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.

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.

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.

Earthquake-induced landslide displacement attenuation models and application in probabilistic seismic landslide displacement analysis

A landslide displacement (DLL) attenuation model has been developed using spectral intensity and a ratio of critical acceleration coefficient to ground acceleration coefficient. In the development of the model,a New Zealand earthquake record data set with magnitudes ranging from 5.0 to 7.2 within a source distance of 175 km is used. The model can be used to carry out deterministic landslide displacement analysis,and readily extended to carry out probabilistic seismic landslide displacement analysis. DLL attenuation models have also been developed by using earthquake source terms,such as magnitude and source distance,that account for the effects of earthquake faulttype,source type,and site conditions. Sensitivity analyses show that the predicted DLL values from the new models are close to those from the Romeo model that was developed from an Italian earthquake record data set. The proposed models are also applied to an analysis of landslide displacements in the Wenchuan earthquake,and a comparison between the predicted and the observed results shows that the proposed models are reliable,and can be confidently used in mapping landslide potential.

A Probabilistic Method for Motion Analysis of Caisson Breakwaters

It is assumed that, during the design period, the waves acting on breakwaters are divided into three types： standing wave, broken wave and breaking wave,and the wave heights fit the Rayleigh distribution while the water depths, wave periods and duration of breaking wave impact force fit normal distribution. Based on the random samples of water depths, wave heights, wave periods and duration of breaking wave impact force, the types of waves acting on breakwaters are distinguished and the time-history model of the wave force is determined. The motions of caisson breakwaters under the wave force are simulated by a dynamic numerical model and the statistic characteristics of the dynamic responses are analyzed with the Monte Carlo method. A probabilistic procedure to analyze the motion of the breakwater is developed therein. The procedure is illustrated by an example.

Success criteria analysis in support of probabilistic risk assessment for nuclear power plants: application on SGTR accident

Success criteria analysis(SCA) bridges the gap between deterministic and probabilistic approaches for risk assessment of complex systems. To develop a risk model,SCA evaluates systems behaviour in response to postulated accidents using deterministic approach to provide required information for the probabilistic model. A systematic framework is proposed in this article for extracting the front line systems success criteria. In this regard, available approaches are critically reviewed and technical challenges are discussed. Application of the proposed methodology is demonstrated on a typical Westinghouse-type nuclear power plant. Steam generator tube rupture is selected as the postulated accident. The methodology is comprehensive and general; therefore, it can be implemented on the other types of plants and complex systems.

An efficient probabilistic design approach for tunnel face stability by inverse reliability analysis

In order to maintain the safety of underground constructions that significantly involve geo-material uncertainties,this paper delivers a new computation framework for conducting reliability-based design(RBD)of shallow tunnel face stability,utilizing a simplified inverse first-order reliability method(FORM).The limit state functions defining tunnel face stability are established for both collapse and blow-out modes of the tunnel face failure,respectively,and the deterministic results of the tunnel face support pressure are obtained through three-dimensional finite element limit analysis(FELA).Because the inverse reliability method can directly capture the design support pressure according to prescribed target reliability index,the computational cost for probabilistic design of tunnel face stability is greatly reduced.By comparison with Monte Carlo simulation results,the accuracy and feasibility of the proposed method are verified.Further,this study presents a series of reliability-based design charts for vividly understanding the limit support pressure on tunnel face in both cohesionless(sandy)soil and cohesive soil stratums,and their optimal support pressure ranges are highlighted.The results show that in the case of sandy soil stratum,the blowout failure of tunnel face is extremely unlikely,whereas the collapse is the only possible failure mode.The parametric study of various geotechnical uncertainties also reveals that ignoring the potential correlation between soil shear strength parameters will lead to over-designed support pressure,and the coefficient of variation of internal friction angle has a greater influence on the tunnel face failure probability than that of the cohesion.

Dynamic probabilistic analysis of stress and deformation for bladed disk assemblies of aeroengine

In order to describe and control the stress distribution and total deformation of bladed disk assemblies used in the aeroengine, a highly efficient and precise method of probabilistic analysis which is called extremum response surface method(ERSM) is produced based on the previous deterministic analysis results with the finite element model(FEM). In this work, many key nonlinear factors, such as the dynamic feature of the temperature load, the centrifugal force and the boundary conditions, are taken into consideration for the model. The changing patterns with time of bladed disk assemblies about stress distribution and total deformation are obtained during the deterministic analysis, and at the same time, the largest deformation and stress nodes of bladed disk assemblies are found and taken as input target of probabilistic analysis in a scientific and reasonable way. Not only their reliability, historical sample, extreme response surface(ERS) and the cumulative probability distribution function but also their sensitivity and effect probability are obtained. Main factors affecting stress distribution and total deformation of bladed disk assemblies are investigated through the sensitivity analysis of the model. Finally, compared with the response surface method(RSM) and the Monte Carlo simulation(MCS), the results show that this new approach is effective.

Probabilistic Analysis for Seismic Stability of Beach Earth Embankment

The current safety factor method for evaluating earth embankment stability is not very rational since the assessment of slope stability is really an uncertainty problem. In order to consider the random property of this problem, the probabilistic analysis is introduced herein. Finally, the stability of a real beach earth embankment is analysed by means of the suggested probabilitic approach. It may be seen that the results of analysis can represent the numerical assessment of the degree of seismic stability.

Fuzzy Probabilistic Analysis of Seismic Stability of Coastal Embankment

The stability of slope is affected by a number of factors, some of which have not only random property but also fuzzy characteristic. Therefore, the analysis of slope stability is really an uncertain problem. The customary safety factor does not in reality reflect stability scientifically, quantitatively and practically. In order to obtain more practical results, the slope stability is treated as a fuzzy random event for the evaluation of its fuzzy probability. Finally, the seismic stability of an existing coastal embankment is analyzed by means of the suggested fuzzy probabilistic method. It may be seen that the results of analysis can more fully represent the numerical assessment of the degree of slope seismic stability.

Probabilistic fragility analysis:A tool for assessing design rules of RC buildings

In this work, fragility analysis is performed to assess two groups of reinforced concrete structures. The first group of structures is composed of buildings that implement three common design practices; namely, fully infilled, weak ground story and short columns. The three design practices are applied during the design process of a reinforced concrete building. The structures of the second group vary according to the value of the behavioral factors used to define the seismic forces as specified in design procedures. Most seismic design codes belong to the class of prescriptive procedures where if certain constraints are fulfilled, the structure is considered safe. Prescriptive design procedures express the ability of the structure to absorb energy through inelastic deformation using the behavior factor. The basic objective of this work is to assess both groups of structures with reference to the limit-state probability of exceedance. Thus, four limit state fragility curves are developed on the basis of nonlinear static analysis for both groups of structures. Moreover, the 95% confidence intervals of the fragility curves are also calculated, taking into account two types of random variables that influence structural capacity and seismic demand.

An aligned mixture probabilistic principal component analysis for fault detection of multimode chemical processes

A novel approach named aligned mixture probabilistic principal component analysis(AMPPCA) is proposed in this study for fault detection of multimode chemical processes. In order to exploit within-mode correlations,the AMPPCA algorithm first estimates a statistical description for each operating mode by applying mixture probabilistic principal component analysis(MPPCA). As a comparison, the combined MPPCA is employed where monitoring results are softly integrated according to posterior probabilities of the test sample in each local model. For exploiting the cross-mode correlations, which may be useful but are inadvertently neglected due to separately held monitoring approaches, a global monitoring model is constructed by aligning all local models together. In this way, both within-mode and cross-mode correlations are preserved in this integrated space. Finally, the utility and feasibility of AMPPCA are demonstrated through a non-isothermal continuous stirred tank reactor and the TE benchmark process.

Semi-supervised learning based probabilistic latent semantic analysis for automatic image annotation

In recent years,multimedia annotation problem has been attracting significant research attention in multimedia and computer vision areas,especially for automatic image annotation,whose purpose is to provide an efficient and effective searching environment for users to query their images more easily. In this paper,a semi-supervised learning based probabilistic latent semantic analysis( PLSA) model for automatic image annotation is presenred. Since it's often hard to obtain or create labeled images in large quantities while unlabeled ones are easier to collect,a transductive support vector machine( TSVM) is exploited to enhance the quality of the training image data. Then,different image features with different magnitudes will result in different performance for automatic image annotation. To this end,a Gaussian normalization method is utilized to normalize different features extracted from effective image regions segmented by the normalized cuts algorithm so as to reserve the intrinsic content of images as complete as possible. Finally,a PLSA model with asymmetric modalities is constructed based on the expectation maximization( EM) algorithm to predict a candidate set of annotations with confidence scores. Extensive experiments on the general-purpose Corel5k dataset demonstrate that the proposed model can significantly improve performance of traditional PLSA for the task of automatic image annotation.

PROBABILISTIC METHODOLOGY OF LOW CYCLE FATIGUE ANALYSIS

The cyclic stress-strain responses (CSSR), Neuber's rule (NR) and cyclic strain-life relation (CSLR) are treated as probabilistic curves in local stress and strain method of low cycle fatigue analysis. The randomness of loading and the theory of fatigue damage accumulation (TOFDA) are considered. The probabilistic analysis of local stress, local strain and fatigue life are constructed based on the first-order Taylor's series expansions. Through this method proposed fatigue reliability analysis can be accomplished.

Probabilistic Model Checking-Based Survivability Analysis in Vehicle-to-Vehicle Networks

Probabilistic model checking has been widely applied to quantitative analysis of stochastic systems, e.g., analyzing the performance, reliability and survivability of computer and communication systems. In this paper, we extend the application of probabilistic model checking to the vehicle to vehicle(V2V) networks. We first develop a continuous-time Markov chain(CTMC) model for the considered V2V network, after that, the PRISM language is adopted to describe the CTMC model, and continuous-time stochastic logic is used to describe the objective survivability properties. In the analysis, two typical failures are considered, namely the node failure and the link failure, respectively induced by external malicious attacks on a target V2V node, and interrupt in a communication link. Considering these failures, their impacts on the network survivability are demonstrated. It is shown that with increasing failure strength, the network survivability is reduced. On the other hand, the network survivability can be improved with increasing repair rate. The proposed probabilistic model checking-based approach can be effectively used in survivability analysis for the V2V networks, moreover, it is anticipated that the approach can be conveniently extended to other networks.

Probabilistic Analysis on Connectivity for Sensor Grids with Unreliable Nodes

This paper mainly investigates the connectivity of the unreliable sensor grid network. We consider an unreliable sensor grid network with mn nodes placed in a certain planar area A, and we assume that each node has independent failure probability p and has the same transmission range R. This paper presents a new method for calculating the connectivity probability of the network, which uses thorough mathematical methods to derive the relationship among the network connectivity probability, the probability that a node is ＂failed＂ （not active）, the numbers of node, and the node＇s transmission range in unreliable sensor networks. Our approach is more useful and efficient for given problem and conditions. Such as the numerical calculating results indicate that, for a 100×100 size sensot network, if node failure probability is bounded 0.5%, even if the transmission range is small （such as R = 10）, we can still maintain very high connectivity probability （reach 95.8%）. On the other hand, the simulation results show that building high connectivity probability is entirely possible on unreliable sensor grid networks.

A Finite-Element Analysis on the Rheorolling Process of Semi-Solid Spring Steel

With a geometrical model of porous material, a 3D finite-element analysis on the rolling process of spring steel60Si2Mn in the semi-solid state is carried out using software MARC. In terms of flat and groove rolling conditions,stress field and strain field are studied. The simulation results show that the rigid-viscoplastic model can accuratelydescribe the semi-solid metal rolling process. Semi-solid slurry has the characteristics of low flow stress and goodfluidity. During groove rolling, distribution of stress and strain on the cross-section of deformation zone is moreuniform than that during flat rolling. The results of simulation are in good agreement with the experiment data, andshow that semi-solid material fits for groove rolling.

Potential rupture surface model and its ap-plication on probabilistic seismic hazard analysis

Potential sources are simplified as point sources or linear sources in current probabilistic seismic hazard analysis （PSHA） methods. Focus size of large earthquakes is considerable, and fault rupture attitudes may have great influence upon the seismic hazard of a site which is near the source. Under this circumstance, it is unreasonable to use the simplified potential source models in the PSHA, so a potential rupture surface model is proposed in this paper. Adopting this model, we analyze the seismic hazard near the Chelungpu fault that generated the Chi-Chi （Jiji） earthquake with magnitude 7.6 and the following conclusions are reached. （1） This model is reasonable on the base of focal mechanism, especially for sites near potential earthquakes with large magnitude; （2） The attitudes of potential rupture surfaces have great influence on the results of probabilistic seismic hazard analysis and seismic zoning.

Probabilistic Analysis of Life Cycle Cost for Power Transformer

The selection of power transformer is very important to power sector. Most methods are utilized according to the initial cost and don’t consider the synthetical evaluation of economy and technology. Based on previous research, this paper addresses a new practical probabilistic life cycle cost model. Then, in order to demonstrate the practicability of probabilistic life cycle cost for the power transformer, illustrative investment alternatives of actual power transformers are discussed. From the result of the numerical investigation, it may be positively stated that the optimum investment alternative for the power transformer based on the probabilistic life cycle cost model proposed in this study will lead to a more rational, economical and effective procedure compared with the conventional method only considering the initial cost.