An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

Guaranteed Cost Consensus for High-dimensional Multi-agent Systems With Time-varying Delays

Guaranteed cost consensus analysis and design problems for high-dimensional multi-agent systems with time varying delays are investigated. The idea of guaranteed cost con trol is introduced into consensus problems for high-dimensiona multi-agent systems with time-varying delays, where a cos function is defined based on state errors among neighboring agents and control inputs of all the agents. By the state space decomposition approach and the linear matrix inequality(LMI)sufficient conditions for guaranteed cost consensus and consensu alization are given. Moreover, a guaranteed cost upper bound o the cost function is determined. It should be mentioned that these LMI criteria are dependent on the change rate of time delays and the maximum time delay, the guaranteed cost upper bound is only dependent on the maximum time delay but independen of the Laplacian matrix. Finally, numerical simulations are given to demonstrate theoretical results.

Analytical Modeling and Mechanism Analysis of Time-Varying Excitation for Surface Defects in Rolling Element Bearings

Surface defects,including dents,spalls,and cracks,for rolling element bearings are the most common faults in rotating machinery.The accurate model for the time-varying excitation is the basis for the vibration mechanism analysis and fault feature extraction.However,in conventional investigations,this issue is not well and fully addressed from the perspective of theoretical analysis and physical derivation.In this study,an improved analytical model for time-varying displacement excitations(TVDEs)caused by surface defects is theoretically formulated.First and foremost,the physical mechanism for the effect of defect sizes on the physical process of rolling element-defect interaction is revealed.According to the physical interaction mechanism between the rolling element and different types of defects,the relationship between time-varying displacement pulse and defect sizes is further analytically derived.With the obtained time-varying displacement pulse,the dynamic model for the deep groove bearings considering the internal excitation caused by the surface defect is established.The nonlinear vibration responses and fault features induced by surface defects are analyzed using the proposed TVDE model.The results suggest that the presence of surface defects may result in the occurrence of the dual-impulse phenomenon,which can serve as indexes for surface-defect fault diagnosis.

Time-varying gravity field model of Sichuan-Yunnan region based on the equivalent mass source model

High-precision time-varying gravity field is an effective way to study the internal mass movement and understanding the spatio-temporal evolution process of the geodynamic system.Compared to the satellite gravity measurement,the repeated terrestrial gravity observation can provide a more high-order signal related to the shallow crust and subsurface.However,the suitable and unified method for gravity model estimation is a key problem for further applications.In this study,we introduce the spherical hexahedron element to simulate the field source mass and forward model the change of gravity field located at the Sichuan-Yunnan region(99—104°E,23—29°N)in the four epochs from 2015 to 2017.Compared to the experimental results based on Slepian or spherical harmonics frequency domain method,this alternative approach is suitable for constructing the equivalent mass source model of regional-scale gravity data,by introducing the first-order smooth prior condition of gravity time-varying signal to suppress the high-frequency component of the signal.The results can provide a higher spatial resolution reference for regional gravity field modeling in the Sichuan-Yunnan region.

Randomized Latent Factor Model for High-dimensional and Sparse Matrices from Industrial Applications

Latent factor(LF) models are highly effective in extracting useful knowledge from High-Dimensional and Sparse(HiDS) matrices which are commonly seen in various industrial applications. An LF model usually adopts iterative optimizers,which may consume many iterations to achieve a local optima,resulting in considerable time cost. Hence, determining how to accelerate the training process for LF models has become a significant issue. To address this, this work proposes a randomized latent factor(RLF) model. It incorporates the principle of randomized learning techniques from neural networks into the LF analysis of HiDS matrices, thereby greatly alleviating computational burden. It also extends a standard learning process for randomized neural networks in context of LF analysis to make the resulting model represent an HiDS matrix correctly.Experimental results on three HiDS matrices from industrial applications demonstrate that compared with state-of-the-art LF models, RLF is able to achieve significantly higher computational efficiency and comparable prediction accuracy for missing data.I provides an important alternative approach to LF analysis of HiDS matrices, which is especially desired for industrial applications demanding highly efficient models.

High-Dimensional Schwarzian Derivatives and Painlevé Integrable Models

Because all the known integrable models possess Schwarzian forms with Mobious transformation invariance,it may be one of the best ways to find new integrable models starting from some suitable Mobious transformation invariant equations. In this paper, we study the Painlevé integrability of some special (3+1)-dimensional Schwarzian models.

Robust Parameter Identification Method of Adhesion Model for Heavy Haul Trains

A robust parameter identification method based on Kiencke model was proposed to solve the problem of the parameter identification accuracy being affected by the rail environment change and noise interference for heavy-duty trains. Firstly, a Kiencke stick-creep identification model was constructed, and the parameter identification task was transformed into a quadratic programming problem. Secondly, an iterative algorithm was constructed to solve the problem, into which a time-varying forgetting factor was added to track the change of the rail environment, and to solve the uncertainty problem of the wheel-rail environment. The Granger causality test was adopted to detect the interference, and then the weights of the current data were redistributed to solve the problem of noise interference in parameter identification. Finally, simulations were carried out and the results showed that the proposed method could track the change of the track environment in time, reduce the noise interference in the identification process, and effectively identify the adhesion performance parameters.

Variance Estimation for High-Dimensional Varying Index Coefficient Models

This paper studies the re-adjusted cross-validation method and a semiparametric regression model called the varying index coefficient model. We use the profile spline modal estimator method to estimate the coefficients of the parameter part of the Varying Index Coefficient Model (VICM), while the unknown function part uses the B-spline to expand. Moreover, we combine the above two estimation methods under the assumption of high-dimensional data. The results of data simulation and empirical analysis show that for the varying index coefficient model, the re-adjusted cross-validation method is better in terms of accuracy and stability than traditional methods based on ordinary least squares.

A Review on High-Dimensional Frequentist Model Averaging

Model averaging has attracted increasing attention in recent years for the analysis of high-dimensional data. By weighting several competing statistical models suitably, model averaging attempts to achieve stable and improved prediction. To obtain a better understanding of the available model averaging methods, their properties and the relationships between them, this paper is devoted to make a review on some recent progresses in high-dimensional model averaging from the frequentist perspective. Some future research topics are also discussed.

Neural Network and GBSM Based Time-Varying and Stochastic Channel Modeling for 5G Millimeter Wave Communications

In this work,a frame work for time-varying channel modeling and simulation is proposed by using neural network(NN)to overcome the shortcomings in geometry based stochastic model(GBSM)and simulation approach.Two NN models are developed for modeling of path loss together with shadow fading(SF)and joint small scale channel parameters.The NN models can predict path loss plus SF and small scale channel parameters accurately compared with measurement at 26 GHz performed in an outdoor microcell.The time-varying path loss and small scale channel parameters generated by the NN models are proposed to replace the empirical path loss and channel parameter random numbers in GBSM-based framework to playback the measured channel and match with its environment.Moreover,the sparse feature of clusters,delay and angular spread,channel capacity are investigated by a virtual array measurement at 28 GHz in a large waiting hall.

Robust Latent Factor Analysis for Precise Representation of High-Dimensional and Sparse Data

High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurately represent them is of great significance.A latent factor(LF)model is one of the most popular and successful ways to address this issue.Current LF models mostly adopt L2-norm-oriented Loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with L2-norm.Yet L2-norm is sensitive to outlier data.Unfortunately,outlier data usually exist in such matrices.For example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious users.To address this issue,this work proposes a smooth L1-norm-oriented latent factor(SL-LF)model.Its main idea is to adopt smooth L1-norm rather than L2-norm to form its Loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS matrix.Experimental results on eight HiDS matrices generated by industrial applications verify that the proposed SL-LF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.

Parameter Estimation of Time-Varying ARMA Model

The auto-regressive moving-average (ARMA) model with time-varying parameters is analyzed. The time-varying parameters are assumed to be a linear combination of a set of basis time-varying functions, and the feedback linear estimation algorithm is used to estimate the time-varying parameters of the ARMA model. This algorithm includes 2 linear least squares estimations and a linear filter. The influence of the order of basis time-(varying) functions on parameters estimation is analyzed. The method has the advantage of simple, saving computation time and storage space. Theoretical analysis and experimental results show the validity of this method.

Comparison of Cox proportional hazards model,Cox proportional hazards with time-varying coefficients model,and lognormal accelerated failure time model:Application in time to event analysis of melioidosis patients

Objective:To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time(AFT),Cox proportional hazards(PH),and Cox PH with time-varying coefficient(TVC)models.Methods:A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah,Kedah and Hospital Tuanku Fauziah,Perlis in Northern Malaysia due to confirmed-cultured melioidosis.The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis,and Cox’s models and the findings were compared by using the goodness of fit methods.The analyses were done by using Stata SE version 14.0.Results:A total of 242 patients(53.4%)survived.In this study,the median survival time of melioidosis patients was 30.0 days(95%CI 0.0-60.9).Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model.In AFT survival analysis,a total of seven significant prognostic factors were identified.The results were found to be only a slight difference between the identified prognostic factors among the models.AFT survival showed better results compared to Cox's models,with the lowest Akaike information criteria and best fitted Cox-snell residuals.Conclusions:AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.

Deep learning-based time-varying channel estimation with basis expansion model for MIMO-OFDM system

For high-speed mobile MIMO-OFDM system,a low-complexity deep learning(DL) based timevarying channel estimation scheme is proposed.To reduce the number of estimated parameters,the basis expansion model(BEM) is employed to model the time-varying channel,which converts the channel estimation into the estimation of the basis coefficient.Specifically,the initial basis coefficients are firstly used to train the neural network in an offline manner,and then the high-precision channel estimation can be obtained by small number of inputs.Moreover,the linear minimum mean square error(LMMSE) estimated channel is considered for the loss function in training phase,which makes the proposed method more practical.Simulation results show that the proposed method has a better performance and lower computational complexity compared with the available schemes,and it is robust to the fast time-varying channel in the high-speed mobile scenarios.

Markov-Switching Time-Varying Copula Modeling of Dependence Structure between Oil and GCC Stock Markets

This paper proposes a Markov-switching copula model to examine the presence of regime change in the time-varying dependence structure between oil price changes and stock market returns in six GCC countries. The marginal distributions are assumed to follow a long-memory model while the copula parameters are supposed to evolve according to the Markov-switching process. Furthermore, we estimate the Value-at-Risk (VaR) based on the proposed approach. The empirical results provide evidence of three regime changes, representing precrisis, financial crisis and post-crisis, in the dependence structure between energy and GCC stock markets. In particular, in the pre- and post-crisis regimes, there is no dependence, while in the crisis regime, there is significant tail dependence. For OPEC countries, we find lower tail dependence whereas in non-OPEC countries, we see upper tail dependence. VaR experiments show that the Markov-switching time- varying copula model performs better than the time-varying copula model.

An Improved Dynamic Modelling for Exploring Ball Bearing Vibrations from Time-Varying Oil Film

Bearings are key components in rotating machinery,which is widely used in many fields,such as CNC machines,wind turbines and induction machines.The increasingly harsh operation environment can lead to wear and tear on raceways and reduce the precision and reliability of bearing or even machinery.Lubrication could relieve the wear to some degree,which is benefit to prolong the bearing’s life.Thus,investigation on the vibration responses under the influence of oil film is of great significance.However,for mechanism analysis,how to include the oil film into the bearing dynamic model affects the result and efficiency of solution.To address this problem,this study proposed a fast algorithm through load distribution and interpolation when calculating oil film stiffness and thickness during the solution of bearing vibration model.Analysis of oil film on vibration is carried out and a bearing test rig is designed to verify the proposed model.Numerical simulation result shows that rotational speed and load have vital effect on oil film and vibration.The experimental result is consistent with the simulation,which shows that the proposed model has a better performance on modeling bearing vibration and the method of considering oil film is reasonable.

Painlev properties and exact solutions for the high-dimensional Schwartz Boussinesq equation

The usual （1＋1）-dimensional Schwartz Boussinesq equation is extended to the （1＋1）-dimensional space-time symmetric form and the general （n＋1）-dimensional space-time symmetric form. These extensions are Painleve integrable in the sense that they possess the Painleve property. The single soliton solutions and the periodic travelling wave solutions for arbitrary dimensional space-time symmetric form are obtained by the Painleve-Backlund transformation.

ICA Based Identification of Time-Varying Linear Causal Model

Recently, several approaches have been proposed to discover the causality of the time-independent or fixed causal model. However, in many realistic applications, especially in economics and neuroscience, causality among variables might be time-varying. A time-varying linear causal model with non-Gaussian noise is considered and the estimation of the causal model from observational data is focused. Firstly, an independent component analysis(ICA) based two stage method is proposed to estimate the time-varying causal coefficients. It shows that, under appropriate assumptions, the time varying coefficients in the proposed model can be estimated by the proposed approach, and results of experiment on artificial data show the effectiveness of the proposed approach. And then, the granger causality test is used to ascertain the causal direction among the variables. Finally, the new approach is applied to the real stock data to identify the causality among three stock indices and the result is consistent with common sense.

ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.