Uncertainty Theory Based Partitioning for Cyber-Physical Systems with Uncertain Reliability Analysis

Model uncertainty is a dominant source of uncertainty in offshore geotechnical reliability. Caused by limitationsin data quantity and quality, model uncertainty leads to uncertainty in the failure rate for a design. [n this paper, an approach is presented for evaluating model uncertainty and incorporating it into reliability analyses. This approach provides the ability to estimate statistics of the failure rate. The failure rate is of interest because (1) it represents an objective measure of performance, (2)it should enter into design decisions since it reflects quality, and (3) it can be observed, providing the ability to reduce model uncertainty by analyzing observed successes and failures. The value of reliability analyses will be enhanced greatly if a physical meaning (i.e., the rate of failure) can be assigned to the results. INTRODUCTION Foundation design for offshore structures represents one of the earliest applications of reliability methods in geotechnical engineering. There are substantialuncertainties associated with the offshore environment concerning storm loads, site characterization and foundation behavior. In addition, costs for offshore construction are large and the consequences of failure are significant. Because of these large uncertainties and costs, considerable attention has been devoted during the past 20 years to develop reliability-based design pproaches for offshore foundations (e.g., Bea Wu et al1). The primary product of a reliability analysis is the probability of failure for a component or system. For example, Tang and Gilbert2 evaluated the reliability three pile foundation systems constructed during the early 1980's. They obtained probabilities of collapse over a 20-year design life ranging from 0.005 to 0.01. Lacasse and Nadim3 presented failure probabilities ranging from 0.00007 for bearing capacity failure of a for gravity structure to 0.02 for failure of a platform system under seismic loading. In both papers, the authors contended that the calculated probabilities were not 'absolutd' quantities but expected probabilities, at best, hich could be used for comparing different designs. 11-wsecalculated probabilities were not based purely on actuarial data, and therefore contained a large measure f subjective judgment and interpretation. In fact, eotechnical reliability analyses are somewhat unique inhat this component of judgment and interpretation due tolimited data, which we will refer to as model ncertainty, is dominant. In recent years, several efforts have been directed at calibrating estimated failure probabilities for offshore structures4,5. Which the value of a reliability analysis is greatly enhanced if a physical meaning can be assigned to the failure probabilities, a clear understanding of model uncertainty is required to achieve this object paper, we provide a definition of model uncertainty anddistinguish it from random uncertainty, identify sources of model uncertainty, and discuss how to evaluate and represent model uncertainty in reliability analyses. DEFINITION OF MODEL UNCERTAINTY Random Events Uncertainties abound in offshore foundation design; soilproperties, loading conditions and foundation behavior are not known with certainty at different points in time and space. There is a risk that a foundation will not perform as designed because of these uncertainties.

This work considers the vibrating system that consists of a snap-through truss absorber coupled to an oscillator under excitation of an electric motor with an eccentricity and limited power, characterizing a non-ideal oscillator. It is aimed to use the non-linearity and quasi-zero stiffness of absorber (snap-through truss absorber) to obtain a significantly attenuation the jump phenomenon. There is also an interest to exhibit the reduction of Sommerfeld effect, to confirm the saturation phenomenon occurrence and show the power transfer in a non-linear structure, evidencing the pumping energy. As shown by simulations in this work, this absorber allows the energy pumping before and during the jump phenomenon, decreasing the higher amplitudes of considered system. Additionally, the occurrence of saturation phenomenon due use of snap-through truss absorber is verified. The analysis of parameter uncertainties was introduced. Sensitivity of system with parametric errors demonstrated a trustable system.

Parameter uncertainty and elasticity analyses of a population model: setting research priorities for shearwaters

Our earlier research work on applying architecture-based software reliability models on a large scale case study allowed us to test how and when they work, to understand their limitations, and to outline the issues that need future research. In this paper we first present an additional case study which confirms our earlier findings. Then, we present uncertainty analysis of architecture-based software reliability for both case studies. The results show that Monte Carlo method scales better than the method of moments. The sensitivity analysis based on Monte Carlo method shows that (1) small number of parameters contribute to the most of the variation in system reliability and (2) given an operational profile, components' reliabilities have more significant impact on system reliability than transition probabilities. Finally, we summarize the lessons learned from conducting large scale empirical case studies for the purpose of architecture-based reliability assessment and uncertainty analysis.

Taking into account a general concept of risk parameters and knowing that natural gas provides very significant portion of energy, firstly, it is important to insure that the infrastructure remains as robust and reliable as possible. For this purpose, authors present available statistical information and probabilistic analysis related to failures of natural gas pipelines. Presented historical failure data is used to model age-dependent reliability of pipelines in terms of Bayesian methods, which have advantages of being capable to manage scarcity and rareness of data and of being easily interpretable for engineers. The performed probabilistic analysis enables to investigate uncertainty and failure rates of pipelines when age-dependence is significant and when it is not relevant. The results of age-dependent modeling and analysis of gas pipeline reliability and uncertainty are applied to estimate frequency of combustions due to natural gas release when pipeline failure occurs. Estimated age-dependent combustion frequency is compared and proposed to be used instead of conservative and age-independent estimate. The rupture of a high-pressure natural gas pipeline can lead to consequences that can pose a significant threat to people and property in the close vicinity to the pipeline fault location. The dominant hazard is combustion and thermal radiation from a sustained fire. The second purpose of the paper is to present the combustion consequence assessment and application of probabilistic uncertainty analysis for modeling of gas pipeline combustion effects. The related work includes performance of the following tasks: to study gas pipeline combustion model, to identify uncertainty of model inputs noting their variation range, and to apply uncertainty and sensitivity analysis for results of this model. The performed uncertainty analysis is the part of safety assessment that focuses on the combustion consequence analysis. Important components of such uncertainty analysis are qualitative and quantitative analysis that identifies the most uncertain parameters of combustion model, assessment of uncertainty, analysis of the impact of uncertain parameters on the modeling results, and communication of the results’ uncertainty. As outcome of uncertainty analysis the tolerance limits and distribution function of thermal radiation intensity are given. The measures of uncertainty and sensitivity analysis were estimated and outcomes presented applying software system for uncertainty and sensitivity analysis. Conclusions on the importance of the parameters and sensitivity of the results are obtained using a linear approximation of the model under analysis. The outcome of sensitivity analysis confirms that distance from the fire center has the greatest influence on the heat flux caused by gas pipeline combustion.

As a safety critical system, affected by cognitive uncertainty and flight environment variability, aircraft electrical power system proves highly uncertain in its failure occurrence and consequences. However, there are few studies on how to reduce the uncertainty in the system design stage, which is of great significance for shortening the development cycle and ensuring flight safety during the operation phrase. For this reason, based on the variance decomposition theory, this paper proposes an importance measure index of the influence of component failure rate uncertainty on the uncertainty of power supply reliability (system reliability). Furthermore, an algorithm to calculate the measure index is proposed by combining with the minimum path set and Monte Carlo simulation method. Finally, the proposed method is applied to a typical series-parallel system and an aircraft electrical power system, and a criteria named as “quantity and degree optimization criteria” is drawn from the case study. Results demonstrate that the proposed method indeed realizes the measurement of the contribution degree of component failure rate uncertainty to system reliability uncertainty, and combined with the criteria, proper solutions can be quickly determined to reduce system reliability uncertainty, which can be a theoretical guidance for aircraft electrical power system reliability design.

References

Conceptual design's intrinsic uncertainty and influence on product life cycle cost make reliability engineering tools during early design phases important. However, typically poor knowledge bases make the prediction of component failure and system performance challenging. Fuzzy techniques are used here during initial conceptual design stages to quantify imprecision and uncertainty in reliability and risk analysis. More specifically, a fuzzy approach is compared to the probabilistic approach presented in Reliability prediction models to support conceptual design by Ormon, et al. (2002). Triangular fuzzy numbers instead of triangular probability distributions represent unknown failure rates here. Two examples of fuzzy reliability analysis in conceptual design are presented where system reliability is evaluated at the subsystem level: The first is to familiarize the reader with fuzzy reliability subsystem level analysis. The second demonstrates fuzzy reliability prediction models for conceptual design tradeoffs. Examples include subsystems operating with active and standby redundancy. In the first example, defuzzified system reliability is a more conservative prediction than that found probabilistically. Recommendations in Example 2 do not differ from those based on the probabilistic models of Ormon, et al.

Uncertainty analysis and modelling in EP evaluation is one of the main focus for the oil industry during the last decade and many progress have been made on the subject, although there are still more improvements to come as the problem is far from being trivial. This key note talk will share with the audience the state of the art we are today with different uncertainty analysis and modelling techniques used by the industry in order to identify and reduce potential risks involved. Uncertainty analysis is the first and crucial step, aiming at identifying correctly the key uncertainties, their related nature (bias or variance errors) and their impact on the results under consideration. Weak signals from measurements should be scrutinized and analogues should be investigated in case of sparse data or information. Uncertainty modelling is the final step using either well known deterministic approach or more complex probabilistic ones. The process is closely linked with the geological and reservoir modelling tasks and must comply with the objective which has been set up beforehand. Their applications and limits are frequently subject of debate, as well as the long time it took to complete the whole process, sometimes with hundreds of models to be generated and investigated. At the end, the communication of the uncertainty results to different parties is not always an easy task, since the probabilistic language is seldom popular among operational staff and especially when the operational needs differ greatly from one group to another. Big challenges still lay ahead for a more comprehensive approach for uncertainty analysis and modelling with a trend towards larger models of the subsurface and more realistic representation of reservoir heterogeneities. However, mastering the uncertainties and risks is the sole way for a better exploration and development.

On the use of uncertainty analyses to test hypotheses regarding deterministic model predictions of environmental processes

Passive containment cooling system is innovatively used in AP1000 reactor design to enhance the safety. Since the system operation is based on natural circulation, physical process failure induced by uncertainties of physical parameters becomes one of the important failure modes (e.g. natural circulation cannot establish or keep and system design function cannot be accomplished because some parameters such as air temperature deviate from their design values), which should be considered in system reliability evaluation. As the heat sink, air temperature with high uncertainty has important effect on system reliability. In this article, we analyze the pressure variation in the containment along with the air temperature based on system thermal–hydraulic model, and the effect of air temperature on system operation is closely related to the thermal–hydraulic performance of the system. Moreover, the system thermal–hydraulic capacity is influenced by the system component configuration, so we evaluate the system physical process failure probability by Monte Carlo simulation and analyze the effect of air temperature distribution under different system component configurations. Finally, we evaluate the whole system reliability considering the logical relationship between physical process failure and equipment fault by fault tree method. The results illustrate that air temperature distribution has important influence on the system reliability, the system failure probability may be difference by several orders and the main contributors may be different at different plant locations, so climate should be considered in system design and reliability analysis.

Parameter uncertainty analysis for simulating streamflow in a river catchment of Vietnam

In reliability analysis of computer systems, models such as fault trees, Markov chains, and stochastic Petri nets (SPN) are built to evaluate or predict the reliability of the system. In general, the parameters in these models are usually obtained from field data, or by the data from systems with similar functionality, or even by guessing. In this paper, we address the parameter uncertainty problem. First, we review and classify three ways to describe the parameter uncertainty in the model: reliability bounds, confidence intervals, and probability distributions. Second, by utilizing the second-order approximation and the normal approximation, we propose an analytic method to derive the confidence interval of the system reliability from the confidence intervals of parameters in the transient solution of Markov models. Then, we study the Monte Carlo simulation method to derive the uncertainty in the system reliability, and use it to validate our proposed analytic method. Our effort makes the reliability prediction more realistic compared with the result without the uncertainty analysis.

Groundwater is a crucial resource for water supply and irrigation in many parts of the world, especially in the Middle East. The Eocene aquifer, located in the northern part of the West Bank, Palestine, is threatened by unsustainable groundwater abstractions and on-ground pollution. Analysis and management of this aquifer are challenging because of limited data availability. This research contributes to the long-term sustainability of the aquifer by model-based design of future abstraction strategies considered within an uncertainty analysis framework. The methodology employed started with development of a single-layer steady-state MODFLOW groundwater model of the area, followed by uncertainty analysis of model parameters using Monte Carlo simulations. The same model was afterwards coupled with a Successive Linear Programming (SLP) optimization algorithm, implemented in the Groundwater Management tool (GWM) of the United States Geological Survey (USGS). The purpose of optimization was deriving five optimal abstraction strategies, each aiming to maximize groundwater abstraction, subject to different constraints regarding groundwater depletion. Given the uncertainty of model parameters, the sensitivity and reliability of these optimal strategies were then tested. Sensitivity was checked for two optimal strategies by performing re-optimization with different values of uncertain model parameters (one at a time). Reliability of the five strategies was tested by analyzing the extent of constraints’ violation for each strategy when varying the uncertain parameters using Monte Carlo simulations. Finally, the model was used for determining capture zones of wells for the five optimal abstraction strategies, land-use in these capture zones, and the associated estimates of on-ground nitrogen loading. The developed strategies were then deployed in a web-based decision support application (named Groundwater Decision Support System—GDSS), together with other relevant information. Users can analyze results of different optimal strategies in terms of groundwater level variations and total water balance results, and test consequences of uncertain parameters. Capture zones of wells for different abstraction strategies, together with land-use and on-ground nitrogen loading in these capture zones, are also presented. Results show that critical uncertain parameters are recharge, hydraulic conductivity, and conductance at key boundary condition locations. Optimal abstraction strategies results indicate that an increase in total abstractions could be between 5% and 20% from the current level (estimated at about 56 × 106 m3/year, which is about 74% of estimated annual recharge). The uncertain parameters, however, are impacting the sensitivity and the reliability of the optimal strategies to variable degrees. Recharge and hydraulic conductivity are the most critical uncertain parameters regarding sensitivity of the optimal strategies, while reliability is also impacted by the level of abstraction proposed in a given strategy (number, locations, and abstraction rates of new wells). The main novelty and contribution of this research is in combining modelling, uncertainty analysis, and optimization techniques in a comprehensive decision support system for the area of the Eocene aquifer, characterized with limited data availability.

Reliable design of mission critical systems requires a special class of engineering methods and tools. As a fundamental technique, Markov modeling has played a significant role in fault-tolerant and fail-safe system reliability analysis dating back to the 1960's. Early applications included flight control system design for military aircraft and spacecraft. Although Markov reliability modeling techniques are well researched, they have not been widely used because of the lack of affordable, easy-to-use reliability modeling and analysis tools. In particular, we need to integrate the capabilities of expert systems (ES) with the computer-aided analysis tools. Thus, our goal is the reuse of the earlier developed Markov methods and tools within the new highly-interactive computing environment.