Stochastic Numerical Analysis for Impact of Heavy Alcohol Consumption on Transmission Dynamics of Gonorrhoea Epidemic

This paper aims to perform a comparison of deterministic and stochastic models. The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic model. Also, the deterministic solution is itself mean of the stochastic solution of the model. For numerical analysis, first, we developed some explicit stochastic methods, but unfortunately, they do not remain consistent in certain situations. Then we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic model. The proposed method is independent of the choice of parameters and behaves well in all scenarios. So, some theorems and simulations are presented in support of the article.     

Risk based probabilistic pavement deterioration prediction models for low volume roads

Accurate prediction of pavement performance is important for efficient management of road infrastructure. Pavement performance prediction models developed for low-volume roads are mainly based on deterministic approach. The deterministic prediction models are inadequate to completely capture the deterioration mechanism. Uncertainties may occur in pavement behaviour under changing traffic loads and environment conditions, which may not be realistically represented by deterministic model. The objective of this paper is to develop pavement deterioration prediction models by probabilistic approach, for various distresses observed on low-volume roads in the state of Kerala in India, with the help of existing deterministic models. The major distresses observed on low-volume roads were ravelling, pothole and edge failure. Load-associated distresses were rarely observed on these roads as the maximum cumulative standard axle observed was only one million standard axle (msa). Hence, lack of proper drainage and construction quality (CQ) could be attributed as the major reasons for the pavement deterioration. Progression of deterioration of pavements with age has been studied and the intensity of distresses along with corresponding probabilities was arrived at. The distresses predicted by probabilistic models were compared with those predicted by deterministic models and the actual distress values observed in the field. The prediction models were validated using Mean Absolute Percentage Error, a statistical method for accuracy measurement of forecasting models. A risk analysis was then conducted to select the critical percentile value for each type of distress corresponding to varying pavement age. A sensitivity analysis was also carried out to study the effect of pavement age and CQ on the progression of pavement deterioration.     

钢筋混凝土梁抗剪承载力计算的概率模型

传统的钢筋混凝土（RC）梁抗剪承载力模型属于确定性模型,难以有效考虑几何尺寸、材料特性、边界约束条件等因素存在的客观（物理）不确定性和在模型推导过程中存在的主观（模型）不确定性的影响,导致计算结果的离散性较大,计算精度和适用性有限。鉴于此,该文首先结合修正压力场理论和考虑剪跨比影响的临界斜裂缝倾角模型,建立了RC梁的确定性抗剪承载力模型;然后综合考虑主观不确定性和客观不确定性因素的影响,结合贝叶斯理论和马尔科夫链蒙特卡洛法（MCMC）,建立了RC梁抗剪承载力计算的概率模型;最后通过与试验数据和传统确定性计算模型的对比分析,验证了该模型的有效性和适用性。分析结果表明,所建立的概率模型不仅可以合理地描述RC梁抗剪承载力的概率分布特性,而且可以校准传统确定性计算模型的计算精度和置信水平,还可以根据预定的置信水平确定RC梁抗剪承载力的概率特征值,具有良好的计算精度和适用性。     

Structure-Preserving Dynamics of Stochastic Epidemic Model with the Saturated Incidence Rate

The structure-preserving features of the nonlinear stochastic models are positivity, dynamical consistency and boundedness. These features have a significant role in different fields of computational biology and many more. Unfortunately, the existing stochastic approaches in literature do not restore aforesaid structure-preserving features, particularly for the stochastic models. Therefore, these gaps should be occupied up in literature, by constructing the structure-preserving features preserving numerical approach. This writing aims to describe the structure-preserving dynamics of the stochastic model. We have analysed the effect of reproduction number in stochastic modelling the same as described in the literature for deterministic modelling. The usual explicit stochastic numerical approaches are time-dependent. We have developed the implicitly driven explicit approach for the stochastic epidemic model. We have proved that the newly developed approach is preserving the structural, dynamical properties as positivity, boundedness and dynamical consistency. Finally, convergence analysis of a newly developed approach and graphically illustration is also presented.     

Condition, safety and cost profiles for deteriorating structures with emphasis on bridges

After an enormous investment in construction of highway networks undertaken in the second half of the 20th century, the highway networks of most European and North American countries are now completed or close to completion. As a result, the need in funding changed from building new highway structures to repair, rehabilitation, and replacement the existing ones. In this paper, a model for analyzing the evolution in time of probabilistic performance indicators of existing structures, in terms of condition, safety, and cost under no maintenance, preventive maintenance, and essential maintenance, is presented. This model integrates the current practice in bridge management systems based on visual inspections (condition index) with structural assessment (safety index) during the lifetime of existing structures. The proposed model allows the consideration of uncertainties in the performance deterioration process, times of application of maintenance actions, and in the effects of maintenance actions on the condition, safety, and life-cycle cost of structures by defining all parameters involved in the model as random variables. Interaction between condition and safety profiles is defined through probabilistic and deterministic relations. The probabilistic characteristics of the condition, safety, and cost profiles of deteriorating structures are computed by Monte-Carlo simulation. Several realistic examples, based on data on highway bridge components gathered in the United Kingdom, are presented.     

Probabilistic models applied to safety assessment of reinforced concrete structures subjected to chloride ingress

This paper addresses the analysis of probabilistic corrosion time initiation in reinforced concrete structures exposed to chloride penetration. Structural durability is an important criterion that must be evaluated for every type of structure. Considering reinforced concrete members, chloride diffusion process is widely used to evaluate durability, especially when these structures are constructed in aggressive atmospheres. The chloride ingress triggers the corrosion of reinforcements; therefore, by modelling this phenomenon, the corrosion process can be better evaluated as well as the structural durability. The corrosion begins when a threshold level of chloride concentration is reached at the steel bars of reinforcements. Despite the robustness of several models proposed in the literature, deterministic approaches fail to predict accurately the corrosion time initiation due the inherent randomness observed in this process. In this regard, structural durability can be more realistically represented using probabilistic approaches. A probabilistic model capable to model chloride ingress is presented in this paper. The chloride ingress is modelled using the Fick’s diffusion law. This law simulates the chloride diffusion process considering time-dependent effects. The probability of failure is calculated using Monte Carlo simulation and the first order reliability method with a direct coupling approach. Some examples are considered in order to study these phenomena. Moreover, a simplified method is proposed to determine optimal values for concrete cover.     

Rutting progression models for light duty pavements

Deterioration models allow road managers to assess current condition and to predict future conditions of their road networks. Due to heavy vehicle axle repetitions and the effect of environmental factors, permanent deformation (rutting) develops gradually in the wheel paths and impacts on structural and surface performance of flexible pavements. This paper reports the approach adopted to develop absolute deterministic models for permanent deformation of low volume roads. A representative large sample network (23 highways) of light duty pavements was selected. For each section, time series data from four consecutive condition surveys were collected. Multiple regression analysis was carried out to develop models to predict pavement rutting progression over time as a function of a number of contributing variables. They include traffic loading, pavement strength, climate and drainage condition. For more powerful prediction, family group data-fitting approach was utilised to estimate future rutting progression based on the average rut depth curve for a series of pavements with similar characteristics. This study highlighted that separate family deterioration models are preferred and needed for more realistic results. The paper concludes that the analysis approach used for developing the models confirmed their accuracy and reliability by well-fitting to the validation data with low standard error values. Also, study results show that higher traffic loading, lower pavement strength, poor drainage and climates with high seasonal variation contribute to increasing rutting progression rate.     

剪切型钢筋混凝土柱抗剪承载力计算的概率模型

现有的钢筋混凝土（RC）柱抗剪承载力计算模型大多属于确定性模型,难以有效考虑几何尺寸、材料特性和外荷载等因素存在的不确定性,导致计算结果的离散性较大,且计算精度和适用性有限。鉴于此,该文结合变角桁架-拱模型和贝叶斯理论,研究建立了剪切型RC柱抗剪承载力计算的概率模型。首先基于变角桁架-拱模型理论,并考虑轴压力对临界斜裂缝倾角的影响,建立了剪切型RC柱抗剪承载力的确定性修正模型;然后考虑主观不确定性和客观不确定性因素的影响,结合贝叶斯理论和马尔科夫链蒙特卡洛（MCMC）法,建立了剪切型RC柱的概率抗剪承载力计算模型;最后通过与试验数据和现有模型的对比分析,验证了该模型的有效性和实用性。分析结果表明,该模型不仅可以合理描述剪切型RC柱抗剪承载力的概率分布特性,而且可以校准现有确定性计算模型的置信水平,并且可以确定不同置信水平下剪切型RC柱抗剪承载力的特征值。     

Probabilistic bond strength model for reinforcement bar in concrete

In order to overcome the disadvantages of traditional deterministic models, a probabilistic bond strength model of reinforcement bar in concrete was presented. According to the partly cracked thick-walled cylinder model, a deterministic bond strength model of reinforcement bar in concrete was developed first by taking into account the influences of various important factors. Then the analytical expression of probabilistic bond strength model of reinforcement bar in concrete was derived by taking into consideration both aleatory and epistemic uncertainties. Subsequently, a probabilistic bond strength model of reinforcement bar in concrete was proposed by determining the statistical characteristics of probabilistic model parameters based on the Markov Chain Monte Carlo method and the Bayesian theory. Finally, applicability of the proposed probabilistic model were validated by comparing with 400 sets of experimental data and four typical deterministic bond strength models. Analysis shows that the probabilistic model provides efficient approaches to describe the probabilistic characteristics of bond strength and to calibrate traditional deterministic bond strength models.     

Mixture probabilistic PCR model for soft sensing of multimode processes

Principal component regression (PCR) has been widely used for soft sensor modeling and quality prediction in last several decades, which is still very popular for both academy researches and industry applications. However, most PCR models are determined by the projection method, which may lack probabilistic interpretation for the process data. In fact, due to the inevitable process noise, most process data are inherently random variables. Several probabilistic PCA methods have already been proposed in the past years. Compared to the deterministic modeling method, the probabilistic model is more appropriate to characterize the behavior of the random variables in the process. This paper first presents a probabilistic derivation of the PCR model (PPCR) and then extends it to the mixture form (MPPCR). For quality prediction of processes with multiple operation modes, a mixture probabilistic soft sensor is developed based on the MPPCR model. Simultaneously, the information of the operation mode can also be located by the proposed soft sensor. To evaluate the performance of the MPPCR model, a numerical example and a benchmark simulation case study of the Tennessee Eastman process are provided. Different methods have been compared with the proposed model, including the global, local, and multi-local PCR models. As a result, the proposed MPPCR model performs the best among these methods.     

Comparison of stochastic parametrization approaches in a single-column model

We discuss and test the potential usefulness of single-column models (SCMs) for the testing of stochastic physics schemes that have been proposed for use in general circulation models (GCMs). We argue that although single-column tests cannot be definitive in exposing the full behaviour of a stochastic method in the full GCM, and although there are differences between SCM testing of deterministic and stochastic methods, SCM testing remains a useful tool. It is necessary to consider an ensemble of SCM runs produced by the stochastic method. These can be usefully compared with deterministic ensembles describing initial condition uncertainty and also with combinations of these (with structural model changes) into poor man's ensembles. The proposed methodology is demonstrated using an SCM experiment recently developed by the GCSS (GEWEX Cloud System Study) community, simulating transitions between active and suppressed periods of tropical convection.     

Dynamic response of structures with uncertain parameters: A comparative study of probabilistic and fuzzy sets models

This paper presents the results of a study on the response of structures with uncertain properties such as mass, stiffness and damping. The effect of the uncertain parameters on the response and the effect of the modelling of the uncertainties on the response are investigated. In particular, two types of uncertainties are distinguished: random and fuzzy uncertainties. Two kinds of models are studied: probabilistic and fuzzy set models. The two approaches to uncertainty modelling are compared with regard to their impacts on the analysis and on the uncertain structural response obtained. The study considers free vibration, forced vibration with deterministic excitation, and forced vibration with Gaussian white noise excitation. It is concluded that, in general, fuzzy models are much easier to implement and the associated analysis easier to perform than their probabilistic counterparts. When the available data on the structural parameters are crude and do not support a rigorous probabilistic model, the fuzzy set approach should be considered in view of its simplicity.     

A nonparametric probabilistic approach for quantifying uncertainties in low‐dimensional and high‐dimensional nonlinear models

A nonparametric probabilistic approach for modeling uncertainties in projection‐based, nonlinear, reduced‐order models is presented. When experimental data are available, this approach can also quantify uncertainties in the associated high‐dimensional models. The main underlying idea is twofold. First, to substitute the deterministic reduced‐order basis (ROB) with a stochastic counterpart. Second, to construct the probability measure of the stochastic reduced‐order basis (SROB) on a subset of a compact Stiefel manifold in order to preserve some important properties of a ROB. The stochastic modeling is performed so that the probability distribution of the constructed SROB depends on a small number of hyperparameters. These are determined by solving a reduced‐order statistical inverse problem. The mathematical properties of this novel approach for quantifying model uncertainties are analyzed through theoretical developments and numerical simulations. Its potential is demonstrated through several example problems from computational structural dynamics. Copyright © 2016 John Wiley & Sons, Ltd.     

磁流变阻尼器MNS模型参数不确定性分析

磁流变阻尼器（Magneto-Rheological damper）因其优异的性能,在地震和风荷载下的结构振动控制中有广阔的应用。采用磁流变阻尼器进行结构控制时,建立相对精确的非线性模型是设计控制策略重要因素之一,也是保证对其进行数值分析时具有较高可信度的关键因素之一。从传统优化方法获得的确定性模型参数无法考虑由于磁流变阻尼器的现象学模型（phenomenological model）内在的不确定性,从而可能导致阻尼器模型出现不准确的预测。使用马尔可夫链蒙特卡洛方法,该研究对磁流变阻尼器的Maxwell Nonlinear Slider（MNS）模型的不确定性分析,并通过与现有200 kN足尺磁流变阻尼器试验结果,证明了概率模型能够更好地预测磁流变阻尼器在预定的正弦曲线位移和实时混合模拟的位移响应下的输出力和能量耗散,从而为进一步分析结构在磁流变阻尼器控制下的响应预测提供了更为有效的工具。     

Verification and validation for a penetration model using a deterministic and probabilistic design tool

The Los Alamos National Laboratory Dynamic Experimentation (DynEx) program is the designing and validating steel blast containment vessels using limited experiments coupled with computational models. Through a need to design portions of the vessel to protect against breeches by projectiles, an analytical model was developed along the lines of the Walker–Anderson penetration model to predict the penetration depth of a projectile in a two- and three-layer target. The three-layer target consists of boron carbide ceramic (B4C), beryllium (Be), and aluminum. The two-layer target removes the Be. This model was integrated in the NESSUS^® probabilistic analysis program to provide a deterministic and probabilistic design tool. Through a verification and validation approach, the model predictions are compared to the experimental results for both target configurations. The probabilistic analysis or uncertainty quantification is an essential part of verification and validation (V&V) and is used to provide confidence in model predictions. Overall, the V&V procedure indicates that the model predicts the two-layer target results well and is biased conservatively. The three-layer target provides reasonable predictions for thinner ceramic layers. The probabilistic results provide additional insight into the model and experimental results comparison over a deterministic analysis alone. The results show that there may be incomplete physics in the modeling of Be and thicker B4C layers. The probabilistic sensitivity factors show that the projectile density, velocity and strength, and Be strength are important variables. This information provides insight into approaches to improve the model predictions and establishes validity for use of the current model for specific configuration ranges.     

A survey of the application of gamma processes in maintenance

This article surveys the application of gamma processes in maintenance. Since the introduction of the gamma process in the area of reliability in 1975, it has been increasingly used to model stochastic deterioration for optimising maintenance. Because gamma processes are well suited for modelling the temporal variability of deterioration, they have proven to be useful in determining optimal inspection and maintenance decisions. An overview is given of the rich theoretical aspects as well as the successful maintenance applications of gamma processes. The statistical properties of the gamma process as a probabilistic stress-strength model are given and put in a historic perspective. Furthermore, methods for estimation, approximation, and simulation of gamma processes are reviewed. Finally, an extensive catalogue of inspection and maintenance models under gamma-process deterioration is presented with the emphasis on engineering applications.     

Analysis of vehicle-bicycle interactions at unsignalized crossings: A probabilistic approach and application

In the last decades, bicycle usage has been increasing in many countries due to the potential environmental and health benefits. Therefore, there is a need to better understand cyclists’ interactions with vehicles, and to build models and tools for evaluating multimodal transportation infrastructure with respect to cycling safety, accessibility, and other planning aspects. This paper presents a modeling framework to describe driver-cyclist interactions when they are approaching a conflicting zone. In particular, the car driver yielding behavior is modeled as a function of a number of explanatory variables. A two-level hierarchical, probabilistic framework (based on discrete choice theory) is proposed to capture the driver’s yielding decision process when interacting with a cyclist. The first level models the probability of the car driver perceiving a situation with a bicycle as a potential conflict whereas the second models the probability of yielding given that a conflict has been perceived by the driver. The framework also incorporates the randomness of the location of the drivers’ decision point. The methodology is applied in a case study using observations at a typical Swedish roundabout. The results show that the conflict probability is affected differently depending on the user (cyclist or driver) who arrives at the interaction zone first. The yielding probability depends on the speed of the vehicle and the proximity of the cyclist.     

An applied mathematics perspective on stochastic modelling for climate

Systematic strategies from applied mathematics for stochastic modelling in climate are reviewed here. One of the topics discussed is the stochastic modelling of mid-latitude low-frequency variability through a few teleconnection patterns, including the central role and physical mechanisms responsible for multiplicative noise. A new low-dimensional stochastic model is developed here, which mimics key features of atmospheric general circulation models, to test the fidelity of stochastic mode reduction procedures. The second topic discussed here is the systematic design of stochastic lattice models to capture irregular and highly intermittent features that are not resolved by a deterministic parametrization. A recent applied mathematics design principle for stochastic column modelling with intermittency is illustrated in an idealized setting for deep tropical convection; the practical effect of this stochastic model in both slowing down convectively coupled waves and increasing their fluctuations is presented here.     

A soft sensor method based on values predicted from multiple intervals of time difference for improvement and estimation of prediction accuracy

Soft sensors are widely used to estimate process variables that are difficult to measure online. However, their predictive accuracy gradually decreases with changes in the state of the plants. We have been constructing soft sensor models based on the time difference of an objective variable, y, and that of explanatory variables (time difference models) for reducing the effects of deterioration with age such as the drift without model reconstruction. In this paper, we have attempted to improve and estimate the prediction accuracy of time difference models, and proposed to handle multiple y-values predicted from multiple intervals of time difference. A weighted average is a final predicted value and the standard deviation is an index of its prediction accuracy. This method was applied to real industrial data and then, could predict more number of data with higher predictive accuracy and estimate the prediction errors more accurately than traditional ones.