Nonbinary ldpc-coded probabilistic shaping scheme for MIMO systems based on signal space diversity

This paper first describes a binary Low-Density Parity-Check(LDPC)-coded Probabilistic Shaping(PS)scheme for Multiple-Input Multiple-Output(MIMO)systems based on Signal Space Diversity(SSD).Second,a Nonbinary(NB)LDPC-coded PS scheme for MIMO systems based on SSD is proposed.The first scheme can be used to obtain a shaping gain,whereas the second can also realize a coding gain.The theoretical average mutual information of the optimized rotated quadrature amplitude modulation constellations is analyzed and the simulated error per-formance with 22 and 44 MIMO schemes is investigated.The theoretical average mutual information analysis and simulation results show that the proposed NB LDPC-coded PS scheme for MIMO systems based on SSD is reliable and robust,and is therefore suitable for future wireless communication systems.

Information Security Evaluation of Industrial Control Systems Using Probabilistic Linguistic MCDM Method

Industrial control systems(ICSs)are widely used in various fields,and the information security problems of ICSs are increasingly serious.The existing evaluation methods fail to describe the uncertain evaluation information and group evaluation information of experts.Thus,this paper introduces the probabilistic linguistic term sets(PLTSs)to model the evaluation information of experts.Meanwhile,we propose a probabilistic linguistic multi-criteria decision-making(PL-MCDM)method to solve the information security assessment problem of ICSs.Firstly,we propose a novel subscript equivalence distance measure of PLTSs to improve the existing methods.Secondly,we use the Best Worst Method(BWM)method and Criteria Importance Through Inter-criteria Correlation(CRITIC)method to obtain the subjective weights and objective weights,which are used to derive the combined weights.Thirdly,we use the subscript equivalence distance measure method and the combined weight method to improve the probabilistic linguistic Visekriterijumska Optimizacija I Kompromisno Resenje(PL-VIKOR)method.Finally,we apply the proposed method to solve the information security assessment problem of ICSs.When comparing with the existing methods such as the probabilistic linguistic Tomada deDecisão Iterativa Multicritério(PL-TODIM)method and probabilistic linguistic Technique for Order Preference by Similarity to Ideal Solution(PL-TOPSIS)method,the case example shows that the proposed method can provide more reasonable ranking results.By evaluating and ranking the information security level of different ICSs,managers can identify problems in time and guide their work better.

Reachability-Based Confidence-Aware Probabilistic Collision Detection in Highway Driving

Risk assessment is a crucial component of collision warning and avoidance systems for intelligent vehicles.Reachability-based formal approaches have been developed to ensure driving safety to accurately detect potential vehicle collisions.However,they suffer from over-conservatism,potentially resulting in false–positive risk events in complicated real-world applications.In this paper,we combine two reachability analysis techniques,a backward reachable set(BRS)and a stochastic forward reachable set(FRS),and propose an integrated probabilistic collision–detection framework for highway driving.Within this framework,we can first use a BRS to formally check whether a two-vehicle interaction is safe;otherwise,a prediction-based stochastic FRS is employed to estimate the collision probability at each future time step.Thus,the framework can not only identify non-risky events with guaranteed safety but also provide accurate collision risk estimation in safety-critical events.To construct the stochastic FRS,we develop a neural network-based acceleration model for surrounding vehicles and further incorporate a confidence-aware dynamic belief to improve the prediction accuracy.Extensive experiments were conducted to validate the performance of the acceleration prediction model based on naturalistic highway driving data.The efficiency and effectiveness of the framework with infused confidence beliefs were tested in both naturalistic and simulated highway scenarios.The proposed risk assessment framework is promising for real-world applications.

Probabilistic modeling of multifunction radars with autoregressive kernel mixture network

The task of modeling and analyzing intercepted multifunction radars(MFRs)pulse trains is vital for cognitive electronic reconnaissance.Existing methodologies predominantly rely on prior information or heavily constrained models,posing challenges for non-cooperative applications.This paper introduces a novel approach to model MFRs using a Bayesian network,where the conditional probability density function is approximated by an autoregressive kernel mixture network(ARKMN).Utilizing the estimated probability density function,a dynamic programming algorithm is proposed for denoising and detecting change points in the intercepted MFRs pulse trains.Simulation results affirm the proposed method's efficacy in modeling MFRs,outperforming the state-of-the-art in pulse train denoising and change point detection.

Uncertainty quantification of inverse analysis for geomaterials using probabilistic programming

Uncertainty is an essentially challenging for safe construction and long-term stability of geotechnical engineering.The inverse analysis is commonly utilized to determine the physico-mechanical parameters.However,conventional inverse analysis cannot deal with uncertainty in geotechnical and geological systems.In this study,a framework was developed to evaluate and quantify uncertainty in inverse analysis based on the reduced-order model(ROM)and probabilistic programming.The ROM was utilized to capture the mechanical and deformation properties of surrounding rock mass in geomechanical problems.Probabilistic programming was employed to evaluate uncertainty during construction in geotechnical engineering.A circular tunnel was then used to illustrate the proposed framework using analytical and numerical solution.The results show that the geomechanical parameters and associated uncertainty can be properly obtained and the proposed framework can capture the mechanical behaviors under uncertainty.Then,a slope case was employed to demonstrate the performance of the developed framework.The results prove that the proposed framework provides a scientific,feasible,and effective tool to characterize the properties and physical mechanism of geomaterials under uncertainty in geotechnical engineering problems.

Probabilistic seismic inversion based on physics-guided deep mixture density network

Deterministic inversion based on deep learning has been widely utilized in model parameters estimation.Constrained by logging data,seismic data,wavelet and modeling operator,deterministic inversion based on deep learning can establish nonlinear relationships between seismic data and model parameters.However,seismic data lacks low-frequency and contains noise,which increases the non-uniqueness of the solutions.The conventional inversion method based on deep learning can only establish the deterministic relationship between seismic data and parameters,and cannot quantify the uncertainty of inversion.In order to quickly quantify the uncertainty,a physics-guided deep mixture density network(PG-DMDN)is established by combining the mixture density network(MDN)with the deep neural network(DNN).Compared with Bayesian neural network(BNN)and network dropout,PG-DMDN has lower computing cost and shorter training time.A low-frequency model is introduced in the training process of the network to help the network learn the nonlinear relationship between narrowband seismic data and low-frequency impedance.In addition,the block constraints are added to the PG-DMDN framework to improve the horizontal continuity of the inversion results.To illustrate the benefits of proposed method,the PG-DMDN is compared with existing semi-supervised inversion method.Four synthetic data examples of Marmousi II model are utilized to quantify the influence of forward modeling part,low-frequency model,noise and the pseudo-wells number on inversion results,and prove the feasibility and stability of the proposed method.In addition,the robustness and generality of the proposed method are verified by the field seismic data.

Development of a DFN-based probabilistic block theory approach for bench face angle design in open pit mining

In open pit mining,uncontrolled block instabilities have serious social,economic and regulatory consequences,such as casualties,disruption of operation and increased regulation difficulties.For this reason,bench face angle,as one of the controlling parameters associated with block instabilities,should be carefully designed for sustainable mining.This study introduces a discrete fracture network(DFN)-based probabilistic block theory approach for the fast design of the bench face angle.A major advantage is the explicit incorporation of discontinuity size and spatial distribution in the procedure of key blocks testing.The proposed approach was applied to a granite mine in China.First,DFN models were generated from a multi-step modeling procedure to simulate the complex structural characteristics of pit slopes.Then,a modified key blocks searching method was applied to the slope faces modeled,and a cumulative probability of failure was obtained for each sector.Finally,a bench face angle was determined commensurate with an acceptable risk level of stability.The simulation results have shown that the number of hazardous traces exposed on the slope face can be significantly reduced when the suggested bench face angle is adopted,indicating an extremely low risk of uncontrolled block instabilities.

Flight Time Minimization of UAV for Cooperative Data Collection in Probabilistic LoS Channel

This paper investigates the data collection in an unmanned aerial vehicle(UAV)-aided Internet of Things(IoT) network, where a UAV is dispatched to collect data from ground sensors in a practical and accurate probabilistic line-of-sight(LoS) channel. Especially, access points(APs) are introduced to collect data from some sensors in the unlicensed band to improve data collection efficiency. We formulate a mixed-integer non-convex optimization problem to minimize the UAV flight time by jointly designing the UAV 3D trajectory and sensors’ scheduling, while ensuring the required amount of data can be collected under the limited UAV energy. To solve this nonconvex problem, we recast the objective problem into a tractable form. Then, the problem is further divided into several sub-problems to solve iteratively, and the successive convex approximation(SCA) scheme is applied to solve each non-convex subproblem. Finally,the bisection search is adopted to speed up the searching for the minimum UAV flight time. Simulation results verify that the UAV flight time can be shortened by the proposed method effectively.

Risk-Informed Model-Free Safe Control of Linear Parameter-Varying Systems

This paper presents a risk-informed data-driven safe control design approach for a class of stochastic uncertain nonlinear discrete-time systems.The nonlinear system is modeled using linear parameter-varying(LPV)systems.A model-based probabilistic safe controller is first designed to guarantee probabilisticλ-contractivity(i.e.,stability and invariance)of the LPV system with respect to a given polyhedral safe set.To obviate the requirement of knowing the LPV system model and to bypass identifying its open-loop model,its closed-loop data-based representation is provided in terms of state and scheduling data as well as a decision variable.It is shown that the variance of the closedloop system,as well as the probability of safety satisfaction,depends on the decision variable and the noise covariance.A minimum-variance direct data-driven gain-scheduling safe control design approach is presented next by designing the decision variable such that all possible closed-loop system realizations satisfy safety with the highest confidence level.This minimum-variance approach is a control-oriented learning method since it minimizes the variance of the state of the closed-loop system with respect to the safe set,and thus minimizes the risk of safety violation.Unlike the certainty-equivalent approach that results in a risk-neutral control design,the minimum-variance method leads to a risk-averse control design.It is shown that the presented direct risk-averse learning approach requires weaker data richness conditions than existing indirect learning methods based on system identification and can lead to a lower risk of safety violation.Two simulation examples along with an experimental validation on an autonomous vehicle are provided to show the effectiveness of the presented approach.

Lychrel Numbers in Base 10: A Probabilistic Approach

For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides some properties which enable a mathematical extraction of new Lychrel numbers from existing ones. This probabilistic approach has the advantage of being extendable to other bases. The results show that palindromes can also be Lychrel numbers.

A Probabilistic Description of the Impact of Vaccine-Induced Immunity in the Dynamics of COVID-19 Transmission

The recent outbreak of COVID-19 has caused millions of deaths worldwide and a huge societal and economic impact in virtually all countries. A large variety of mathematical models to describe the dynamics of COVID-19 transmission have been reported. Among them, Bayesian probabilistic models of COVID-19 transmission dynamics have been very efficient in the interpretation of early data from the beginning of the pandemic, helping to estimate the impact of non-pharmacological measures in each country, and forecasting the evolution of the pandemic in different potential scenarios. These models use probability distribution curves to describe key dynamic aspects of the transmission, like the probability for every infected person of infecting other individuals, dying or recovering, with parameters obtained from experimental epidemiological data. However, the impact of vaccine-induced immunity, which has been key for controlling the public health emergency caused by the pandemic, has been more challenging to describe in these models, due to the complexity of experimental data. Here we report different probability distribution curves to model the acquisition and decay of immunity after vaccination. We discuss the mathematical background and how these models can be integrated in existing Bayesian probabilistic models to provide a good estimation of the dynamics of COVID-19 transmission during the entire pandemic period.

DAMAGE CLASSIFICATION BY PROBABILISTIC NEURAL NETWORKS BASED ON LATENT COMPONENTS FOR TIME-VARYING SYSTEM

A new approach to damage classification for health monitoring of a time-varylng system is presented. The functional-series time-dependent auto regressive moving average （FS-TARMA） time series model is applied to the vibration signal observed in the time-varying system for estimating the TAR/TMA parameters and the innovation variance. These parameters are the functions of the time, represented by a group of projection coefficients on the certain functional subspace with specific basis functions. The estimated TAR/TMA parameters and the innovation variance are further used to calculate the latent components （LCs） as the more informative data for health monitoring evaluation, based on an eigenvalue decomposition technique. LCs are then combined and reduced to numerical values （NVs） as feature sets, which are input to a probabilistic neural network （PNN） for the damage classification. For the evaluation of the proposed method, numerical simulations of the damage classification for a tlme-varylng system are used, in which different classes of damage are modeled by the mass or stiffness reductions. It is demonstrated that the method can identify the damages in the course of operation and the change of parameters on the time-varying background of the system.

Probabilistic small signal stability analysis of power system with wind power and photovoltaic power based on probability collocation method

Recently, with increasing improvements in the penetration of wind power and photovoltaic power in the world, probabilistic small signal stability analysis(PSSSA) of a power system consisting of multiple types of renewable energy has become a key problem. To address this problem, this study proposes a probabilistic collocation method(PCM)-based PSSSA for a power system consisting of wind farms and photovoltaic farms. Compared with the conventional Monte Carlo method, the proposed method meets the accuracy and precision requirements and greatly reduces the computation; therefore, it is suitable for the PSSSA of this power system. Case studies are conducted based on a 4-machine 2-area and New England systems, respectively. The simulation results show that, by reducing synchronous generator output to improve the penetration of renewable energy, the probabilistic small signal stability(PSSS) of the system is enhanced. Conversely, by removing part of the synchronous generators to improve the penetration of renewable energy, the PSSS of the system may be either enhanced or deteriorated.

Robust Beamforming for Secured Wireless Power Transfer in MIMO Magnetic Resonant Coupling System:A Probabilistic Approach

Wireless power transfer(WPT) to support mobile and portable devices is an emerging wireless technique.Among all kinds of approaches,magnetic resonance coupling(MRC) is an excellent one for mid-range WPT,which provides better mobility,flexibility,and convenience due to its simplicity in hardware implementation and longer transmission distances.In this paper,we consider an MRCWPT system with multiple power transmitters,one intended power receiver and multiple unintended power receivers.We investigate the probabilistic robust beamforming designs and provide efficient algorithms to achieve the local optimums under two different criteria,i.e.,total source power minimization problem and min-max unintended receiving power restriction problem.As the problems are quite typical in robust design situations,our proposed robust beamformers can be conveniently applied to other probabilistic robust design problems,thus reduce the complexity as well as improve the beamforming performance.Numerical results demonstrate that the proposed algorithms can significantly improve the performance as well as the robustness of the WPT system.

Dynamic probabilistic design technique for multi-component system with multi-failure modes

For unacceptable computational efficiency and accuracy on the probabilistic analysis of multi-component system with multi-failure modes,this paper proposed multi-extremum response surface method(MERSM).MERSM model was established based on quadratic polynomial function by taking extremum response surface model as the sub-model of multi-response surface method.The dynamic probabilistic analysis of an aeroengine turbine blisk with two components,and their reliability of deformation and stress failures was obtained,based on thermal-structural coupling technique,by considering the nonlinearity of material parameters and the transients of gas flow,gas temperature and rotational speed.The results show that the comprehensive reliability of structure is 0.9904 when the allowable deformations and stresses of blade and disk are 4.78×10–3 m and 1.41×109 Pa,and 1.64×10–3 m and 1.04×109 Pa,respectively.Besides,gas temperature and rotating speed severely influence the comprehensive reliability of system.Through the comparison of methods,it is shown that the MERSM holds higher computational precision and speed in the probabilistic analysis of turbine blisk,and MERSM computational precision satisfies the requirement of engineering design.The efforts of this study address the difficulties on transients and multiple models coupling for the dynamic probabilistic analysis of multi-component system with multi-failure modes.

The Approach to Probabilistic Decision-Theoretic Rough Set in Intuitionistic Fuzzy Information Systems

For the moment, the representative and hot research is decision-theoretic rough set (DTRS) which provides a new viewpoint to deal with decision-making problems under risk and uncertainty, and has been applied in many fields. Based on rough set theory, Yao proposed the three-way decision theory which is a prolongation of the classical two-way decision approach. This paper investigates the probabilistic DTRS in the framework of intuitionistic fuzzy information system (IFIS). Firstly, based on IFIS, this paper constructs fuzzy approximate spaces and intuitionistic fuzzy (IF) approximate spaces by defining fuzzy equivalence relation and IF equivalence relation, respectively. And the fuzzy probabilistic spaces and IF probabilistic spaces are based on fuzzy approximate spaces and IF approximate spaces, respectively. Thus, the fuzzy probabilistic approximate spaces and the IF probabilistic approximate spaces are constructed, respectively. Then, based on the three-way decision theory, this paper structures DTRS approach model on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. So, the fuzzy decision-theoretic rough set (FDTRS) model and the intuitionistic fuzzy decision-theoretic rough set (IFDTRS) model are constructed on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. Finally, based on the above DTRS model, some illustrative examples about the risk investment of projects are introduced to make decision analysis. Furthermore, the effectiveness of this method is verified.

Probabilistic rainfall thresholds in Chibo, India: estimation and validation using monitoring system

The Himalayan region has been severely affected by landslides especially during the monsoons. In particular, Kalimpong region in Darjeeling Himalayas has recorded several landslides and has caused significant loss of life, property and agricultural land. The study region, Chibo has experienced several landslides in the past which were mainly debris and earth slide. Globally, several types of rainfall thresholds have been used to determine rainfall-induced landslide incidents. In this paper, probabilistic thresholds have been defined as it would provide a better understanding compared to deterministic thresholds which provide binary results, i.e., either landslide or no landslide for a particular rainfall event. Not much research has been carried out towards validation of rainfall thresholds using an effective and robust monitoring system. The thresholds are then validated using a reliable system utilizing Microelectromechanical Systems(MEMS) tilt sensor and volumetric water content sensor installed in the region. The system measures the tilt of the instrument which is installed at shallow depths and is ideal for an early warning system for shallow landslides. The change in observed tilt angles due to rainfall would give an understanding of the applicability of the probabilistic model. The probabilities determined using Bayes' theorem have been calculated using the rainfall parameters and landslide data in 2010-2016. The rainfall values were collected from an automatic rain gauge setup near the Chibo region. The probabilities were validated using the MEMS based monitoring system setup in Chibo for the monsoon season of 2017. This is the first attempt to determine probabilities and validate it with a robust and effective monitoring system in Darjeeling Himalayas. This study would help in developing an early warning system for regions where the installation of monitoring systems may not be feasible.

A Satellite Communication System Transmission Scheme Based on Probabilistic Shaping

In this paper, A transmission scheme based on probabilistic shaping applied to satellite communication systems is proposed. 16QAM is taken as an example to establish a 1GBaud ROF experimental system working in Ka-band. The experiment results show that the PS-16QAM signal has better performance in terms of bit error rate than the uniform 16QAM, and its performance is close to the uniform 8QAM scheme.

A direct probabilistic approach to solve state equations for nonlinear systems under random excitation

In this paper, a direct probabilistic approach（DPA） is presented to formulate and solve moment equations for nonlinear systems excited by environmental loads that can be either a stationary or nonstationary random process.The proposed method has the advantage of obtaining the response＇s moments directly from the initial conditions and statistical characteristics of the corresponding external excitations. First, the response＇s moment equations are directly derived based on a DPA, which is completely independent of the It？/filtering approach since no specific assumptions regarding the correlation structure of excitation are made.By solving them under Gaussian closure, the response＇s moments can be obtained. Subsequently, a multiscale algorithm for the numerical solution of moment equations is exploited to improve computational efficiency and avoid much wall-clock time. Finally, a comparison of the results with Monte Carlo（MC） simulation gives good agreement.Furthermore, the advantage of the multiscale algorithm in terms of efficiency is also demonstrated by an engineering example.

Countermeasure against probabilistic blinding attack in practical quantum key distribution systems

In a practical quantum key distribution（QKD） system, imperfect equipment, especially the single-photon detector,can be eavesdropped on by a blinding attack. However, the original blinding attack may be discovered by directly detecting the current. In this paper, we propose a probabilistic blinding attack model, where Eve probabilistically applies a blinding attack without being caught by using only an existing intuitive countermeasure. More precisely, our countermeasure solves the problem of how to define the bound in the limitation of precision of current detection, and then we prove security of the practical system by considering the current parameter. Meanwhile, we discuss the bound of the quantum bit error rate（QBER） introduced by Eve, by which Eve can acquire information without the countermeasure.