Variation In Probability Research Articles

Probabilistic modeling of rockfall trajectories: a review

Probabilistic approaches are widely adopted for the modeling of rockfall trajectories, but are not widely discussed in the literature. This paper aims to help fill this gap by reviewing probabilistic models of rockfall trajectories, while providing some perspectives for future study. We first make it clear that, from a theoretical point of view, the probabilistic approach is necessitated by both the ontic (inherent) uncertainty associated with rockfalls and the epistemic (information) uncertainty associated with numerical modeling. The review suggests that there may be the potential to improve the probabilistic modeling of rockfall trajectories in various aspects, including the systematic probabilistic modeling criterion, the random sampling approaches employed for probabilistic variables, the probabilistic modeling of rock shape, and the probabilistic prediction of rockfall intensity. However, there are still some open questions regarding the promotion of probabilistic modeling in practice. It is not clear whether probabilistically treating all of the variables of rockfall trajectory model with reasoned distributions will lead to significantly improved results, or whether the improvements will be great enough (given the difficulties and costs involved) that it is worth quantifying all of the uncertainties involved in rockfall trajectory modeling. The answers to these questions can be found in the practice of probabilistic modeling itself.

Towards Active Diagnosis of Hybrid Systems leveraging Multimodel Identification and a Markov Decision Process

Active diagnosis is defined as the association of fault detection and isolation algorithms with the execution of control plans that optimize fault research performance. This paper addresses active diagnosis of hybrid systems. It proposes to associate a diagnosis method based on multimodel identification and a framework for optimal conditional planning relying on a Markov decision process (MDP). The multimodel diagnosis algorithm identifies the most probable fault by measuring a distance between residual vectors generated from the test system and a set of REFERENCE fault models. Moreover a criterion called the correct diagnosis rate (CDR) is set up to evaluate the accuracy of the diagnosis results depending on the applied operation sequence. Conditional planning is formulated as a MDP, which is a model mixing a discrete structure and probabilistic variables. It is based on a reward function weighing diagnosis accuracy and the cost of actions and the optimal conditional plan is characterized thanks to the recursive Bellman function. An application to a diesel engine airpath model is presented so as to illustrate the diagnosis and planning methods in practice.

Optimization based on reliability and confidence interval design for the structural-acoustic system with interval probabilistic variables

In practice, the uncertain parameters whose unique distributions cannot be identified on the basis of limited data existed in the structural-acoustic system extensively. The uncertain parameters with limited data can be modeled as interval probabilistic variables whose distribution parameters are expressed as interval variables instead of unique values. For the optimization of the structural-acoustic system with interval probabilistic variables, a new optimization technique named as the optimization based on reliability and confidence interval design (O-RCID) is developed. O-RCID is a nested loop optimization whose computational cost during the evaluation of the confidence interval of sound pressure response and the system reliability is considerable. To improve the computational efficiency of O-RCID, a change-of-variable interval probabilistic perturbation method (CV-IPPM) which is based on the perturbation approach and change-of-variable technique is proposed to calculate the confidence interval of sound pressure response and the system reliability. By introducing CV-IPPM, the nested loop O-RCID is converted into an approximate single-loop one which can be efficiently solved. Numerical examples demonstrate the effectiveness and efficiency of O-RCID based on CV-IPPM for the optimization of the structural-acoustic system with interval probabilistic variables.

PENGENDALIAN PERSEDIAAN PADA KONDISI STOKASTIK DAN HARGA BERTINGKAT MENGGUNAKAN SIMULASI

investment value of the company in the form of supplies could reach 50 % of the value of all assets . Basically resource inventory is idle resources, which means that if the excess inventory will lead to wasted investment , but if there is no inventory would be difficult to anticipate fluctuations in demand can lead to stockout . So, we need a good inventory management to manage the balance between inventory investment and customer service . This research took a case study in Olla Bakery where there is demand and uncertain lead time , which affects the supply of raw material flour . To control the supply of the raw material , in this study using Monte Carlo simulation due to the properties of probabilistic variables , fluctuating demand , lead time is uncertain , and also considering the quantity discounts in the purchase of raw materials as a consideration in the simulation . The results obtained from this study that the Monte Carlo simulation method can reduce inventory costs by 6.83% , so it can be taken into consideration for the company in the purchase of raw materials. Keywords : Probabilistic, Quantity Discount, Monte Carlo

A collocation reliability analysis method for probabilistic and fuzzy mixed variables

The main bottleneck of the reliability analysis of structures with aleatory and epistemic uncertainties is the contradiction between the accuracy requirement and computational efforts. Existing methods are either computationally unaffordable or with limited application scope. Accordingly, a new technique for capturing the minimal and maximal point vectors instead of the extremum of the function is developed and thus a novel reliability analysis method for probabilistic and fuzzy mixed variables is proposed. The fuzziness propagation in the random reliability, which is the focus of the present study, is performed by the proposed method, in which the minimal and maximal point vectors of the structural random reliability with respect to fuzzy variables are calculated dimension by dimension based on the Chebyshev orthogonal polynomial approximation. First-Order, Second-Moment (FOSM) method which can be replaced by its counterparts is utilized to calculate the structural random reliability. Both the accuracy and efficiency of the proposed method are validated by numerical examples and engineering applications introduced in the paper.

Assessment of the Internal Pressure Fragility of the PWR Containment Building Using a Nonlinear Finite Element Analysis

Abstract In this study, the probabilistic internal pressure fragility analysis was performed by using the non-linear finite element analysis method. The target structure is one of the containment buildings of typical domestic pressurized water reactors(PWRs). The 3-dimensional finite element model of the containment building was developed with considering the large equipment hatches. To consider uncertainties in the material properties and structural capacities, we performed the sensitivity analysis of the ultimate pressure capacity with respect to the variation of four important uncertain parameters. The results of the sensitivity analysis were used to the selection of the probabilistic variables and the determination of their probabilistic parameters. To reflect the present condition of the tendon pre-stressing force, the data of the pre-stressing force acquired from the in-service inspections of tendon forces were used for the determination of the median value. Two failure modes(leak, rupture) were considered and their limit states were defined to assess the internal pressure fragility of target containment building. The internal pressure fragilities for each failure mode were evaluated in terms of median internal pressure capacity, high confidence low probability of failure(HCLPF) capacity, and fragility curves with respect to the confidence levels. The HCLPF capacity was 115.9 psig for leak failure mode, and 125.0 psig for rupture failure mode.

Perpetual extraction of work from a nonequilibrium dynamical system under Markovian feedback control

By treating both control parameters and dynamical variables as probabilistic variables, we develop a succinct theory of perpetual extraction of work from a generic classical nonequilibrium system subject to a heat bath via repeated measurements under a Markovian feedback control. It is demonstrated that a problem for perpetual extraction of work in a nonequilibrium system is reduced to a problem of Markov chain in the higher-dimensional phase space. We derive a version of the detailed fluctuation theorem, which was originally derived for classical nonequilibrium systems by Horowitz and Vaikuntanathan [Phys. Rev. E 82, 061120 (2010)], in a form suitable for the analyses of perpetual extraction of work. Since our theory is formulated for generic dynamics of probability distribution function in phase space, its application to a physical system is straightforward. As simple applications of the theory, two exactly solvable models are analyzed. The one is a nonequilibrium two-state system and the other is a particle confined to a one-dimensional harmonic potential in thermal equilibrium. For the former example, it is demonstrated that the observer on the transitory steps to the stationary state can lose energy and that work larger than that achieved in the stationary state can be extracted. For the latter example, it is demonstrated that the optimal protocol for the extraction of work via repeated measurements can differ from that via a single measurement. The validity of our version of the detailed fluctuation theorem, which determines the upper bound of the expected work in the stationary state, is also confirmed for both examples. These observations provide useful insights into exploration for realistic modeling of a machine that extracts work from its environment.

A Method for the Analysis of Behavioural Uncertainty in Evacuation Modelling

Evacuation models generally include the use of distributions or probabilistic variables to simulate the variability of possible human behaviours. A single model setup of the same evacuation scenario may therefore produce a distribution of different occupant-evacuation time curves in the case of the use of a random sampling method. This creates an additional component of uncertainty caused by the impact of the number of simulated runs of the same scenario on evacuation model predictions, here named behavioural uncertainty. To date there is no universally accepted quantitative method to evaluate behavioural uncertainty and the selection of the number of runs is left to a qualitative judgement of the model user. A simple quantitative method using convergence criteria based on functional analysis is presented to address this issue. The method permits (1) the analysis of the variability of model predictions in relation to the number of runs of the same evacuation scenario, i.e. the study of behavioural uncertainty and (2) the identification of the optimal number of runs of the same scenario in relation to pre-defined acceptance criteria.

Probabilistic Power Flow Analysis With Generation Dispatch Including Photovoltaic Resources

This paper proposes a novel probabilistic power flow (PPF) algorithm considering generation dispatch. The intent is to examine the influence of uncertainty due to photovoltaic (PV) generation resources and loads. PV generation uncertainty may have a significant impact on transmission systems since this resource is easily influenced by changing environmental conditions. However, it is prudent to include generation dispatch in the PPF algorithm since the dispatching strategy compensates for PV generation injections and influences the uncertainty in the results. The proposed PPF algorithm is based on the cumulant method. The Gram-Charlier expansion is applied to approximate the distribution of probabilistic variables. Furthermore, this paper also proposes a probabilistic optimal power dispatching strategy which considers uncertainty problems in the economic dispatch and optimizes the expected value of the total cost with the overload probability as a constraint. The Arizona area of the Western Electricity Coordinating Council (WECC) system is used to test the proposed PPF algorithm and compare results with Monte Carlo simulation (MCS).

Modulating robustness in control design: Principles and algorithms

Many problems in systems and control, such as controller synthesis and state estimation, are often formulated as optimization problems. In many cases, the cost function incorporates variables that are used to model uncertainty, in addition to optimization variables, and this article employs uncertainty described as probabilistic variables. In a probabilistic setup, a cost value can only be guaranteed with a certain probability. Like pulling down one end of a rope wrapped around a pulley lifts the other end, decreasing the probability improves the cost value. This article analyzes this trade-off and describes quantitative tools to drive the user's choice toward a suitable compromise.

Weakening of Intervocalic /s/ in the Nijmegen Corpus of Casual Spanish

This study describes the weakening of intervocalic /s/ in the Nijmegen Corpus of Casual Spanish and investigates the role of several potential conditioning factors, including morphological, lexical and probabilistic variables. Three acoustic parameters were examined: voicing, the difference in high-band (4–8 kHz) intensity between /s/ and the following vowel, and the duration of the dip in low-band (0–1.5 kHz) intensity in /s/. Over a third of the /s/ consonants exhibited uninterrupted voicing. All three parameters were highly sensitive to speech rate and, less consistently, to prosodic factors such as word position and stress. We also found that /s/ suffixes in redundant morphosyntactic contexts were more prone to weakening than other word-final /s/ segments. Several high-frequency words were particularly prone to weakening, but no general probabilistic effects were observed for factors claimed to favor reduction such as word frequency, contextual predictability or grammatical class. These findings demonstrate the complex variability characteristic of reduction phenomena in spontaneous speech.

In situ measured cross section geometry of old timber structures and its influence on structural safety

Old timber structures may show significant variation in the cross section geometry along the same element, as a result of both construction methods and deterioration. As consequence, the definition of the geometric parameters in situ may be both time consuming and costly. This work presents the results of inspections carried out in different timber structures. Based on the obtained results, different simplified geometric models are proposed in order to efficiently model the geometry variations found. Probabilistic modelling techniques are also used to define safety parameters of existing timber structures, when subjected to dead and live loads, namely self-weight and wind actions. The parameters of the models have been defined as probabilistic variables, and safety of a selected case study was assessed using the Monte Carlo simulation technique. Assuming a target reliability index, a model was defined for both the residual cross section and the time dependent deterioration evolution. As a consequence, it was possible to compute probabilities of failure and reliability indices, as well as, time evolution deterioration curves for this structure. The results obtained provide a proposal for definition of the cross section geometric parameters of existing timber structures with different levels of decay, using a simplified probabilistic geometry model and considering a remaining capacity factor for the decayed areas. This model can be used for assessing the safety of the structure at present and for predicting future performance.

Characterisations of multivalued dependency implication over undetermined universes

In relational databases the original definition of a multivalued dependency is dependent on the underlying relation schema. In this context, the implication of multivalued dependencies has been characterised from multiple perspectives. Logically, it is equivalent to the logical implication of certain material implications in Boolean propositional logic. Proof-theoretically, the Chase procedure offers a convenient tool to decide implication. And algebraically, the implication can be characterised by the notion of closed attribute sets with respect to multivalued dependencies. The assumption of having a fixed underlying relation schema is not always feasible in practice, and also distinguishes multivalued dependencies from other classes of data dependencies. In this paper, we establish logical, proof-theoretical and algebraic characterisations for Biskupʼs notion of multivalued dependency implication over undetermined universes. That is, we unburden the current theory of the assumption of having a fixed underlying relation schema. From the perspective of probability theory this means that is unnecessary to fix the set of discrete probabilistic variables in order to utilise conditional independencies.

Probabilistic Simulation for Combined Cyclic Fatigue in Composites

The combined cyclic fatigue is computationally simulated by a judicious combination of three independent computational modules: composite mechanics, a multi-factor equation module (MFIM) and probabilistic algorithm (FPI). The inputs to each module are constituent material properties, processing variables, loading and environmental conditions and probabilistic variables. The composite fatigue is simulated by considering an inplane loaded-component in a structure which is subjected to fatigue because of cyclic loading. Typical results show that the low probability fatigue cycle is about 50 percent of the corresponding static value.

Safety Evaluation of Timber Structures through Probabilistic Analysis

This work presents a procedure for the use of probabilistic modelling techniques in the assessment of safety parameters of existing timber structures, when influenced by two types of actions. The parameters of the models have been defined as probabilistic variables, and Monte Carlo simulation technique was taken into account for safety evaluation. The case study here examined concerns four king post trusses on which a safety evaluation method was conducted to determine a target reliability index. Since the structures presented a high level of deterioration, a model considering the variation of the residual cross-section and the influence of environment in resistance was taken into account. Time dependent deterioration models have also been considered. With the results given by the different used models, it was possible to obtain probabilities of failure and respective reliability indices, as well as time evolution deterioration curves for a deteriorated historical structure.

XU-RSM: Diffuse response surface model for reliability-based design optimization

We focus on a new response surface methodology (XU-RSM) adapted to RBDO, based on Diffuse Approximation. This method uses simultaneously the points in the space of probabilistic variables (U-space) and the points in the space of physical variables (X-space). The two grids form a "virtual design of experiments" and are progressively explored in order to minimize the number of the "exact" function evaluations. A variant of the first order reliability method FORM is chosen to calculate the safety index. A case study is investigated for the numerical control (NC) machining operations of ultrahigh strength steel. We show how the proposed method can decrease the amount of function calculations and reduce the computing time.

The influence of the axial, antero-posterior and lateral positions of the center of rotation of a ball-and-socket disc prosthesis on the cervical spine biomechanics

Background Previous studies documented the importance of the positioning and the design parameters of the prosthesis in determining the biomechanics of the implanted spine. However, a comprehensive biomechanical evaluation of the significance of these parameters is still lacking. Therefore, the paper is aimed to the quantification of their influence on the flexibility of the implanted spine and the force transmitted through the facet joints. Methods A finite element model of the C5–C6 spine unit including a ball-and-socket disc prosthesis was built. Three probabilistic variables were considered: the axial, antero-posterior and lateral positions of the center of rotation. Randomized input parameters were generated with the Monte Carlo method. Pure moments of 1.6 Nm in flexion, extension, lateral bending and axial rotation were imposed to the upper endplate of C5; 100 simulations were conducted for the each of the considered loading conditions. Findings Axial position of the center of rotation influenced the spine flexibility in all loading conditions and the facet force in extension, lateral bending and axial rotation. The antero-posterior position was found to influence the spine flexibility in flexion and extension, and the facet force in lateral bending and axial rotation. The lateral position was not significant. Interpretation The effects of the positioning of a cervical disc prosthesis were estimated. A wide range of mechanical behaviors can be obtained by the manufacturers by appropriately manipulating the position of the center of rotation. A proper positioning of the artificial disc during the surgery, in particular in the antero-posterior direction, was found to be of critical importance.

選択肢集合形成のプロセスモデルを用いた観光地間の魅力の相互作用に関する分析

In this Paper, we analyzed the destination set of excursion of sightseeing tour. The adopted model assumes exploring process on the destination set decision in order to avoid computational problem. The Inter-correlation between destinations was considered using static and probabilistic variables in utility function. The result showed significant negative inter-correlation at the combination of different categories. This result helps to analyze excursion behaviors of tourists and to suggest advisable routes for tourists.

Effect of manufacturing tolerances on dynamic equilibria of multibody systems undergoing prescribed rotational motion

A general formulation is developed for the tolerance analysis of dynamic equilibria in a multibody system undergoing prescribed rotational motion, with applications including robots, spacecraft, propulsion and power generation systems, and sensors and actuators. In a state of dynamic equilibrium, a subset of the generalized coordinates assumes constant values while the remaining coordinates vary and respond in time. Manufacturing tolerances can be mathematically represented by probabilistic distributions or statistical variables through either an analytical approach or a Monte Carlo simulation. In the present tolerance work, the tolerances of design parameters including lengths, stiffnesses, inertias, and attachment positions are examined. In order to analytically calculate the statistical response of the dynamic equilibrium positions to such tolerances, the first-order sensitivities of the equilibria with respect to parameters are calculated. To illustrate the method’s accuracy and computational efficiency, two numerical examples are considered, and the statistical results obtained analytically for the equilibria are compared with those calculated through Monte Carlo simulation. In some cases, an equilibrium configuration can have an operating condition for which the response has zero standard deviation to perturbations of a design parameter. That condition can be a useful design point to the extent that typical manufacturing tolerances or other sources of variation would have no effect on the dynamic equilibrium configuration.

The Time Dependent Reliability Analysis for the Deteriorated Reinforced Concrete Columns Using the Monte Carlo Simulation

his study was prosecuted to analyze a structural resistance degradation model for the existing column in the 3-story building to be remodeled. The probabilistic random variables in this study were dealt with an initial member strength, current maximum crack width, current density and diameter of reinforcement with elapsed time and corrosion initiation time, TDRA has been performed to calculate the reliability index, the failure probability, the degradation level according to the member strength loss in reinforced concrete columns due to corrosion of steel reinforcement.