Probabilistic Analysis Approach Research Articles

Challenges Related to Probabilistic Decision Analysis for Bridge Testing and Reclassification

This paper reviews historical developments and recent challenges in full scale bridge testing and introduces results- and hypotheses related to an ongoing bridge testing research project. This research project encompasses full scale bridge testing in conjunction with bearing capacity analysis as well as related contact- and non-contact monitoring procedures combined with a decision analytical approach. Results from the first steps of the project, focusing on full scale load testing of bridges, are presented. The next part approaches the interfaces between three project areas namely the bearing capacity analysis, the utilization of monitoring procedures and a decision analytical approach. The proposed probabilistic decision analysis approach is described for two scenarios: (1) The decision support for the actual proof load test providing decision rules for a safe and efficient in-situ test and (2) for the identification of efficient strategies for the bridge reclassification accounting for modeling, simulation, and monitoring information. The paper concludes with a summary highlighting deemed challenges in the used approaches.

Probabilistic model-checking based reliability analysis for failure correlation of multi-state systems

Many conventional reliability analysis methods for multi-state systems assume independence among the various subsystems. To avoid this, we propose a probabilistic model checking-based approach for failure correlation analysis of multi-state systems. First, an improved Apriori algorithm is used to determine the effect of a subsystem failure on the associated subsystems. Next, a copula function is applied to establish the relationship between failures of the associated subsystems. Finally, probabilistic model-checking is used to analyze the reliability of the entire system and all its subsystems. The effectiveness of the proposed method is verified using an application involving offshore wind turbines. The results show that the proposed method can be used flexibly and effectively for multi-state system reliability analysis. Moreover, the proposed method lays the foundation for system maintenance strategy formulation and other engineering applications.

Corrosion-induced cracking fragility of RC bridge with improved concrete carbonation and steel reinforcement corrosion models

Corrosion-induced cracking is one important limit state in the durability performance analysis of the reinforcement concrete (RC) structures. A comprehensive probabilistic approach is established for the corrosion-induced cracking fragility analysis of the RC bridge in the urban atmospheric condition with improved concrete carbonation and steel reinforcement corrosion models. The improved deterioration models have a probabilistic formation by adding correction and error terms to the existing deterministic models. The deterministic parts are selected from reviews and discussions on existing models. The correction terms are sets of explanatory functions representing the influencing factors related to the potential bias in the deterministic models. The statistical distributions of unknown model parameters are calibrated and the optimum collections of the explanatory functions are selected through the Bayesian rule based on long-term data from onsite tests or natural exposure experiments. The probabilistic analysis approach for the corrosion-induced cracking fragility are generated based on the improved deterioration models. Fragility curves, parameter sensitivities and random variable importance are achieved for the example RC bridge. The results show that increases on the concrete strength, cover depth and steel bar diameter, or decrease on the CO2 density, are efficient countermeasures to improve the durability performance of the RC bridge against corrosion-induced cover cracking and the uncertainty of the problem mainly comes from the concrete carbonation model.

Probabilistic stability analysis of earth dam slope under transient seepage using multivariate adaptive regression splines

Earth dams are widespread throughout the world and their safety has gained increasing concern from geotechnical engineering societies. Although probabilistic stability analysis approach has been widely applied to the safety assessment of geotechnical structures, few studies have been performed to investigate the effects of water level fluctuations on earth dam slope stability considering uncertainties of soil parameters. This study proposes an efficient probabilistic stability analysis approach by integrating a soft computing algorithm of multivariate adaptive regression splines (MARS). The calibration of a MARS model generally requires a large number of training samples, which are obtained from repeated runs of deterministic seepage and slope stability analyses using the GeoStudio software. Based on the established MARS model, the earth dam slope failure probability can be conveniently evaluated. As an illustration, the proposed approach is applied to the probabilistic stability analysis of Ashigong earth dam under transient seepage. The effects of the uncertainties of soil parameters and water level fluctuation velocity on the earth dam slope failure probability are explored systematically. Results show that the MARS-based probabilistic stability analysis approach evaluates the earth slope failure probability with satisfactory accuracy and efficiency. The earth dam slope failure probability is significantly affected by the water level fluctuation velocity and the coefficient of variation of the effective friction angle.

Tsallis Entropy-Based Fuzzy Latent Semantics Analysis

In this study, we present a fuzzy counterpart to the probabilistic latent semantic analysis (PLSA) approach. It is derived by solving the optimization problem of Tsallis entropy-penalizing free energy of a pseudo PLSA model by using a modified i.i.d. assumption. This derivation is similar to that of the conventional fuzzy counterpart of the PLSA, which involves solving the optimization problem of Shannon entropy-penalizing free energy. Furthermore, the proposed method is validated using numerical examples.

Bayesian Approach for Sequential Probabilistic Back Analysis of Uncertain Geomechanical Parameters and Reliability Updating of Tunneling‐Induced Ground Settlements

This paper proposes a new sequential probabilistic back analysis approach for probabilistically determining the uncertain geomechanical parameters of shield tunnels by using time‐series monitoring data. The approach is proposed based on the recently developed Bayesian updating with subset simulation. Within the framework of the proposed approach, a complex Bayesian back analysis problem is transformed into an equivalent structural reliability problem based on subset simulation. Hermite polynomial chaos expansion‐based surrogate models are constructed to improve the computational efficiency of probabilistic back analysis. The reliability of tunneling‐induced ground settlements is updated in the process of sequential back analyses. A real shield tunnel project of No. 1 Nanchang Metro Line in China is investigated to assess the effectiveness of the approach. The proposed approach is able to infer the posterior distributions of uncertain geomechanical parameters (i.e., Young’s moduli of surrounding soil layers and ground vehicle load). The reliability of tunneling‐induced ground settlements can be updated in a real‐time manner by fully utilizing the time‐series monitoring data. The results show good agreement with the variation trend of field monitoring data of ground settlement and the post‐event investigations.

Probabilistic analysis of flood embankment stability: the case study of the Adige River embankment in Italy

Flooding is a worldwide phenomenon. Over the last few decades the world has experienced a rising number of devastating flood events and the trend in such natural disasters is increasing. Furthermore, escalations in both the probability and magnitude of flood hazards are expected as a result of climate change. Flood defence embankments are one of the major flood defence measures and stability assessment for these structures is therefore a very important process. Traditional deterministic approaches to stability analysis do not allow taking into account and quantifying the uncertainties in soil characterisation. For this reason they may not be sufficient to capture the failure of flood embankments. The paper presents a probabilistic approach for the stability analysis of flood embankments taking into account the probabilistic distribution of soil hydro-mechanical properties. The approach is validated against the failure case study of the Adige river embankment in Italy, by comparing the probability of failure of two sections, within and outside the failure segment respectively.

Correction to: Frequency domain approach for probabilistic flutter analysis using stochastic finite elements

Due to an unfortunate turn of events, this article was published with a erroneous version of Table 1.

Application of Probabilistic and Machine Learning Models for Groundwater Potentiality Mapping in Damghan Sedimentary Plain, Iran

Groundwater is one of the most important natural resources, as it regulates the earth’s hydrological system. The Damghan sedimentary plain area, located in the region of a semi-arid climate of Iran, has very critical conditions of groundwater due to massive pressure on it and is in need of robust models for identifying the groundwater potential zones (GWPZ). The main goal of the current research is to prepare a groundwater potentiality map (GWPM) considering the probabilistic, machine learning, data mining, and multi-criteria decision analysis (MCDA) approaches. For this purpose, 80 wells collected from the Iranian groundwater resource department and field investigation with global positioning system (GPS), have been selected randomly and considered as the groundwater inventory datasets. Out of 80 wells, 56 (70%) wells have been brought into play for modeling and 24 (30%) for validation purposes. Elevation, slope, aspect, convergence index (CI), rainfall, drainage density (Dd), distance to river, distance to fault, distance to road, lithology, soil type, land use/land cover (LU/LC), normalized difference vegetation index (NDVI), topographic wetness index (TWI), topographic position index (TPI), and stream power index (SPI) have been used for modeling purpose. The area under the receiver operating characteristic (AUROC), sensitivity (SE), specificity (SP), accuracy (AC), mean absolute error (MAE), and root mean square error (RMSE) are used for checking the goodness-of-fit and prediction accuracy of approaches to compare their performance. In addition, the influence of groundwater determining factors (GWDFs) on groundwater occurrence was evaluated by performing a sensitivity analysis model. The GWPMs, produced by technique for order preference by similarity to ideal solution (TOPSIS), random forest (RF), binary logistic regression (BLR), weight of evidence (WoE) and support vector machine (SVM) have been classified into four categories, i.e., low, medium, high and very high groundwater potentiality with the help of the natural break classification methods in the GIS environment. The very high groundwater potentiality class is covered 15.09% for TOPSIS, 15.46% for WoE, 25.26% for RF, 15.47% for BLR, and 18.74% for SVM of the entire plain area. Based on sensitivity analysis, distance from river, and drainage density represent significantly effects on the groundwater occurrence. validation results show that the BLR model with best prediction accuracy and goodness-of-fit outperforms the other five models. Although, all models have very good performance in modeling of groundwater potential. Results of seed cell area index model that used for checking accuracy classification of models show that all models have suitable performance. Therefore, these are promising models that can be applied for the GWPZs identification, which will help for some needful action of these areas.

Frequency domain approach for probabilistic flutter analysis using stochastic finite elements

In this work, a stochastic finite element method based on first order perturbation approach is developed for the probabilistic flutter analysis of aircraft wing in frequency domain. Here, both bending and torsional stiffness parameters of the wing are treated as Gaussian random fields and represented by a truncated Karhunen–Loeve expansion. The aerodynamic load on the wing is modeled using Theodorsen’s unsteady aerodynamics based strip theory. In this approach, Theodorsen’s function, which is a complex function of reduced frequency, is also treated as a random field. The applicability of the present method is demonstrated by studying the probabilistic flutter of cantilever wing with stiffness uncertainties. The present method is also validated by comparing results with Monte Carlo simulation (MCS). From the analysis, it is observed that torsional stiffness uncertainty has significant effect on the damping ratio and frequency of the flutter mode as compared to bending stiffness uncertainty. The probability density functions of damping ratio and frequency using perturbation technique and MCS are also discussed at various free stream velocities due to stiffness uncertainties. Furthermore, the flutter probability of the cantilever wing is studied by defining implicit limit state function in conditional sense on flow velocity for the flutter mode. Both perturbation and MCS are considered to study the flutter probability of the wing. From the cumulative distribution functions of flutter velocity, it is noticed that the presence of uncertainty in torsional rigidity lowers the predicted flutter velocity in comparison to uncertainty in bending rigidity.

Cost-Benefit Analysis for Supporting Intermunicipal Decisions on Drinking Water Supply

Several countries promote a regionalization of the drinking water sector; however, few decision support tools are adapted to the intermunicipal level to aid in regional decisions. The aim of this paper is to describe and demonstrate a probabilistic cost-benefit analysis approach to assess the societal effects of regional water supply interventions to constitute support for decision makers. A special focus is given to the quantification of effects on consumers’ health, water supply reliability, and operation and maintenance costs. The uncertainties of the quantified values are represented by probability distribution functions and analyzed by means of Monte Carlo simulations. The proposed approach was demonstrated in the Goteborg region in Sweden, for which five alternative interventions were evaluated. In conclusion, the proposed approach facilitates the identification and prioritization of societal effects so that costs and benefits normally overlooked in evaluation processes can be explicitly considered and addressed. The paper provides a transparent handling of uncertainties and enables a structured approach to improve decision makers’ ability in making informed choices on regional water supply alternatives.

Life-cycle probabilistic geotechnical model for energy piles

Although energy piles are widely used worldwide as green foundations, currently no approach is available to quantify the design uncertainties in their long-term performance. Based on the cyclic load-transfer curves, this paper presents a probabilistic model for life-cycle analysis of energy piles under seasonal thermal loading. For computational efficiency, the subdomain sampling method is adopted for estimating the failure probability due to excessive settlement, and is compared with Monte Carlo simulation. This probabilistic analysis approach for energy piles is illustrated through a case study. The life-cycle failure probability of energy piles for various mechanical loading and thermal loading scenarios is investigated.

A novel extension of DEMATEL approach for probabilistic safety analysis in process systems

Quantitative risk assessment (QRA) techniques methodically assess the likelihood, impact, and subsequently the risk of adverse events. In a typical QRA method, one of the main intentions is to identify the critical root events which mostly contribute to the risk of the top event (TE) and requiring subsequent corrective actions (CAs). Finding the critical events which contribute to the risk is significantly dependent on the assumptions and methods applied to integrate the probabilities of different events and these events may have really low probability of occurrence. Thus, the probability reduction of the critical root events and subsequently the system’s failure does not lead to an optimal solution. For this reason, ranking the CAs without consideration of several aspects such as their influence on root events probability, inter-relationships, and direct/indirect cost, is not an appropriate approach. This study aims to introduce an approach to deal with the aforementioned situations. A novel extension to DEMATEL (decision making trial and evaluation laboratory) named Pythagorean fuzzy DEMATEL is proposed on a common probabilistic safety analysis. As a case study, a collapse in an offshore facility platform (including 42 basic events and corresponding 30 CAs) is considered to illustrate the effectiveness of the presented approach. The application of the model confirms its robustness in prioritizing critical root events and CAs compared with a conventional model, consideration of the influencing factors, and a dynamic and flexible structure.

Activity in human visual areas reflects the precision of motion perception

Any neural representation of a visual stimulus is necessarily uncertain, due to sensory noise and ambiguity in the inputs. Recent advances in fMRI decoding provide a principled approach for estimating the amount of uncertainty in cortical stimulus representations (van Bergen, Ma, Pratte & Jehee, 2015, Nature Neuroscience). However, these previous findings were limited to orientation perception. We here demonstrate that a similar decoding approach can be used to characterize the degree of uncertainty in cortical representations of motion. Participants viewed stimuli consisting of dots that moved coherently into a random direction, while their brain activity was measured with fMRI. Shortly after the dots disappeared from the screen, observers reported the direction of motion. Using a probabilistic analysis approach, we decoded the posterior probability distribution of motion direction from activity in visual areas V1–V4, and hMT+. We found that the decoded posterior distributions were generally bimodal, with two distinct peaks separated by roughly 180 degrees. One peak was reliably larger than the other, and centered on the true direction of stimulus motion. This bimodality suggests that the decoded distributions reflected not only motion, but also orientation information in the patterns of cortical activity. To assess the degree to which the decoded distributions reflected perceptual uncertainty, we computed the entropy of the decoded distributions. We compared this measure of uncertainty with behavioral variability, reasoning that a more precise representation in cortex should result in less variable (more precise) behavior. We found that uncertainty decoded from visual cortex was linked to participant behavior. Specifically, the entropy of the decoded distributions reliably predicted the variability in the observers’ estimates of motion direction. This suggests that the precision of motion perception can be reliably extracted from activity in human visual cortex.

Bayesian pharmacokinetic modeling of dynamic contrast-enhanced magnetic resonance imaging: validation and application

Tracer-kinetic analysis of dynamic contrast-enhanced magnetic resonance imaging data is commonly performed with the well-known Tofts model and nonlinear least squares (NLLS) regression. This approach yields point estimates of model parameters, uncertainty of these estimates can be assessed e.g. by an additional bootstrapping analysis. Here, we present a Bayesian probabilistic modeling approach for tracer-kinetic analysis with a Tofts model, which yields posterior probability distributions of perfusion parameters and therefore promises a robust and information-enriched alternative based on a framework of probability distributions. In this manuscript, we use the quantitative imaging biomarkers alliance (QIBA) Tofts phantom to evaluate the Bayesian tofts model (BTM) against a bootstrapped NLLS approach. Furthermore, we demonstrate how Bayesian posterior probability distributions can be employed to assess treatment response in a breast cancer DCE-MRI dataset using Cohen’s d. Accuracy and precision of the BTM posterior distributions were validated and found to be in good agreement with the NLLS approaches, and assessment of therapy response with respect to uncertainty in parameter estimates was found to be excellent. In conclusion, the Bayesian modeling approach provides an elegant means to determine uncertainty via posterior distributions within a single step and provides honest information about changes in parameter estimates.

A FORM‐based approach for probabilistic analysis in geotechnics: Application to a reinforced concrete drainage culvert

SummaryAs numerical models are increasingly used as a design tool in geotechnical engineering, it is highly desirable if geotechnical reliability analysis can be conducted based on numeral models. Currently, the practical use of geotechnical reliability analysis‐based numerical models is still quite limited. In this study, an easy to access method is derived to conduct geotechnical reliability analysis based on numerical models. To facilitate its application, a procedure is outlined to implement the suggested method such that geotechnical reliability analysis can be automated using existing geotechnical numerical packages. The procedure is illustrated in detail with an example, and the source codes provided can be easily adapted to analyze other similar problems. The method described in this paper is used to study the reliability of a deteriorating reinforced concrete drainage culvert in Shanghai, China. The suggested method provides a convenient means for reliability analysis of complex geotechnical problems.

Probabilistic approach for open pit bench slope stability analysis – A mine case study

The geotechnical slope design of an open pit wall starts at the bench scale configuration. At this scale, the rock slope stability is governed primarily by the geological discontinuities within the rock mass and as a result, structurally-controlled failures (e.g. planar, wedge or toppling) are most likely to occur. The probabilistic approach offers a major advantage over the traditional deterministic method in that it accounts for the different degrees of variability and uncertainty often encountered in rock properties. This paper presents a bench slope stability assessment for an open pit mine in Peru using a probabilistic-based approach by coupling a kinematic analysis based on stereographic projection techniques followed by a kinetic analysis by means of the limit equilibrium method. Finally, these two probabilities are combined to provide an overall measure of the probability of failure (PoF) of the bench slope system. The case study is characterized by significant scatter in the geometrical and mechanical properties of the joints. Extensive surface mapping was conducted at 36 different sites following the ISRM suggested procedures. Several direct shear tests were carried out. It is shown that by combining field and laboratory measurements and engineering judgment, the probability density functions (PDF) of the discontinuity parameters can be obtained. These are then used in a Monte Carlo simulation process to compute both kinematic and kinetic probabilities of failure. The overall probability of failure aims to provide the design engineer with a tool to critically evaluate the bench performance from a geotechnical risk perspective and to provide a basis for future bench design optimization.

Monte Carlo approach to fuzzy AHP risk analysis in renewable energy construction projects.

The construction of large renewable energy projects is characterized by the great uncertainties associated with their administrative complexity and their constructive characteristics. For proper management, it is necessary to undertake a thorough project risk assessment prior to construction. The work presented in this paper is based on a hierarchical risk structure identified by a group of experts, from which a Probabilistic Fuzzy Sets with Analysis Hierarchy Process (PFSAHP) was applied. This probabilistic analysis approach used expert opinion based on the Monte Carlo Method that allows for extracting more information from the original data. In addition, the coherence of the experts’ opinions is assessed using a novel parameter known as Confidence Level, which allows for adjusting the opinions of experts and weighting their judgments regarding impact and probability according to their coherence. This model has the advantage of offering a risk analysis in the early stages of the management of renewable energy projects in which there is no detailed information. This model is also more accurate than the classic fuzzy methodology when working with complete distribution functions, whilst it avoids the loss of information that results from the traditional mathematical operations with Fuzzy numbers. To test the model, it was applied to a 250 MW photovoltaic solar plant construction project located in southeast of Spain (Region of Murcia). As a result of the application of the proposed method, risk rankings are obtained with respect to the cost, the time, the scope and from a general point of view of the project.

Probabilistic analysis and design of stabilizing piles in slope considering stratigraphic uncertainty

The uncertainty involved in the interpreted geological model may be categorized as the stratigraphic uncertainty and the properties uncertainty. Note that although the influence of the properties uncertainty on the behavior or performance of the geotechnical system and the geotechnical design has been extensively reported in the literature, the studies that address the stratigraphic uncertainty are limited. This paper presents a study regarding the influence of the stratigraphic uncertainty on the behavior of the geotechnical system and the geotechnical design. In which, the uncertainty in the stratigraphic configuration is characterized using the stochastic Markov random field-based approach with a large number of potential stratigraphic realizations. With these stratigraphic realizations as inputs, the influence of the stratigraphic uncertainty on the behavior of the geotechnical system is evaluated in a probabilistic manner; then, the design of the geotechnical system is formulated as a bi-objective optimization-based problem that considers the design safety and the cost simultaneously. To demonstrate the effectiveness of the proposed probabilistic analysis and design approach, the problem of designing stabilizing piles in a slope consisting of multiple strata is studied. The parametric study is further conducted to analyze how the probabilistic analysis results are influenced by the pile parameters and how the probabilistic design results are influenced by the additional boreholes.

Probabilistic adaptive model predictive power pinch analysis (PoPA) energy management approach to uncertainty

This paper proposes a probabilistic power pinch analysis (PoPA) approach based on Monte–Carlo simulation (MCS) for energy management of hybrid energy systems uncertainty. The systems power grand composite curve is formulated with the chance constraint method to consider load stochasticity. In a predictive control horizon, the power grand composite curve is shaped based on the pinch analysis approach. The robust energy management strategy effected in a control horizon is inferred from the likelihood of a bounded predicted power grand composite curve, violating the pinch. Furthermore, the response of the system using the energy management strategies (EMS) of the proposed method is evaluated against the day-ahead (DA) and adaptive power pinch strategy.