Rosenblueth's Point Estimate Research Articles

A point-estimate based method for soil amplification estimation using high resolution model under uncertainty of stratum boundary geometry

This study provides a practical technique for stochastically estimating soil amplification under uncertainty of the geometry of stratum boundary. To evaluate the possible values of the non-linear soil response under ambiguity, a nonlinear dynamic analysis with a high resolution 3D-FEM model is preferable, although the computations still represent a rigorous task. This study modifies Rosenblueth's point estimate method (PEM), which is greatly advantageous from the viewpoint of computational time, and demonstrates that the proposed method can provide good estimations with a very small number of calculations compared to the Monte-Carlo method. To evaluate the ground response stochastically, the preferable probability density function (PDF) is also examined. Furthermore, the estimation accuracy of the exceedance probability and the limitations of the proposed method are also discussed.

Methodology for quantitative landslide risk analysis in residential projects

This paper provides a quantitative assessment for the hazard, the vulnerability and the risk associated to slope instability as a tool for urban planners and policy makers. Analysis methodologies and overall numerical procedures are presented in detail. In order to assess a hazard, which is expressed as a temporal probability, FOSM technique was used along with Rosenblueth's point estimate method. Reliability index (β) was used as a standard measure to compare the results assessed with other information presented in published literature for a number of geotechnical projects. Concerning the analysis of vulnerability, a new approach was proposed by combining local methodology for seismic vulnerability designed for buildings in Medellin with generic analysis methodology for vulnerability of people when exposed to landslides. The risk was assessed by a simple mathematical crossing between hazard and vulnerability. A database of 120 residential projects located on natural slopes in the city of Medellin (Colombia) was used for the analysis. The results were presented as FN charts relating the calculated frequency of landslides to the number of potential life or economic losses.

Application of Neural Network for Prediction of Unmeasured Mode Shape in Damage Detection

The major problem in the vibration-based damage detection field is still a limited number of sensors and the existence of uncertainties. In this paper, a new approach combines a multi-stage ANN model and statistical method to detect damage based on the limited number of sensors with consideration of uncertainties. The first stage of the ANN is used to predict the unmeasured mode shapes data based on limited measured modal data. The second stage ANN is devoted to predicting the damage location and severity using the complete modal data from the first-stage ANN. To incorporate the uncertainties in modal data, Gaussian noise is applied to the input variables and the probability of damage existence is calculated using Rosenblueth's point estimate method. The feasibility of the proposed method is demonstrated using an analytical model of a continuous two-span reinforced concrete slab. The application of a multi-stage ANN showed results having a high potential of overcoming the issue of using a limited number of sensors in structural health monitoring.

Assessing the impact of uncertainty on flood risk estimates with reliability analysis using 1-D and 2-D hydraulic models

Abstract. This paper addresses the use of reliability techniques such as Rosenblueth's Point-Estimate Method (PEM) as a practical alternative to more precise Monte Carlo approaches to get estimates of the mean and variance of uncertain flood parameters water depth and velocity. These parameters define the flood severity, which is a concept used for decision-making in the context of flood risk assessment. The method proposed is particularly useful when the degree of complexity of the hydraulic models makes Monte Carlo inapplicable in terms of computing time, but when a measure of the variability of these parameters is still needed. The capacity of PEM, which is a special case of numerical quadrature based on orthogonal polynomials, to evaluate the first two moments of performance functions such as the water depth and velocity is demonstrated in the case of a single river reach using a 1-D HEC-RAS model. It is shown that in some cases, using a simple variable transformation, statistical distributions of both water depth and velocity approximate the lognormal. As this distribution is fully defined by its mean and variance, PEM can be used to define the full probability distribution function of these flood parameters and so allowing for probability estimations of flood severity. Then, an application of the method to the same river reach using a 2-D Shallow Water Equations (SWE) model is performed. Flood maps of mean and standard deviation of water depth and velocity are obtained, and uncertainty in the extension of flooded areas with different severity levels is assessed. It is recognized, though, that whenever application of Monte Carlo method is practically feasible, it is a preferred approach.

Influence of Uncertain Source Parameters on Strong Ground Motion Simulation with the Empirical Green's Function Method

A combined stochastic and Green's function approach was developed to simulate strong ground motions in Southwest Western Australia (SWWA) in a previous study. Although it was demonstrated that adopting the source parameters derived from other regions yielded reasonable simulation of ground motions in SWWA as compared with a few available strong motion records, the effect of source parameter variations on simulated ground motions was not known. This article performs a statistical study of the effects of random fluctuations of the seismic source parameters on simulated strong ground motions. The uncertain source parameters, i.e., stress drop ratio, rupture velocity, and rise time corresponding to the empirical source models are assumed to be the respective mean value of the parameter and normally distributed with an assumed coefficient of variation. The Rosenblueth's point estimate method [Rosenblueth, 1981] is used to calculate the statistics of the simulate ground motion parameters corresponding to different magnitudes and epicentral distances. The accuracy of the Rosenblueth's point estimate method in estimating the mean and standard deviation of ground motion PGA, PGV, and response spectrum is proven by simulating the ground motions from an ML6.0 and epicentral distance 100 km event with both the Rosenblueth's point estimate method and the Monte Carlo simulation method. A sensitivity analysis is preformed to investigate the effect of random fluctuations of each source parameters on strong ground motion simulation. A coefficient of variation model for ground motion parameters is developed based on the simulated data as a function of the variations of the three source parameters and earthquake magnitude, which can be used in probabilistic predictions of earthquake ground motions with uncertain source parameters.

Distinctive and fuzzy failure probability analysis of an anisotropic rock mass to explosion load

AbstractThis paper estimates failure probability of an anisotropic rock mass with random initial damage and random critical tensile strain to explosion loads. The initial random damage and critical tensile strain of the rock mass are estimated by approximate statistical methods. They are incorporated into the constitutive law of the anisotropic damage model. The statistical estimation of the rock‐mass response to underground explosion is evaluated by the Rosenblueth's point estimate method. A statistical anisotropic continuum damage model considering both the anisotropic initial damage and cumulative damage dependent on tensile strain is suggested. A beta distribution is proposed to represent the probabilistic distribution of the damage variable of the rock mass under blasting loads. Using the theory of reliability, failure probabilities are calculated according to different levels of failure criteria of the rock mass. A fuzzy definition is also proposed to describe the fuzzy nature of failure phenomenon of the rock mass. Based on the fuzzy random probabilistic theory, a model including both the effects of randomness of the rock‐mass properties and fuzziness of its failure criterion is proposed for the failure analysis of the rock mass. The suggested models are coded and linked with an available computer programe Autodyn3D as its user's subroutines. Using the Autodyn3D together with the suggested model, a series of field blasting tests are simulated. Numerical results of stress wave propagation are compared with field‐recorded data. The failure probabilities of the rock mass around the charge hole are estimated. Copyright © 2002 John Wiley & Sons, Ltd.

Numerical Analysis of Blast-Induced Stress Waves in a Rock Mass with Anisotropic Continuum Damage Models Part 2: Stochastic Approach

This paper reports the second part of the study carried out by the authors on the underground explosion-induced stress wave propagation and damage in a rock mass. In the accompanying paper reporting the first part of the study, equivalent material properties were used to model the effects of existing cracks and joints in the rock mass. The rock mass and its properties were treated as deterministic. In this paper, existing random cracks and joints are modeled as statistical initial damage of the rock mass. In numerical calculation, an anisotropic continuum damage model including both the statistical anisotropic initial damage and cumulative damage dependent on principal tensile strain and stochastic critical tensile strain is suggested to model rock mass behavior under explosion loads. The statistical estimation of stress wave propagation in the rock mass due to underground explosion is evaluated by Rosenblueth's point estimate method. The suggested models and statistical solution process are also programmed and linked to Autodyn3D as its user's subroutines. Numerical results are compared with the field test data and those presented in the accompanying paper obtained with equivalent material property approach.

Computational stochastic analysis of earth structure settlements

Abstract A stochastic method and its computer implementation to evaluate the earth structure settlements that occur under static loading is presented in this paper. The settlements are calculated with a commercial finite difference program called Dynard, which considers a non-linear elasto-plastic soil model based on the shear and bulk moduli and the undrained strength of the soil. The Monte Carlo simulation technique and the Rosenblueth's point estimate methods are considered in the proposed approach. To illustrate the suitability and accuracy of the proposed procedure, the settlements arising on an earth dam model under gravity loads are calculated. The results are compared and validated with the settlements obtained with a boundary element method program codified by the authors.

Dynamic response analysis of rock mass with stochastic properties subjected to explosive loads

Abstract This paper carries out probabilistic analysis of dynamic responses of rock mass under blast loads. Statistical analysis of the initial damage and strength constants of the rock mass is performed by using both the field and laboratory test data. The initial damage of the rock mass is found having the beta distribution, while the critical tensile strain has the normal distribution. These statistical properties are incorporated into the constitutive law and cumulative damage model for rock mass. The statistical estimation of stress wave propagation in the rock mass due to underground explosion is evaluated by Rosenblueth's point estimate method. In numerical calculation, an isotropic continuum damage model considering both the initial damage and the cumulative damage dependent on an equivalent tensile strain is suggested to model rock mass behaviour under blast loads. The suggested models are programmed and linked to an available computer program Autodyn2D through its user's subroutine capability. U...

Uncertainty Analysis by Point Estimate Methods Incorporating Marginal Distributions

The model performance of an engineering system is affected by many variables subject to uncer­ tainty. Point estimate (PE) methods are practical tools to assess the uncertainty features of a model involving multivariate stochastic parameters. Two PE methods have been developed for engineering applications. One is Rosenblueth's PE method, which preserves the first three moments of random variables and the other is Hare's PE method, which reduces the computations of Rosenblueth's method but only as appropriate for application to random variables with normal distributions. In this study, two algorithms are proposed to encompass the advantages of the two PE methods: computational practicality and the handling of mixture distributions. Through a numerical experiment, the proposed methods yielded more accurate estimations than those of Rosenblueth's method with about the same amount of computation as Hare's method. The two proposed methods were also applied to estimate statistical moments of a pier scouring model output to demonstrate their performance in an engineering application.

Calibration and Control for Estuary System under Uncertainty

A comprehensive stochastic management methodology is developed for a distributed-parameter estuary system (DPES) which is described by partial differential equations (PDEs). The proposed stochastic management methodology consists of uncertainty-based calibration (i.e. parameter estimation under uncertainty) and uncertainty-based control (i.e. determination of optimal freshwater inflows into the estuary under uncertainty). The technique for uncertainty-based calibration is based on Gauss–Newton minimization method and uncertainty analysis method such as Rosenblueth's point estimate method or Harr's point estimate method. The uncertainty-based calibration technique is used to estimate the optimal parameters such as Manning's roughness coefficient and dispersion coefficient in the PDEs while considering the uncertainties in the boundary conditions or initial conditions for the PDEs. The technique for uncertainty-based control is based on a real-time control method which is discrete-time stochastic linear quadratic feedback control. Real-time control is achieved by feedback control which uses salinities at test stations in the estuary as the state vector and controlled freshwater inflows as the control vector. The feedback control law determines the real-time control vector using observed states in a manner that best approximates desired states and controls (freshwater inflows). This new methodology for real-time control has been applied to the Lavaca–Tres Palacios Estuary in Texas for purposes of testing and illustration.

Uncertainty and Risk Analyses for FEMA Alluvial-Fan Method

Alluvial fans along mountain bases pose quite interesting problems for the design of hydraulic structures and highway crossings and for flood insurance studies. The Federal Emergency Management Agency (FEMA) alluvial-fan method is subject to uncertainties because it is an approximate method. In this paper, Rosenblueth's point-estimate is applied to the FEMA alluvial fan method to compute the mean and standard deviation for the 100-yr discharge at any point on the fan and the mean and standard deviation for the fan arc width. The mean and standard deviation for the 100-yr discharge are used to obtain the risk that the 100-yr discharge will exceed the discharge capacity of hydraulic structures on the fan. The mean and standard deviation for the fan arc width are used to estimate the risk that a given location on the fan is within the hazard flood zone. The HEC-1 rainfall-runoff computer model is used to compute inputs to the FEMA method. The proposed uncertainty and risk analyses are applied to an alluvial fan in north Scottsdale, Ariz.

Analysis of random anisotropic damage mechanics problems of rock mass

Probabilistic analysis of random anisotropic damage mechanics problems is proposed in Parts of I and II. In Part I, a probabilistic law of damage variables for rock mass was presented as a Beta distribution by using the Monte-Carlo statistical simulation method. In part II, statistical estimation of a damage state and properties of random damaged rock mass are evaluated by Rosenblueth's point estimate method. Two stability problems involving randomly damaged rock mas have been analyzed using the finite element method

Analysis of random anisotropic damage mechanics problems of rock mass

A probabilistic analysis method of random anisotropic damage mechanics problems is proposed in parts I and II. In part I, based on the measured characteristics of random crack distribution on the surface of a rock specimen, a probabilistic distribution law of damage variables for rock mass is presented as a Beta distribution by using the Monte-Carlo statistical simulation method. In part II, statistical estimation of a damage state and properties of random damaged rock mass are evaluated by Rosenblueth's point estimate method. Combining with the F. E. method, rock mechanics problem for random damaged state have been analyzed.

Probabilistic estimates for multivariate analyses

The ways in which engineering systems fail (i.e., their occurence and frequency) demonstrate considerable differences between hypothetical models assumed for design and actual performance. All materials contain imperfections. All systems are subject to complex interrelationships, material defects, structural deficiencies, human errors, ambient fluctuations, and, hence, to varying degrees of randomness (uncertainties). Various methods have been offered to accomodate uncertainty. The most common, by far, is to assign single-valued point estimates that reflect central tendencies or implied levels of conservatism. Analyses are then reduced to deterministic treatments. More direct probabilistic methods employ Monte Carlo simulations or truncated Taylor series. However, analyses rapidly become exceedingly difficult, if not impossible, for these methods for all but a very few uncorrelated random variables. These matters and others have been ameliorated by Rosenblueth's point estimate method. 1 Many problems are encountered that require numerous correlated random variables. For such systems all of the above methods become untractable. This paper presents a simple procedure that accomodates the analyses of such systems.

Simulation for risk analysis with correlated variables

A Monte-Carlo simulation technique for geotechnical risk analysis with correlated random variables is presented. The proposed method is illustrated by an example of time required for water-table draw-down near a box cut of an open strip coal mine. The permeability and storage coefficient are considered as correlated stochastic variables. The results are compared with those achieved by using Rosenblueth's point estimate method for finding statistical moments as well as the well-known Taylor series approach. Excellent agreement is achieved for the first two moments. For higher moments the Rosenblueth method provides a better approximation to the simulation solution than does the Taylor series method. The role of a valid risk analysis technique for correlated variables is discussed and the application of the Paper to stability analysis of slopes is highlighted. L'article présente une technique de simulation type Monte-Carlo pour l'analyse géotechnique des risques avec des variables aléatoires corrélatives. La méthode proposée est illustrée à l'aide de l'exemple du temps nécessaire pour le rabattement de la nappe aquifére dans le voisinage d'une tranchée rectangulaire dans une mine à ciel découvert. La perméabilité et le coefficient d'accumulation sont considérés comme des variables aléatoires corrélatives. On compare les résultats avec ceux obtenus par la méthode d'évaluation par pointes (Rosenblueth) pour découvrir les moments statistiques aussi bien qu'avec la méthode connue des séries de Taylor. Pour les deux premiers moments on obtient un accord excellent. Pour des moments supérieurs la méthode de Rosenblueth offre une meilleure approximation à la solution par simulation que ne le fait la méthode des séries de Taylor. L'article discute le rôle joué par une technique analytique valable des risques pour les variables aléatoires corrélatives et souligne la validité de la méthode présentée pour l'analyse de la stabilité des talus