Applications of Stochastic Analyses for Collaborative Learning and Cognitive Assessment

Fatigue crack growth (FCG) in welded joints of orthotropic steel decks (OSDs) is highly stochastic, which complicates the accurate assessment of fatigue reliability. To consider the stochastic factors affecting fatigue performance in welded joints, this study proposed a stochastic FCG analysis method that incorporates machine learning to evaluate the fatigue reliability. Firstly, a probabilistic model for fatigue stress spectrum in welded joints was developed using site-specific traffic data. Subsequently, stochastic FCG analysis method assisted by a random forest model was developed to replace the time-consuming finite element solution. Finally, a fracture limit state function was established to evaluate fatigue reliability with consideration of the stochastic FCG process. Results indicate that a lognormal distribution accurately fits fatigue characteristic of the equivalent stress intensity factor range, with mean values consistently lower at the crack tip compared to the crack edge. Additionally, the deterioration rate of welded joints accelerates significantly at a crack depth of 5 mm, resulting in a shift of the remaining fatigue life distribution from lognormal to exponential. The reliability indices decrease significantly under overloading conditions. A 20% increase in vehicle weight reduces the fatigue life from the expected 100 years to 82 years.

Power system stability has become an increasing concern in renewable power integration because the active power generated by renewable energy varies randomly. Thus, we focus on random outside excitations in this study. Since the power obeys Non‐Gaussian distribution in most case, a novel small disturbance stochastic stability analysis method based on entropy is presented. First, the dynamic model of power system with random outside excitation is established by stochastic differential equation. Then, the values of mean and mean square stability are efficiently derived by transforming the stochastic differential equation into a deterministic mean or variance equation. For non‐Gaussian disturbance, entropy stability is presented by this transformation. At last, the numerical simulations are presented on a WSCC three‐generator nine‐bus power system with a wind farm © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

A new, efficient algorithm is developed for the sensitivity analysis of a class of continuous-time recurrent neural networks with additive noise signals. The algorithm is based on the stochastic sensitivity analysis method using the variational approach, and formal expressions are obtained for the functional derivative sensitivity coefficients. The present algorithm uses only the internal states and noise signals to compute the gradient information needed in the gradient descent method, where the evaluation of derivatives is not necessary. In particular, it does not require the solution of adjoint equations of the back-propagation type. Thus, the algorithm has the potential for efficiently learning the network weights with significantly fewer computations. The effectiveness of the algorithm in a statistical sense is shown, and the method is applied to the familiar layered network.

Multi-scale stochastic dynamic response analysis of offshore risers with lognormal uncertainties

Dynamic reliability analysis of slopes based on the probability density evolution method

The performance of a railway turnout (switch and crossing) is influenced by a large number of input parameters of the complex train–turnout system. To reach a robust design that performs well for different traffic situations, random distributions (scatter) of these inputs need to be accounted for in the design process. Stochastic analysis methods are integrated with a simulation model of the dynamic interaction between train and turnout. For a given nominal layout of the turnout, using design of experiments methodology and a two-level fractional factorial screening design, four parameters (axle load, wheel–rail friction coefficient, and wheel and rail profiles) are identified to be the most significant. These parameters are further investigated using a three-level full factorial design and stochastic analysis. The random distributions of transverse wheel profile and set of transverse rail profiles along the switch panel are accounted for by the Karhunen–Loève expansion technique. The influence of the random distributions of the input parameters on the statistical outputs of wheel–rail contact forces, wear and rolling contact fatigue is assessed using Latin hypercube sampling to generate a number of stochastic load realizations.

This paper describes the fatigue analysis of Kizomba 'A' FPSO based on the FPSO Fatigue Methodology Specification (FMS) [1] which is developed on the direct stochastic calculation. The FMS provides designers with technical guidance for fatigue control of newly built FPSO and can be characterized as integrated fatigue analysis to ensure the structural safety of all critical FPSO details by means of full stochastic analysis as well as component based one. At the cost of modeling complexity and computer resources, the full stochastic method gives the accurate fatigue damage for FPSO-specific details such as topside, piperack, flare etc., which are governed by hull-wave interactions. On the other hand, the component based one provides the cost-effective tools to screen the most fatigue prone area in topside supports for full stochastic analysis. Besides, the spectrum combination method that is suggested in order to consider both wave-line and wave-hull interactions, is adopted in fatigue damage calculation of the supports for FTL, OOL, riser and mooring. Apart from technical aspect, the interface management between other groups in charge of FPSO-hull, topside, riser and mooring system turns out very important due to tight project schedule. This paper proves the practical possibility and appropriateness of full stochastic fatigue analysis for FPSO and envisions its usefulness for other floating structures such as TLP, semisubmersibles and etc. The considered Kizomba 'A' FPSO to be installed on Angola Block 15 is 285 meters long, 63 meters wide, and 32 meters high, and can store 2.2 million barrels of crude oil in its lower hull facilities [2]. Introduction As the offshore oilfields shift into the deeper waters with little infrastructures, FPSOs have become the more popular solution. Currently one of the most active areas in FPSO installation is the West Africa where the weather is benign and the swell from the south is dominant. Whereas strength of the FPSO in such a calm site is mostly controlled on towing route, the fatigue control is directly dependent on the site-specific environment. It should be ensured that FPSOs could stay for decades without drydocking for maintenance. ExxonMobil has developed FPSO Fatigue Methodology Specification (FMS) with DNV for providing designers with technical guidance for fatigue control of newly built shipshaped FPSOs [3]. The aim of the fatigue control is to ensure that all critical structural details meet the fatigue design requirements. Also, the calculated fatigue lives form the basis of FPSO design and are used as inputs to the inspection plans during fabrication and in-service. The focus of the FMS is a full stochastic fatigue analysis method that gives the accurate fatigue damage for the FPSOspecific details like topside support, piperack, flare tower foundation etc. The structural behaviors of these supports are governed by wave-hull interactions and describable using linear analysis. The wave loads based on the metocean data of installation site are directly calculated and transferred to the structural model. Generally, full-ship structural model is utilized in the analysis. Figure 1 shows the general procedure of full stochastic fatigue analysis.

The aim of the study is to systematize current methods for assessing the economic efficiency of the best available food and agri-biotechnologies in domestic and international science and practice. The research applies methods of comparative analysis, systematization, and critical evaluation of scientific publications focused on the economic and environmental effectiveness of best available technologies (BAT). A classification-based approach was also employed to identify and group methods according to their orientation and application area. The empirical base includes regulatory documents, in particular, methodological guidelines for identifying technologies as BAT, national standards (GOST), and scientific publications on biotechnology, precision agriculture, organic waste processing, alternative protein sources, and more. The study examines methods such as investment feasibility analysis, life cycle environmental impact assessment, life cycle costing, multi-criteria decision analysis (MCDA), stochastic analysis, cluster analysis, among others. The findings demonstrate that integration of several methods enables assessment of both the financial and environmental viability of technology adoption. For example, in the case of cultivated meat, key indicators include both unit production cost and carbon footprint, which necessitates a shift from narrow economic assessment to eco-efficiency evaluation. The use of stochastic frontier analysis and clustering methods reveals that differences in farm efficiency are influenced not only by technology type, but also by the degree of its adoption. Overall, the systematization of methods for evaluating the efficiency of BAT indicates a clear trend toward transitioning from isolated economic indicators to comprehensive, data-driven approaches that combine economic and environmental metrics and validate results through empirical evidence.

Stochastic methods in quantum field theory and hydrodynamics

A household's financial satisfaction is one of the most significant factors driving subjective well-being. However, Poland ranks close to the lowest position, 22nd out of the 28 EU members, in self-reported financial status. The paper investigates the problem of determining patterns of Polish households' behaviour and shows the evolution of the subjective assessment of financial situation based on the eight waves of the Polish Household panel data. The analysis is carried out on the basis of latent Markov (LM) models, which allow for socio-economic features affecting the parameters of the latent process. We compare different types of LM models considering: (1) different numbers of latent structures; (2) different types of the latent process constraints; (3) socio-economic background characteristics; and (4) survey weights (being excluded in most of the empirical analyses). The final model identifies three latent states, specifies common initial and transition probabilities over a 15-year period and, as a result, enables us to better characterise the families likely to change their position, especially families reporting worsening in their financial situation. To show the main direction of self-reporting financial condition, we present the predicted path for respondents characterised by the selected socio-economic features, relying on algorithm maximising posterior probabilities of the selected LM model.

Natural gas should be distributed and consumed optimally in a given country since it is an important intermediate good for producers and a necessary final good for households with a low-income elasticity. Thus, this study aims to measure the efficiency of natural gas distribution companies responsible for delivering natural gas to economic units. The efficiency of 63 natural gas distribution companies operating in Turkey is estimated by the Stochastic Frontier Analysis method for 2013-2018. According to the findings, it is found that no firm operates within full efficiency. It is also concluded that while Bursa Natural Gas Distribution firm has the highest efficiency, Aksa Çanakkale Natural Gas Distribution firm has the lowest efficiency for the period studied. The findings show that inefficiency mainly stems from technical inefficiency rather than measurement errors and that natural gas distribution firms experience increasing returns to scale.

This paper presents a stochastic fracture analysis method for random non-homogenous cracked structures using the scaled boundary finite element method (SBFEM). The analyzed cracked domain is divided into polygon-based sub-domains such that the material property of each sub-domain can be modeled differently in the SBFEM. The spatial variability of the material property is represented as random field which is then incorporated directly into the coefficient matrices of the SBFEM. The stochastic global stiffness matrix and the stochastic equilibrium equation of the SBFEM through which the stochastic structural responses can be successfully calculated are further formulated. The stochastic stress intensity factors (SIFs) considering the spatial variability of the material property are then directly extracted from the stress solution of the cracked polygon. Numerical examples are given to demonstrate the validity of the proposed method and investigate the effect of the spatial distribution of the material property on the SIFs.

With the scale of wind power integration expanding continuously, the random characteristic of power system is more and more prominent due to the volatility and intermittency of wind energy. Because of the fluctuations brought by wind power integration, the traditional deterministic analysis methods and the conventional stochastic differential equations are difficult to accurately analyze wind power system. In this paper, Markov theory is utilized to establish a stochastic Markov dynamic model for wind power systems by considering various uncertainties. Then, based on the developed model, Lyapunov energy function and M matrix are combined together to present the analytical method of stochastic mean stability and stochastic mean square stability of wind power system. Compared with the conventional stochastic differential equation analysis method, the proposed method can overcome the shortcomings that the stochastic stability cannot be analyzed when the system operating conditions change. Finally, simulation results are provided to verify the validity and correctness of the proposed method.

Stochastic response analysis of the scaled boundary finite element method and application to probabilistic fracture mechanics

This paper presents an original essay that explains how managerial psychology affects the efficiency of transport firms. Stochastic frontier analysis methods are applied to our sample over a 12-year period from 2000 to 2011, where we aim to detect the potential effect of a well-documented bias in behavioral economic and finance theory: the managerial optimism bias. We initiate a debate concerning the potential role of Chief Executive Officers’ (CEO) irrationalities in explaining the inefficiency of public transport operators, such as the shortfall between the optimal production function and the observed production level. We find strong evidence of the negative impact of CEOs’ optimism bias on transport firms’ technical efficiency, meaning that managerial optimism decreases transport firms’ technical efficiency.