Probabilistic Analysis Approach Research Articles

Assessing Model Prediction Control (MPC) Performance. 1. Probabilistic Approach for Constraint Analysis

Advanced process control (APC)in particular, model predictive control (MPC)has emerged as the most effective control strategy in process industry, and numerous applications have been reported. Nevertheless, there are several factors that limit the achievable performance of MPC. One of the limiting factors considered in this paper is the presence of constraints. To exploit optimal control performance, continuous performance assessment, with respect to the constraints of MPC, is necessary. MPC performance assessment has received increasing interest, both in academia and in industry. This paper is concerned with a practical aspect of performance assessment of industrial MPC by investigating the relationship among process variability, constraints, and probabilistic economic performance of MPC. The proposed approach considers the uncertainties induced by process variability and evaluates the economic performance through probabilistic calculations. It also provides a guideline for the constraint tuning, to improve MPC performance.

A Probabilistic Analysis Approach to Making Decision on Retirement of Aged Equipment in Transmission Systems

Determining the retirement time of aged equipment in power systems has been a challenge in the utility industry for many years. The paper presents a probabilistic analysis approach to making decision on retirement of aged equipment in transmission systems. The basic idea is to quantify and compare the expected damage cost and capital saving due to delaying the retirement of aged equipment. An actual example of an aged underground cable in a regional transmission system of a utility is used to demonstrate the application of the presented approach step by step.

The use of stochastic stresses in the static approach of probabilistic limit analysis

AbstractIn the framework of the structural reliability theory, the probabilistic limit analysis (PLA) represents a powerful tool for the evaluation of the safety of structures with stochastic strengths with respect to the ultimate limit state of plastic collapse. Aim of the PLA is to evaluate the conditional probability of collapse (CPC), that is, the probability of plastic collapse of the structural system for assigned value of the acting loads. In this paper the focus is on the static approach of the limit analysis theory, which is particularly attractive for engineers, because it gives upper bounds of the CPC, that is, safe bounds. The classical static approach, introduced more than 30 years ago, however, cannot in any case evaluate the exact CPC of the structural system, and moreover generally the bounds obtained are not very close, especially in the range of very small probabilities. In this paper an alternative static approach is proposed, which can obtain the exact CPC of the structural system considering a finite number of suitable chosen stochastic stress vectors through the use of the partial admissible domains; moreover, it gives good safe bounds of the CPC considering only a few stochastic stress vectors. Some simple numerical examples show the accuracy and effectiveness of the method. Copyright © 2007 John Wiley & Sons, Ltd.

Approaches for Categorization of Reusable Software Components

Reuse repositories manager manages the reusable software components in different categories and needs to find the category of reusable software components. In this paper, we have used different pure and hybrid approaches to find the domain relevancy of the component to a particular domain. Probabilistic Latent Semantic Analysis (PLSA) approach, LSA, Singular Value Decomposition (SVD) technique, LSA Semi-Discrete Matrix Decomposition (SDD) technique and Naive Bayes Approach purely as well as hybrid, are evaluated to determine the Domain Relevancy of software components. It exploits the fact that Feature Vector codes can be seen as documents containing terms -the identifiers present in the components- and so text modeling methods that capture co-occurrence information in low-dimensional spaces can be used. The FV code representation of clusters or domains is used to find the domain-relevancy of the software components. PLSA has provided better results than LSA retrieval techniques in terms of Precision and Recall but its time complexity is too high. SVD Transformation with Naive Bayes scheme has outperformed all other approaches and shows better results than the existing approach (LSA) being used by some open source code repositories e.g. Sourceforge. The DR-value determined is close to the manual analysis, used to be performed by the programmers/repository managers. Hence, the tool can also be utilized for the automatic categorization of software components and this kind of automation may improve the productivity and quality of software development.

Fuzzy Logic Pavement Maintenance and Rehabilitation Triggering Approach for Probabilistic Life-Cycle Cost Analysis

Life-cycle cost analysis (LCCA) is an important tool in transportation asset management. Transportation agencies have used both deterministic and probabilistic LCCA approaches. Probabilistic approaches allow decision makers to evaluate the risk of an investment by using uncertain input variables, assumptions, or estimates. The incorporation of fuzzy logic–based models into the risk analysis process is explored to enhance further the traditional probabilistic LCCA method. It proposes a fuzzy logic approach for determining the timing of pavement maintenance, rehabilitation, and reconstruction (MR&R) treatments in a probabilistic LCCA model for selecting pavement MR&R strategies. Instead of using predefined service life for initial construction and future rehabilitations, the proposed approach uses performance curves and fuzzy logic triggering models to determine the most effective timing of MR&R activities. The new approach is compared with the deterministic and traditional probabilistic approaches in a simple case study. The case study demonstrates that the fuzzy logic–based risk analysis model for LCCA can effectively produce results that are at least comparable to those of the benchmark methods while effectively considering some of the uncertainty inherent to the process.

A probabilistic approach for analysis of uncertainty in the evaluation of watershed management practices

Summary A computational framework is presented for analyzing the uncertainty in model estimates of water quality benefits of best management practices (BMPs) in two small ( 2 ) watersheds in Indiana. The analysis specifically recognizes the significance of the difference between the magnitude of uncertainty associated with absolute hydrologic and water quality predictions, and uncertainty in estimated benefits of BMPs. The Soil and Water Assessment Tool (SWAT) is integrated with Monte Carlo-based simulations, aiming at (1) adjusting the suggested range of model parameters to more realistic site-specific ranges based on observed data, and (2) computing a scaled distribution function to assess the effectiveness of BMPs. A three-step procedure based on the One-factor-At-a-Time (OAT) sensitivity analysis and the Generalized Likelihood Uncertainty Estimation (GLUE) was implemented for the two study watersheds. Results indicate that the suggested range of some SWAT parameters, especially the ones that are used to determine the transport capacity of channel network and initial concentration of nutrients in soils, required site-specific adjustment. It was evident that uncertainties associated with sediment and nutrient outputs of the model were too large, perhaps limiting its application for point estimates of design quantities. However, the estimated effectiveness of BMPs sampled at different points in the parameter space varied by less than 10% for all variables of interest. This suggested that BMP effectiveness could be ascertained with good confidence using models, thus making it suitable for use in watershed management plans such as the EPA’s Total Maximum Daily Load (TMDL) program. The potential impact of our analysis on utility of models and model uncertainties in decision-making process is discussed.

A probabilistic approach for economic analysis of a shopping center in seismic zone

The occurrence of an earthquake causes direct and indirect losses in economy. Performance of the built environment can determine both the magnitude of the losses and the speed of recovery from earthquakes. Earthquake losses can be minimized by the use of planning techniques. This paper presents a probabilistic approach for economic evaluation of a shopping center constructed in a seismic zone. Decision-makers can benefit from this approach, before and after an earthquake occurrence, by considering the probability distribution and variability. Life cycle cost concept is taken into account in the formulation of future worth estimation. Therefore, the approach simulates all the benefits and costs, which are prone to variation within Monte Carlo framework. The probabilistic approach can be used to assess the effects of recovery periods.

Power system equipment aging

This article discussed the issues around power system equipment aging, including concepts of equipment lifetime, approaches to estimating the mean life and age, Weibull and normal-distribution-based models to assess the end-of-life failure probability. The relationship between aging and maintenance activities, limitations of maintenance in extending equipment life, and determination of timing of retirement were also discussed. A few examples showing actual data of transformers, cables, and reactors at BCTC have been presented. Maintenance activities can extend the life of equipment but could be very costly for equipment at their end-of-life stage. A compromise between maintenance and replacement must be carefully considered. RCM and probabilistic analysis approaches are available for utilities to guide maintenance activities and manage aged assets in a more efficient and economic manner

On the assessment of the impact of reducing parameters and identification of parameter uncertainties for a hydrologic model with applications to ungauged basins

In this paper, we investigate model parameter uncertainties associated with hydrological process parameterizations and their impacts on model simulations in the Three-Layer Variable Infiltration Capacity (VIC-3L) land surface model. We introduce an alternative subsurface flow parameterization into VIC-3L to reduce the impacts of model parameter uncertainties on model simulations by reducing the number of model parameters that need to be estimated through a calibration process. The new subsurface flow parameterization is based on the concepts of kinematic wave and hydrologic similarity, and has one parameter for calibration. Results from the 12 MOPEX (Model Parameter Estimation Experiment) basins obtained by applying the VIC-3L model with the new subsurface flow formulation show that the performance of the new parameterization is comparable to the original subsurface flow formulation, which has three parameters for calibration. In addition, a probabilistic approach based on Monte Carlo simulations is used to evaluate model performance and uncertainties associated with model parameters over different ranges of streamflow. Studies based on the 12 MOPEX watersheds show that compared to the parameter associated with the new subsurface flow parameterization, the VIC shape parameter (i.e. the b parameter that represents the shape of the heterogeneity distribution of effective soil moisture capacity over a study area) has a larger impact on model simulations and could introduce more uncertainty if not estimated appropriately. Furthermore, investigations on the b parameter suggest that the ensembles (i.e. the mean response and its bounds) from the Monte Carlo simulations could provide reasonable predictions and uncertainty estimates of streamflows, which have important implications for applications to ungauged basins. The study also shows that appropriate reduction of the number of model parameters is an effective approach to reduce the impacts of parameter uncertainties on model simulations. This is more so for applications to ungauged basins or basins with limited data available for calibration. The new subsurface flow parameterization and the probabilistic uncertainty analysis approach are general and can be applied to other modeling studies.

Spatial risk analysis of Li-shan landslide in Taiwan

By coupling limit equilibrium analysis and Monte Carlo analysis with a geography information system (GIS), this study implements a method that can evaluate the risk (corresponding to probability of failure in this study) of landslide with consideration of spatial uncertainties. The GIS can adopt the three-dimensional information including surface topography, underground geomaterial distribution and groundwater level to determine slope profiles for analysis. Then the safety of defined slope can be evaluated by limit equilibrium analysis. In this study, the mechanical properties of geomaterial were considered as random variables instead of single values. The slope and groundwater profiles are also randomly adopted. Through a Monte Carlo sampling process, a distribution of safety factor and probability of failure can be determined. This probabilistic risk analysis approach was applied to Li-shan landslide in Central Taiwan. Due to heavy rains, the sites near the highway 7A (mileage 73 k + 150) and the highway 8 (mileage 82 k) in the Li-shan Township began to subside in mid April 1990. Topography, geology, and groundwater condition of this area were first reviewed. Based on this review, together with field investigations and a series of limit equilibrium back analyses, a general hypothetic model was established to illustrate the failure mechanism of this landslide area. Then the developed probabilistic risk analysis model is applied to spatially evaluate the risk of this landslide area as well as the performance of the remediation treatment.

Investigations into resting-state connectivity using independent component analysis

Inferring resting-state connectivity patterns from functional magnetic resonance imaging (fMRI) data is a challenging task for any analytical technique. In this paper, we review a probabilistic independent component analysis (PICA) approach, optimized for the analysis of fMRI data, and discuss the role which this exploratory technique can take in scientific investigations into the structure of these effects. We apply PICA to fMRI data acquired at rest, in order to characterize the spatio-temporal structure of such data, and demonstrate that this is an effective and robust tool for the identification of low-frequency resting-state patterns from data acquired at various different spatial and temporal resolutions. We show that these networks exhibit high spatial consistency across subjects and closely resemble discrete cortical functional networks such as visual cortical areas or sensory-motor cortex.

Relative Entropy Based Method for Probabilistic Sensitivity Analysis in Engineering Design

Abstract In this paper, a new Probabilistic Sensitivity Analysis (PSA) approach based on the concept of relative entropy is proposed for design under uncertainty. The relative entropy based method evaluates the impact of a random variable on a design performance by measuring the divergence between two probability density functions of the performance response, obtained before and after the variation reduction of the random variable. The method can be applied both over the whole distribution of a performance response [called global response probabilistic sensitivity analysis (GRPSA)] and in any interested partial range of a response distribution [called regional response probabilistic sensitivity analysis (RRPSA)]. Such flexibility of our approach facilitates its use under various scenarios of design under uncertainty, for instance in robust design, reliability-based design, and utility optimization. The proposed method is applicable to both the prior-design stage for variable screening when a design solution is yet identified and the post-design stage for uncertainty reduction after an optimal design has been determined. The saddlepoint approximation approach is introduced for improving the computational efficiency of applying our proposed method. The proposed method is illustrated and verified by numerical examples and industrial design cases.

Probabilistic Failure Analysis by Importance Sampling Markov Chain Simulation

A probabilistic approach for failure analysis is presented in this paper, which investigates the probable scenarios that occur in case of failure of engineering systems with uncertainties. Failure analysis can be carried out by studying the statistics of system behavior corresponding to the random samples of uncertain parameters that are distributed as the conditional distribution given that the failure event has occurred. This necessitates the efficient generation of conditional samples, which is in general a highly nontrivial task. A simulation method based on Markov Chain Monte Carlo simulation is proposed to efficiently generate the conditional samples. It makes use of the samples generated from importance sampling simulation when the performance reliability is computed. The conditional samples can be used for statistical averaging to yield unbiased and consistent estimate of conditional expectations of interest for failure analysis. Examples are given to illustrate the application of the proposed simulation method to probabilistic failure analysis of static and dynamic structural systems.

Uncertainty and the value of diagnostic information, with application to axillary lymph node dissection in breast cancer.

In clinical decision making, it is common to ask whether, and how much, a diagnostic procedure is contributing to subsequent treatment decisions. Statistically, quantification of the value of the information provided by a diagnostic procedure can be carried out using decision trees with multiple decision points, representing both the diagnostic test and the subsequent treatments that may depend on the test's results. This article investigates probabilistic sensitivity analysis approaches for exploring and communicating parameter uncertainty in such decision trees. Complexities arise because uncertainty about a model's inputs determines uncertainty about optimal decisions at all decision nodes of a tree. We present the expected utility solution strategy for multistage decision problems in the presence of uncertainty on input parameters, propose a set of graphical displays and summarization tools for probabilistic sensitivity analysis in multistage decision trees, and provide an application to axillary lymph node dissection in breast cancer.

Early probabilistic noise estimation for capacitively coupled interconnects

One of the critical challenges in today's high-performance IC design is to take noise into account as early as possible in the design cycle. Current noise analysis tools are effective at analyzing and identifying noise in the postroute design stage when detailed parasitic information is available. However, noise problems identified at this stage of the design cycle are very difficult to correct due to the limited flexibility in design and may cause additional iterations of routing and placement which adds costly delays in its time to market. In this paper, we introduce a probabilistic preroute noise analysis approach to identify postroute noise failures before the actual detailed route is completed. We introduce new methods to estimate the RC characteristics of victim and aggressor lines, their coupling capacitances, and the aggressor transition times before routing is performed. The approach is based on congestion information obtained from a global router. Since the exact location and relative position of wires in the design are not yet available, we propose a novel probabilistic method for capacitance extraction. We present results on two high-performance microprocessors in 0.18 /spl mu/m technology that demonstrate the effectiveness of the proposed approach.

Probabilistic finite element analysis of residual stress formation in shrink-fit ceramic/steel gun barrels

The development of residual stresses in a hybrid α-SiC lining/CrMoV steel jacket gun barrel during shrink fitting of the jacket over the lining is studied using a probabilistic finite element analysis. Particular attention is given to understanding the development of the axial compressive stress in the ceramic lining, since this stress (if sufficiently high) can prevent lining failure caused by formation and growth of circumferential cracks near the barrel ends. To quantify the effect of variability in various design, material and process parameters on the magnitude and the distribution of the axial residual stress, a probabilistic structural analysis approach, known as the advanced mean value (AMV) method, is used, enabling determination of the cumulative distribution function for failure of the lining. The results obtained are validated using the adaptive importance sampling (AIS) method, an efficient direct statistical sampling technique. Lastly, the corresponding sensitivity factors which quantify the effect of variability in each parameter on the magnitude of axial residual stresses in the ceramic lining are computed. The results indicate that the loss of the compressive axial stress in the lining near the barrel ends is affected to the greatest extent by the magnitude of the friction coefficient at the lining/barrel interface.

Probabilistic finite element analysis of residual stress formation in shrink-fit ceramic/steel gun barrels

The development of residual stresses in a hybrid α-SiC lining/CrMoV steel jacket gun barrel during shrink fitting of the jacket over the lining is studied using a probabilistic finite element analysis. Particular attention is given to understanding the development of the axial compressive stress in the ceramic lining, since this stress (if sufficiently high) can prevent lining failure caused by formation and growth of circumferential cracks near the barrel ends. To quantify the effect of variability in various design, material and process parameters on the magnitude and the distribution of the axial residual stress, a probabilistic structural analysis approach, known as the advanced mean value (AMV) method, is used, enabling determination of the cumulative distribution function for failure of the lining. The results obtained are validated using the adaptive importance sampling (AIS) method, an efficient direct statistical sampling technique. Lastly, the corresponding sensitivity factors which quantify the effect of variability in each parameter on the magnitude of axial residual stresses in the ceramic lining are computed. The results indicate that the loss of the compressive axial stress in the lining near the barrel ends is affected to the greatest extent by the magnitude of the friction coefficient at the lining/barrel interface.

Probabilistic slope stability analysis for practice

The impact of uncertainty on the reliability of slope design and performance assessment is often significant. Conventional slope practice based on the factor of safety cannot explicitly address uncertainty, thus compromising the adequacy of projections. Probabilistic techniques are rational means to quantify and incorporate uncertainty into slope analysis and design. A spreadsheet approach for probabilistic slope stability analysis is developed. The methodology is based on Monte Carlo simulation using the familiar and readily available software, Microsoft® Excel 97 and @Risk. The analysis accounts for the spatial variability of the input variables, the statistical uncertainty due to limited data, and biases in the empirical factors and correlations used. The approach is simple and can be applied in practice with little effort beyond that needed in a conventional analysis. The methodology is illustrated by a probabilistic slope analysis of the dykes of the James Bay hydroelectric project. The results are compared with those obtained using the first-order second-moment method, and the practical insights gained through the analysis are highlighted. The deficiencies of a simpler probabilistic analysis are illustrated. Key words: probabilistic analysis, slope stability, Monte Carlo simulation, spatial variability.

Limit Analysis of Structures with Stochastic Strengths by a Static Approach

A procedure for the evaluation of the conditional probability of collapse of elastic–plastic structures with stochastic strengths is presented. The procedure represents an extension to the stochastic framework of the static approach, coupled with the method of redundant unknowns, well established in the classical deterministic limit analysis. In this paper, a kinematic approach for probabilistic limit analysis, provided in the literature, is also recalled in order to show the duality with the proposed static approach. A beam of elastic perfectly plastic material with correlated stochastic strengths is studied and the influence of the degree of correlation between cross-sections is evidenced. When a low correlation is encountered an accurate discretisation is necessary. Furthermore, investigation of the influence of different collapse events on the conditional probability of collapse is conducted for a frame structure.

Seismic reliability analysis of earth slopes under short term stability conditions

Different models were developed for evaluating the probabilistic three-dimensional (3-D) stability analysis of earth slopes and embankments under earthquake loading. The 3-D slope stability model assumed is that of a simple cylindrical failure surface. The probabilistic models evaluate the probability of failure under seismic loading considering the randomness of earthquake occurrence, and earthquake induced acceleration and uncertainties stemming from the discrepancies between laboratory-measured and in-situ values of shear strength parameters. The models also takes into consideration the spatial variabilities and correlations of soil properties. The probabilistic analysis and design approach is capable of obtaining the 2-D and 3-D static and dynamic safety factors, the probability of slope failure, the earthquake induced acceleration coefficient, the yield acceleration coefficient, the earthquake induced displacement, and the probability of allowable displacement exceedance taking into account the local site effect. The approach is applied to a well known landslide case: Congress Street Landslide in Chicago. A sensitivity analysis was conducted on the different parameters involved in the models by applying those models to the Congress Street landslide considering different levels of seismic hazard. Also, a sensitivity analysis was carried out to study the sensitivity of computed results to input parameters of undrained shear strength, and corrective factors. A comparison was made between the different models of failure. The parametric study revealed that the hypocentral distance and earthquake magnitude have major influence on the earthquake induced displacement, probability of failure and dynamic 2-D and 3-D safety factors.