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model error and reliability of reinforced concrete beams in shear designed according to the Modified Compression Field Theory

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STRUCTURAL CONCRETE 2021年第6期22卷 3711-3726页

作者： Agarwal, Ankit Foster, Stephen J. Stewart, Mark G. Western Sydney Univ Sydney City CampusLevel 4255 Elizabeth St Sydney NSW 2000 Australia Univ New South Wales Fac Engn Sydney NSW Australia Univ Newcastle Ctr Infrastruct Performance & Reliabil Callaghan NSW Australia

model error (or model uncertainty) were probabilistically characterized for modified compression field theory (MCFT) Simplified and General Method approaches using experimental databases that contained reinforced concrete (RC) beams having shear failures with and without stirrups (168 and 368 specimens, respectively). It was found that when compared to the design shear model currently used in ACI-318, the General Method produced low model error variability indicating better consistency for the determination of shear strength. Structural reliabilities were then calculated for RC beams in shear designed to MCFT General Method (AASHTO LRFD, CSA A23.3-14, AS3600-2018) for a live-to-dead load ratio between 0 and 5, and for capacity reduction factor phi = 0.70, 0.75, and 0.80. It was concluded that the phi-factor for shear failure for Australian standards can be increased from 0.70 to 0.75 for RC beams with stirrups, providing a 7.1% increase in the design shear capacity and contributing to sustainable design and reduction in greenhouse gas emissions due to more efficient usage of materials.

关键词： MCFT model error RC beams reliability shear

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model error and Structural Reliability for Reinforced Concrete Block Masonry Walls in Shear

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ADVANCES IN STRUCTURAL ENGINEERING 2012年第3期15卷 389-398页

作者： Zhai, Ximei Zhong, Zhifeng Stewart, Mark G. Harbin Inst Technol Sch Civil Engn Harbin 150090 Peoples R China Univ Newcastle Ctr Infrastruct Performance & Reliabil Sch Engn Newcastle NSW 2308 Australia

The present paper develops a probabilistic model to calculate the structural reliability of typical reinforced grouted concrete block masonry walls designed to Chinese standards, loaded in horizontal shear. The statistical parameters for model error used for the structural reliability analysis are obtained from a database of wall test data from China. The effect of probability distribution of model error, the compressive strength for grouted concrete block masonry, live load type, load effect ratio, reinforcement ratio, wall length, wall size or strength discretization, vertical compressive load and ratio of shear span to depth were considered when calculating the structural reliability of reinforced masonry walls in shear. The structural reliability for reinforced concrete block masonry walls in shear is sensitive to the probability distribution of model error. The recommended lognormal distribution of model error based on test data provided a high reliability index, and when using Gamma and Gumbel distributions for typical structures the existing (design) safety levels were also found to exceed the target reliability of 3.7, whereas the safety levels were less than the target reliability using Normal and Weibull distributions of model error.

关键词： concrete block reinforced masonry reliability model error probability distribution shear

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model error covariance estimation in particle and ensemble Kalman filters using an online expectation-maximization algorithm

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QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY 2021年第734期147卷 526-543页

作者： Cocucci, Tadeo J. Pulido, Manuel Lucini, Magdalena Tandeo, Pierre Univ Nacl Nordeste FaCENA Corrientes Argentina Consejo Nacl Invest Cient & Tecn Corrientes Argentina CNRS IMT Atlantique Lab STICC UMR 6285 Paris France

The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are not usually known and have to be inferred. Many approaches have been proposed to tackle this problem, including fully Bayesian, likelihood maximization and innovation-based techniques. This work focuses on maximization of the likelihood function via the expectation-maximization (EM) algorithm to infer the model error covariance combined with ensemble Kalman filters and particle filters to estimate the state. The classical application of the EM algorithm in a data assimilation context involves filtering and smoothing a fixed batch of observations in order to complete a single iteration. This is an inconvenience when using sequential filtering in high-dimensional applications. Motivated by this, an adaptation of the algorithm that can process observations and update the parameters on the fly, with some underlying simplifications, is presented. The proposed technique was evaluated and achieved good performance in experiments with the Lorenz-63 and Lorenz-96 dynamical systems designed to represent some common scenarios in data assimilation such as nonlinearity, chaoticity and model mis-specification.

关键词： expectation‐ maximization model error parameter estimation uncertainty quantification

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model error assessment of burst capacity models for energy pipelines containing surface cracks

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INTERNATIONAL JOURNAL OF PRESSURE VESSELS AND PIPING 2014年第1期120卷 80-92页

作者： Yan, Zijian Zhang, Shenwei Zhou, Wenxing Univ Western Ontario Dept Civil & Environm Engn London ON N6A 5B9 Canada

This paper develops the probabilistic characteristics of the model errors associated with five well-known burst capacity models/methodologies for pipelines containing longitudinally-oriented external surface cracks, namely the Battelle and CorLAS (TM) models as well as the failure assessment diagram (FAD) methodologies recommended in the BS 7910 (2005), API RP579 (2007) and R6 (Rev 4, Amendment 10). A total of 112 full-scale burst test data for cracked pipes subjected internal pressure only were collected from the literature. The model error for a given burst capacity model is evaluated based on the ratios of the test to predicted burst pressures for the collected data. Analysis results suggest that the CorLAS (TM) model is the most accurate model among the five models considered and the Battelle, BS 7910, API RP579 and R6 models are in general conservative;furthermore, the API RP579 and R6 models are markedly more accurate than the Battelle and BS 7910 models. The results will facilitate the development of reliability-based structural integrity management of pipelines. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Pipeline Surface crack Burst capacity model error Probability distribution

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model error correction from truncated modal flexibility sensitivity and generic parameters: Part I - Simulation

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2004年第6期18卷 1381-1399页

作者： Wu, D Law, SS Hong Kong Polytech Univ Dept Civil & Struct Engn Kowloon Hong Kong Peoples R China

A great advantage of the flexibility based method is the availability of the large amount of measured information from a few lower modes which can be practically measured. But the modal truncated errors would be significant for a structure with high modal density, and this poses a limitation on the usage of existing flexibility methods. This paper presents the truncated modal flexibility sensitivity with respect to the generic parameters, and a model updating method is proposed based on this sensitivity and incomplete measurement. The loss of contribution from the higher modes to the modal flexibility will not be a source of error in the proposed method. The effect of spatial incompleteness and measurement noise is investigated with numerical studies. The proposed approach is found capable of updating both the systematic model error and local stiffness error separately in a single or two stages under noisy environment. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： vibration model updating generic element modal flexibility sensitivity finite element method model error

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model error assessments of burst capacity models for corroded pipelines

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INTERNATIONAL JOURNAL OF PRESSURE VESSELS AND PIPING 2012年 99卷 1-8页

作者： Zhou, W. Huang, G. X. Univ Western Ontario Dept Civil & Environm Engn London ON N6A 5B9 Canada TransCanada Corp Calgary AB Canada

The model errors associated with eight well-known burst capacity models for corroded pipelines, namely B31G, B31G Modified, CPS, the CSA model, the DNV model, PCORRC, RSTRENG and SHELL92, are characterized based on a full-scale burst test database that consists of 150 data points collected from the literature for pipe specimens containing single isolated real corrosion defects. The probabilistic characteristics of the model errors, including the mean values, coefficients of variation and probability distributions, for the burst models are obtained by analyzing the ratios between the test and predicted burst pressures corresponding to the test data applicable to the model. For each of the burst models, separate model errors for short and long defects are also evaluated, whereby the short and long defects are separated by the transition normalized defect length that is identified using the weighted average COV approach. (c) 2012 Elsevier Ltd. All rights reserved.

关键词： Pipeline Corrosion Burst capacity model error Test-to-predicted ratio

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A flexible additive inflation scheme for treating model error in ensemble Kalman filters

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QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY 2018年第716期144卷 2026-2037页

作者： Sommer, Matthias Janjic, Tijana Ludwig Maximilians Univ Munchen Hans Ertel Ctr Weather Res Deutsch Wetterdienst Munich Germany

Data assimilation algorithms require an accurate estimate of the uncertainty of the prior (background) field that cannot be adequately represented by the ensemble of numerical model simulations. Partially, this is due to the sampling error that arises from the use of a small number of ensemble members to represent the background-error covariance. It is also partially a consequence of the fact that the geophysical model does not represent its own error. Several mechanisms have been introduced so far to alleviate the detrimental effects of misrepresented ensemble covariances, allowing for the successful implementation of ensemble data assimilation techniques for atmospheric dynamics. One of the established approaches is additive inflation, which consists of perturbing each ensemble member with a sample from a given distribution. This results in a fixed rank of the effective model-error covariance matrix. In this article, a more flexible approach is introduced, where the model error samples are treated as additional synthetic ensemble members, which are used in the update step of data assimilation but are not forecast. This way, the rank of the model-error covariance matrix can be chosen independently of the ensemble. The effect of this altered additive inflation method on the performance of the filter is analyzed here in an idealized experiment. It is shown that the additional synthetic ensemble members can make it feasible to achieve convergence in an otherwise divergent parameter setting of data assimilation. The use of this method also allows for a less stringent localization radius.

关键词： additive inflation additive noise data assimilation ensemble Kalman filter model error numerical methods NWP

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An approach to estimating and extrapolating model error based on inverse problem methods:towards accurate numerical weather prediction

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Chinese Physics B 2014年第8期23卷 669-677页

作者：胡淑娟邱春雨张利云黄启灿于海鹏丑纪范 College of Atmospheric Sciences Lanzhou University School of Mathematics and Statistics Lanzhou University

model error is one of the key factors restricting the accuracy of numerical weather prediction （NWP）. Considering the continuous evolution of the atmosphere, the observed data （ignoring the measurement error） can be viewed as a series of solutions of an accurate model governing the actual atmosphere. model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers＇ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.

关键词： numerical weather prediction model error past data inverse problem

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ACCURACY OF SOME APPROXIMATE GAUSSIAN FILTERS FOR THE NAVIER-STOKES EQUATION IN THE PRESENCE OF model error

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MULTISCALE modelING & SIMULATION 2018年第4期16卷 1756-1794页

作者： Branicki, M. Majda, A. J. Law, K. J. H. Univ Edinburgh Sch Math Edinburgh Midlothian Scotland British Lib Alan Turing Inst Data Sci London England NYU Courant Inst Dept Math New York NY 10012 USA Univ Manchester Sch Math Manchester Lancs England

Bayesian state estimation of a dynamical system from a stream of noisy measurements is important in many geophysical and engineering applications where high dimensionality of the state space, sparse observations, and model error pose key challenges. Here, three computationally feasible, approximate Gaussian data assimilation/filtering algorithms are considered in various regimes of turbulent 2D Navier-Stokes dynamics in the presence of model error. The first source of error arises from the necessary use of reduced models for the forward dynamics of the filters, while a particular type of representation error arises from the finite resolution of observations which mix up information about resolved and unresolved dynamics. Two stochastically parameterized filtering algorithms, referred to as cSPEKF and GCF, are compared with 3DVAR-a prototypical time-sequential algorithm known to be accurate for filtering dissipative systems for a suitably inflated "background" covariance. We provide the first evidence that the stochastically parameterized algorithms, which do not rely on detailed knowledge of the underlying dynamics and do not require covariance inflation, can compete with or outperform an optimally tuned 3DVAR algorithm, and they can overcome competing sources of error in a range of dynamical scenarios.

关键词： data assimilation 3DVAR SPEKF Navier-Stokes equation model error stochastic parameterization

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Triple Collocation-Based model error Estimation of VIC-Simulated Soil Moisture at Spatial and Temporal Scales in the Continental United States in 2010-2020

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WATER 2024年第21期16卷 3049页

作者： Li, Yize Lu, Jianzhong Huang, Pingping Chen, Xiaoling Jin, Heping Zhu, Qiang Luo, Huiheng Inner Mongolia Univ Technol Coll Informat Engn Hohhot 010051 Peoples R China Wuhan Univ State Key Lab Informat Engn Surveying Mapping & Re Wuhan 430079 Peoples R China China Three Gorges Corp Wuhan 430010 Peoples R China

The model error is a direct reflection of the accuracy of the model simulation. However, it is challenging to estimate the model error due to the presence of numerous uncertainties inherent to the atmospheric and soil data, as well as the structure and parameters of the model itself. This paper addresses the fundamental issue of error estimation in the simulation of soil moisture by the Variable Infiltration Capacity (VIC) model, with a particular focus on the continental United States from 2010 to 2020. The paper develops a model error estimation method based on the Triple Collocation (TC) error estimation and in situ data validation of the VIC model at different temporal and spatial scales. Furthermore, it addresses the issue of failing to consider the variability of temporal and spatial scales in model error estimations. Furthermore, it generates the standard product data on soil moisture simulation errors for the VIC model in the continental United States. The mean of the simulation error variance of the VIC model, estimated using the TC method for spatially scaled soil moisture in the continental United States, is found to be 0.0045 (m3/m3)2, with a median value of 0.0042 (m3/m3)2. The mean time-scale error variance of the VIC model, validated using ground station data, is 0.0096 (m3/m3)2, with a median value of 0.0078 (m3/m3)2. Concurrently, the paper employs K & ouml;ppen climate classification and land cover data as supplementary data, conducting a comprehensive investigation and analysis of the characteristics and alterations of the VIC model error in the study area from both temporal and spatial perspectives. The findings indicate a proclivity for reduced error rates during the summer months and elevated rates during the winter, with lower rates observed in the western region and higher rates in the eastern region. The objective of this study is twofold: firstly, to conduct a quantitative assessment and analysis of the VIC model's simulation capabilities;s

关键词： soil moisture variable infiltration capacity model error triple collocation continental United States spatiotemporal error

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