent- field-based optimization methods, by following multiple trajectories, and local-gradient- descent-field-based optimization methods, by using multiple agents, in order to allow for parallel computation and increased computational efficiency. Various embodiments of the present invention further include approaches for relatively continuous adjustment of solutions to optimization problems in time, to respond to various events, changes in priorities, and changes in forecasts, without needing to continuously recalculate optimization solutions de novo. While many embodiments of the present invention are specifically directed to various classes of optimization problems, other embodiments of the present invention provide a more general approach for constructing complex hierarchical computational processes and for optimally or near optimally controlling general computational processes.

A pulse circuit to solve a system of differential equations in the pulse domain based on analog or inputs or time-encoded pulse inputs. Intrinsically linear 1-bit digital to analog converters are used as feedback elements within circuits implementing solutions to a differential equation or to a system of differential equations. The circuits may be used to implement filters. While the input to the circuit may be an analog signal, the internal signals of the circuit are time-encoded current or voltage pulses. Output of the circuit is a time-encoded pulse or a series of time-encoded pulses from which an analog output may be recovered by time decoding.

The present invention provides a fluorescence-based modeling method that is capable of capturing the dynamic changes of different membrane foulant fractions that occur in fluid filtration operations. Principal component analysis is utilized to de-convolute spectral information captured within fluorescence EEMs into principal component scores that are related to different known foulant groups. The principal component scores are then used as states within a system of differential equations representing approximate mass balances of the main foulant groups to obtain a dynamic forecasting of membrane fouling. Based on the fouling dynamics forecasted by this modeling method, an optimization strategy can be developed for estimating the optimal membrane back-washing scenario for minimizing energy consumption while maximizing clean fluid production.

The present invention relates to an attack and defense differential game-based network security defense decision determination method and a device. The method comprises the steps of constructing a state evolution model NIRM for network nodes according to an SIR model during the network attack and defense process; according to a network node state migration path, acquiring a node state change differential equation set based on the state evolution model NIRM; according to the node state change differential equation set, constructing an attack and defense differential game model ADDG; according to an attack and defense return strategy and a corresponding execution cost, executing a revenue function of the attack party and the defense party during the differential game process; according to the revenue function and the attack and defense differential game model ADDG, solving out a saddle point strategy for the attack party and the defense party through the dynamic planning method, determining an optimal defense strategy and outputting the optimal defense strategy. According to the technical scheme of the invention, the problem that actual requirements cannot be met through the traditional dynamic game analysis method can be solved. Compared with the existing network security defense strategy, the attack and defense process in the continuous and real-time engagement condition is analyzed. The timeliness, the pertinence and the guiding significance of network defense decision results are better.

The invention relates to a simulation analysis method of the vibratory response of a variable working condition single-stage heavy gear case containing a crackle fault, which comprises the following steps: establishing a gear pair 3D solid model containing a crackle fault on the basis of 3D design software SolidWorks; leading the model into finite element analysis software ansys, programming a program capable of calculating the gear meshing rigidity of any meshing positions by combining menu operations of the ansys and APDL languages and outputting a result data file of the meshing rigidity; establishing a damping gear case system kinetic model of 8 degrees-of-freedom and kinetic simultaneous differential equations considering factors of the rigidity and the damping of a shaft and the case, an input torque and a load torque of a motor, and the like and utilizing MATLAB to solve the equations so as to simulate the system vibratory response of the single-stage heavy gear case containing a crackle fault. The invention integrates the advantages of the SolidWorks, the ansys and the MATLAB and can quickly and accurately simulate the vibratory responses of variable working condition heavy single-stage heavy gear cases containing various different forms of crackle faults.

The invention relates to a city-wide infectious disease simulation method and a city-wide infectious disease simulation device. The method includes the steps of: 1) partitioning the city and classifying the people; 2) building a 4p ordinary simultaneous differential equation set which describes the dynamic process of the transmission of the disease in p (number) areas; 3) discretizing the equation set to obtain a difference equation set; 4) converting the discretized difference equation set into an open equation set by taking the connections of other cities into consideration; and 5) resolving the parameters of the equation set and visually expressing the infected people in the manner of dot density and piled bar graph. According to the epidemiological characteristics of the infectious disease and based on the data of interregional population flow across the city, the city-wide infectious disease simulation method and the city-wide infectious disease simulation device can predict and simulate the dynamic contagion process of the disease spatially in a period of time in the future, and the spatial propagation process of a typical infectious disease can be analyzed on a map in a visual way. The city-wide infectious disease simulation method and the city-wide infectious disease simulation device provide a decision support to infectious disease propagation prevention and control.

The invention discloses an evaluation method for unconventional reservoir volume transformation multi-pore media productivity contribution. The evaluation method comprises the following steps that firstly, based on the principle of effective stress and flow characteristics of a transformation zone, and a fluid-solid coupling mathematical model of interaction between a geotechnical deformation field (stress field) and a fluid flow field (seepage field) of the unconventional reservoirs is established; then a perfectly coupled method solution of the seepage field and the stress field is realizedby solving a fluid-solid perfectly coupled system of partial differential equations in a general formula mode; and finally, fluid-solid coupling interactions under different combinations of pore mediaare simulated, and the contribution ratio of three systems of base materials, natural cracks and grid cracks to the cumulative production of a volume transformation well is obtained. A set of evaluation method for unconventional reservoir volume transformation multi-pore media productivity contribution is established eventually. The evaluation method for unconventional reservoir volume transforming multi-pore media productivity contribution has the advantages that the model factor consideration is comprehensive, the evaluation method is simple and results are quantifiable, an oil and gas field can be guided timely to be subjected to development measure adjustment and comprehensive management, and a theoretical basis and technical support are provided to the unconventional reservoir to realize economic recovery.

The invention relates to a vibration response simulation analyzing method for a rolling bearing with single-point failures. On the basis of a Hertz contact theory, related knowledge about kinematics and kinetics are utilized to establish a five-degree-of-freedom nonlinear vibration mode of a rolling bearing and kinetic differential equations of the rolling bearing while influencing factors like slipping of rolling balls, oil slick rigidity and the like are taken into consideration, according to that the rolling balls change due to contact deformation is caused when the rolling balls roll through partial failures, a partial failure model of the rolling bearing is introduced into the kinetic differential equations of the rolling bearing, and the single-point failures of the rolling bearing are classified according to length-width ratios of the failures and size ratios between the failures and the rolling balls so as to establish different failure shape functions; the differential equations are solved by an ode solver in MATLAB (matrix laboratory) software, and vibration responses of the rolling bearing are simulated when an inner ring, an outer ring and the rolling balls of the rolling bearing are suffered from the single-point failures. By the aid of the vibration response simulation analyzing method, vibration responses of the bearings with failures in different sizes can be simulated. Compared with traditional methods for acquiring vibration responses of failed bearings, the vibration response simulation analyzing method has the advantages that an experimental period is short and experimental cost is saved. The computation for the vibration responses for the failed rolling bearings can lay the foundation of late failure diagnosis for the rolling bearings.

The invention discloses a method for improving simulation capacity of HVDC transmission system in the technical field of electric power system operation and control technique. The technical program includes: singlet dynamic phasor is expanded to polymorphic dynamic phasor; switch function is used for indicating the characteristic of a converter valve, polymorphic dynamic phasor model of HVDC system is built considering the non-ideal state that alternating current fundamental voltage is asymmetric and direct current is mixed with ripples; curves indicating that each variable changes with time are obtained according to algebraic differentiation equations of the model; complete curves indicating that direct voltage at rectification side of the HVDC transmission system, direct voltage at contravariance side, direct line current and current at alternating current side change with time are calculated respectively by inverse Fourier transform; and finally values at the alternating current side and the direct current side of the HVDC transmission system are calculated, thus realizing the simulation of the HVDC transmission system. The invention has the advantages that the adaption to unsymmetrical fault is good, computational efficiency is high and computation is accurate.

A method use line-frequency disturb the zero-sequence impedance parameter of resource charge measure mutual inductance circuit, cuts the power of a certain circuit in the mutual inductance circuit in order, puts one three-phase of the power cut circuit to earth, measures the induction voltage of the other one after it is in short-circuit; at the same time measures the zero-sequence voltage pressure loss and zero-sequence current in the other run circuit; uses the GPS technology sample the zero-sequence voltage, zero-sequence current in the mutual inductance circuit in-phase, gets the zero-sequence voltage, zero-sequence current data in the mutual inductance circuit; collects the data of each measurement point to the center computer; gets the zero-sequence impedance parameter of the mutual inductance circuit by using the least square law solute the algebraic equations, differential equations or integral equations; this equipment is composed of GPS antenna, signal input connection interface, signal transducer, embedded DPS synchromesh data collection card, launch amount card, relay group, embed PC card, the electrical source card.

The invention discloses a power distribution network CPS protective method based on bounded rationality. Equipment data of a power distribution network, running data of the power distribution network,the residence time of a historical attacker, the average reaction time, the average restoration time and other types of power grid multi-source data are fully utilized, and comprehensive power distribution network CPS risk assessment indexes are established on the basis of two aspects including a physical system and an information system, so that all line risk assessment results effectively helpa defense building party to select defense building strategies through a game learning method based on bounded rationality. A defense building efficiency value corresponding to each attack and defensebuilding strategy is obtained from two aspects of economic benefits and safety, a logarithm synthetic method is adopted to obtain final expected efficiency and average efficiency when the defense building party employs different strategies, dynamic differential equations are adopted to represent dynamic change rates when the attacker and the defense building party select certain strategies, and then a dynamic differential equation group of a game learning model is established to obtain power distribution network CPS protective satisfactory strategies.

The invention provides an under-actuated release control method based on a nonlinear space tether system. The method comprises the following steps: 1, a dumbbell model is adopted, system dynamics differential equations are built according to a second kind Lagrange equation, and a dimensionless form is introduced in the differential equations; 2, based on a normal form expression for the above dynamics differential equations, expected values for a system in-plane pitching angle and an out-plane rolling angle are set, and the balance position of the system in the release process is obtained; 3, starting from the balance position of the system, a tether length change control law for realizing tether release is deduced and obtained; and 4, the range for the expected in-plane pitching angle is determined to ensure the tether release process to be asymptotically stable under effects of the control law. Numerical simulations show that the space tether can be released asymptotically stably under effects of the release control method provided by the invention, and an attractor capable of covering the balance point and an attraction domain with enough thickness can be found out.

The invention discloses an electric power system transient stability calculation method based on a semi-implicit Runge-Kutta method. The method includes: establishing a dynamic element model for transient stability simulation calculation of the power system; forming a whole system differential algebraic equation set; inputting raw data and information, carrying out tide calculation, obtaining an operation parameter initial value before system disturbance; calculating an initial value of the state variable; generating a Jacobian matrix and a network admittance matrix of each dynamic element; performing system disturbance judgment; generating a Jacobian matrix of the differential equation set of the whole system; solving and obtaining the value of each state variable at the next moment; carrying out machine network alternate iterative computation, obtaining an operation parameter value at the next moment until a convergence condition is met, and taking the operation parameter value as aninitial value to calculate the next step length. The calculation is simple and stable, the larger step length can be used, the problem that the numerical stability and the calculation efficiency of the algorithm are difficult to consider at the same time in the transient stability simulation calculation is solved, and the method is more efficient, accurate and stable.

Recursive digital pre-distortion (DPD) techniques are provided. Digital pre-distortion is performed by applying a signal to a recursive system to generate a state vector; providing the state vector as a feedback value to the recursive non-linear system; and applying the state vector to a second function to generate an output signal, wherein at least one of the recursive system and the second function comprise a non-linear function. The recursive non-linear system can be initialized to a known initial value. The recursive system is defined by a system of non-linear differential equations.

A method and system for image segmentation by evolving radial basis functions (RBFs) is disclosed. A set of RBFs define a contour on an image. The contour is the zero level set of an implicit function defined by the RBFs. The RBFs are weighted and parameterized by multiple parameters, such as center point, standard deviation, and orientation. The contour is iteratively deformed by updating the weight and each of the parameters of each of the RBFs based on each pixel of the contour, until the contour converges. The parameters and the weight of each RBF is updated using coupled set of differential equations derived based from a region-based or boundary-based image segmentation energy formulation. The final contour at a convergence defines boundaries of a target object or region in the image.

OptimizationA computer-implemented method and system are disclosed for solving an optimization problem in which nodes of a population have a probability of undergoing a state transition in response to an input. Transition probabilities are modelled in a matrix T, where T is an N×N matrix, N being the number states, and T_ab is the transition probability from state a to state b. The matrix T is multiplied by a vector of coupled differential equations to determine a system of differential equations. From an initial state of nodes of the population, the system of differential equations is solved for each of a plurality of time increments.

The invention discloses a backup structure-oriented fault tree analysis method, wherein a dynamic fault tree model is built based on working principles and failure processes of a backup structure, and the failure process of the backup structure is transformed to a fuzzy Markov model; Kolmogorov state transfer differential equations corresponding to the fuzzy Markov model are built and solved, so as to obtain fuzzy state probabilities of the backup structure at any time point. The invention efficiently resolves the problems of "small sample" and "inaccuracy" in fault tree analysis processes, and dynamic characteristic and sequential characteristic of the backup structure and the problem of imperfect coverage of backup switching are also considered, thereby a relatively accurate reliability quantitative analysis result is obtained, which helps to find the weak link affecting the reliability of the system and provides a guidance in optimizing design of the system.

The invention disclose a method for analyzing dynamic transferred water quality based on a fugacity theory, relating to a water quality analysis method, and solving the problem of larger deviation between a simulated result and an actual condition caused by actually unobtainable required parameters and randomly non-modifiable inner parameters in a traditional water quality analysis method. The method comprises the following steps of: firstly, confirming environment facies of a water area to be detected and acquiring geographic information parameters of the water area to be detected, environmental parameters of various environment and materialization parameters of a target pollutant; then computing fugacity capacity of each environmental facies, speed constant of reaction dynamics and transfer parameters among each environmental face; then establishing a system of differential equation by taking the fugacity of each environmental face as an unknown and solving the system of differential equation through a Runge-Kutta algorithm to obtain the fugacity of each environmental face; and calculating out pollutant concentration by the fugacity of each environmental facies and the fugacity capacity. The invention overcomes defects of the prior art, and can be applied to the field of analyzing transferring transformation of organic pollutants in the water area and distribution law of multi-medium environment.

The invention discloses a real time parameter identification method of an air-conditioning belonged building second order equivalent thermal parameter model, and a real time built air-conditioning belonged building second order equivalent thermal parameter model, which are used to build and real time control an air-conditioning load equivalent polymerization model; a second order differential equation group of the air-conditioning load belonged building is built and the input & output quantity and the parameter needs to be identified are determined; the real time data acquisition of the input & output quantity is conducted through a high-grade metering terminal of an intelligent power grid; data transmission to a load aggregator is conducted; and the real time parameter identification is conducted through the cooperation particle swarm algorithm by the load aggregator. According to the invention, research insufficient in domestic air-conditioning load real time modeling is made up; an accurate air-conditioning load model is constructed; and technical support for demand response is provided.

The invention discloses a social network double-rumor model-based rumor propagation range estimation method, which comprises the following steps: according to an SI model, considering propagation of two rumor and interaction between the two rumor, constructing a double-rumor SI model, and obtaining a differential equation set of time-varying user number proportions in different states under the double-rumor SI model; on the basis of the SI model, considering the condition of an immunization person, constructing a double rumor model based on the SIR model, and respectively considering a degreeuniformity network and a degree nonuniformity network to obtain a differential equation set of time-varying user number proportions under the double rumor SIR model; and the equation is simplified, propagation threshold expressions in the two networks are derived, and the relationship between the propagation threshold and the propagation range in the final state steady state is obtained, so that the propagation range of the rumor is estimated. The method can be applied to finding appropriate time to control diffusion of the rumor under different network conditions, the influence of the rumor is reduced, the rumor propagation range can be estimated, and rumor propagation is effectively inhibited.

The invention discloses a distributed energy-saving method based on an unlicensed frequency band D2D system. The method comprises the following steps: S1) establishing a system model with a minimum total power as a target function, restricting a throughput demand of each pair of D2D users, restricting the power of the k-th D2D user on the k-th unlicensed frequency band channel, restricting the proportion of distributing the frequency spectrum of the k-th unlicensed frequency band to the k-th D2D user time-division factor, and restricting the total interference on each licensed frequency band sub-channel n by all D2D users; S2) establishing differential equations to perform the solving, and solving the differential equations constructed by the target function based on a gradient projectionalgorithm; and S3) performing simulation analysis by adopting a simlink module in the matlab. The method disclosed by the invention has the advantages that each D2D user reuses the licensed frequencyband of an LTE system and the unlicensed frequency band on a Wi-Fi system station (APs), and a distributed algorithm is proposed to accomplish the power and spectrum resource allocation of the D2D users.