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Integrated sensing and communication (ISAC) is increasingly recognized as a pivotal technology for next-generation cellular networks, offering mutual benefits in both sensing and communication capabilities. This advancement necessitates a re-examination of the fundamental limits within networks where these two functions coexist via shared spectrum and infrastructures. However, traditional stochastic geometry-based performance analyses are confined to either communication or sensing networks separately. This paper bridges this gap by introducing a generalized stochastic geometry framework in ISAC networks. Based on this framework, we define and calculate the coverage and ergodic rate of sensing and communication performance under resource constraints. Then, we shed light on the fundamental limits of ISAC networks by presenting theoretical results for the coverage rate of the unified performance, taking into account the coupling effects of dual functions in coexistence networks. Further, we obtain the analytical formulations for evaluating the ergodic sensing rate constrained by the maximum communication rate, and the ergodic communication rate constrained by the maximum sensing rate. Extensive numerical results validate the accuracy of all theoretical derivations, and also indicate that denser networks significantly enhance ISAC coverage. Specifically, increasing the base station density from $1~\text {km}^{-2}$ to $10~\text {km}^{-2}$ can boost the ISAC coverage rate from 1.4% to 39.8%. Further, results also reveal that with the increase of the constrained sensing rate, the ergodic communication rate improves significantly, but the reverse is not obvious.

Cross-coupling catalysts typically react and unite functionally distinct partners via sequential inner-sphere elementary steps: coordination, migratory insertion, reductive elimination, etc. Here, we report a single catalyst that cross-couples styrenes and benzyl bromides via iterative outer-sphere steps: metal–ligand-carbon interactions. Each partner forms a stabilized radical intermediate, yet heterocoupled products predominate. The system is redox-neutral and, thus, avoids exogenous oxidants, resulting in simple and scalable conditions. Numerous variations of alkene hydrobenzylation are made possible, including access to the privileged heterodibenzyl (1,2-diarylethane) motif and challenging quaternary carbon variants.

An integrated sensing and communication (ISAC) system assisted by distributed passive intelligent reflecting surfaces (IRSs) is proposed in this paper, which enables simultaneous signal demodulation and location sensing, without channel state information (CSI). A detailed workflow of the proposed IRS-based ISAC system is designed, including transmission protocol, joint location sensing and demodulation, as well as beamforming optimization. Specifically, each coherent block consists of two stages, and each stage is divided into two time blocks, where the signal demodulation, channel estimation, and location sensing are conducted by the proposed integrated localization and demodulation (I-LAD) algorithm, simultaneously. Simulation results show that the signal demodulation performance of the proposed I-LAD algorithm is close to that of the benchmark scheme assuming perfect CSI. At the same time, the channel estimation performance is comparable to that of the parallel factor decomposition (PAPRFAC) method or the compressive sensing-based channel estimation (CS-EST) method. In addition, the proposed location sensing scheme almost achieves the Cramér-Rao lower bound (CRLB) for distributed IRS-assisted localization-only systems, confirming the effectiveness of the proposed I-LAD algorithm.

Metal-hydride hydrogen atom transfer (MHAT) has emerged as a useful tool to form quaternary carbons from alkenes via hydrofunctionalization. Methods to date that cross-couple alkenes with sp3partners rely on heterobimetallic catalysis to merge the two cycles. Here, we report an iron-only cross-coupling via putative MHAT/SH2 steps that solves a key stereochemical problem in the synthesis of meroterpenoid eugenial C and obviates the need for nickel. The concise synthesis benefits from a conformationally locked o,o′-disubstituted benzyl bromide and a locally sourced chiral pool terpene coupling partner.

In this letter, we envision the integration of holographic reconfigurable intelligent surface (HRIS) into a millimeter-wave (mmWave) localization system. The large aperture of HRIS in the mmWave band allows the system to operate in the near-field propagation regime, where the wavefront tends to be spherical and contains distance information. To investigate the fundamental limits of localization accuracy of the proposed system, we obtain the Fisher information matrix (FIM) and Cramér-Rao lower bound (CRLB) taking into account the radiation patterns of antennas. The analytical results reveal that the FIM quadratically increases with the size of HRIS. Then, to explore the potential of HRIS passive beamforming for improving localization quality, we formulate the HRIS phases optimization problem to minimize a worst-case CRLB with respect to an uncertainty set of user equipment (UE) positions. To address this formulated problem, an iterative entropy regularization (IER) based method is proposed. Numerical results evaluate the effect of key parameters on the squared position error bound and verify the effectiveness of the proposed IER-based method.

In this letter, we propose an unscented Kalman filtering (UKF)-based method to track the channel parameters of the intelligent reflecting surface (IRS) aided millimeter wave (mmWave) multi-input single-output (MISO) systems. To minimize the mean squared error (MSE) of the tracking parameters, the beamforming vector of the base station (BS) and the reflecting vector of the IRS are designed iteratively, considering the transmit power constraint of the BS and the unit module constraint of the IRS. The resulting sub-problems can be transformed into quadratic constraint quadratic problems (QCQPs), which are solved by the semidefinite relaxation (SDR) method and Gaussian randomization. Simulation results demonstrate that the proposed method outperforms existing benchmark methods.

To investigate the characteristics of intestinal flora in overweight pregnant women and the correlation with gestational diabetes mellitus (GDM).A total of 122 women were enrolled and divided into four groups according to their pre-pregnancy BMI and the presence of GDM: group 1 (n= 71) with a BMI <24 kg/m2, without GDM; group 2 (n= 27) with a BMI <24 kg/m2, with GDM; group 3 (n= 17) with a BMI ≥24 kg/m2, without GDM; and group 4 (n= 7) with a BMI ≥24 kg/m2with GDM. Feces were collected on the day that the oral glucose tolerance test was conducted. The V3–V4 variable region of 16S rRNA was sequenced using the Illumina Hiseq 2500 platform, and a bioinformatics analysis was conducted.There were differences between the four groups in the composition of intestinal flora, and it was significantly different in group 4 than in the other three groups. Firmicutesaccounted for 36.4% of the intestinal flora in this group, the lowest among the four groups, while Bacteroidetesaccounted for 50.1%, the highest among the four groups, making ratio of these two bacteria approximately 3:5, while in the other three groups, this ratio was reversed. In women with a BMI <24 kg/m2, the insulin resistance index (homeostatic model assessment for insulin resistance (HOMA-IR)) in pregnant women with GDM was higher than in those without (P3= 0.026).The composition of the intestinal flora of pregnant women who were overweight or obese before pregnancy and suffered from GDM was significantly different than women who were not overweight or did not suffer from GDM.

This Synopsis covers recent reports of metal-catalyzed alkene functionalizations that likely involve iterative outer-sphere reactions in which the substrate reacts directly with a metal ligand instead of with the metal center itself. Traditional metal hydride-catalyzed alkene functionalizations involve this latter pathway whereby the alkene forms part of the metal ligand sphere (i.e. an inner-sphere reaction). In contrast, alkenes do not ligate the metal in so-called outer-sphere reactions and instead react with a metal ligand. These transformations have proved crucial for the synthesis of high fraction sp3(Fsp3) targets, especially in hindered fragment couplings of relevance to natural product space.

An asymmetric three-component reaction of Bis(pinacolato)diboron ((BPin)2), 1,3-enynes, and fluoroalkyl ketones was carried out by using a copper(I)-Ph-BPE complex as the catalyst, which afforded a series of chiral fluoroalkyl diols in good to high yield, good to high diastereoselectivity, and high enantioselectivity after an oxidative workup. The reaction exhibits advantages that include a broad substrate scope, high functional group compatibility, high stereoselectivity, and an easy reaction protocol. The synthetic utility of the reaction was showcased by several transformations.

A copper(I)-catalyzed asymmetric borylative propargylation of simple ketones was disclosed. Additive NaBARF was found to be pivotal to achieve excellent enantioselectivity. This reaction enjoyed advantages of broad substrate scope, good tolerance of functional groups, high diastereo- and enantioselectivities, and reaction robustness. The borylative product served as a suitable cross-coupling partner in a palladium-catalyzed Suzuki–Miyaura reaction. Finally, the synthetic utility of the methodology was showcased by the asymmetric synthesis of a chiral piperidine derivative.

•Cellular automata traffic flow model, linear regression safety evaluation model.•Case studies with four types of paths in a freeway, namely two straight lanes, three straight lanes, ramps, and roundabouts.•Effective rules and alternatives, left driving norms and intelligent system as extension.

A quasi 1D model of two-phase flow for a urea-selective catalytic reduction (SCR) system is developed which can calculate not only the generation of reducing agent but also the formation of deposits in the exhaust pipe. The gas phase flow is solved through Euler method, variables are stored on staggered grids, and the semi-implicit method for pressure-linked equation (SIMPLE) algorithm is applied to decouple the pressure and velocity. The liquid phase is treated in a Lagrangian way, which solves the equations of droplet motion, evaporation, thermolysis, and spray wall interaction. A combination of a direct decomposition model and a kinetic model is implemented to describe the different decomposition behaviors of urea in the droplet phase and wall film, respectively. A new 1D wall film model is proposed, and the equations of wall film motion, evaporation, thermolysis, and species transport are solved. The position, weight, and components of deposits can be simulated following implementation of the semi-detailed kinetic model. The simulation results show that a decrease in the exhaust temperature will increase the wall film region and the weight of deposits. Deposit components are highly dependent on temperature. The urea-water-solution (UWS) injection rate can affect the total mass of wall film and expand the film region, but it has little influence on deposit components. An increase in exhaust mass flow can decrease the total weight of deposits on the pipe wall because of the promotion of the mass and heat transfer process both in the droplets and wall film.

Smooth Support Vector Regression (SSVR) is new modified edition of traditional support vector regression for better performance. To further improve the modeling capability of SSVR, it is necessary to take into account the feature extraction based on Independent Component Analysis (ICA) before SSVR. Simulation on the example of function approximation shows that the result of SSVR based on ICA feature extraction is better than that of SSVR without ICA preprocess.

In order to improve the modeling efficiency of RBF neural network, an Artificial Fish Swarm Algorithm (AFSA) training algorithm with an adaptive mechanism is proposed. In the training algorithm, the search step size and visible domain of AFSA algorithm can be adjusted dynamically according to the convergence characteristics of artificial fish swarm, and then the improved AFSA algorithm is used to optimize the parameters of RBF neural network. The example shows that, the proposed model is a better approximation performance for the nonlinear function.

The model capability of Support Vector Machine (SVM) relies on the selection of kernel function. To obtain a better application modeling of SVM, the wavelet kernel function that satisfies Merce condition is introduced to use the kernel function of SVM, achieving a good effect. In the paper, on the basis of wavelet kernel function, a wavelet derivation kernel function is proposed in the application of SVM for higher accuracy. An actual example on nonlinear function approximation shows that SVM regression model has a satisfactory approximation effect, and also support an effective nonlinear modeling method.

To predict the fault severity of aircraft and its equipments, a modeling and predicting method based on Relevance Vector Machine (RVM) under Bayesian framework is proposed to solve the problem. First the principle and realization step of RVM are detailed, and then RVM is introduced in prediction of fault severity of aircraft and its equipments. The prediction result indicates that the proposed model has a good prediction to fault severity of aircraft and its equipments.

BP neural network has a good nonlinear mapping ability, and can describe the relationship between frequency characteristics and fault. However, the multi-resolution wavelet neural network has the simple learning rules, fast training speed with the avoidance of local minima. So a multi-resolution wavelet neural network based on UKF is proposed to solve the problem of fault diagnosis for rotating machinery. The simulation result shows that the proposed multi-resolution wavelet neural network based on UKF value has a good diagnosis capability, and is better than that of traditional BP neural network and wavelet neural network.

In order to formulate the medium-and long-term planning of aviation safety development, a qualitative prediction and analysis method known as scenario analysis method is introduced in the field of safety strategic planning. An actual example on an airline safety development in the future 5 years shows that the proposed qualitative prediction and analysis method has a good feasibility and effectiveness.

The selection of kernel function in Support Vector Machine (SVM) has a great influence on the model performance. In the paper, Mexico hat wavelet kernel is introduced to employ the kernel function of SVM, and theoretically it has be prove that, Mexico hat wavelet kernel satisfies the Merce condition, that is the necessary condition as the kernel function of SVM. Simulation on the anomaly detection shows that the capability of SVM based on Mexico hat wavelet kernel is better than that of SVM based on RBF kernel with a satisfactory result for anomaly intrusion detection.

To solve some problems in fault diagnosis for analog circuit, a neural network diagnosis method using improved PSO algorithm is proposed. For the appearance on local convergence and prematurity in the application of standard PSO algorithm, an information sharing strategy is introduced, and then improved PSO algorithm is used to train the neural network for overcoming the deficiency of BP algorithm. The simulation indicates that the proposed fault diagnosis method has the fast convergence and accuracy without local convergence and prematurity for analog circuit.

To optimize the parameters of LS-SVM effectively, an improved Particle Swarm Optimization (PSO) algorithm is proposed to select the optimal parameters combination. For the improvement of the precocity in PSO algorithm, an multi-particles sharing strategy is introduced in simple PSO algorithm to enhance the convergence. The simulation indicates that the proposed PSO algorithm has a better selection on LS-SVM parameters.

To realize the reasonable and effective safety management and decision-making in aviation productive activity, the flight safety time series can be used to mine the statistical law for the assistant of accident prevention. Based on this purpose, Grey modeling theory is introduced in the field of the aviation safety analysis. The actual example shows that, the established GM (1, 1) model for flight mishap data of USAF has a good prediction for future years, especially for the accident data that follows or approximates the exponential law.

To assist the aviation safety management and decision-making, it is important to effectively predict the flight incident 10000-hour-rate for preventing the aviation accidents. For improvement of prediction level, a simple regression model is proposed. The prediction result obtained in actual example indicates that the proposed single regression model has a good prediction on CAAC flight incident 10000-hour-rate.

To accurately depict the dynamic characteristics for aircraft stall by aerodynamic model, a Wavelet Neural Network (WNN) stall aerodynamic modeling method based on Particle Swarm Optimization (PSO) algorithm and Artificial Fish Swarm (AFS) algorithm is proposed. Numerical examples show that the proposed method has a good prediction precision, and it is also effective and feasible to build the aerodynamic model from flight data for aircraft stall.

To accurately identify the nonlinear model for aircraft, maximum likelihood method is introduced to analyze the flight test data for compatibility check, which can satisfy the kinematics equations of aircraft at the same time. The experiment shows that the proposed method has a good compatibility check effect, and it is also effective and feasible for flight test data for aircraft.

For the aerodynamic modeling problem from measured flight data for aircraft stall, a WNN aerodynamic modeling method is proposed. According to the aerodynamic modeling flow from flight data for aircraft stall, WNN is introduced to establish the aerodynamic model of aircraft for stall phenomenon. Experiment shows that the method can improve the modeling ability of WNN, and is suitable for actual aerodynamic modeling for aircraft stall.

To understand the characteristics of aircraft stall for better aerodynamic model, the physical essence of the stall phenomena of aircraft is first introduced, and then a Wavelet Neural Network (WNN) is proposed to set up the stall aerodynamic model. Numerical examples indicates that through the deep cognition of the stall phenomena of aircraft the proposed stall aerodynamic method has a better accuracy than the traditional neural network and is also effective and feasible.

An aerodynamic modeling method based on WNN with Partial Least Squares (PLS) is proposed. In the method, PLS first is applied to extract the feature of original aerodynamic data samples, and then the obtained feature is used to establish the WNN aerodynamic model for aircraft stall from flight test data. Simulation results are given to illustrate that the proposed method is effective and feasible.

To improve the ability of fault diagnosis for mechanical equipment, a Radial Basis Function Neural Network (RBFNN) diagnosis method based on Unscented Kalman Filter (UKF) algorithm is proposed. In the algorithm, at first, UKF algorithm is used to estimate the parameters of RBFNN, and then the proposed method is introduced into the fault diagnosis of mechanical equipment. The simulation indicates that the established model has a good diagnosis performance for mechanical fault diagnosis.

To describe the complex nonlinear characteristics of a system accurately, a Wavelet Neural Network (WNN) identification model based on Artificial Fish Swarm (AFS) algorithm is proposed. In the identification model, AFS algorithm is introduced to optimize the parameters combination of the network for the satisfactory WNN model. The simulation shows that, the proposed method is a good nonlinear identification capability, and is feasible to identify the nonlinear system.

It is difficult to realize an accurate and reliable diagnosis in the rotating machinery. To solve this problem, a Wavelet Neural Network (WNN) diagnosis model based on EKF algorithm is proposed. In the model, EKF algorithm is introduced to optimize the parameters of WNN, and then the built WNN model is used to diagnose the faults of the rotating machinery. The experiment shows that, the proposed model has a good diagnosis capability in the field of the rotating machinery.

To diagnose the fault that occurs in rotating machinery, a neural network diagnosis method based on an improved GA algorithm is proposed. In this diagnosis method, a case injected idea is introduced to improve the strong global search capability of traditional GA algorithm; and then the improved GA algorithm is used to optimize the parameters of neural network, fulfilling the training of neural network. Simulation result indicates that, the proposed diagnosis method has a good practicability in the field of fault diagnosis for rotating machinery.

To improve the learning capability of Radial Basis Function (RBF) neural network, a RBF neural network algorithm based on Extended Kalman Filter (EKF) is proposed. First the basic idea of EKF algorithm and RBF neural network are introduced, and then EKF is used to optimize the parameters combination of RBF neural network to obtain the better model. The experiment proves its feasibility.

To assess the safety situation in air traffic control effectively, a comprehensive assessment method based on RBF neural network is proposed. At first, the safety assessment principle based on RBF neural network is introduced, and then the safety assessment index system for air traffic control is established from four aspects of human, machine, environment and management. Simulation example of ATC safety assessment gives us a satisfactory result for RBF neural network.

To improve the prediction of properties of engineering materials, a Relevance Vector Machine (RVM) regression algorithm based on Kernel Partial Least Squares (KPLS) is proposed. In the algorithm, firstly execute the feature extraction from the original samples using KPLS, and then use obtained feature to realize RVM regression. The simulation shows that the hybrid regression algorithm can effectively reduce the difficulty on RVM modeling and has a wide application in prediction of properties of engineering materials.

To improve the level of aviation safety management and decision-making, an aviation unsafe event model based on neural network trained by an improved Particle Swarm Optimization (PSO) algorithm is proposed. First a gradient acceleration idea is introduced in standard PSO algorithm to improve the search efficiency, and then the improved PSO algorithm is used to optimize the parameters of neural network, finishing the training of model. An actual example on unsafe event data of an airline shows that the proposed method can achieve a good prediction effect.

To improve the optimization design of Radial Basis Function (RBF) neural network, a RBF neural network based on a hybrid Genetic Algorithm (GA) is proposed. First the hierarchical structure and adaptive crossover probability is introduced into the traditional GA algorithm for the improvement, and then the hybrid GA algorithm is used to optimize the structure and parameters of the network. The simulation indicates that the proposed model has a good modeling performance.

A combination regression algorithm of PLS-SVM is proposed for the properties of engineering materials. The algorithm first extracts the feature from the primal sample sets by PLS, and then carries out SVM regression estimation using the new sample sets attained. Thus the algorithm will have the ability of extracting feature. The simulation results indicate that the new combined SVM regression algorithm can effectively solve the regression estimation problem including dimensions reduction, noise elimination and multiple correlations between independent variables. The algorithm has good and wide application foreground in research of properties of engineering materials.

The mechanical engineering for flight are important for flight safety to prevent the flight accident, improve the management and decision-making level of flight safety. In order to improve the safety of flight system, a flight safety evaluation method based on relevance vector machine and flight mechanical engineering is proposed. First, based on system viewpoint, according to the actual situation of flight safety, the factors that influence the safety of flight system are found out on four sides of human, flight mechanical engineering, environment and management and the flight safety evaluation index system is constructed; then the flight safety evaluation model based on relevance vector machine developed in the framework of Bayesian theory is briefly introduced; finally using the index system the relevance vector machine evaluation model of flight safety is establish. The actual example confirms its feasibility.

In order to diagnose the fault in analog circuit correctly, a Wavelet Neural Network (WNN) method is proposed that uses the Particle Swarm Optimization (PSO) algorithm to optimize the network parameters. For the improvement of convergence rate in WNN based on PSO algorithm, a compressing method in research space is introduced into the traditional PSO algorithm to improve the convergence in WNN training. The simulation shows that the proposed method has a good diagnosis with fast convergence rate for the fault in analog circuit.

To better master the development law of flight safety for flight materials, the spectral analysis method is introduced to analyze the cycle fluctuation of flight accident for flight materials. The basic principle of spectrum analysis of cycle fluctuation is first introduced, and then the calculation method of spectral density function is given. The actual example of flight accident shows that the method is an effective and feasible for analyzing the cycle fluctuation of flight accident. The research also has both theoretical and applicable value of flight safety management for flight materials.

In order to better describe the dynamic characteristics of aircraft through aerodynamic modeling, a Wavelet Neural Network (WNN) aerodynamic modeling method based on Kernel Principal Components Analysis (KPCA) is proposed. Firstly, the training samples are used to execute KPCA for extracting basic features of samples, and then using the extracted basic features, WNN aerodynamic model was established. The simulation result shows that, the modeling ability of the method proposed is better than that of another 3 methods. It can easily determine of model parameters. This enables it to be effective and feasible to establish the aerodynamic modeling for aircraft.

n order to improve the prediction of aviation unsafe events, a hybrid prediction method of aviation unsafe events based on grey catastrophe and regression analysis method is proposed. At first, the catastrophe points (date) are found from original unsafe events data to establish the grey catastrophe model for predicting the future catastrophe points, and then the grey prediction model for these catastrophe points is built to calculate the catastrophe value corresponding to future catastrophe points. For non-catastrophe points, the appropriate regression analysis model needs to be established. Example validates its effectiveness.

n order to reinforce the efficiency and initiative of accident prevention for reducing accident loss, the surest way is to strengthen the prediction. In view of difficulties in aviation accident prediction, a prediction method based on Auto-Regressive Integrating Moving Average (ARIMA) is proposed. In this method, a trial model is first identified for an accident time series, and then the diagnosis is executed with the necessary adjustments. The calculation process including identification, estimation and diagnosis is repeated until obtain a satisfactory model. The example shows that, ARIMA has a good prediction for aviation accident and provides an important technique support for decision-making of aviation safety.

A design of the fuzzy self-tuning immune PID controller is proposed. The controller, which combines immune feedback mechanism and fuzzy PID control, executes the self-tuning of PID parameters in the control system. A simulation experiment is presented in light of a tactical missile autopilot transfer function. Simulation result shows that the performance of fuzzy self-tuning immune PID controller is better than that of fuzzy PID controller, especially in its robust performance for variable parameter system.

n order to improve the safety level of aircraft anti-collision, an anti-collision risk assessment methods based on Relevance Vector Machine (RVM) is proposed. First, RVM learning under Bayesian framework is introduced as well as its basic principle and modeling process, and then on the basis of system point of view an anti-collision risk assessment index system is established, finally, on this basis, RVM assessment model for aircraft anti-collision risk is constructed. It can adaptively adjust the weights of influence factors without analyzing the relationship between various factors in the system. Examples show that, for anti-collision risk assessment, RVM has a novel structure and convenient application, and the result can reflect the actual safety situation.

Accessibility is an important criterion that reflects the quality of aviation equipment maintenance, especially prominent to maintenance time. To obtain the better accessibility for maintenance efficiency and reducing maintenance costs, it is necessary to choose an optimal scheme in many accessibility designs. This requires the comprehensive appraisement for the parts accessibility of the entire functional system. This paper introduces the correlation analysis method to appraise the accessibility, and propose the mathematical model of the appraisement, which has practical application value to improve the maintenance of aviation equipment.

The main target of flight accident prediction is to prevent the accident. To improve the pertinence and efficiency, the prediction must be strengthened to raise initiative of accident prevention. A hybrid prediction method, based on Auto-Regressive Integrating Moving Average (ARIMA) and Support Vector Machine (SVM), is proposed. First, ARIMA model is established to describe the linear relation in historical data, and then SVM model is built with regard to the residual error of ARIMA model in order to simulate the nonlinear law in historical data. The sum of prediction value of two models is to final hybrid prediction result. An application example show that the model based on this hybrid method has a good prediction to flight accident, and also is better than ARIMA or SVM model.

Based on the study of adaptive wavelet neural networks, a hierarchy genetic algorithm is proposed to training network. Compared with standard genetic algorithm, the method can not only optimize network parameters such as scale factor, transform factor parameter and connection weights, but also solve structure problem of adaptive wavelet neural network. The result of simulation indicates that the algorithm can efficiently determinate the parameter and structure of adaptive wavelet neural network, and has better higher training efficiency and forecasting precision.

To describe the dynamic characteristics of flight vehicle accurately, a Relevance Vector Machine (RVM) aerodynamic modeling method is proposed. RVM is a learning method which is based on Bayesian learning theory. Compared with Support Vector Machine (SVM), it has the benefits such as probabilistic predictions, sparser model, facilities to select arbitrary basis function and so on. Experimental results show that the proposed method can obtain the aerodynamic model with higher accuracy by less relevance vector. It is also effective and feasible for aerodynamic modeling.