86 results about "Approximation error" patented technology

The invention discloses a free-form surface three-axis ball-end cutter equal approximation error finish machining tool path generation method which comprises the following steps: firstly, importing a free-form surface model to be machined, and setting data such as the radius, the line spacing, the approximation error maximum allowable value and the precision of a ball-end cutter; secondly, a group of section planes are planned according to the row spacing to intersect with the curved surface, the intersecting line serves as a cutter contact curve, and an equal-bow-height-error cutter contact iterative search method for driving cutter contact adjustment through the geometric distance is provided for the cutter contact curve on the section planes; the maximum distance between a cutter cutting envelope surface and a cutter contact track line is used as an approximation error, and an adaptive discrete method is adopted to carry out approximation error calculation; and finally, the cutter location points of the equal-bow-height-error cutter contact points serve as initial values, an equal-error cutter location point calculation method of step length self-adaptive adjustment iteration is provided, approximation errors between the cutter location points are all within an allowable range, and therefore the free-form surface three-axis ball-end cutter equal approximation error finish machining cutter path is obtained.

The invention discloses a transformer sound signal adaptive wavelet optimization and feature extraction method and system, and the method comprises the steps: calling a Pywt wavelet analysis library, decomposing an original signal according to a decomposition layer number J, and obtaining a multi-layer detail signal; for each layer of detail signals, the following steps are executed: introducing an M estimator to improve a noise variance calculation model, and calculating a standard deviation and a unified monitoring threshold value; constructing a dynamic threshold value based on a denoising signal approximation error minimization criterion; designing a correction factor; correcting the wavelet coefficient of each layer of detail signal; reconstructing a pure signal by using an inverse decomposition method; dividing the pure signal into a plurality of short-time signals; extracting an MFCC feature vector of each short-time signal; weighting and screening MFCC feature vectors by adopting a support vector machine recursive feature elimination method; and compressing the dimension of the feature vector in combination with a principal component analysis algorithm to generate a final feature matrix. According to the method, the problems of contradiction between noise suppression and signal fidelity and low recognition rate caused by high-dimensional feature redundancy in a traditional method are solved.

The invention relates to the field of nonlinear system control, and provides a preset time reinforcement learning method and system of a continuous nonlinear system, and an electronic device, and the method comprises the steps: constructing a zero-sum game framework based on a kinetic model and a performance index of the nonlinear system; determining a value function and a Hamiltonian function based on a zero-sum game framework; applying a preset neural network model to carry out approximation on the value function, and determining an approximation error; based on the Hamiltonian function and the approximation error, an approximate optimal control strategy and a worst interference strategy are determined; constructing a Lyapunov function based on the value function and the weight error of the value function; and based on a Lyapunov function, an approximate optimal control strategy and a worst interference strategy, a reinforcement learning result is verified. The method and the device are used for overcoming the defects that convergence time cannot be dynamically adjusted, parameter complexity is high and robustness is insufficient in the prior art, and the scheme of the invention can meet dual requirements of a continuous nonlinear system on dynamic convergence and anti-interference performance.

The invention provides a finite time cooperative tracking control method based on an adaptive RBF neural network, and belongs to the technical field of networked multi-agent control strategies. Constructing a dynamic mathematical model of a high-order all-drive uncertain nonlinear multi-agent system comprising a virtual leader and a follower; according to a cooperative tracking control target and uncertain items in the system, constructing an error dynamic system comprising an adaptive RBF neural network estimation compensation item; designing a finite time integral sliding mode surface based on a high-order all-drive system theory; designing linearization parameters of a finite time integral sliding mode surface based on a pole assignment method according to system dynamic performance and finite time convergence requirements, and obtaining a finite time integral sliding mode controller; and designing a self-adaptive updating law of an upper bound of an RBF neural network weight and an approximate error, and substituting the network weight and the approximate error into a finite time integral sliding mode controller to realize cooperative tracking control of finite time.

The invention discloses a self-adaptive cooperative control strategy based on a variable speed reaching law and a neural network, belongs to the field of intelligent control, and mainly aims at estimating and compensating uncertainty, external disturbance and actuator saturation existing in a queue in queue control and improving the stability, robustness and control performance of the whole queue. The method comprises the following steps: establishing a queue system model with uncertainty, external disturbance and actuator saturation; establishing a Gaussian error function approximation strategy; establishing a tracking error; establishing a variable speed reaching law; establishing a queue integral sliding mode error; establishing a queue coupling sliding mode error; establishing an adaptive parameter estimation mechanism for external disturbance and Gaussian function approximation errors in the queue; establishing a neural network estimation mechanism for uncertainty in the queue; and establishing a queue integral sliding mode control strategy based on a variable speed reaching law, a Gaussian error function approximation strategy, an adaptive parameter estimation mechanism and a neural network estimation mechanism. The method is used for queue cooperative intelligent control.

A label noise estimation method based on a manifold regularization transfer matrix provided by the present invention pre-trains a first network in a second network, and after distilling a data set, inputs the obtained sub-data set into the second network to obtain the probability of the class to which the data instances in the sub-data set belong and obtain a transfer matrix related to the data instances; further calculates the cross-entropy loss of the second network according to the data instance labels, and combines an association matrix expressing the consistency of the data instances belonging to the same manifold and a penalty matrix of the data instances belonging to different manifolds to calculate the loss function of the second network; adjusts the loss function to reduce the training of the second network to obtain a trained second network, thereby completing the estimation of the class to which the data instances belong. The present invention can reduce the estimation error without affecting the approximation error of the transfer matrix, and experiments prove that the present invention can achieve excellent performance in label noise learning.

Methods and systems for performing an operation on at least one homomorphically encrypted ciphertext, the method include determining, by a computing device, a value that is an initial approximation of a result of the operation on the at least one homomorphically encrypted ciphertext; and iteratively improving, by the computing device, the value using a recurrence relation wherein a number of iterations is determined based on a predetermined accuracy to minimize an approximation error.

The embodiment of the invention discloses a harmonic compensation method for an angle error of a magnetic encoder, and the method comprises the steps: enabling the magnetic encoder to rotate at a constant speed in a setting mode, collecting sine and cosine signals outputted by the magnetic encoder, and carrying out the calculation through CORDIC, thereby obtaining an initial angle sequence containing a fundamental wave error and a harmonic wave error; extracting each harmonic component through an adaptive wave trap, constructing a harmonic compensation polynomial, and storing each coefficient; in an application mode, a magnetic encoder signal is collected in real time, a current initial angle value is solved, a harmonic compensation amount is calculated according to a current fundamental wave angular frequency and a stored coefficient, and an accurate angle value is obtained by subtracting the compensation amount from the initial angle value. According to the method, external reference signals and a large amount of storage space are not needed, each harmonic error is directly eliminated through a harmonic compensation polynomial, and approximate errors caused by traditional linear interpolation are avoided; and the compensation precision can be improved only by increasing polynomial terms, and the storage requirement is not obviously increased.

The invention discloses a CKKS fully homomorphic encryption scheme approximation error reduction method, and solves the problems of low efficiency and rapid increase of error scale in practical application in the prior art. The method comprises the following steps: generating a public parameter, a public key and a private key; generating a relinear key and a self-isomorphic key according to the public key and the private key; performing multi-layer coding on the received multiple message vectors to obtain a coded plaintext polynomial corresponding to each layer; performing encryption to obtain a ciphertext corresponding to each layer; operation is carried out according to the encryption requirement of a user and the ciphertext, and a ciphertext operation result corresponding to each layer is obtained; carrying out relinearization on the ciphertext operation result and scaling the ciphertext operation result to the next layer step by step to obtain scaled ciphertext corresponding to each layer; a multiplication ciphertext is obtained; decrypting and decoding to obtain a message vector; according to the method, the noise introduced by the ciphertext in the initial encryption process and the noise generated in the key switching process are reduced, and meanwhile, the rounding error introduced in the operation process is greatly reduced.

An information processing apparatus obtains measurement data representing measurement values measured after a quantum gate sequence including first and second quantum gates is executed a plurality of times, defines, in representing the first quantum gate as the product of a first matrix representing an ideal value of the first matrix and a matrix exponential of a second matrix representing an error, a variable representing the second matrix, generates a function that linearly approximates an effect of the error on the measurement values, by approximating a composite quantum gate that is a combination of the first and second quantum gates by the product of the first matrix, a third matrix representing an ideal value of the second quantum gate, and a matrix exponential of a transformation result of transforming a value of the variable using the third matrix, and estimates the error using the function and measurement data.

The invention discloses an air-space-ground Internet of Things performance analysis method and system based on SWIPT and NOMA, and belongs to the technical field of air-space-ground integrated Internet of Things. Comprising the following steps: constructing an air-space-ground Internet of Things system model comprising an LEO satellite, an unmanned aerial vehicle relay and a ground user, and considering heterogeneous channel characteristics and node dynamics; deducing a closed-form solution of the outage probability of the system through joint transformation of a moment generation function and a characteristic function of a random variable; a high-order Taylor expansion and moment matching method is adopted to carry out approximation on the closed-form solution, a first-order approximate solution and a second-order approximate solution are obtained, and an upper bound of an approximate error is deduced. According to the method, the problem of accurate modeling of the outage probability under heterogeneous link coupling in the air-space-ground Internet of Things is solved, theoretical preciseness and engineering practicability are both achieved, and an effective tool is provided for network reliability analysis and optimization.

The invention discloses a roadside multi-mode fusion sensing method. According to the method, an initial 3D view cone tensor with depth information is generated through a depth estimation network, features of pixel points are projected to a coordinate system in combination with internal and external parameter matrixes of a camera, then a three-dimensional space point coordinate set is generated according to projected feature position information, a Gaussian function is adopted to distribute weights of neighborhood grids, and a three-dimensional space point coordinate set is obtained. And finally, inputting the image features and the features into a fusion unit, respectively carrying out uncertainty modeling on the two types of features, automatically generating a fusion weight, and finally, carrying out normalization weighted aggregation on the features in the neighborhood so as to reduce the position approximation error and obtain the calibrated image features, and finally, inputting the image features and the features into the fusion unit, and respectively carrying out uncertainty modeling on the two types of features and automatically generating a fusion weight. And dynamic optimization is carried out according to a self-supervised loss function in the fusion process, so that the stability of multi-modal feature fusion is ensured, the detection accuracy is high, the performance is relatively good, and the problem of global feature dislocation caused by external parameter deviation and depth error can be avoided.

The invention discloses a five-axis numerical control finish machining tool path approximation error calculation method based on an Optuna optimization BiLSTM-TCRA (BiLSTM, Bidirectional Long Short Term Memory Network, a Bidirectional Long Short Term Memory Network, a Temporal-Channel Residual Attention, a Time-Channel Residual Attention mechanism) neural network, and relates to a tool path approximation error calculation method based on an Optuna optimization method of a BiLSTM-TCRA (BiLSTM, Bidirectional Long Short Term Memory Network, a Bidirectional Long Short Term Memory Network, a Time-Channel Residual Attention Mechanism) neural network and a tool path approximation error calculation method based on the BiLSTM-TCRA neural network. The method comprises the following steps: firstly, acquiring core parameters required by calculation of a neural network model, and mapping the parameters to the same scale by using mean variance normalization to eliminate the influence of dimensional difference between different features on the performance of the model; then, each hyper-parameter of the BiLSTM model is optimized by using an Optuna hyper-parameter optimization framework; a TCRA attention mechanism module is introduced to dynamically distribute different time step feature weights, so that the model can pay more attention to effective information which greatly influences an approximation error, the learning ability of the model is enhanced, and the training precision is improved; dropout mechanism sparsity is added to optimize a network structure, and part of neurons are randomly discarded in each iteration process, so that interference of non-core knife contacts on an approximation error value is reduced, and model overfitting is avoided; finally, the effectiveness of the method is verified in combination with actual curved surface model data, and efficient and accurate prediction of the five-axis machining approximation error is achieved.

Diffusion models are machine learning algorithms implemented as neural network-based denoisers that are uniquely trained to generate high-quality data from an input lower-quality data. However, for complex datasets, the samples generated by a diffusion model can still fail to reproduce the quality and diversity of the training data, due to approximation errors made by the finite-capacity network. Diffusion guidance addresses this issue by steering the sampling process away from a less desired model, toward a preferred one. However, current guidance methods rely on a single additional denoiser and manual tuning of guidance weights, which is suboptimal for large, complex models and leads to inefficiencies. The present disclosure employs a mixture of denoisers to guide a diffusion model, which can increase the expressiveness of the guidance and substantially improve sample quality and diversity in the output of the diffusion model.

This invention discloses a floating-point-fractional hybrid anchoring method and computational system for suppressing iteration errors, belonging to the field of high-precision numerical computation technology. It solves the technical problems of pseudo-chaos caused by the accumulation of iteration errors in pure floating-point calculations, the computational power explosion in pure high-precision fractional calculations, and the inability to simultaneously achieve both computational power and precision. This invention completes high-speed iterative computations of nonlinear systems using a general floating-point format. After each floating-point calculation, an optimal rational number approximation algorithm is used to convert the calculation result into a simplified rational number with a denominator not exceeding a preset threshold, eliminating the original errors introduced by floating-point truncation and rounding. The purified rational number is then converted back to floating-point format to participate in the next iteration, relying on a bounded rational number anchoring mechanism to progressively block the error amplification chain. The denominator threshold is set to 10¹²~10¹ based on the effective number of bits of the floating-point number. 5 This invention can adaptively adjust to various scenarios such as embedded terminals, supercomputing, and industrial control, and optimizes the continued fraction algorithm to achieve the globally optimal rational approximation under a given upper limit of the denominator. It requires no dedicated large number hardware and combines the advantages of high-speed, low-load floating-point operations with zero approximation error in rational numbers. It can be stably used in nonlinear computing scenarios that are sensitive to initial values ​​and require long-term stable iterations, such as chaotic simulation, vehicle trajectory prediction, industrial PID closed-loop control, 5G / 6G communication channel simulation, microscale meteorological simulation, and large-scale number theory zero-point verification. It effectively eliminates numerical trajectory drift, reduces equipment computing power consumption, and minimizes the workload of manual calibration and data screening, possessing extremely high engineering and academic application value.

The present invention provides a stable control method for the libration of an electrodynamic tethered satellite. Compared with existing control methods based on optimization theory, this control method has an analytical form, a small computational effort, and can handle the effects of control current saturation nonlinearity and unknown system disturbances. The method comprises: establishing orbital dynamics equations based on the six elements of the vernal equinox; establishing attitude dynamics equations based on in-plane and out-of-plane angles; obtaining control equations describing the libration of the tethered satellite through dimensionless transformation; designing an auxiliary dynamics system to compensate for the saturation nonlinearity of the control current; using a radial basis function neural network to approximate multiple disturbances, such as model perturbations and external interferences, and estimating the weight matrix and approximation error to compensate for the disturbances; designing an analytical control law for the current in the electrodynamic tether; correcting singular terms in the analytical control law using a dynamic scaling generalized inverse method; and controlling the libration process of the electrodynamic tethered satellite system using the analytical control law.

The invention belongs to the technical field of laser interference precision measurement, and provides a full geometric error displacement calculation method based on non-approximate simplification of a light beam track. All optical machine geometric errors can be completely calculated, the real refraction condition can be completely calculated, no approximate error is introduced in the simplification process, and the displacement calculation process conforms to the real light beam track condition; according to the method provided by the invention, all reflection phenomena in the interferometer are simplified, parameter integration is carried out on a reflecting surface and a receiving surface of a reflected light beam, an originally complicated multi-beam calculation process is optimized, the number of parameter items required for completely describing geometric errors is reduced, and the calculation efficiency is improved. And meanwhile, the light beams which do not influence the calculation of the total optical path difference are deleted, so that the calculation efficiency is high.

The invention discloses an uplink outage probability analysis method and system for an unmanned aerial vehicle cooperating with a wolfberry picking trolley, and the method comprises the steps: constructing a joint effect model in a non-static multi-input multi-output scene, and determining an unmanned aerial vehicle and wolfberry picking trolley uplink cooperative communication scheme for achieving the maximum channel gain; deducing to obtain an uplink outage probability closed expression containing transmitting power, interference statistical characteristics and mobility parameters by adopting an interference statistic calculation method based on Laplacian transformation; based on the obtained uplink outage probability closed expression, an improved Gaussian approximation method is adopted, and an uplink outage probability approximate expression is obtained through a dynamic truncation criterion; and based on the obtained uplink outage probability approximate expression, obtaining the total error upper bound of approximate errors by using Gaussian approximation errors and space average errors, and realizing efficient and accurate evaluation and guaranteeing the reliability of agricultural automation communication through dynamic interference modeling and improved Gaussian approximation.

The invention discloses a large model similar channel sharing weight lightening method and device, and belongs to the field of artificial intelligence. The method comprises the steps of performing K-Means clustering on a Q / K projector weight matrix of a self-attention layer of a Transform architecture large model according to columns, and generating a cluster representative vector and a cluster label list to replace an original weight matrix to complete compression; restoring the approximate weight matrix based on the representative vector and the cluster label, and constructing an error matrix of the original matrix and the approximate matrix; performing singular value decomposition on the error matrix and retaining a key singular value to obtain two low-dimensional matrixes; during reasoning, multiplying the two low-dimensional matrixes to obtain an approximate error matrix, and adding the approximate error matrix with the approximate weight matrix to obtain a final reasoning weight; the total storage size after compression is calculated through a unified formula, and accurate quantification of storage overhead is achieved. According to the method, the performance degradation under low-bit compression is effectively relieved, the resource demand of model deployment is reduced, and the method is adaptive to various mainstream large models and different-dimension weight matrixes.

The invention discloses a chromatin contact atlas-based topological correlation domain division method, which comprises the following steps of: acquiring and preprocessing chromatin contact atlas data, and constructing a normalized contact matrix; according to the normalized contact matrix, calculating single-segment Infomap entropy values of all possible division intervals; solving an Infomap entropy value of a minimum part in each state through dynamic programming recursion, and calculating a complete Infomap entropy value under each step number according to the Infomap entropy value of the minimum part in each state; selecting the step number corresponding to the minimum integral Infomap entropy value, and obtaining the optimal topological correlation structure domain division through backtracking; an approximation error of the partition structure is calculated to assess partition accuracy. According to the method, a machine learning model does not need to be trained, whole genome chromatin contact information can be fully utilized, optimal division of TAD is automatically achieved, the division accuracy and repeatability are improved, meanwhile, the calculation complexity and cost are reduced, and an efficient and reliable tool is provided for chromatin three-dimensional structure and gene regulation and control research.

The application discloses an underactuated unmanned ship route tracking control system based on extreme learning, which comprises an establishing module I, an establishing module II, an establishing module III, an identifying module and a control module. Based on the identified unmodeled dynamics, parameter disturbance, external environment disturbance and the rest dynamic unknown items, and the longitudinal sight line guidance law, a robust adaptive route tracking control method based on extreme learning is adopted, the output weight based on the single hidden layer feedforward network SLFN approximation and the corresponding estimated error adaptive rate are designed to approximate the unknown items and reduce the approximation error, the identification precision is improved, the longitudinal controller and the bow controller are designed to compensate for the unmodeled dynamics, parameter disturbance, external environment disturbance and the rest dynamic unknown items, so that the unmanned ship is asymptotically stable at the dynamics level, the tracking control of the unmanned ship sailing along the expected path is realized, the tracking precision is improved, and the global asymptotic stability of the whole closed loop system is improved.

An apparatus for computing functions using polynomial-based approximation, comprising one or more processing circuitries configured for computing a polynomial-based approximant approximating a function by executing one or more iterations. Each iteration comprising computing the polynomial-based approximant using scaled fixed-point unit(s) according to a constructed set of coefficients, minimizing an approximation error of the computed polynomial-based approximant compared to the function while complying with one or more constraints selected from a group comprising at least: an accuracy, a compute graph size, a computation complexity, and a hardware utilization of the processing circuitry(s), adjusting one or more of the coefficients in case the approximation error is incompliant with the constraint(s) and initiating another iteration. The polynomial-based approximant and its adjusted set of coefficients for which the computed polynomial-based approximant complies with the constraint(s) may be output to one or more processing circuitries configured to approximate the function by computing the polynomial-based approximant.

The invention belongs to the field of computational electromagnetism numerical simulation, and particularly relates to a non-uniform conformal FDTD method based on a sub-grid technology. According to the method, non-uniform conformal geometric correction is introduced into the sub-grids, so that high-precision fitting of a curved surface boundary is realized, step approximation errors are reduced, and the calculation precision of field quantities near the boundary is improved; according to the method, bidirectional coupling transfer which simultaneously meets line integral conservation and flux conservation is established on a main-sub grid interface, and a conservation relation required by a non-uniform conformal FDTD method is prevented from being damaged, so that interface numerical value reflection is effectively inhibited, energy non-physical errors are reduced, and long-term stability is improved; and fine grids are only adopted in the local fine structure neighborhood and are matched with time sub-cycle propulsion, so that global grid encryption and limitation of global time step length to a minimum unit are avoided, and the storage and calculation time overhead is remarkably reduced while the precision is ensured. According to the method, geometric modeling precision, interface stability and calculation efficiency are considered, and the method has high engineering application value.

The invention discloses a sonar image imaging method, system and device based on a two-step interpolation method. The sonar image imaging method comprises the following steps: calculating a two-dimensional frequency domain system function; second-order approximation is carried out on the distance-direction instantaneous frequency, and a high-order phase approximation error is calculated; for the approximated function, calculating the maximum range migration of the scene and the multiple # imgabs0 # to be interpolated in the subsequent steps, and performing first zero padding on the front end and the rear end of the sonar data in a range direction time domain; performing high-order phase error compensation and range-direction matched filtering in a two-dimensional frequency domain for the zero-filled data; calculating the total number # imgabs 1 # of the range-direction frequency domain data, supplementing # imgabs 2 # zero values to the rear end of the range-direction frequency domain data, and converting the range-direction frequency domain data to a range-direction time domain; aiming at the data of the distance-Doppler domain, according to the distance migration amount corresponding to each distance target, adopting a rounding-off interpolation method to carry out distance migration correction; and carrying out azimuth matched filtering in the distance-Doppler domain and converting to a two-dimensional time domain to obtain a high-resolution image.

This application discloses an adaptive wavelet optimization and feature extraction method and system for transformer acoustic signals. The method includes: calling the Pywt wavelet analysis library to decompose the original signal according to the decomposition layer number J to obtain multi-layer detail signals; for each layer of detail signals, performing the following: introducing the M-estimator to improve the noise variance calculation model, calculating the standard deviation and a unified monitoring threshold; constructing a dynamic threshold based on the criterion of minimizing the approximation error of the denoised signal; designing a correction factor; correcting the wavelet coefficients of each layer of detail signals; reconstructing the pure signal using an inverse decomposition method; dividing the pure signal into multiple short-time signals; extracting the MFCC feature vector of each short-time signal; using the support vector machine recursive feature elimination method to weightedly screen the MFCC feature vectors; and combining the principal component analysis algorithm to compress the feature vector dimension and generate the final feature matrix. This application solves the problems of the contradiction between noise suppression and signal fidelity in traditional methods, and the low recognition rate caused by high-dimensional feature redundancy.

The point spread function calculation method and system provided in the present application construct an optical analysis model, obtain the image plane intersection point in the optical analysis model, obtain the intersection point of the lower edge light of the specified field of view of the optical analysis model and the last optical surface as the boundary of the tracing grid, establish ray tracing grid points, and perform reverse ray tracing based on the image plane intersection point and the grid point to obtain the pupil function. Compared with the traditional method that needs to find the entrance pupil boundary and involves complex logical processes, the present application will avoid the complex entrance pupil, exit pupil and their boundary determination process, and directly calculate the ray tracing boundary based on the surface aperture. The calculation process is closer to the real physical process, with low implementation complexity and good stability. Through reverse ray tracing, the calculation error introduced by Fourier grid distortion and the approximation error of the traditional Fraunhofer propagation method are avoided, and an accurate ideal point light source diffraction image, that is, the point spread function of the optical system, can be obtained in the image space.

This invention discloses a method, system, and electronic device for preparing stable substates based on graph states. The method includes: acquiring and preprocessing stable substate generators to obtain complete stable substate generators; generating an initial parity-check matrix based on the complete stable substate generators; converting the initial parity-check matrix into a graph state parity-check matrix and recording the conversion operations performed during the conversion; constructing a graph state preparation circuit based on the graph state parity-check matrix; constructing a stable substate reduction circuit based on the conversion operations; merging the graph state preparation circuit and the stable substate reduction circuit into a total circuit; acquiring an initial quantum state and executing the total circuit with the initial quantum state to obtain a stable substate. This invention uses graph states as an intermediary, reducing the complexity of circuit design and improving computational efficiency, making it suitable for large-scale quantum systems. Furthermore, the precise mapping relationship between stable substates and graph states avoids approximation errors.

The invention belongs to the technical field of computer-aided manufacturing, and relates to a variable-step-size high-precision approximation method for a complex spline curve. The method comprises the following steps: selecting an approximation curve as a straight line or a circular arc according to a local geometric characteristic of an approximated curve, namely a curve curvature, measuring an approximation error between the approximated curve and the approximation curve by using a bidirectional Hausdorff distance, controlling an approximation precision fluctuation range and an approximation curve segment length based on a variable step size method, and controlling an approximation iteration process by using a termination discrimination strategy, therefore, on the premise that the approaching progress is guaranteed, the length of the minimum approaching curve section and the number of machining codes are increased as much as possible, and then the machining efficiency and the machining quality are guaranteed.

To provide an information processing device, information processing method, and program that can reduce the scale of computations and improve the uniformity of approximation error of a square root of an input value.SOLUTION: An information processing device 1 includes a determination unit configured to calculate the largest integer n that satisfies the expression [1] for an input numerical value x, and a first calculation unit configured to output a numerical value y obtained by performing, on the numerical value x, a computation that includes a term of the expression [2], in which a numerical value α is a predetermined constant. The numerical value α is a predetermined constant close to 1 / 3. The numerical value y obtained in this manner is an approximation of the square root of the numerical value x (i.e., √x).SELECTED DRAWING: Figure 2

The application provides a real-time security evaluation method and device. The method comprises the following steps: acquiring a monitoring data stream, and extracting security level information corresponding to each time point of all data blocks from the monitoring data stream; updating the weight change of the security index based on the security level information through a KernelSHAP method; incrementally updating an evaluation model by using the updated security index and weight, and predicting a security evaluation result by using the updated evaluation model; and determining a security evaluation result according to a preset decision threshold and the security evaluation result. By using the KernelSHAP method, the importance of the newly collected monitoring data stream is determined based on a wide learning system structure, the negative influence caused by the approximation error is reduced, the drift detection is combined with the adaptive and generated explanation ranking preference, and therefore the result of the real-time security evaluation task can be better predicted.