Using the Kriging Response Surface Method for the Estimation of Failure Values of Carbon-Fibre-Epoxy Subsea Composite Flowlines under the Influence of Stochastic Processes

This paper investigates the use of the Kriging response surface method to estimate failure values in carbon-fibre-epoxy composite flow-lines under the influence of stochastic processes. A case study of a 125 mm flow-line was investigated. The maximum stress, Tsai-Wu and Hashin failure criteria was used to assess the burst design under combined loading with axial forces, torsion and bending moments. An extensive set of measured values was generated using Monte Carlo simulation and used as the base case population to which the results from the response surfaces was compared. The response surfaces were evaluated in detail in their ability to reproduce the statistical moments, probability and cumulative distributions and failure values at low probabilities of failure. In addition, the optimisation of the response surface calculation was investigated in terms of reducing the number of input parameters and size of the response surface. Finally, a decision chart that can be used to build a response surface to calculate failures in a carbon fibre-epoxy-composite (CFEC) flow-line was proposed based on the findings obtained. The results show that the response surface method is suitable and can calculate failure values close to that calculated using a large set of measured values. The results from this paper provide an analytical framework for identifying the principal design parameters, response surface generation, and failure prediction for CFEC flow-lines.

Possibilistic response surfaces: incorporating fuzzy thresholds into bottom-up flood vulnerability analysis

Several alternatives have been proposed to shift the paradigms of water management under uncertainty from predictive to decision-centric. An often-mentioned tool is the response surface mapping system performance with a large sample of future hydroclimatic conditions through a stress test. Dividing this exposure space between acceptable and unacceptable states requires a criterion of acceptable performance defined by a threshold. In practice, however, stakeholders and decision-makers may be confronted with ambiguous objectives for which the acceptability threshold is not clearly defined (crisp). To accommodate such situations, this paper integrates fuzzy thresholds to the response surface tool. Such integration is not straightforward when response surfaces also have their own irreducible uncertainty from the limited number of descriptors and the stochasticity of hydroclimatic conditions. Incorporating fuzzy thresholds, therefore, requires articulating categories of imperfect knowledge that are different in nature, i.e., the irreducible uncertainty of the response itself relative to the variables that describe change and the ambiguity of the acceptability threshold. We, thus, propose possibilistic surfaces to assess flood vulnerability with fuzzy acceptability thresholds. An adaptation of the logistic regression for fuzzy set theory combines the probability of an acceptable outcome and the ambiguity of the acceptability criterion within a single possibility measure. We use the flood-prone reservoir system of the Upper Saint François River basin in Canada as a case study to illustrate the proposed approach. Results show how a fuzzy threshold can be quantitatively integrated when generating a response surface and how ignoring it might lead to different decisions. This study suggests that further conceptual developments could link the reliance on acceptability thresholds in bottom-up assessment frameworks with the current uses of fuzzy set theory.

EXPERIMENTAL RESEARCH OF PARTIAL REGULAR MICRORELIEFS FORMED ON ROTARY BODY FACE SURFACES

The basic regularities in the influence of processing parameters on the geometrical characteristics of the partially regular microreliefs, formed on the rotary body face surface, are established. Combinations of partially regular microreliefs are formed by using a contemporary CNC milling machine, and an advanced programing method, based on previously developed mathematical models. Full factorial experimental design is carried out, which consist of three factors, varied on three levels. Regression stochastic models in coded and natural form, which give the relations between the width of the grooves and the deforming force, feed rate and the pitch of the axial grooves, are derived as a result. Response surfaces and contour plots are built in order to facilitate the results analysis. Based on the dependencies of the derived regression stochastic models, it is found that the greatest impact on the width of the grooves has the magnitude of the deforming force,followed by the feed rate. Also, it is found that the axial pitch between adjacent toolpaths has the least impact on the width of the grooves. As a result of the full-factorial experiment, the average geometric parameters of the microrelief grooves were obtained on their basis. When used, these values will provide for the required value of the relative burnishing area of the surface with regular microreliefs, and, accordingly, the specified operational properties.

The need for unrealistic experiments in global change biology

Climate change is an existential threat, and our ability to conduct experiments on how organisms will respond to it is limited by logistics and resources, making it vital that experiments be maximally useful. The majority of experiments on phytoplankton responses to warming and CO2 use only two levels of each driver. However, to project the characters of future populations, we need a mechanistic and generalizable explanation for how phytoplankton respond to concurrent changes in temperature and CO2. This requires experiments with more driver levels, to produce response surfaces that can aid in the development of predictive models. We recommend prioritizing experiments or programmes that produce such response surfaces on multiple scales for phytoplankton.

Response Surface Mesh with the Outer Input Method

Artificial intelligence in general and optimization tasks applied to the design of very efficient structures rely on response surfaces to forecast the output of functions, and are vital part of these methodologies. Yet they have important limitations, since greater precisions require greater data sets, thus, training or updating larger response surfaces become computationally expensive or unfeasible. This has been an important bottle neck limitation to achieve more promising results, rendering many optimization and AI tasks with a low performance.To solve this challenge, a new methodology created to segment response surfaces is hereby presented. Differently than other similar methodologies, this algorithm named outer input method has a very simple and robust operation, generating a mesh of near isopopulated partitions of inputs which share similitude. The great advantage it offers is that it can be applied to any data set with any type of distribution, such as random, Cartesian, or clustered, for domains with any number of coordinates, significantly simplifying any metamodel with a mesh ensemble.This study demonstrates how one of the most known and precise metamodel denominated Kriging, yet with expensive computation costs, can be significantly simplified with a response surface mesh, increasing training speed up to 567 times, while using a quad-core parallel processing. Since individual mesh elements can be parallelized or updated individually, its faster operational speed has its speed increased.

Robust optimization of multistage process: response surface and multi-response optimization approaches

A multistage system refers to a system contains multiple components or stages which are necessary to finish the final product or service. To analyze these problems, the first step is model building and the other is optimization. Response surfaces are used to model multistage problem as an efficient procedure. One regular approach to estimate a response surface using experimental results is the ordinary least squares (OLS) method. OLS method is very sensitive to outliers, so some multivariate robust estimation methods have been discussed in the literature in order to estimate the response surfaces accurately such as multivariate M-estimators. In optimization phase, multi-response optimization methods such as global criterion (GC) method and ε-constraints approaches are different methods to optimize the multi-objective-multistage problems. An example of the multistage problem had been estimated considering multivariate robust approaches, besides applying multi-response optimization approaches. The results show the efficiency of the proposed approaches.