Advanced Probabilistic Methods Research Articles

ProPTV: A probability-based particle tracking velocimetry framework

We present proPTV, a comprehensive framework for particle tracking velocimetry. The framework is an open-source software project and written in Python. It provides the user with all tools needed to process raw camera images of a particle-seeded flow in order to reconstruct the particle dynamics and to assimilate pressure fields. The advanced probabilistic tracking method enables accurate reconstruction of the most probable particle trajectories. Its performance is studied applying it to the numerical test case of turbulent Rayleigh-Bénard convection (Pr=6.9, Ra=1010) in a cubic cell generated by direct numerical simulation. For the highest tracer particle density of about 0.125ppp of this test case, 83% of the reconstructed tracks are correct. To check the performance also for experimental data, proPTV is additionally applied to particle measurements of turbulent Rayleigh-Bénard convection in a water-filled cell for similar Ra- and Pr-numbers as the numerical test case. Thereby, a tracer particle density of about 0.02 ppp is estimated. The obtained results are then compared with those obtained using LaVision's commercial particle tracking software DaVis (v10.2.1). Both frameworks provide velocity fields that have small deviations. However, the particle tracks generated by proPTV are on average 5 times longer than those generated with DaVis. proPTV including the numerical test case is available at: https://github.com/RobinBarta/proPTV.

Modeling of horizontal pleiotropy identifies possible causal gene expression in systemic lupus erythematosus.

Systemic lupus erythematosus (SLE) is a chronic autoimmune condition with complex causes involving genetic and environmental factors. While genome-wide association studies (GWASs) have identified genetic loci associated with SLE, the functional genomic elements responsible for disease development remain largely unknown. Mendelian Randomization (MR) is an instrumental variable approach to causal inference based on data from observational studies, where genetic variants are employed as instrumental variables (IVs). This study utilized a two-step strategy to identify causal genes for SLE. In the first step, the classical MR method was employed, assuming the absence of horizontal pleiotropy, to estimate the causal effect of gene expression on SLE. In the second step, advanced probabilistic MR methods (PMR-Egger, MRAID, and MR-MtRobin) were applied to the genes identified in the first step, considering horizontal pleiotropy, to filter out false positives. PMR-Egger and MRAID analyses utilized whole blood expression quantitative trait loci (eQTL) and SLE GWAS summary data, while MR-MtRobin analysis used an independent eQTL dataset from multiple immune cell types along with the same SLE GWAS data. The initial MR analysis identified 142 genes, including 43 outside of chromosome 6. Subsequently, applying the advanced MR methods reduced the number of genes with significant causal effects on SLE to 66. PMR-Egger, MRAID, and MR-MtRobin, respectively, identified 13, 7, and 16 non-chromosome 6 genes with significant causal effects. All methods identified expression of PHRF1 gene as causal for SLE. A comprehensive literature review was conducted to enhance understanding of the functional roles and mechanisms of the identified genes in SLE development. The findings from the three MR methods exhibited overlapping genes with causal effects on SLE, demonstrating consistent results. However, each method also uncovered unique genes due to different modelling assumptions and technical factors, highlighting the complementary nature of the approaches. Importantly, MRAID demonstrated a reduced percentage of causal genes from the Major Histocompatibility complex (MHC) region on chromosome 6, indicating its potential in minimizing false positive findings. This study contributes to unraveling the mechanisms underlying SLE by employing advanced probabilistic MR methods to identify causal genes, thereby enhancing our understanding of SLE pathogenesis.

Assessing the Quality of Student-Generated Content at Scale: A Comparative Analysis of Peer-Review Models

Engaging students in creating learning resources has demonstrated pedagogical benefits. However, to effectively utilize a repository of student-generated content (SGC), a selection process is needed to separate high- from low-quality resources as some of the resources created by students can be ineffective, inappropriate, or incorrect. A common and scalable approach is to use a peer-review process where students are asked to assess the quality of resources authored by their peers. Given that judgments of students, as experts-in-training, cannot wholly be relied upon, a redundancy-based method is widely employed where the same assessment task is given to multiple students. However, this approach introduces a new challenge, referred to as the consensus problem: How can we assign a final quality to a resource given ratings by multiple students? To address this challenge, we investigate the predictive performance of 18 inference models across five well-established categories of consensus approaches for inferring the quality of SGC at scale. The analysis is based on the engagement of 2141 undergraduate students across five courses in creating 12 803 resources and 77 297 peer reviews. Results indicate that the quality of reviews is quite diverse, and students tend to overrate. Consequently, simple statistics such as mean and median fail to identify poor-quality resources. Findings further suggest that incorporating advanced probabilistic and text analysis methods to infer the reviewers' reliability and reviews' quality improves performance; however, there is still an evident need for instructor oversight and training of students to write compelling and reliable reviews.

Global diversity dynamics in the fossil record are regionally heterogeneous

Global diversity patterns in the fossil record comprise a mosaic of regional trends, underpinned by spatially non-random drivers and distorted by variation in sampling intensity through time and across space. Sampling-corrected diversity estimates from spatially-standardised fossil datasets retain their regional biogeographic nuances and avoid these biases, yet diversity-through-time arises from the interplay of origination and extinction, the processes that shape macroevolutionary history. Here we present a subsampling algorithm to eliminate spatial sampling bias, coupled with advanced probabilistic methods for estimating origination and extinction rates and a Bayesian method for estimating sampling-corrected diversity. We then re-examine the Late Permian to Early Jurassic marine fossil record, an interval spanning several global biotic upheavals that shaped the origins of the modern marine biosphere. We find that origination and extinction rates are regionally heterogenous even during events that manifested globally, highlighting the need for spatially explicit views of macroevolutionary processes through geological time.

Uncertainty Quantification Analysis of Wind Power: A Data-Driven Monitoring-Forecasting Framework

Advances in wind power system modeling have produced widespread socioeconomic benefits for alleviating global environmental problems. However, previous studies mainly payed attention to point forecasts of wind power system, with the absence of its uncertainty quantification analysis and outlier detection, which cannot facilitate further development in this field. In this paper, a novel monitoring-forecasting system, including the analysis module, the outlier detection module, the probabilistic forecasting module, and the evaluation module, is proposed for uncertainty modeling of wind power. In the analysis module, recurrence analysis techniques are developed, aiming at characterizing complicated patterns of wind power. Furthermore, the interval partitioning-based isolation forest algorithm, which can effectively address the effects of swamping and masking, is first developed in the outlier detection module for wind power. Superior to the traditional point forecasting method that cannot perform quantitative characterization of the intrinsic uncertainties in wind power forecasting, an advanced probabilistic forecasting method based on Gaussian process regression (GPR) with an optimal kernel function scenario, cooperating with a feature selection method, is first presented in the probabilistic forecasting module, indicating that the forecast skill of GPR is significantly enhanced. Finally, the proposed system is validated using real wind power data with high resolution from Spain in the evaluation module, solidly demonstrating its high reliability and flexibility compared to benchmarks considered in this study.

Risk-based decision making and the calibration of structural design codes – prospects and challenges

ABSTRACTTo date, our built environment is broadly developed and maintained on the basis of structural design standards. Most design standards contain simplified semi-probabilistic safety concepts that help daily structural engineering decision making using simple calculus. For few projects, the semi-probabilistic safety concept is replaced by advanced probabilistic methods that allow for reliability-based design. Neither include explicit consideration of optimality criteria. However, for the development and the calibration of the semi-probabilistic and probabilistic safety concepts it is important that societal preferences in regard to risk acceptance and the optimal use of natural resources are explicitly considered. In the present contribution, the development and calibration of semi-probabilistic and probabilistic structural design standards is represented as a formal decision problem allowing an optimal combination of reliability elements to be identified.

Stability Analysis of a Large Gold Mine Open-Pit Slope Using Advanced Probabilistic Method

A large gold reserve was recently discovered at Haveri district of Karnataka state of India where open-pit mining was planned to extract these deposits. Stability analysis for open-pit mine slope at this site is presented in the article. Extensive geological investigations and laboratory testing suggested high variability in geological features of discontinuities, rock mass quality and intact rock properties. Hence, it was decided to perform stability analysis of the rock slope using probabilistic approach along with deterministic approach. Deterministic analysis was carried out with average properties of rock, and reliability analysis of the rock slope was carried out using both traditional and advanced probabilistic methods. In traditional probabilistic method, rock mass strength properties were treated as random variables without considering spatial variation of rock properties and reliability index was evaluated by Monte Carlo (MC) simulation on augmented radial basis function-based response surface. In advanced probabilistic analysis, spatial variability of rock mass strength properties was considered by generating anisotropic random field using Fourier series method with spatial averaging over finite difference zones. Reliability index was then estimated by performing MC simulation using random finite difference method. A comparison was provided between the results of stability analysis of slope from all these approaches. Rock slope was found to be stable in both deterministic and probabilistic approaches; however, the degree of stability predicted was different for both methods. Deterministic approach was found to be inappropriate to analyse the stability of slope having rock mass with variable properties. Further, reliability index and expected performance level of slope were highly underestimated by traditional probabilistic method as compared to advanced probabilistic method.

Probabilistic design of fibre concrete structures

Advanced computer simulation is recently well-established methodology for evaluation of resistance of concrete engineering structures. The nonlinear finite element analysis enables to realistically predict structural damage, peak load, failure, post-peak response, development of cracks in concrete, yielding of reinforcement, concrete crushing or shear failure. The nonlinear material models can cover various types of concrete and reinforced concrete: ordinary concrete, plain or reinforced, without or with prestressing, fibre concrete, (ultra) high performance concrete, lightweight concrete, etc. Advanced material models taking into account fibre concrete properties such as shape of tensile softening branch, high toughness and ductility are described in the paper. Since the variability of the fibre concrete material properties is rather high, the probabilistic analysis seems to be the most appropriate format for structural design and evaluation of structural performance, reliability and safety. The presented combination of the nonlinear analysis with advanced probabilistic methods allows evaluation of structural safety characterized by failure probability or by reliability index respectively. Authors offer a methodology and computer tools for realistic safety assessment of concrete structures; the utilized approach is based on randomization of the nonlinear finite element analysis of the structural model. Uncertainty of the material properties or their randomness obtained from material tests are accounted in the random distribution. Furthermore, degradation of the reinforced concrete materials such as carbonation of concrete, corrosion of reinforcement, etc. can be accounted in order to analyze life-cycle structural performance and to enable prediction of the structural reliability and safety in time development. The results can serve as a rational basis for design of fibre concrete engineering structures based on advanced nonlinear computer analysis. The presented methodology is illustrated on results from two probabilistic studies with different types of concrete structures related to practical applications and made from various materials (with the parameters obtained from real material tests).

An Advanced Bayesian Method for Short-Term Probabilistic Forecasting of the Generation of Wind Power

Currently, among renewable distributed generation systems, wind generators are receiving a great deal of interest due to the great economic, technological, and environmental incentives they involve. However, the uncertainties due to the intermittent nature of wind energy make it difficult to operate electrical power systems optimally and make decisions that satisfy the needs of all the stakeholders of the electricity energy market. Thus, there is increasing interest determining how to forecast wind power production accurately. Most the methods that have been published in the relevant literature provided deterministic forecasts even though great interest has been focused recently on probabilistic forecast methods. In this paper, an advanced probabilistic method is proposed for short-term forecasting of wind power production. A mixture of two Weibull distributions was used as a probability function to model the uncertainties associated with wind speed. Then, a Bayesian inference approach with a particularly-effective, autoregressive, integrated, moving-average model was used to determine the parameters of the mixture Weibull distribution. Numerical applications also are presented to provide evidence of the forecasting performance of the Bayesian-based approach.

Stochastic assessment for the behaviour of systems of dry soil mix columns

The mechanical properties of dry soil mix (DSM) columns can be highly variable. Variability can be accounted for in the construction specification for deterministic design and directly in reliability based design. Design methods and specifications to date adopt simplifications that do not take the variability of the columns fully into account. This paper uses both simple and advanced probabilistic methods to assess the performance/failure and system redundancy of dry soil mix columns. Reliability-based design methods and examples are given for the design of column strength and the adjustment of the column spacing to achieve a target probability of unacceptable performance or failure. An acceptance criteria chart is developed. The pull-out resistance tests on the DSM columns constructed for the Ballina Bypass motorway construction project in NSW Australia are compared to the chart to provide guidance with respect to acceptance criteria required to achieve the desired performance.

FULLY PROBABILISTIC DUNE SAFETY ASSESSMENT USING AN ADVANCED PROBABILISTIC METHOD

In this paper, an advanced probabilistic method - Adaptive Directional Importance Sampling (ADIS) - is used in concert with a process-based dune erosion model - XBeach - to perform a dune safety assessment. The efficiency of the probabilistic method removes the restriction of only using simple empirical dune erosion models for probabilistic calculations. The proposed combination of ADIS and XBeach is able to handle complex cross-shore profiles that empirical dune erosion models cannot, as shown in several case studies.

Probabilistic aspects of finance

In the past decades, advanced probabilistic methods have had significant impact on the field of finance, both in academia and in the financial industry. Conversely, financial questions have stimulated new research directions in probability. In this survey paper, we review some of these developments and point to some areas that might deserve further investigation. We start by reviewing the basics of arbitrage pricing theory, with special emphasis on incomplete markets and on the different roles played by the "real-world" probability measure and its equivalent martingale measures. We then focus on the issue of model ambiguity, also called Knightian uncertainty. We present two case studies in which it is possible to deal with Knightian uncertainty in mathematical terms. The first case study concerns the hedging of derivatives, such as variance swaps, in a strictly pathwise sense. The second one deals with capital requirements and preferences specified by convex and coherent risk measures. In the final two sections we discuss mathematical issues arising from the dramatic increase of algorithmic trading in modern financial markets.

Probabilistic Aspects of Finance

In the past decades, advanced probabilistic methods have had significant impact on the field of finance, both in academia and in the financial industry. Conversely, financial questions have stimulated new research directions in probability. In this survey paper, we review some of these developments and point to some areas that might deserve further investigation. We start by reviewing the basics of arbitrage pricing theory, with special emphasis on incomplete markets and on the different roles played by the 'real-world' probability measure and its equivalent martingale measures. We then focus on the issue of model ambiguity, also called Knightian uncertainty. We present two case studies in which it is possible to deal with Knightian uncertainty in mathematical terms. The first case study concerns the hedging of derivatives, such as variance swaps, in a strictly path wise sense. The second one deals with capital requirements and preferences specified by convex and coherent risk measures. In the final two sections we discuss mathematical issues arising from the dramatic increase of algorithmic trading in modern financial markets.

Time-Dependent Reliability of PSC Box-Girder Bridge Considering Creep, Shrinkage, and Corrosion

Bridge performance undergoes time-varying changes when exposed to aggressive environments. While much work has been done on bridge reliability under corrosion, little is known about the effects of creep and shrinkage on the reliability of concrete bridges. In this paper, the CEB-FIP model for creep and shrinkage is applied by using finite-element (FE) analysis in conjunction with probabilistic considerations. Verification is made by comparing the analytical findings with existing test data. More specifically, a time-dependent reliability assessment is made for a composite prestressed concrete (PSC) box-girder bridge exposed to a chloride environment. This realized via an advanced probabilistic FE method. The postcracking behavior of the thin-walled box girder is described using composite degenerated shell elements, and importance sampling is used to improve the efficiency of the reliability analyses. It is shown that concrete creep and shrinkage dominate during the early stages of bridge structure deterio...

Influence of Spatial Variability on Slope Reliability Using 2-D Random Fields

The paper investigates the probability of failure of slopes using both traditional and more advanced probabilistic analysis tools. The advanced method, called the random finite-element method, uses elastoplasticity in a finite-element model combined with random field theory in a Monte-Carlo framework. The traditional method, called the first-order reliability method, computes a reliability index which is the shortest distance (in units of directional equivalent standard deviations) from the equivalent mean-value point to the limit state surface and estimates the probability of failure from the reliability index. Numerical results show that simplified probabilistic analyses in which spatial variability of soil properties is not properly accounted for, can lead to unconservative estimates of the probability of failure if the coefficient of variation of the shear strength parameters exceeds a critical value. The influences of slope inclination, factor of safety (based on mean strength values), and cross correlation between strength parameters on this critical value have been investigated by parametric studies in this paper. The results indicate when probabilistic approaches, which do not model spatial variation, may lead to unconservative estimates of slope failure probability and when more advanced probabilistic methods are warranted.

Usage of meshfree methods in reliability analysis

This paper describes the use of meshfree methods for response and design sensitivity calculations within structural reliability analysis when geometric shape is a random variable. Brief descriptions of meshfree methods and advanced probabilistic methods are provided. An existing interface between the probabilistic analysis and traditional finite element method is modified to allow the use of meshfree methods for response and design sensitivity calculations within the probabilistic analysis routine. Three examples that treat design shape and thickness as random variables are presented to assess the accuracy and use of meshfree methods for reliability analysis.

NUMERICAL PROBABILISTIC ANALYSIS OF STRUCTURAL/ACOUSTIC SYSTEMS1*

ABSTRACT A methodology that accounts for structural variability in the acoustic response of structural/acoustic systems is presented. The new methodology integrates an advanced mean value first-order probabilistic method with finite element analysis (FEA) and boundary element analysis (BEA) in order to compute the probabilistic acoustic response of a structural/acoustic system subjected to a deterministic excitation. The advanced mean value (AMV) method is used to evaluate the probabilistic response from a linear response surface that is corrected for higher-order terms. FEA and BEA are combined for computing the performance function (i.e., acoustic response) each time that it is requested by the AMV algorithm. The AMV/FEA/BEA methodology is used to illustrate the difference between the probabilistic response of a system and the equivalent deterministic simulation through examples. The interaction between the distinct acoustic normal modes and the structural normal modes that shift due to structural variability constitutes the main source of the difference between the probabilistic and deterministic acoustic results. The non-monotonic nature of the structural/acoustic response is also considered in this development. Results are validated using a Monte Carlo simulation and a standard radius-based importance-sampling algorithm. On the basis of computational time and accuracy, the methodology is concluded to be a viable method of numerically calculating the probabilistic acoustic response of a structural/acoustic system due to structural variability. *Communicated by F. Ziegler

Concrete strength and durability of prototype tetrapods and dolosse: results of field and laboratory tests

A number of destructive and nondestructive tests have been carried out on 15 t slender-type concrete armour blocks from three Italian breakwaters, in order to investigate the material properties after a long-term exposure at sea. Measured surface hardness from rebound hammer tests in situ appears to be correlated to the results of laboratory breakage tests on core samples. The core position on the unit shows to have an influence on the concrete strength, with weaker points generally occurring at legs' intersections. Further laboratory results from porosity, carbonatation and ultrasonic pulse velocity tests and finally from destructive split-out tests on core samples generally show the good quality of aged pozolanic marine concretes, as typically used in Italian coastal structures. Despite the data scatter, also due to the necessarily limited number of cores, the average value of the tensile strength achieves 4 MPa (with a variation coefficient around 20%) and increases with concrete density (mean value of 24.5 kN with variation coefficient of 2%). These test results from prototype armour blocks can be useful for the application of advanced probabilistic methods for the design of rubble mound breakwaters.