Review of the book ＂Probabilistic Mechanics of Quasibrittle Structures＂

Reliability-based structural analysis and design are of paramount importance since no structures can be designed to be risk-free.It has been generally accepted that the design of engineering structures must often guarantee an extremely low failure risk on the order of 10^（-6）,which is difficult to achieve through direct verification by histogram testing or stochastic computations.

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.

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.

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.

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.

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 back-analysis of rainfall-induced landslides for slope reliability prediction with multi-source information

Probabilistic back-analysis is an important means to infer the statistics of uncertain soil parameters,making the slope reliability assessment closer to the engineering reality.However,multi-source information(including test data,monitored data,field observation and slope survival records)is rarely used in current probabilistic back-analysis.Conducting the probabilistic back-analysis of spatially varying soil parameters and slope reliability prediction under rainfalls by integrating multi-source information is a challenging task since thousands of random variables and high-dimensional likelihood function are usually involved.In this paper,a framework by integrating a modified Bayesian Updating with Subset simulation(mBUS)method with adaptive Conditional Sampling(aCS)algorithm is established for the probabilistic back-analysis of spatially varying soil parameters and slope reliability prediction.Within this framework,the high-dimensional probabilistic back-analysis problem can be easily tackled,and the multi-source information(e.g.monitored pressure heads and slope survival records)can be fully used in the back-analysis.A real Taoyuan landslide case in Taiwan,China is investigated to illustrate the effectiveness and performance of the established framework.The findings show that the posterior knowledge of soil parameters obtained from the established framework is in good agreement with the field observations.Furthermore,the updated knowledge of soil parameters can be utilized to reliably predict the occurrence probability of a landslide caused by the heavy rainfall event on September 12,2004 or forecast the potential landslides under future rainfalls in the Fuhsing District of Taoyuan City,Taiwan,China.

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.

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.

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.

Evaluation of the Added Value of Probabilistic Nowcasting Ensemble Forecasts on Regional Ensemble Forecasts

Ensemble forecasting systems have become an important tool for estimating the uncertainties in initial conditions and model formulations and they are receiving increased attention from various applications.The Regional Ensemble Prediction System(REPS),which has operated at the Beijing Meteorological Service(BMS)since 2017,allows for probabilistic forecasts.However,it still suffers from systematic deficiencies during the first couple of forecast hours.This paper presents an integrated probabilistic nowcasting ensemble prediction system(NEPS)that is constructed by applying a mixed dynamicintegrated method.It essentially combines the uncertainty information(i.e.,ensemble variance)provided by the REPS with the nowcasting method provided by the rapid-refresh deterministic nowcasting prediction system(NPS)that has operated at the Beijing Meteorological Service(BMS)since 2019.The NEPS provides hourly updated analyses and probabilistic forecasts in the nowcasting and short range(0-6 h)with a spatial grid spacing of 500 m.It covers the three meteorological parameters:temperature,wind,and precipitation.The outcome of an evaluation experiment over the deterministic and probabilistic forecasts indicates that the NEPS outperforms the REPS and NPS in terms of surface weather variables.Analysis of two cases demonstrates the superior reliability of the NEPS and suggests that the NEPS gives more details about the spatial intensity and distribution of the meteorological parameters.

Pythagorean probabilistic hesitant triangular fuzzy aggregation operators with applications in multiple attribute decision making

As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.

Physics-Informed AI Surrogates for Day-Ahead Wind Power Probabilistic Forecasting with Incomplete Data for Smart Grid in Smart Cities

Due to the high inherent uncertainty of renewable energy,probabilistic day-ahead wind power forecasting is crucial for modeling and controlling the uncertainty of renewable energy smart grids in smart cities.However,the accuracy and reliability of high-resolution day-ahead wind power forecasting are constrained by unreliable local weather prediction and incomplete power generation data.This article proposes a physics-informed artificial intelligence(AI)surrogates method to augment the incomplete dataset and quantify its uncertainty to improve wind power forecasting performance.The incomplete dataset,built with numerical weather prediction data,historical wind power generation,and weather factors data,is augmented based on generative adversarial networks.After augmentation,the enriched data is then fed into a multiple AI surrogates model constructed by two extreme learning machine networks to train the forecasting model for wind power.Therefore,the forecasting models’accuracy and generalization ability are improved by mining the implicit physics information from the incomplete dataset.An incomplete dataset gathered from a wind farm in North China,containing only 15 days of weather and wind power generation data withmissing points caused by occasional shutdowns,is utilized to verify the proposed method’s performance.Compared with other probabilistic forecastingmethods,the proposed method shows better accuracy and probabilistic performance on the same incomplete dataset,which highlights its potential for more flexible and sensitive maintenance of smart grids in smart cities.

A Novel Smart Beta Optimization Based on Probabilistic Forecast

Rule-based portfolio construction strategies are rising as investmentdemand grows, and smart beta strategies are becoming a trend amonginstitutional investors. Smart beta strategies have high transparency, lowmanagement costs, and better long-term performance, but are at the risk ofsevere short-term declines due to a lack of Risk Control tools. Although thereare some methods to use historical volatility for Risk Control, it is still difficultto adapt to the rapid switch of market styles. How to strengthen the RiskControl management of the portfolio while maintaining the original advantagesof smart beta has become a new issue of concern in the industry. Thispaper demonstrates the scientific validity of using a probability prediction forposition optimization through an optimization theory and proposes a novelnatural gradient boosting (NGBoost)-based portfolio optimization method,which predicts stock prices and their probability distributions based on non-Bayesian methods and maximizes the Sharpe ratio expectation of positionoptimization. This paper validates the effectiveness and practicality of themodel by using the Chinese stock market, and the experimental results showthat the proposed method in this paper can reduce the volatility by 0.08 andincrease the expected portfolio cumulative return (reaching a maximum of67.1%) compared with the mainstream methods in the industry.

Echo State Network With Probabilistic Regularization for Time Series Prediction

Recent decades have witnessed a trend that the echo state network(ESN)is widely utilized in field of time series prediction due to its powerful computational abilities.However,most of the existing research on ESN is conducted under the assumption that data is free of noise or polluted by the Gaussian noise,which lacks robustness or even fails to solve real-world tasks.This work handles this issue by proposing a probabilistic regularized ESN(PRESN)with robustness guaranteed.Specifically,we design a novel objective function for minimizing both the mean and variance of modeling error,and then a scheme is derived for getting output weights of the PRESN.Furthermore,generalization performance,robustness,and unbiased estimation abilities of the PRESN are revealed by theoretical analyses.Finally,experiments on a benchmark dataset and two real-world datasets are conducted to verify the performance of the proposed PRESN.The source code is publicly available at https://github.com/LongJinlab/probabilistic-regularized-echo-state-network.

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.

Part II: Explaining Black Hole Growth due to Universal Expansion: Probabilistic Spacetime versus GEODEs

Recent research indicates that black holes can grow based on the expansion of the universe and not just through accretion and mergers. Two different models independently predicted that finding. One model, describing the relevant massive star remnants as “generic objects of dark energy”, rejects the traditional view of black holes while hypothesizing that dark energy causes the cosmologically coupled growth of these objects. The other model, based on the probabilistic spacetime theory, indicates the growth of black holes is based on the same spacetime mechanism underlying all universal expansion, and does so while leaving the traditional black hole conceptualization essentially intact. The fact these two models predicted this observational finding but did so from different perspectives suggests more can be learned by further study of their differences. This paper explores similarities and differences in the two models’ explanations for massive star remnants’ growth, concluding with suggestions for research testing their relative veracity. An exploration of the relative utility and parsimony of the two models is also described.

Novel Decision Making Methodology under Pythagorean Probabilistic Hesitant Fuzzy Einstein Aggregation Information

This research proposes multicriteria decision-making(MCDM)-based real-time Mesenchymal stem cells(MSC)transfusion framework.The testing phase of the methodology denotes the ability to stick to plastic surfaces,the upregulation and downregulation of certain surface protein markers,and lastly,the ability to differentiate into various cell types.First,two scenarios of an enhanced dataset based on a medical perspective were created in the development phase to produce varying levels of emergency.Second,for real-timemonitoring ofCOVID-19 patients with different emergency levels(i.e.,mild,moderate,severe,and critical),an automated triage algorithmbased on a formal medical guideline is proposed,taking into account the improvement and deterioration procedures fromone level to the next.For this strategy,Einstein aggregation information under the Pythagorean probabilistic hesitant fuzzy environment(PyPHFE)is developed.Einstein operations on PyPHFE such as Einstein sum,product,scalar multiplication,and their properties are investigated.Then,several Pythagorean probabilistic hesitant fuzzy Einstein aggregation operators,namely the Pythagorean probabilistic hesitant fuzzy weighted average(PyPHFWA)operator,Pythagorean probabilistic hesitant fuzzy Einstein weighted geometric(PyPHFEWG)operator,Pythagorean probabilistic hesitant fuzzy Einstein ordered weighted average(PyPHFEOWA)operator,Pythagorean probabilistic hesitant fuzzy Einstein ordered weighted geometric(PyPHFEOWG)operator,Pythagorean probabilistic hesitant fuzzy Einstein hybrid average(PyPHFEHA)operator and Pythagorean probabilistic hesitant fuzzy Einstein hybrid geometric(PyPHFEHG)operator are investigated.All the above-mentioned operators are helpful in design the algorithm to tackle uncertainty in decision making problems.In last,a numerical case study of decision making is presented to demonstrate the applicability and validity of the proposed technique.Besides,the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.

Multidimensional Quality Evaluation of Graduate Thesis:Based on the Probabilistic Linguistic MABAC Method

Graduate education is the main way to train high-level innovative talents,the basic layout to cope with the global talent competition,and the important cornerstone for implementing the innovation-driven development strategy and building an innovation-driven country.Therefore,graduate education is of great remarkably to the development of national education.As an important manifestation of graduate education,the quality of a graduate thesis should receive more attention.It is conducive to promoting the quality of graduates by supervising and examining the quality of the graduate thesis.For this purpose,this work is based on textmining,expert interviews,and questionnaire surveys to obtain the factors influencing the quality of a graduate thesis first.Then,through three rounds of expert consultation,a multidimensional evaluation indicator system for the graduate thesis quality is built.Furthermore,probabilistic linguistic termsets(PLTSs)are utilized to obtain the initial evaluation information and apply the stepwise weight assessment ratio analysis method to determine the weights of attributes.In the ensuing step,the novel multi-attribute border approximation area comparison based on the PLTS method is established.Finally,the proposed method is employed in a case study concerning the quality evaluation of a graduate thesis and the effectiveness of this approach is further illustrated.

Resolving the Information Paradox with Probabilistic Spacetime

It has been 50 years since Hawking described the black hole (BH) information paradox. The combination of BH radiation and subsequent BH evaporation was found to take trapped information into oblivion contrary to the law of conservation of quantum information. Numerous attempts have been made since to resolve this paradox. A brief review herein documents how all these attempts have significant shortcomings, meaning the paradox is still unresolved. A relatively new cosmological theory offers a resolution despite not being developed for that purpose. The theory, entitled the probabilistic spacetime theory (PST), starts with an alteration in one basic assumption compared to all current cosmological theories. Spacetime, instead of being seen as a void or container of other entities, is viewed as the most fundamental entity in the universe, composed of energy fragments, and (in keeping with the conservation principle) impermeable to destruction. The potential contribution of the PST in resolving the information paradox is delineated, with the finding that the single change in the conceptualization of spacetime results in the disappearance of the paradox and not information.