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Recommended properties for advanced numerical analysis
Published in Paulo B. Lourenço, Angelo Gaetani, Finite Element Analysis for Building Assessment, 2022
Paulo B. Lourenço, Angelo Gaetani
The probabilistic method (sometimes referred to as fully probabilistic design method) is the most sophisticated tool for safety assessment and allows the analyst to explicitly include the reliability requirements in terms of reliability index β and reference period. The numerical simulation resembles real testing of a representative group of samples, statistically analysed for the assessment of safety. Basically, by assuming a random distribution of the input variables (material properties, dimensions, boundary conditions, etc.), the consequent distribution of resistance values implicitly considers all possible causes of failure. For instance, the method can reveal reserves of capacity or alternative force redistributions not easily identifiable with conventional methods. Certainly, the results are sensitive to the initial random distribution selected (in terms of function, average and standard deviation), marginally supported by a wide number of destructive and nondestructive tests. The latter aspect should be carefully evaluated for not compromising the authenticity of the building at hand. As a consequence, also due to its computational demands and the consequent economical effort, a full probabilistic analysis is suggested only in those cases where the consequences of failure justify the effort, or where real random properties need to be exploited.
Presentation ofstatistical data
Published in John Bird, Bird's Basic Engineering Mathematics, 2021
Statistics is the study of the collection, organisation, analysis and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments. Statistics is applicable to a wide variety of academic disciplines, including natural and social sciences, engineering, government and business. Statistical methods can be used for summarising or describing a collection of data. Engineering statistics combines engineering and statistics. Design of experiments is a methodology for formulating scientific and engineering problems using statistical models. Quality control and process control use statistics as a tool to manage conformance to specifications of manufacturing processes and their products. Time and methods engineering use statistics to study repetitive operations in manufacturing in order to set standards and find optimum manufacturing procedures. Reliability engineering measures the ability of a system to perform for its intended function (and time) and has tools for improving performance. Probabilistic design involves the use of probability in product and system design. System identification uses statistical methods to build mathematical models of dynamical systems from measured data. System identification also includes the optimal design of experiments for efficiently generating informative data for fitting such models. This chapter introduces the presentation of statistical data.
Principles of rock slope design
Published in Duncan C. Wyllie, Christopher W. Mah, Rock Slope Engineering, 2017
Duncan C. Wyllie, Christopher W. Mah
There is sometimes reluctance to use probabilistic design when there is a limited amount of design data that may not be representative of the population. In these circumstances, it is possible to use subjective assessment techniques that provide reasonably reliable probability values from small samples (Roberds, 1990). The basis of these techniques is the assessment and analysis of available data, by an expert or group of experts in the field, in order to arrive at a consensus on the probability distributions that represent the opinions of these individuals. The degree of defensibility of the results tends to increase with the time and cost that is expended in the analysis. For example, the assessment techniques range from, most simply, informal expert opinion to more reliable and defensible techniques such as Delphi panels (Rohrbaugh, 1979). A Delphi panel comprises a group of experts who are each provided with the same set of data and are required to produce a written assessment of these data. These documents are then provided anonymously to each of the other assessors who are encouraged to adjust their assessments in light of their peer’s results. After several iterations of this process, it should be possible to arrive at a consensus that maintains anonymity and independence of thought.
A simple Monte Carlo simulation method for geotechnical reliability-based design
Published in Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 2023
Bin Li, Lianyu Zhang, Jinquan Yuan
Note that almost all the RBD methods involve iterations, i.e., repetitive forward reliability analyses (Soubra and Youssef Abdel Massih 2010), which are desirable to be avoided to improve both efficiency and simplicity (Ji et al. 2018; Ji et al. 2019). This has motivated the development of the full probabilistic design framework (Wang 2011) and the expanded reliability-based design framework (Cao et al. 2019; Wang, Au, and Kulhawy 2011), in which the failure probability of each possible design is estimated using a Bayesian analysis Zhang et al. (2022b) based on the results of a single run of MCS. The main shortcoming of this framework is that the required number of MCS samples increases as the number of possible designs. To reduce the computational cost, this framework has been combined with advanced MCS techniques like subset simulation (Wang 2013) and generalized subset simulation (Li et al. 2016).
A systematic and probabilistic approach for optimal design and on-site adaptive balancing of building central cooling systems concerning uncertainties
Published in Science and Technology for the Built Environment, 2020
Recently, the probabilistic design method or uncertainty-based design method has drawn increasing attention in the building field (Wit and Augenbroe 2002; Corrado and Mechri 2009; Spitz et al. 2012; Wang, Mathew, and Pang 2012; Shan et al., 2013; Shan et al., 2013; Nguyen, Reiter, and Rigo 2014; Huang, Huang, and Augenbroe 2017; Kang and Wang 2018; Tian et al. 2018). Probabilistic design methods quantify uncertainties based on a probabilistic approach, enabling risk-based decisions, rather than sizing systems with safety margins to consider uncertainties approximately like the conventional design methods, which may lead to oversizing (Sowden 2002). A number of studies have been conducted on probabilistic optimal design for the components of cooling systems. Gang et al. (2015) proposed an optimal design method for chillers in district cooling systems by quantifying uncertainties in outdoor weather, building design/construction, and indoor conditions. Sun et al. (2014) explored a new framework for uncertainty analysis and sensitivity analysis for HVAC system sizing. Cheng, Wang, and Yan (2016) proposed a robust optimal design for chilled water systems by quantifying the uncertainties of design inputs and the reliability of system components in operation.