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Comparison of RSM, ANN, Factorial DoE, and Fuzzy Logic Network for Diesel Engine Performance Parameter and Emission Analysis
Published in C. S. P. Rao, G. Amba Prasad Rao, N. Selvaraj, P. S. C. Bose, V. P. Chandramohan, Mechanical Engineering for Sustainable Development, 2019
Pramod K. Tiwari, Atul G. Lodhekar, Suhas C. Kongre
Factorial is a good statistical technique for designing experiments; creating models, aiming effects of multiple variables, and finding optimum conditions for propose responses.7 For designing model, D-optimal approach of factorial design with statistical approach was employed to reduce the number of experiment for various blended fuels. One of advantage over the statistical method is that it enables all possible main effect and interaction effect of all variables at different levels. The response could be written as a function of variables by arranging multiple regressions using the least squares method to fit the equation below: () Y=a0+a1X1+a2X2+a3X3+a12X1X2+…
Probability and Its Distribution in Statistics
Published in Seong-woo Woo, Design of Mechanical Systems Based on Statistics, 2021
The numeral of permutations of n discrete objects is n factorial, usually expressed as n!, which means that the product of all positive integers is less than or equal to n. That is, Pnn=n(n−1)(n−2)⋯1=n!
General Mathematical Functions
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
The factorial of a number is the product of all positive integers less than or equal to the number, for example: 5! = 5⋅4⋅3⋅2⋅1 = 120
A simplified method for seismic assessment of unreinforced masonry buildings
Published in Civil Engineering and Environmental Systems, 2022
I. Capanna, F. Di Fabio, M. Fragiacomo
The macro-seismic method (Lagomarsino and Giovinazzi 2006) was then applied, based on the predictive indices, to estimate the mean damage μD for each building, see Figure 11, using the Equation (22): where I is the seismic input in terms of macroseismic intensity, Q is the ductility coefficient (set to 2.3), and V is the vulnerability coefficient, evaluated as reported in Equation (23), from the vulnerability index iv, expressed in a range between 0 and 100: A binomial distribution estimated the probability pk of occurrence of the damage grade Dk (k from 0 to 5) (Grünthal 1998) as a function of μD, according to Equation (24): where the symbol ! indicates the factorial operator. In order to compare the numerically obtained binomial distributions with the experimental one, the mean damage μD is evaluated based on the peak ground acceleration of the site, set to 0.255 g. The authors correlated the peak ground acceleration, ag, with the macro-seismic intensity I, following the correlation law in Equation (25) (Lagomarsino and Giovinazzi 2006):
Consultation sequencing of a hospital with multiple service points using genetic programming
Published in Engineering Optimization, 2018
Katsumi Morikawa, Katsuhiko Takahashi, Keisuke Nagasawa
To highlight the performance of the rules obtained by GP, an alternative dispatching rule named the permutation rule is prepared. Figure 3 indicates that at most three patients should be compared when selecting the next patient. As each queue corresponds to a term of the objective function defined by Equation (1), it is a reasonable idea to set a fixed order of priority among these three queues. The factorial of three produces six permutations, such as and . The expression , for example, means that the patient in queue x is always selected first. If queue x is empty, then the patient in y is selected. If both x and y are empty, then the patient in queue z is selected. The performance of the permutation rule was evaluated by simulating 100,000 sessions under the condition described earlier.
Roza: a new and comprehensive metric for evaluating classification systems
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2022
In the first step, to demonstrate the power of the Roza metric, the BUPA dataset was classified according to the LOO-CV strategy with eight different classifiers popular in machine learning systems. These classifiers are decision trees with 3 different numbers of splits (that denoted by DT (100), DT (20), and DT (4)), linear discriminant analysis (LDA), k- nearest neighbor (k-NN), support vector machine with polynomial and radial basis function kernels (that denoted by SVM (pl) and SVM (rbf), respectively), and ensemble boosted tree. Then, 10 different metrics that are frequently used to measure the performance of machine/deep learning systems, especially in imbalanced datasets, were calculated for each classifier. In this case, the permutation of the general polygon was 10!, where "!" denotes the factorial. Thus, through the decagon of these 10 metrics, the Roza metric and the inverse of the Roza metric were calculated, the results of which are shown in Table 6. Additionally, in order to show that the Roza metric behaves more fairly and comprehensively, the ranking of the classifiers from the most successful to the most unsuccessful according to the different metrics frequently used in imbalanced datasets is given in Table 7. As can be seen, according to all other metrics except the ACC metric, the decision tree with 20 splits, and the ensemble boosted tree were the most successful classifiers. However, after the second successful classifier, the success order changed according to the metrics. This, as has been said before, made the selection of the successful system quite difficult. However, the Roza metric offered the most comprehensive and accurate ranking as it was obtained by considering all the metrics.