Analysis of variance

Summary

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means. History While the analysis of variance reached fruition in the 20th century, antecedents extend centuries into the past according to Stigler. These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. Laplace was performing hypothesis testing in

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https://en.wikipedia.org/wiki/Analysis_of_variance

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2021

Auto-tuning deep forest for shear stiffness prediction of headed stud connectors

Yuqing Liu

The shear stiffness of headed stud connector is a critical parameter for the calculation of deflection and inter-facial shear force for steel-concrete composite structure. Thus, this study presented a promising data-driven model auto-tuning Deep Forest (ATDF) to precisely predict the stud shear stiffness, where the novel Deep For-est algorithm is integrated with the Sequential Model-Based Optimization method to achieve automatic hyper -parameter optimization. Six variables having causal relationships with shear stiffness were extracted via mechanism and model analysis, including the effect of weld collar that cannot be considered in existing models and subsequently constituting a database of 425 push-out tests. Then the ATDF model was trained by combining the advantages of deep learning, ensemble learning, and auto-tuning techniques. It was approved to significantly outperform representative benchmark models with R values of 0.91 and 0.87 for training and testing sets. The ATDF was subjected to attribute importance analysis, which quantified the stud diameter and concrete elastic modulus as the most significant variables for shear stiffness, with the stud elastic modulus having the minimal effect. The model uncertainty of ATDF was further evaluated, revealing that it had the lowest bias and variability than those in existing empirical or semi-empirical models. Finally, the reliability analysis was conducted and the partial factors of ATDF under specified target reliability were derived.

2022

The Goals of the Analysis Model

When developing an analysis model, the notation itself does not suffice for determining the content of the analysis model and the end of the analysis process. For this, the goals and intents of the analysis model are used, either implicitly or explicitly. In this report we take a look at various possibilities to define the term analysis and the goals of the analysis model. We start with considering the reference model of the problem solving cycle. We examine the definitions that refer to analysis as the "what" in opposite to the "how", or as the problem definition phase of a problem solving cycle. We then continue with a discussion of various criteria (like technology independence, real word model, unambiguous or essential model) that are often used to specify the goals of an analysis model. Difficulties that arise with these criteria are that they cannot be combined arbitrarily and that some of them are very vague; we propose therefore also some more concrete formulations. In the last part of the report we take a closer look at some misconceptions and intent clashes that are due to a too idealistic model of the software development process. Objective real world models, analysis models that are stable after the analysis phase and analysis models that are equal to the high-level view of the final software system are often attempted, but are normally not realistic. This leads to intent clashes with the desire for a seamless and easy controllable development process. We explain these intent clashes and we also describe the three different approaches taken by software development methods to cope with these intent clashes.

1996