Probabilistic Analysis Method Research Articles

Asymptotic stability of fractional order switching nonlinear system based on short memory principle

AbstractFractional order derivatives have memory effects and are widely used in real world applications. However, they require large storage space and lead to low computational efficiency. Therefore, fractional order systems based on the short memory principle have gradually attracted the scholars' attention. In this paper, the asymptotic stability of Caputo fractional order switching nonlinear systems is investigated based on the Markov process and short memory principle. Firstly, a model of Caputo fractional order Markovian switching nonlinear systems (CFMNSs) based on the short memory principle is constructed so that the lower bound initial time and the corresponding initial state values are updated synchronously with switching. Secondly, the stability of the system is investigated based on the probabilistic analysis method and stochastic multi‐Lyapunov functions and the sufficient conditions for the asymptotic stability of the system are given. Using a similar method, we also study the asymptotic stability of CFMNs with variable fractional order. Finally, the simulation results show that the proposed stability scheme is effective and reasonable.

Study of Earthquake Hazard Probability Based on PGA (Peak Ground Acceleration) Using the PSHA Method in Semarang Regency, Indonesia

Semarang Regency was one of the areas affected by the earthquake. This happens because it is located north of the subduction zone and has active faults, so research is needed to identify the impact of earthquakes in Semarang Regency as an initial action in disaster mitigation efforts. This research aims to determine the distribution of PGA values in the Semarang Regency area and to assess the seismic hazard due to earthquakes based on a map of the distribution of PGA values in the Semarang Regency area. The method used is the Probabilistic Seismic Hazard Analysis (PSHA) method, which uses earthquake catalogues from BMKG, USGS, IRIS, and ISC. The earthquake source data was the n processed using ZMAP and R-CRISIS software. The results of seismic hazard analysis in the Semarang Regency area for a probability of exceeding 10% in 50 years or an earthquake return period of 475 years in bedrock with a period of 0 seconds obtained a PGA value ranging from 0.368–0.844 g, for a short period of 0.2 seconds the PGA value obtained ranged from 0.647. –1.773 g, for 1 second, the PGA value obtained ranges from 0.320–0.852 g. The highest PGA value is in West Ungaran District, with a value of 0.844 g. The lowest PGA value is in Kaliwungu District, which has a value of 0.458 g. The active fault zones influence the danger of earthquakes in the Semarang Regency area in Semarang Regency.

Quantitative analysis of subway station seismic deformation under random earthquakes and uncertain soil properties using the equivalent linearization method

The seismic performance of underground structures is strongly influenced by the characteristics of both the surrounding soil and the earthquake. In contrast to traditional deterministic analysis methods, this study uses a stochastic analysis approach to investigate the effect of uncertainties in nonlinear soil characteristics, shear wave velocity, density, and earthquake randomness on the response of underground stations. The equivalent linearization method is employed to approximate the nonlinear behavior of the soil. The soil was modeled using a linear elastic constitutive model combined with Rayleigh damping in the finite element model. Inter-story displacements are used to determine structural damage. Probabilistic analysis methods are used to obtain their statistical characteristics, and the probability of failure is calculated. The results show that, according to single parameter analysis, random ground motion results in the greatest probability of exceeding the threshold (PET), while ground shear wave velocity significantly affects the coefficient of variation (COV), and the effect of density is the smallest. The study also found that when soil nonlinearity, shear wave velocity, and random ground motion are considered simultaneously, the range, mean, standard deviation, and COV of interstory displacement all increase significantly, but the PET slightly decreases. In summary, the analysis results indicate that random ground motion has the greatest impact on interstory displacement, followed by shear wave velocity, with nonlinear soil characteristics having a smaller effect, and density the least. Therefore, the impact of various uncertainties should be fully considered in the analysis of underground structures, especially random ground motion and shear wave velocity.

Shale Fracture Static Stability Evaluation Method Based on 3D Discrete Fracture Model: A Case Study on the Luzhou Area in Southern Sichuan Basin, SW China

Abstract The stress interference in deep shale may lead to shale fracturing and instability and consequently results in engineering risks such as casing deformation in horizontal wells. Therefore, in the early stages of shale gas exploration and development, it is of great significance to evaluate the stability of shale fractures in advance. The stability evaluation of shale reservoir faults can be mainly divided into two categories at present: quantitative evaluation of single faults and qualitative evaluation of wide-range faults. The quantitative evaluation of single faults primarily relies on numerical simulation techniques, while the qualitative evaluation of wide-range faults primarily employs geophysical methods. Both methods are difficult to meet the needs of shale gas exploration and development. The shale fracture stability evaluation method based on 3D discrete fracture model which is developed in this article can quantitatively evaluate the static stability of wide-range shale fractures in the early stage of exploration and development. In this article, seismic geometric attributes were calculated, and fracture seismic facies was established by means of the Bayesian probabilistic cluster analysis method. Then, 3D discrete fracture modeling under the constraint of fracture seismic facies was performed to establish a discrete fracture model. Finally, according to the Mohr–Coulomb criterion, the shear stress and effective normal stress of discrete fracture were calculated by using the formation pressure data in other exploration and development results and the regional in situ stress obtained through seismic prestack inversion. And thus, the stability evaluation of the fractures in shale reservoirs was eventually completed. In addition, this method was verified by using the casing deformation points in some actual shale-gas horizontal wells, the actual small fault points, and microseismic data. It indicates that the method has higher accuracy and is better applicable to the early shale gas exploration and development.

A novel probabilistic analysis method for long-term dynamical response analysis

A novel probabilistic analysis method for long-term dynamical response analysis

A novel framework for debris flow susceptibility assessment considering the uncertainty of sample selection

The uncertainty arising from random sampling of non-debris flow samples significantly impacts the accuracy of debris flow susceptibility assessments (DFSA). This study introduces a novel uncertainty elimination method, Kernel Density Estimation (KDE), and compares it with Mean and Maximum Probability Analysis (MPA) methods. Furthermore, we investigate the responses of four commonly used machine learning models to sampling uncertainty, comparing two structurally similar models (Random Forest (RF) and Extremely Randomized Trees (ERT)) with two structurally different models (Support Vector Machine (SVM) and Multilayer Perceptron (MLP)). The results indicate that the application of these uncertainty elimination methods can significantly enhance AUC values and zoning accuracy, with the KDE method outperforming the others. Specifically, the AUC values based on KDE for RF, ERT, SVM, and MLP are 0.995, 0.999, 0.999, and 0.853, respectively. The corresponding zoning accuracy for these models is 1.00, 1.00, 1.00, and 0.78, respectively. The study further reveals that the responses to sampling uncertainty vary by model architecture: RF, ERT, and SVM typically exhibit bimodal normal distributions, while the MLP model shows a unimodal distribution. Additionally, MLP is more sensitive to variations in negative samples, whereas RF and ERT are less affected due to the ensemble structure.

Probabilistic seismic demand analysis for bridges based on earthquake scenarios

The current probabilistic seismic demand analysis of structures predominantly considers the correlation between the ground motion intensity measure (IM) and structural seismic demand, but fails to effectively capture regional source characteristics. It is essential to integrate earthquake engineering with seismic response of structures using source parameters to quantify regional ground motion uncertainties and determine appropriate IMs. This study presented a probabilistic seismic demand analysis method for structures based on earthquake scenarios, characterized by 1) utilizing the stochastic finite-fault method to simulate ground motions at a specific site instead of employing multiple seismic waves from different source areas, and 2) incorporating the correlation between IMs and the key indicator of source parameters, stress drop, into the probabilistic seismic demand analysis. Taking a continuous girder bridge as an example, the performance of the stress drop and 14 individual IMs in predicting the longitudinal seismic demand and reflecting source characteristics was evaluated. The results revealed that it was difficult to establish a reliable relationship between the stress drop and structural seismic demand. Owing to the complexities of ground motion and structural parameters, the individual IMs were challenging to effectively capture their characteristics simultaneously. Therefore, composite IMs have been proposed to cover the characteristics of both the source and seismic demand. The optimal solutions were derived using a multi-objective genetic algorithm, which exhibited desirable capabilities in both aspects, providing a comprehensive guide for the seismic performance assessment of regional transportation networks.

I-vector and variability compensation techniques for mobile phone recognition

Mobile phone recognition consists of trying to identify the mobile phone brand or model, which is very important in forensic analysis. In this paper, we exploit the audio recordings to realize this task. Audio data conveys many information, one of them is related to the source of records, i.e., is a specific audio was captured by a given mobile phone. In order to separate between this particular information and the rest of audio content, we introduce the I-vector technique. Additionally, Linear Discriminant Analysis (LDA) and Within-Class Covariance Normalization (WCCN) methods were used in different ways to compensate the speaker and channel variability. We evaluate the performance of our proposed system by correct rate recognition based on Gaussian Probabilistic Linear Discriminant Analysis (GPLDA) and Cosine Similarity Score (CSS) methods. To train the mobile phone models and do tests, two datasets were prepared: the public MOBIPHONE database and a novel local database. Experiments done with different configurations demonstrate the effectiveness of I-vectors models with the combination of LDA – WCCN compensation techniques and CSS as a similarity measurement method. A correct recognition rates of 97.23 %, 98.91 %, and 99.45 % were obtained for MOBIPHONE, the local Same Environment (SE) and Different Environment (DE) databases, respectively.

Data-model driven probability model of branch power flow for distribution networks and its application to analysis of overload and line loss

The fluctuation of highly penetrated distributed generations (DGs) in distribution networks (DNs) increases branch overload risks, which makes the analysis uncertainty of branch power flow more complex. The probability analysis of branch power can grasp the power flow operation characteristics under uncertain conditions, which supports the power flow optimization management and ensures the safe and economic operation of DNs. Therefore, this paper proposes a data-model driven probability analysis method for branch power flow in DNs. An approximate branch power model is first derived to reveal the analytical relationship between branch power and node power. Then, based on the branch power approximation model and the forecasting error, the datasets of branch apparent power are constructed to capture the complex nonlinear characteristics of the power flow. The non-Gaussian distribution characteristics of branch apparent power and line loss are described by the optimal probability fitting method. Finally, the probability level of branch overload is evaluated and the probability distribution of line loss is analyzed. The case studies demonstrate that the branch power approximation model is highly accurate, and the probability distribution of the branch apparent power presents different characteristics. The proposed method can quickly and accurately calculate the branch overload probability level.

A time-varying non-probabilistic reliability analysis method using surrogate model for the reinforcement effectiveness of damaged concrete gravity dam

Evaluation of the effectiveness of reinforcement measures for the diseased concrete gravity dam is a critical issue in the field of hydraulic structural health control. The traditional probabilistic reliability analysis method is constrained by factors such as the randomness of the uncertain parameters, the high nonlinearity of the performance function, etc., when it is applied to the evaluation of the effectiveness evolution of reinforcement measures for the diseased concrete gravity dam. Therefore, a time-varying non-probabilistic reliability (NR) analysis method is proposed in the research. To characterize the uncertainty of the parameters, we adopt the form of interval numbers to present parameters and construct the interval parameter-based reliability analysis framework. Specifically, combining interval mathematics and non-probabilistic reliability theory, the NR calculation model for the gravity dam is proposed. In addition, considering of the aging of the structure, the time-varying NR (TV-NR) calculation model utilized to evaluate the long-term reinforcement effectiveness is established. To tackle the issue of expensive computation existed in the TV-NR model, response surface method (RSM) is coupled in the TV-NR calculation model to replace the original high nonlinearity performance function. Ultimately, the proposed method is verified in engineering examples that it can detect the most possible initial locations and failure processes of the gravity dam varying with time and can efficiently and accurately evaluate the reinforcement effectiveness of the gravity dams. The results indicate that the use of reinforcement measures can provide an improvement for the safety service of gravity dams.

Probabilistic assessment of earthquake casualties in residential areas

Accurately and reasonably assessing earthquake casualties is crucial for seismic disaster planning and governmental decision-making. However, current research on earthquake casualty assessments often lacks sufficient consideration of the uncertainties related to seismic scenarios and influencing factors. To enhance the authenticity and reliability of casualty assessments, this study proposes a seismic casualty assessment model capable of simultaneously considering multiple influencing factors. It quantitatively evaluates each influencing factor and comprehensively integrates the uncertainty characteristics associated with seismic occurrence time, building damage states, and the number of occupants. Using a residential area as an example, the research compares casualty assessment results with and without considering apartment layouts and the age structure of residents. It also explains the probabilistic method for quantifying casualties and constructing vulnerability models for seismic events in the residential area. Additionally, a simplified analytical method applicable to probabilistic assessment of earthquake casualties in masonry residential areas in Beijing is proposed. The research findings indicate that the apartment layouts within buildings have a relatively minor impact on the assessment results of casualties in the residential area, while the age structure of residents significantly affects earthquake casualty estimates. Casualty rates in the residential area, considering uncertainties in the three factors, approximately follow a log-normal distribution. For seismic intensities ranging from VI(0.05g) to IX(0.40g), the standard deviation of casualty rates across different seismic intensities exceeds 0.4. The probabilistic analysis method proposed in this study enhances existing models for earthquake casualty assessments and addresses the shortcomings in probabilistic evaluation research.

Research on column overdesign factor of reinforced concrete frame structures in the 2022 Ms 6.8 Luding earthquake

The strong column-weak beam failure mode of reinforced concrete (RC) frame structures is one of the most important targets of structural seismic design and is primarily realized by a reasonable column overdesign factor (COF). However, most RC frame structures in previous earthquakes were often subjected to strong beam-weak column failure modes. To address this issue, the RC frame with a strong column-weak beam failure mode and a typical strong beam-weak column RC frame in the 2022 Ms 6.8 Luding earthquake were intensively studied in this study. The differences between the two failure modes of the RC frame structure were comparatively analyzed at both the overall structure and member levels. A numerical simulation was conducted to obtain the structural response under actual ground motion. Finally, a probabilistic analysis method was adopted to process the COF data of the RC frame joints. The results indicate that the structural safety redundancy of the RC frame with the undesired failure mode cannot be fully utilized, whereas the RC frame with the strong column-weak beam failure mode allows more structural members to participate in the energy dissipation through a complex redistribution mechanism of internal forces. Damage to the infill wall further mitigates the degree of damage to the main structure and reduces the risk of soft-story failure. The COF of the actual RC frame structure shows a non-uniform distribution, and it is recommended that the COF be higher than 1.5 for the seismic design of the structure following the Chinese code.

Multidimensional Seismic Fragility Study of Intake Towers Based on Incremental Dynamic Analysis

Assessing the fragility of intake towers using a single damage index does not allow for accurate evaluation of the potential for structural damage under seismic conditions. In this study, based on the probabilistic seismic demand analysis method, the effects of ground motion intensity on maximum displacement, local damage index, and global damage index are considered, and the seismic fragility of an intake tower structure is analyzed. First, 10 natural ground motion records were selected from the ground motion database (PEER) and 2 artificial seismic waves were synthesized. These seismic waves were amplitude-modulated for incremental dynamic analysis (IDA). The trends of the IDA curves were analyzed to divide the performance levels of the intake tower structure. Furthermore, a two-dimensional fragility curve for the intake tower structure was plotted in this study. The maximum displacement in the direction of parallel flow and the damage index were taken into account in the two-dimensional fragility curve. The results show that, under the designed seismic acceleration, the two-dimensional fragility curve for the intake tower structure was lower than the one-dimensional curve. This indicates that the seismic design based on the one-dimensional performance index was unstable. This provides a theoretical reference for seismic optimization design and the strengthening of intake towers. Therefore, it is recommended to use multidimensional fragility analysis to study the seismic performance of intake tower structures in seismic design.

End-to-end probability analysis method for multi-core distributed systems

End-to-end probability analysis method for multi-core distributed systems

Fully analytical method for probabilistic stability analysis of the rainfall-induced landslide considering variability of saturated hydraulic conductivity and rainfall uncertainty

Fully analytical method for probabilistic stability analysis of the rainfall-induced landslide considering variability of saturated hydraulic conductivity and rainfall uncertainty

The psycho-social impact of video games on K12 Spanish students

This research aims to study the psycho-social impact of video games on K12 students. For this, a probabilistic topic modelling analysis method based on text mining approach has been performed. This process is based on nodes’ connectivity and it has been developed through K Means approach; by launching the Jenks-Breaks algorithm. The sex differences are calculated according to a nonlinear dynamics approach based on Hurst exponent and multifractal function and the influence of time with the application of the Sobel test. The results show which are the most used video games by K12 and their psycho-social impact on students based on four categories: (1) boredom and sadness, (2) happiness and socialization, (3) immersion, and (4) families' conflicts. There are significant differences between boys and girls depending on the games they use, a factor that increases when playing more than two hours a day. For boys, games like FIFA and Fortnite produce higher levels of immersion and family conflict, while for girls, games are perceived as sources of greater happiness and a means to reinforce friendship and camaraderie, particularly with games like Brawl Stars, Rocket League, and PKXD.

Probabilistic assessment of complex corrosion in pipelines considering River-Bottom Profile information

One of the important causes of failure and incidents in pipelines is corrosion. Due to the severe consequences and impact in several social, economic, and environmental areas, pipelines must be regularly inspected. The possibilities for pipeline assessment are standard equations and numerical simulations. While the first is simple and fast, it tends to be conservative and the second is expensive. The finite element method (FEM) has been successfully used to predict the failure pressure of pipelines under different conditions. Commonly assessment methods overlook the uncertainties for failure predictions, often relying on safety factors. However, it is imperative to consider uncertainties to ascertain the reliability and risk of corroded pipes. While the reliability analysis of pipelines with idealized defects has been extensively explored in the literature, studies considering complex corrosion profiles, are still demanding. This paper addresses this gap considering the traditional Monte Carlo (MC) and first-order reliability (FORM) methods. The assessment is based on the Effective Area Method (EAM) within the failure function. As well know, MC can be expensive due to the high number of function evaluations. To mitigate this, FORM is employed as it requires fewer function evaluations. However, function gradients are required as it relies on an iterative optimization algorithm. Particularly challenges arise when computing the gradient using EAM for burst pressure estimation. The EAM is an iterative procedure, and small perturbations can yield incorrect sensitivity values, causing problems for FORM convergence. To address this, we propose a novel procedure for efficiently and less conservatively obtaining the gradients required by FORM using EAM as a failure function. The modified FORM method achieved convergence within 15 iterations for all test cases. This alternative approach offers a faster, more precise and less conservative method for Level-2 probabilistic failure analysis of complex-shaped corrosion defects compared to traditional Level-1 methods.

Physics-informed probabilistic slow feature analysis

This paper presents a novel approach called physics-informed probabilistic slow feature analysis. The probabilistic slow feature analysis method has been employed to extract slowly varying latent patterns from high-dimensional measured data. The extracted slow features have proven effective in industrial applications such as soft sensing and process monitoring. However, industrial processes come with various physical constraints that must be taken into account, such as energy requirements, equipment limitations, and safety considerations. The conventional black-box nature of the slow feature model often leads to physically inconsistent or unacceptable results. To address this issue, we propose integrating physics principles into the probabilistic slow feature model, ensuring that the extracted features adhere to physics laws. Our formulation incorporates two types of physical constraints: linear algebraic equality and inequality constraints. Through an industrial case study, we demonstrate the effectiveness of our methodology, showcasing the advantages of incorporating physics in feature extraction. These advantages include improved interpretability, reduced data dimensionality, and enhanced generalization performance.

Robust multi-objective optimization under multiple uncertainties using the CM-ROPAR approach: case study of water resources allocation in the Huaihe River basin

Abstract. Water resources managers need to make decisions in a constantly changing environment because the data relating to water resources are uncertain and imprecise. The Robust Optimization and Probabilistic Analysis of Robustness (ROPAR) algorithm is a well-suited tool for dealing with uncertainty. Still, the failure to consider multiple uncertainties and multi-objective robustness hinders the application of the ROPAR algorithm to practical problems. This paper proposes a robust optimization and robustness probabilistic analysis method that considers numerous uncertainties and multi-objective robustness for robust water resources allocation under uncertainty. The copula function is introduced for analyzing the probabilities of different scenarios. The robustness with respect to the two objective functions is analyzed separately, and the Pareto frontier of robustness is generated. The relationship between the robustness with respect to the two objective functions is used to evaluate water resources management strategies. Use of the method is illustrated in a case study of water resources allocation in the Huaihe River basin. The results demonstrate that the method opens a possibility for water managers to make more informed uncertainty-aware decisions.

Moving Beyond Medical Statistics: A Systematic Review on Missing Data Handling in Electronic Health Records.

Background: Missing data in electronic health records (EHRs) presents significant challenges in medical studies. Many methods have been proposed, but uncertainty exists regarding the current state of missing data addressing methods applied for EHR and which strategy performs better within specific contexts. Methods: All studies referencing EHR and missing data methods published from their inception until 2024 March 30 were searched via the MEDLINE, EMBASE, and Digital Bibliography and Library Project databases. The characteristics of the included studies were extracted. We also compared the performance of various methods under different missingness scenarios. Results: After screening, 46 studies published between 2010 and 2024 were included. Three missingness mechanisms were simulated when evaluating the missing data methods: missing completely at random (29/46), missing at random (20/46), and missing not at random (21/46). Multiple imputation by chained equations (MICE) was the most popular statistical method, whereas generative adversarial network-based methods and the k nearest neighbor (KNN) classification were the common deep-learning-based or traditional machine-learning-based methods, respectively. Among the 26 articles comparing the performance among medical statistical and machine learning approaches, traditional machine learning or deep learning methods generally outperformed statistical methods. Med.KNN and context-aware time-series imputation performed better for longitudinal datasets, whereas probabilistic principal component analysis and MICE-based methods were optimal for cross-sectional datasets. Conclusions: Machine learning methods show significant promise for addressing missing data in EHRs. However, no single approach provides a universally generalizable solution. Standardized benchmarking analyses are essential to evaluate these methods across different missingness scenarios.