84 results about "Unconstrained optimization" patented technology

The invention provides a delay compensation control method for a double-vibrator wave energy conversion device, which comprises the following steps of: performing numerical modeling and hydrodynamic analysis on the double-vibrator wave energy conversion device, establishing a time domain motion equation of the double-vibrator wave energy conversion device, and introducing a time delay function into the time domain motion equation to simulate control signal transmission delay; simulating the execution delay of the brake by using a partial differential equation; establishing a state-space equation of the device, replacing a convolution term of the time-domain motion equation with the state-space equation, and calculating to obtain a motion state of the device; a Hamiltonian function is defined to convert a constrained optimization problem into an unconstrained optimization problem, and the Hamiltonian function is solved to obtain an optimal control criterion considering control delay so as to realize maximization of energy capture under the optimal control criterion. According to the method, the operation characteristics of a physical system are truly reflected by introducing control delay, so that the locking control method is effectively implemented in an actual physical device, and the energy capture efficiency of a wave energy conversion device and the reliability of system operation are effectively improved.

The invention relates to the technical field of intelligent traffic and road disaster early warning, in particular to a transportation risk optimization method and system, and the method comprises the steps: S1, carrying out the multi-mode event-infrared-optical fiber data collection, and synchronously generating a unified index data package; s2, the physical information neural network combines energy conservation and causal inference assimilation to output a digital twin state tensor; s3, executing forward noise scheduling and reverse denoising by the conditional diffusion model, generating an icing probability field and extracting a high-frequency attention spectrum; s4, road structure factors are calculated according to the probability field and the attention spectrum, a binary unconstrained optimization model is constructed and mapped to an optical coherence Ising machine to be solved, an intervention scheduling scheme is formed through strategy network soft updating and safety verification, and an execution effect is written back and circularly updated. According to the method, sub-second risk identification and millisecond optimization decision are realized, and the accident rate and the salt spreading cost are reduced.

The invention discloses a zero-order primal dual method and device for a black-box constraint optimization problem, and the method comprises the steps: constructing a corresponding black-box constraint optimization problem based on a preset constraint optimization scene, and determining a tightly convex feasible region containing an original variable; converting the black box constraint optimization problem into an unconstrained optimization sub-problem which can be solved iteratively; on the basis of a function value query result of the black box constraint optimization problem, gradient correlation information of the unconstrained optimization sub-problem about an original variable is estimated, iterative solution is carried out on the unconstrained optimization sub-problem on the basis of the gradient correlation information, and the original variable after iterative updating is limited in the tightly convex feasible region; and when a preset convergence condition is met, obtaining a final original variable as an optimization result. A black box constraint optimization problem is converted into an unconstrained sub-problem which can be solved iteratively by introducing a near-end Lagrangian fusion optimization framework, so that efficient optimization is realized under the black box condition that only function values can be obtained.

The invention discloses a satellite remote sensing image random stripe noise suppression method and system based on low-rank tensor approximation. The method specifically comprises the following steps: establishing a random stripe mixed noise image model; then converting a core task of satellite image denoising into an unconstrained optimization problem, and determining a target function; lRA operation is carried out on a noisy data matrix / tensor for random noise in a satellite image to realize random noise suppression, and stripe noise separation is realized through direction selective regularization by using a stripe noise removal model based on one-way total variation UTV for stripe noise in the satellite image; a UTV-LRTA mixed denoising model is established, and the mixed stripe noise in the satellite image is effectively suppressed through combination of low-tube-rank tensor constraint and one-way total variation regularization. According to the method, the random stripe mixed noise is effectively suppressed, the image quality is improved, and the visual effect is improved, so that the accuracy of information identification and analysis is improved.

The invention discloses an aircraft recovery scheduling method and device based on a self-adaptive Lagrange multiplier, and relates to the technical field of aviation traffic control automation, and the method comprises the steps: building a constrained Markov decision process model of an aircraft recovery scheduling problem; introducing and initializing a Lagrangian multiplier by using a Lagrangian relaxation technology, and converting the constrained Markov decision process model into an unconstrained optimization problem to obtain a Lagrangian function; and performing main dual collaborative iterative optimization based on a Carlo demander-Kuhn-Tucker condition, and adaptively adjusting the Lagrange multiplier until the Lagrange multiplier converges to obtain an optimal strategy. According to the method, the constraint weight is dynamically adjusted in the main dual collaborative iteration mechanism, so that the rationality and accuracy of large-scale cluster recovery scheduling are improved.

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

According to the carbon dioxide absorbent formula optimization method, the electronic equipment and the storage medium, by introducing an adaptive particle swarm optimization (APSO) and a dynamic penalty function, a large amount of absorbent physical property and performance data are integrated and intelligently analyzed, dynamic adjustment of constraint conditions and conversion of an unconstrained optimization problem are achieved, and the carbon dioxide absorbent formula optimization efficiency is improved. Furthermore, an absorbent formula with the lowest cost and performance indexes such as the absorption rate, the circulation capacity and the desorption energy consumption meeting the requirements is efficiently and accurately screened out, so that the economical efficiency and the operation stability of a CO2 trapping technology are remarkably improved.

The invention discloses a safety reinforcement learning control method and device for a maglev train suspension system and a medium, and relates to the technical field of maglev control, and the method comprises the following steps: S1, constructing a suspension system dynamic model as a training environment; s2, modeling a control problem of the suspension system as a constraint optimization problem; s3, converting a constrained optimization problem into an unconstrained optimization problem, and performing iterative solution on the target function; s4, constructing a cost function, accelerating solution of an unconstrained optimization problem, and designing a penalty term to guide a system state to be away from a security boundary; and S5, in a reinforcement learning environment, combining a cost function, and carrying out iterative training solution on the unconstrained optimization problem. The method does not depend on an accurate suspension system model, an independent control strategy does not need to be designed for each specific challenge, the optimal control strategy can be adaptively learned through interaction with the suspension system, and the method has high robustness and flexibility.

The invention discloses a high-degree-of-freedom MIMO radar waveform design method capable of accurately controlling ISL, and relates to the technical field of radars, and the method comprises the steps: S1, carrying out MIMO radar constant modulus waveform design modeling, and constructing a bivariate problem under CMC and CSC constraints; s2, introducing a penalty mechanism, constructing a unified constraint space, and converting a bivariate problem into an unconstrained optimization problem; and S3, calculating the gradient of the objective function of the converted problem in the unified constraint space, and then using an adaptive conjugate gradient algorithm to optimize the two variables in parallel to solve. According to the invention, the problem can be directly solved without loosening, and the DOF of waveform design can be enhanced.

The invention provides a radio frequency fingerprint identification method and system based on distributed robust optimization, and the method comprises the steps: collecting a radio frequency signal as an original radio frequency input sample, carrying out the adversarial training, and carrying out the adversarial disturbance and distribution constraint modeling in the adversarial training; minimizing a maximum loss function after disturbance is added in the adversarial training process, and converting the maximum loss function into a solvable unconstrained optimization problem to form a new optimization target; based on the new optimization target, generating a disturbance sample meeting distribution constraints by adopting an adversarial attack mechanism; and carrying out feature extraction on the generated adversarial sample, and outputting a radio frequency fingerprint classifier with high robustness to potential attacks. According to the method, the distribution robust optimization technology is introduced, changes of different data distributions are considered, and the performance loss of the model under the worst condition is minimized. Even in the face of different training data distributions, the model can maintain good performance, so that the stability and reliability of the model in practical application are improved.

The application provides a delay compensation control method for a double pendulum wave energy conversion device, which comprises the following steps: numerical modeling and hydrodynamic analysis are performed on the double pendulum wave energy conversion device, time domain motion equations are established, a time delay function is introduced into the time domain motion equations to simulate control signal transmission delay, and partial differential equations are used to simulate the execution delay of the brake; state space equations of the device are established, the convolution items in the time domain motion equations are replaced by the state space equations, and the motion state of the device is calculated; a Hamilton function is defined to convert a constrained optimization problem into an unconstrained optimization problem, the optimal control criterion considering the control delay is obtained by solving the Hamilton function, and the maximization of energy capture under the optimal control criterion is realized. The application truly reflects the operation characteristics of the physical system by introducing the control delay, so that the closed-loop control method is effectively implemented in the actual physical device, and the energy capture efficiency of the wave energy conversion device and the reliability of the system operation are effectively improved.

The application belongs to the technical field of wireless communication, and relates to a RIS-assisted integrated sensing and communication joint beamforming design method and system, which comprises the following steps: constructing an RIS-assisted ISAC system; initializing a digital beamforming matrix and a phase shift matrix according to a base station total power constraint; constructing an unconstrained optimization problem by using a penalty function method; designing a sending end phase shift matrix based on the unconstrained optimization problem; designing a sending end digital beamforming matrix based on the phase shift matrix; repeating the previous two steps until the change of the system objective function values before and after the two times is less than a preset threshold value, so that the optimal phase shift matrix and the corresponding digital beamforming matrix are obtained. The application effectively improves the performance of the overall system sensing mutual information by alternately optimizing the phase shift matrix and the digital beamforming matrix.

The invention relates to the technical field of multi-agent systems, in particular to a multi-unmanned-vehicle obstacle avoidance pursuit game method and a multi-unmanned-vehicle obstacle avoidance pursuit game system. The method comprises the following steps: constructing a pursuit cost function and an obstacle avoidance cost function of an escaper unmanned vehicle and each pursuit unmanned vehicle, wherein the pursuit cost function is constructed based on a local error function and a pursuit strategy; an obstacle avoidance problem is converted into an unconstrained optimization problem through a gradient weight center self-coordination obstacle function, the obstacle avoidance problem is weighted and introduced into an obstacle avoidance cost function, the obstacle avoidance cost function is constructed by using a relative safety function, an obstacle avoidance strategy and an obstacle penalty term converted by a safety distance constraint, and the obstacle avoidance strategy and a pursuit strategy are optimized based on a value iteration algorithm. And the Nash equilibrium of pursuit game in the obstacle environment is realized. According to the invention, it can be effectively ensured that the unmanned vehicle always keeps a safe distance from the obstacle in the process of pursuit game, and the stability and safety of the unmanned vehicle are improved.

The application provides a kind of space target ISAR image component intelligent segmentation and attitude estimation method, through inverse synthetic aperture radar to space target is continuously observed, and utilize distance-Doppler imaging algorithm to the echo is sequentially imaged, obtain the ISAR image sequence of space target;Utilize deep learning network Pix2pixGAN to the ISAR image sequence is segmented, and the segmentation accuracy is higher;After removing the invalid connected region in each component segmentation result, obtain the final segmentation image of each component;Linear structure extraction is carried out to the final each component segmentation image using the minimum circumscribed rectangle method, and the method is lower to the image component segmentation accuracy requirement, and the robustness is stronger;Finally, according to the imaging principle of radar observation and ISAR image, an unconstrained optimization problem for solving three-dimensional attitude is constructed, and a particle swarm optimization algorithm is used for solving, and the solving efficiency is higher, to realize the attitude inversion of space target key component.

The application provides a kind of intelligent car multi-constraint trajectory planning method based on multi-dimensional laser radar point cloud information, it is related to intelligent car motion planning technical field, the method of the present application first constructs dense point cloud map using A-LOAM algorithm according to the point cloud information emitted by multi-dimensional laser radar, then on the basis of obtaining the dense point cloud map of surrounding environment, the method of curve fitting based on minimum jerk is used, the optimal trajectory is solved in state space by giving the planning starting point and end point position, velocity, acceleration, and the time is further discretized to generate front path point. The uniform B-spline curve without control points is used for curve fitting, and the unconstrained optimization problem about curve smoothness, intelligent car driving speed, intelligent car driving acceleration, obstacle avoidance distance, end point arrival distance is further constructed according to the existing dense occupancy grid map, the quasi-Newton method is used to solve the unconstrained optimization problem, and the optimal trajectory of the intelligent car in complex environment is obtained.

The present application relates to the technical field of power system simulation, and more particularly to a Thevenin equivalent parameter estimation method and system based on multivariate coefficient of variation, an electronic device and a medium; the method comprises: collecting the measured voltage and the measured current at the equivalent point in the target time window; based on the measured voltage, the measured current and the preset Thevenin equivalent impedance prediction value, an indirect statistical model is constructed; the multivariate coefficient of variation is set as an evaluation index for measuring the dispersion degree of Thevenin equivalent potential; an unconstrained optimization model is established; the unconstrained optimization model is solved to obtain the estimated value of Thevenin equivalent impedance, and the estimated value of Thevenin equivalent potential is determined based on the estimated value of Thevenin equivalent impedance. In this way, the technical problem of insufficient estimation accuracy of the existing Thevenin equivalent parameter estimation method when facing complex and variable load fluctuation conditions is solved, and the accuracy and reliability of parameter estimation are improved.

The present application relates to a diffusion kurtosis imaging method, apparatus, computer device, storage medium, and computer program product. The method comprises: acquiring a scanned image signal of a scanned object, fitting the scanned image signal using an unconstrained optimization algorithm to obtain elements of a first diffusion tensor and elements of a first kurtosis tensor, determining diffusion tensor imaging parameters and / or kurtosis tensor imaging parameters based on the elements of the first diffusion tensor and the elements of the first kurtosis tensor, and generating a parametric image based on the diffusion tensor imaging parameters and / or kurtosis tensor imaging parameters. Because the unconstrained optimization algorithm requires a shorter computation time and higher computational efficiency, the time required to obtain the elements of the first diffusion tensor and the elements of the first kurtosis tensor using the unconstrained optimization algorithm in this embodiment is shorter, thereby improving the efficiency of generating the parametric image and reducing the computation time required to generate the parametric image.

A method comprising: setting and training a plurality of classifiers for classification of data in two or more classes; defining a cost function with error functions; optimizing weighting factors associated with each classifier of the plurality of classifiers by converting the cost function into an Unconstrained Optimization problem and solving it with a Tensor Network; setting a boosted classifier based on the optimized weighting factors; solving a problem requiring classification of datapoints in a dataset in the two or more classes using the boosted classifier, the problem defining either a configuration or operation of an apparatus or system, or behavior of a process; and determining at least one of: whether a potential anomaly exists in the operation or the behavior; and a configuration of the apparatus or the system intended to at least one of improve the operation and solve the potential anomaly thereof.

This invention discloses a novel method and apparatus for identifying large branches in a distribution network based on the whale swarm optimization algorithm, addressing the technical problem of low solution efficiency in existing large branch identification methods. The method includes responding to an identification request and constructing objective functions for main distribution transformers and branch transformer load calculations; constructing identification models for main distribution transformers and branch transformers based on the main distribution transformer and branch transformer identification objective functions and preset main distribution transformer and branch transformer identification constraints; constructing branch transformer load calculation models based on the branch transformer load calculation objective functions and preset branch transformer load calculation constraints; using relaxation techniques to transform the identification models for main distribution transformers and branch transformers, and the branch transformer load calculation models, respectively, generating a first unconstrained optimization problem and a second unconstrained optimization problem; and using the whale swarm optimization algorithm to solve the first and second unconstrained optimization problems, outputting the large branch identification results of the distribution network.

The application discloses a kind of meta-heuristic test design optimization methods based on matrix transformation, belong to computer-aided test design and statistical modeling technical field, this method uses a two-stage optimization framework: first, in global exploration stage, with minimizing global uniformity index as target to carry out unconstrained optimization, to obtain well space coverage sample set;Subsequently in local development stage, with minimizing adjacent distance variance as target, optimization is carried out under the constraint of maintaining the good global coverage obtained, to fine adjustment sample point local spacing distribution, improve uniformity;The application encodes test design scheme into matrix form individual, is updated iteratively by meta-heuristic algorithm, and adopts global normalization strategy to ensure that sample is always located in design space;The application can systematically consider the global coverage of sample and local uniformity, significantly improve the sample distribution quality in high-dimensional space, generate comprehensive performance excellent test design scheme.

The present disclosure provides an optimal scheduling method and system for a combined heat and power system facing operational flexibility, and relates to the technical field of power system scheduling, comprising: firstly constructing an optimization function with the minimum heat consumption rate as the target, and establishing a system constraint system covering the heat and power coupling feasible region; then converting the constraint optimization into an unconstrained optimization problem by using a hierarchical penalty function; finally, an improved hybrid genetic particle swarm optimization (IHGPSO) is proposed to solve it, which focuses on introducing the opposite learning initialization, cosine inertia weight, Lévy flight and elite injection mechanism on the hybrid framework of genetic crossover mutation and particle swarm update. The present disclosure overcomes the defect that the existing algorithm is easy to fall into local optimum, significantly reduces the system heat consumption rate under the premise of meeting complex constraints, and realizes the coordinated improvement of the operational flexibility and economy of heterogeneous units.

The invention discloses a single-user dynamic controllable waveform design method for a dual-function radar communication system, which relates to the technical field of radars and comprises the following steps of: constructing a joint waveform optimization model of the dual-function radar communication system, establishing a multivariable coupling problem of user dynamic controllable communication service quality constraint under constant modulus constraint; according to the method, a stack Riemannian manifold space is constructed through time domain stack reconstruction and accurate penalty conversion, a non-convex constraint problem is converted into an unconstrained optimization problem of the manifold space, a parallel Riemannian gradient of a penalty function in the manifold space is derived, and joint optimization of a waveform and a filter is realized by adopting a parallel conjugate gradient algorithm of an adaptive step length. According to the invention, a controllable communication QoS (Quality of Service) is provided for a single user; under the condition that the user has better communication quality, the obtained ASR is better, reliable communication QoS is provided, and the communication quality is high.

The invention discloses a high-directivity phased array synthesis method based on circular polarization axial ratio control, and belongs to the technical field of satellite communication. The method comprises the following steps: firstly, establishing a one-to-one correspondence relationship between an axial ratio and an electric field; then, an array directivity coefficient maximization problem model with strict axial ratio constraint is established; a non-convex fractional programming problem is converted into a Rayleigh entropy form, axial ratio constraint is converted into linear constraint, the axial ratio constraint is replaced with first-dimension excitation through excitation dimension reduction, an original problem is converted into an unconstrained optimization problem, and the converted unconstrained optimization problem is further converted into the Rayleigh entropy form; and finally, carrying out eigendecomposition on the converted standard Rayleigh entropy form to obtain an eigenvector corresponding to the maximum eigenvalue, and recovering the excitation of the original problem according to the conversion form. According to the method, accurate axial ratio control can be achieved, meanwhile, the maximum directivity coefficient can be obtained under the condition that the current axial ratio is limited, and the iteration process is avoided.

The present invention discloses a method and system for rapid post-outage partitioning of power networks based on a coherent Ising machine. By constructing a Laplace matrix of the power network, building a sub-region partitioning model for parallel recovery after a network outage, converting the model into a binary quadratic unconstrained optimization model, solving the binary quadratic unconstrained optimization model using a coherent Ising machine, and converting the coherent Ising machine solution into a network partitioning result, the method provides a novel quantum computing-based solution to the problem of network partitioning after a power system outage. The method avoids the "curse of dimensionality" problem that may be encountered when using classical computers to solve the above partitioning problem, and proposes a quantum bit expansion method to address the problem of excessive number of variables during the solution process, thereby accelerating the solution of the power network partitioning problem.

Aspects discussed herein may relate to methods and techniques for embedding constrained and unconstrained optimization programs as layers in a neural network architecture. Systems are provided that implement a method of solving a particular optimization problem by a neural network architecture. Prior systems required use of external software to pre-solve optimization programs so that previously determined parameters could be used as fixed input in the neural network architecture. Aspects described herein may transform the structure of common optimization problems / programs into forms suitable for use in a neural network. This transformation may be invertible, allowing the system to learn the solution to the optimization program using gradient descent techniques via backpropagation of errors through the neural network architecture. Thus these optimization layers may be solved via operation of the neural network itself.

The invention discloses a hyperspectral anomaly detection method based on prior coupling driving non-convex tensor representation, and belongs to the technical field of hyperspectral image processing. Aiming at the problem that background representation is not ideal due to the fact that an existing tensor representation method depends on a plurality of independent regularization items for background prior modeling and a loose convex substitute is adopted for approximation, a basic tensor representation model is constructed, and meanwhile, a prior-coupled non-convex background regularization item and an abnormal regularization item are constructed; constructing an augmented Lagrangian equation, converting the model into an unconstrained optimization problem, performing model iteration according to the augmented Lagrangian equation, and taking an abnormal tensor when the iteration is completed as an optimal abnormal tensor; and obtaining an anomaly detection result according to the optimal anomaly tensor. According to the method, the global low-rank priori and the local smoothness priori of the background are coupled in a non-convex regularization item, and the background priori is better described, so that the accuracy of anomaly detection is improved, and the false alarm rate is reduced.

The application provides a clutch damping control method for a wave energy device, considers the survival problem of the wave energy device in actual sea conditions, establishes a time domain motion equation and a state space equation, simplifies the time domain motion equation by using the state space equation, rewrites the time domain motion equation into a linear differential equation, represents whether the inner oscillator and the wave energy device are connected by loading and unloading control commands in the linear differential equation, and obtains the motion state of the wave energy device by solving the motion differential equation with the control. A Hamilton function about the control command is defined, a constraint problem of displacement minimization is converted into an unconstrained optimization problem, the Hamilton function is expanded according to the state space equation of the wave energy device, the Hamilton function is solved, the optimal control sequence of the displacement of the optimized wave energy device in the extreme environment is obtained when the Hamilton function is minimum, the motion of the wave energy device is adjusted by using the optimal control sequence, and the effect of maximizing the survival ability of the optimized wave energy device is realized.

The present invention discloses a method, apparatus, device, and medium for unmanned aerial vehicle (UAV) trajectory planning. The method comprises obtaining phase difference measurement data between a first receiving device and a second receiving device at the current moment; calculating a cost surface based on the phase difference measurement value, then performing a grid search within a preset range centered on the UAV's initial position to find the UAV's initial estimated position; performing iterative least squares convergence on the local neighborhood of the corresponding grid point to complete the positioning of the UAV and obtain the UAV's position estimate at the current moment; establishing an optimization model using the UAV's heading angle as the state vector and minimizing the Cramer-Rao lower bound trajectory as the objective function, and converting the constrained optimization model into an unconstrained optimization model using a penalty function multiplier method; solving the unconstrained optimization model to obtain the UAV's optimal heading angle at the current moment; and calculating the next optimal track point based on the current UAV speed and the optimal heading angle. The present invention improves positioning accuracy and sensitivity.

The invention discloses a low sidelobe waveform design method and system based on a Riemannian manifold, and the method comprises the steps: introducing a peak-to-average power ratio as a constraint condition based on an MIMO radar system, and constructing an unconstrained optimization problem of the manifold; introducing a tangent plane, and performing iterative search on the unconstrained optimization problem of the flow shape to obtain new data points on the tangent plane; and constructing a remapping function to map the new data points on the tangent plane into the back flow form, thereby realizing the design of the minimum low-sidelobe waveform. According to the embodiment of the invention, a manifold structure in Riemannian geometry can be introduced into a non-convex waveform design optimization problem, the calculation complexity is reduced, and the algorithm convergence speed and the solving precision are effectively improved. The method can be widely applied to the technical field of radar waveform design.

The present invention discloses a bridge reliability prediction method based on dynamic characteristics and response surface method, which includes the following steps: collecting and preprocessing the vibration characteristic information of existing bridges; establishing a structural analysis model in combination with bridge design data and operation conditions, and using sensitivity analysis method to screen out the design parameters to be corrected in the structural analysis model; obtaining output samples, forming training samples with input samples, and correcting the initial structural analysis model; based on the corrected structural analysis model, output samples, constructing training samples again, and normalizing the sample points to construct a response surface model; standard normalizing random variables, transforming the constrained optimization problem into an unconstrained optimization problem by using penalty function, and obtaining the optimal weights of random variables by using optimization algorithms; establishing a mathematical model for solving the structural reliability index through the prediction results of the constructed response surface model. The beneficial effects of the present invention are: high calculation accuracy and fast estimation speed.