34results about How to "Reduce truncation error" patented technology

A local extremum of a function ƒ is determined by computing a Jacobian of ƒ at a test point x by adding an imaginary part to x and a Hessian of ƒ by adding two imaginary parts to a multicomplex copy of x and extracting a third imaginary part. Solving a system of equations defined by the Jacobian and Hessian yields a delta; the process is repeated until convergence. This method is used in each of a series of time intervals to compute an insulin-delivery amount for an insulin pump. ƒ is a model-predictive-control cost function; x is a set of successive candidate insulin delivery amounts beginning from a selected time interval. A system includes a glucose monitor and a controller using glucose measurement data therefrom to determine an insulin delivery amount for a time interval by minimizing ƒ; an insulin pump provides insulin corresponding to the delivery amount.

The invention discloses a double-rate Kalman filtering method based on GNSS/INS deep integrated navigation. The method comprises the following steps of 1, building a state equation according to the initial position, the rate and the attitude information of a carrier, and initializing the parameters of the Kalman filtering; 2, performing state prediction updating on M step lengths and obtaining a predicted value of a prior state quantity which is described in the specification; 3 correcting the prior state quantity which is described in the specification to obtain a predicted value of a posterior state quantity which is described in the specification; 4, adaptively updating the errors of the state quantities and a systematic error covariance matrix, and compensating an inertial navigation result by using the predicted value of the posterior state quantity which is described in the specification to obtain the position, the rate and attitude information of the carrier; and 5, updating thepredicted value of a posterior state quantity which is described in the specification after the compensation. The method can reduce a truncation error caused by the low update frequency of GNSS satellite data or the losing lock of the satellite data during a data fusion algorithm of the GNSS/INS deep integrated navigation, and simultaneously solve a navigation positioning error caused by the non-synchronization of INS data and GNSS data.

The invention relates to a state estimation method based on high-order unscented Kalman filtering. A high-order unscented Kalman filter is used for finishing the state estimation task in the target tracking process. According to the state estimation method based on the high-order unscented Kalman filtering, the state estimation task in the target tracking process is finished by the high-order unscented Kalman filter. In the target tracking process, the state equation and the measurement equation of target tracking are established; a sigma point required for the target tracking filter is obtained by high-order unscented transformation, and the weight of the sigma point is calculated; and the state estimation is obtained by iterating the sigma point and the weight of the sigma point to realize the real-time tracking of the target. The tracking precision of the state estimation method is higher than those of the existing target tracking methods based on other filters, a proper performance parameter k is selected to further improve the precision of the proposed high-order unscented Kalman filtering (UKF) target tracking method, and the high-precision real-time tracking to the target is realized. The state estimation method disclosed by the invention is applied to the technical field of the target tracking.

The invention relates to an electromagnetic transient simulation method containing a switching characteristic sub-network, and belongs to the technical field of electromagnetic transient analysis in electric power systems. According to the simulation method, a breaker and electronic power switching elements are designed into an independent switching sub-network; the network only comprises an electronic power sub-switch, the breaker and related elements (resistors, inductors, capacitors and the like); the network performs modeling through a rational polynomial approximation based exponential fitting method provided by the invention; and the rest of networks perform modeling by a conventional method (an implicit trapezoid method, a backward Euler method, a damping trapezoidal method or a modified combining form thereof). In offline/real-time calculation, only the switching sub-network performs iteration or interpolation calculation, and the rest of networks do not participate in iteration or interpolation. The switching sub-network adopts a high-order algorithm provided by the invention, so that numerical oscillation can be immunized; and meanwhile, the workload of model modification is relatively low, so that engineering promotion is facilitated.

The invention discloses a new WENO (Weighted Essentially Non-oscillatory) format construction method under a trigonometric function framework. Compared with a classic essentially non-oscillatory format constructed through utilization of an algebraic polynomial, a weighted essentially non-oscillatory format constructed through utilization of a trigonometric function polynomial has the advantage that the weighted essentially non-oscillatory format is easier to simulate wave or high frequency oscillation problems, can obtain high order numerical precision can be obtained in a smooth area, and keeps essentially non-oscillatory property at shock wave and contact discontinuity locations. Even if the new TWENO format and the classic five-order WENO format employ information at the same five points, according to the new TWENO format, the lower global L<1> and L<infinite> norm truncation errors can be obtained. According to linear weights employed by the new TWENO format, the optimum solutiondoes not need to be obtained through burdensome numerical calculation, the linear weights can be set as any positive numbers satisfying the fact that the sum is 1. Compared with the classic WENO format, the new TWENO format has the advantages that the new TWENO format is simpler, has higher robustness and is easier to popularize to a high-dimensional space. According to the new TWENO format, a plurality of classic Euler problems are effectively and numerically simulated, and the effectiveness is sufficiently verified.

An apparatus, method and program storage device for determining high-energy neutron/ion transport to a target of interest. Boundaries are defined for calculation of a high-energy neutron/ion transport to a target of interest; the high-energy neutron/ion transport to the target of interest is calculated using numerical procedures selected to reduce local truncation error by including higher order terms and to allow absolute control of propagated error by ensuring truncation error is third order in step size, and using scaling procedures for flux coupling terms modified to improve computed results by adding a scaling factor to terms describing production of j-particles from collisions of k-particles; and the calculated high-energy neutron/ion transport is provided to modeling modules to control an effective radiation dose at the target of interest.

The invention relates to a 0+ error immune electromagnetic transient simulation algorithm used under the sudden change of input quantity and belongs to the technical field of electromagnetic transient analysis of an electric system. According to the method, by means of the impulse response invariable principle, numerical sampling of a continuous signal of the system corresponds to Z conversion of a discrete signal, and the fundamental form of an element based on operation conductance and a history current item is given. Based on the form, a system network equation is obtained according to the node analysis method, and a system electromagnetic transient simulation result is obtained according to the same steps. The method has the advantages that the truncation error is smaller than that generated through currently adopted methods and the 0+ error purpose is realized under the sudden change of the immune input quantity, achieves non-linear load modeling of the electric system, solves the problem of oscillation of an electronic power switch model state variable outburst value, and provides a new way for electromagnetic transient branch-level modeling of the electric system.

The invention discloses a finite difference multi-resolution trigonometric function WENO format simulation method which comprises the following steps: S1, discretizing a hyperbolic conservation law equation into a space semi-discrete ordinary differential equation, and reconstructing a high-order approximation value of numerical flux by adopting a novel finite difference multi-resolution trigonometric function WENO format; S2, adopting a four-order TVB Runge-Kutta time discrete formula to discretize the space semi-discrete finite difference format into a space-time full-discrete high-precisionfinite difference format; S3, obtaining an approximate value on the next time layer according to the space-time full-discrete high-precision finite difference format; and sequentially iterating to obtain a numerical result of the flow field at the termination moment in the calculation area. According to the method, high-precision numerical simulation can be carried out on various compressible flow field problems, especially the low-pressure low-density problem and the high-frequency oscillation problem, numerical simulation of the compressible flow field problems and the low-pressure low-density problem of waves and high-frequency oscillation is achieved, robustness is higher, and the method is easier to popularize to a high-dimensional space.

The invention relates to a method for simulating a compressible flow field problem in a multi-resolution TWENO format, and provides a brand new finite difference multi-resolution trigonometric function weighted essentially non-oscillatory format, and is used for numerical simulation of a compressible flow field problem. Innovative points of the method are as follows: only information on a spatialcenter nesting hierarchical structure is used, and any equivalent multi-resolution is not introduced; the adopted linear weight does not need to be calculated through complicated numerical values to obtain a theoretically optimal solution, and the solution can be artificially set to be any positive number meeting the sum of 1. Compared with a classical WENO format, the method is simpler and more convenient, higher in robustness and easier to popularize to a high-dimensional space. Finally, the novel finite difference multi-resolution TWENO format effectively simulates a plurality of classicalhyperbolic conservation law equation problems in a numerical mode, and the effectiveness and reliability of the method are fully verified.

The invention discloses a method applied to an unmanned aerial vehicle for improving navigation calculating precision, and belongs to the field of aerial automation control. The method specifically comprises the following steps: 1, acquiring starting point information, destination point information and current position information of the unmanned aerial vehicle; 2, splitting longitude data, latitude data and height data of forty floating point types in the starting point, the destination point and the current position, so as to obtain a trigonometric function equation of the data of the forty floating point types; and 3, acquiring laterodeviation distance and laterodeviation speed according to the starting point information, the destination point information and the current position information obtained in step 1 of the unmanned aerial vehicle, and rectifying the deviation of a track route of the unmanned aerial vehicle according to the laterodeviation distance and the laterodeviation speed. According to the method applied to the unmanned aerial vehicle for improving navigation calculating precision, the navigation calculation of the forty floating point types is carried out, thus the intercepting error occurring in the operation can be reduced, and the calculation precision can be improved; once the position precision of a DGPS (Differential Global Positioning System) is 0.1m, the laterodeviation distance output precision under the navigation calculation of the forty floating point types can reach 0.3m, and thus the purposes of precise guiding, taking off and landing control can be met.

A direct digital frequency synthesis method comprises the following steps: calculating, by a phase accumulation module, a first phase according to a frequency synthesis word (S101); finding an amplitude value by a preset sinusoidal lookup table according to the first phase (S102); finding a second phase by a preset phase lookup table according to the amplitude value (S103); if the second phase is less than the first phase, adjusting and outputting the amplitude value (S105); or else, outputting the original amplitude value (S106); and performing, by a digital-to-analog converter, a digital-to-analog conversion according to the output amplitude value to obtain a sinusoidal wave (S107); wherein, for a N-bit phase accumulation module and a D-bit digital-to-analog converter, the preset phase lookup table has 2^D−1-1 phase boundary value records corresponding to 0˜2^D−1-2 amplitudes, each phase boundary value is stored in N-2 bits. A direct digital frequency synthesizer applying the above method is also disclosed.

The invention discloses a sine windowing electromagnetism band gap band-stop filter which comprises an upper-layer microstrip line structure, a middle-layer medium substrate and a lower-layer grounding metal face. The upper-layer microstrip line structure is attached to the upper surface of the middle medium substrate and the grounding metal face is attached to the lower surface of the middle medium substrate. The upper-layer microstrip line structure comprises an input port, an output port and a periodical microstrip line which is modulated by a windowing function, wherein the input port and the output port are formed in the two ends of the upper-layer microstrip line structure. The weighting technology with a grounded flaw face is directly applied to microstrip transmission line design of the one-dimension sine EBG band-stop filter. A signal is weighted through a window function, thus, truncation errors generated when limited truncation is carried out on an infinite time-domain signal are reduced. Thus, under the condition that performances of the device are not changed, the device can be miniaturized through a small sine periodical amount. Passband ripples and reflected sidelobe performances of the band-stop filter are improved, thus, the manufacturing technology of the sine windowing electromagnetism band gap band-stop filter is simpler.

The invention relates to the technical field of high-speed milling, and discloses a milling chatter stability prediction method, which uses Renyi entropy to judge the stability of a time domain signal obtained by simulation, and comprises the following steps: S1, establishing a milling process dynamic differential equation considering a regeneration effect; S2, solving the milling dynamics differential equation by adopting a numerical method to obtain a time domain signal; S3, applying a stability criterion to the time domain signal in the S2; and S4, changing the cutting condition, and repeating the steps S1 to S3 until a stability lobe graph is obtained. The Renyi entropy is used for carrying out stability judgment on the obtained time domain signal, so that the criterion universality is greatly enhanced; the variable-step Runge-Kutta algorithm is adopted to solve the milling dynamics differential equation, the truncation error is greatly reduced compared with the Runge-Kutta algorithm, and the stability prediction precision can be fully improved.