Lambda Plots Research Articles

A multi-objective chimp optimization algorithm for seismicity de-clustering

Earthquakes are random triggering phenomenons that generate clusters in space and time, thus creating a bias in a seismic catalog. Seismic de-clustering separates seismic catalog into mainshocks, aftershocks–foreshocks, and backgrounds, widely used in earthquake prediction models and seismic hazard assessment. The segregation of an optimal number of earthquake clusters and backgrounds is formulated as an unsupervised problem. This manuscript introduces a multi-objective chimp-optimization algorithm (MOCOA) to de-cluster seismicity of earthquake-prone regions. The chimp optimization is inspired by the natural hunting behavior of the chimp to catch the prey. The algorithm effectively balances the exploration of search space (Driving and Chasing) and exploitation around the best solution achieved so far (Attack). In MOCOA, archive controller and archive grid-based approaches are incorporated for selecting non-dominated solutions. The proposed MOCOA is tested on fifteen mathematical test problems and compared with popular algorithms like MOEA/D, MODE, MOPSO, and SPEA2. The binary version of MOCOA is designed for the de-clustering problem. In the time and space domain, respectively, two objective functions, m-Morisita Index (m-MI) and coefficient of variance (COV), are analyzed. The proposed de-clustering algorithm is applied on thirty-two-year historical seismic catalogs of the Himalayas, California, Indonesia, Japan, Iran, and Mexico. Comparative analysis between five existing benchmark de-clustering techniques is performed to check the potential of the proposed MOCOA. The simulation results generated by the proposed algorithm show that obtained de-clustered catalogs COV values lying near unity and m-MI values achieved maximum values. Validation of results using cumulative plots, lambda plots, and inter-event time versus inter-event distance plots signify the accurate discrimination of aftershocks and background events in the catalogs.

Tetra‐stage cluster identification model to analyse the seismic activities of Japan, Himalaya and Taiwan

From the decades, due to the independent and Poisson nature of background seismicity, they are extensively used for hazard analysis, modelling of prediction phenomenon and also used for earthquake simulations. In this study, a tetra-stage cluster identification model is proposed for accurate estimation of background seismicity and triggered seismicity. The proposed method considers a seismic event's occurrence time, location, magnitude and depth information available in the given catalogue to classify the event as a background or aftershock. The model has flexible threshold parameters which can be tuned to a proper value according to the specific seismic zone to be analysed. It exploits the current seismic activities of the region by taking care the past samples of the region over last 25 years. The analyses of Japan, Himalaya and Taiwan catalogues are carried out using the proposed model. Superior results with the proposed model are achieved, compared with benchmark models by Nanda et al., Gardner–Knopoff and Uhrhammer et al. in terms of percentage of background seismicity, lambda plot and cumulative plot. The ergodicity present in the original seismic catalogue and catalogue after de-clustering are compared using Thirumalai-Mountain metric to justify the stationary and linearity.

Robust Parameter Design of an EDM Process

AbstractThe paper details a robust parameter design of an electrical discharge machining process. The influence of capacitance, pulse off‐time, pulse on‐time and pulse current on both the average and variability of surface roughness and material removal rate of a titanium alloy was investigated. The analysis revealed that to attain robustness against the impact of noise parameters, no capacitance should be applied. Furthermore, increasing pulse on‐time and its current increased the average of both the surface roughness and material removal rate. Two approaches were suggested to deal with the trade‐off between minimizing the former and maximizing the latter. The study confirmed empirically the inferiority of Taguchi's S/N ratios to a robust design method involving the use of log(s) together with a simple graphical tool for determining the appropriate data transformation called lambda plot. In fact, it was revealed that the employed S/N ratios were driven mainly by the average and involved unaided, unexplained and unjustified transformations. The log(s), on the other hand, provided an independent means of quantifying the variability and, when integrated with lambda plot, rendered not only a simplified analysis but also a better process understanding. The study is the first to report the use of this powerful approach in the context of electrical discharge machining parameter design. Copyright © 2012 John Wiley & Sons, Ltd.

Plotting Scaled Effects from Unreplicated Orthogonal Experiments

Box proposed on empirical procedure, called the lambda plot, to search for a simplifying transformation in the context of replicated orthogonal experiments. This paper shows that, by appropriately scaling the factor effects, the lambda plot procedure ca..

Signal-to-Noise Ratios, Performance Criteria, and Transformations

For the analysis of designed experiments, Taguchi uses performance criteria that he calls signal-to-noise (SN) ratios. Three such criteria are here denoted by SN T , SN L , and SN S . The criterion SN T was to be used in preference to the standard deviation for the problem of achieving, for some quality characteristic y, the smallest mean squared error about an operating target value. León, Shoemaker, and Kacker (1987) showed how SN T was appropriate to solve this problem only when σ y was proportional to μ y . On that assumption, the same result could be obtained more simply by conducting the analysis in terms of log y rather than y. A more general transformation approach is here introduced for other, commonly met kinds of dependence between σ y and μ y (including no dependence), and a lambda plot is presented that uses the data to suggest an appropriate transformation. The criteria SN L and SN S were for problems in which the objective was to make the response as large or as small as possible. It is argued here that these predecided “portmanteau” criteria can provide an inadequate summary of data and that, regarded as measures of location, they can be extremely inefficient. In preference to such performance criteria, the merits of simple methods of data analysis that can uncover information both expected and unexpected are urged. A reanalysis of an interesting experiment due to Quinlan (1985) illustrates the value of this approach and its contribution to the art of discovery. It is argued that improvement of quality will best be catalyzed by engineers using elementary data analysis with computer graphics rather than by those trained only to employ more rigid predecided criteria.