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Crush Energy in Accident Vehicles and Nonlinear Structures
Published in Donald E. Struble, John D. Struble, Automotive Accident Reconstruction, 2020
Donald E. Struble, John D. Struble
To follow this advice and understand how the coefficients were determined, an example was considered: Toyota Sienna vans produced between model years 1998 and 2003, involved in full-width frontal crashes. For such vehicles, NEI produced data obtained from reports of two tests: DOT 2766, a barrier crash at approximately 35 mph, and Transport Canada 99–144, a barrier crash at approximately 30 mph. The data appeared in a table showing the pertinent test data, and the A and B parameters were calculated for each test by itself. A crash plot was also produced having two data points, presumably reflecting the two tests, plus what appears to be a regression fit. The equation of the regression line, its slope, and its intercept were not given. Thus, it was not possible to trace the derivation of A and B from the crash plot. However, the table indicates values of A and B from the crash plot of 380 lb/in. and 150 lb/in.2, respectively.
Curve Fitting and Regression Analysis
Published in Bilal M. Ayyub, Richard H. Mccuen, Numerical Analysis for Engineers, 2015
Bilal M. Ayyub, Richard H. Mccuen
in which b0 = the intercept coefficient and b1 = the slope coefficient; b0 and b1 are called regression coefficients because they are obtained from a regression analysis. Because Equation 10.15 involves two variables, Y and X, it is sometimes referred to as the bivariate model. The intercept coefficient represents the value of Y when X equals zero. The slope coefficient represents the rate of change in Y with respect to change in X. Whereas b0 has the same dimensions as Y, the dimensions of b1 equal the ratio of the dimensions of Y to X.
Linear transformation: Making bent lines straight
Published in Alan R. Jones, Best Fit Lines and Curves, and Some Mathe-Magical Transformations, 2018
Unsurprisingly, the family name under which we classify straight lines is Linear Function. As a general rule, taking the log of a Linear Function distorts its shape into a curve, so we would not apply a transformation in this case. The only exception would be in the case where the straight line passes through the origin, i.e. the intercept equals zero. In this case alone, the straight line remains a straight line if we transform both the x and y-values (but only for positive values, as we cannot take the log of zero or a negative value.)
Nonlinear elastic constitutive model of clayey sand reservoirs during depressurization exploitation of natural gas hydrate
Published in Marine Georesources & Geotechnology, 2023
Huie Chen, Hua Du, Fansheng Kong, Wenchong Shan
According to Equation (3), a linear correlation can be observed between and In the context of coordinate system, the y-intercept of the line is represented by while the slope of the line is denoted by (Figure 3). According to the previous research results (Duncan and Chang 1970), the middle section of the curve with a better linear relationship was selected to determine the parameters and
Adsorptive of vanadium and palladium ions using chitin-extracted from shrimp shell wastes: genetic programming modeling
Published in Journal of Dispersion Science and Technology, 2023
Maryam Omidinasab, Zahra Noorimotlagh, Maryam Faraji, Behrouz Bayati, Mohammad Reza Valizadeh, Jalel Labidi, Zeinab Ghaedrahmat, Kourosh Rahmani, Saba Fouladvand, Neamatalah Jaafarzadeh Haghighi Fard, Majid Nozari
In this part of the study, the efficiency of chitin was examined at the adsorbent dose of 0.8 g/L, pH = 9, V and Pd concentration of 25 mg/L, contact time of 15 minutes and temperature of 298–338˚K. Thermodynamic parameters, for example, entropy changes (ΔS˚), enthalpy changes (ΔH˚), and free energy changes (ΔG˚) were estimated to determine the spontaneity of a process. The values of ΔH˚ and ΔS˚ were achieved by plotting a linear graph of LnKd versus 1/T. In the linear graph, ΔH˚ and ΔS˚ were the slope and y-intercept of the linear equation, respectively. The value of ΔG˚ was obtained from the following equation:[37,38]
A model for predicting Acceleration Severity Index in impacts with road safety barriers
Published in International Journal of Crashworthiness, 2019
Andrew Burbridge, Rod Troutbeck
Subsequent review and analysis by Burbridge and Troutbeck [20], introducing new analysis of data reported earlier by Hammonds and Troutbeck [21] and by Anghileri et al. [22], suggested that the relationship between barrier flexibility and the reciprocal of ASI (1/ASI) is a linear function, and that the shape (slope and y-intercept) of the linear function could be a function of impacting vehicle mass, speed and angle. This is depicted in Figure 1 and is described as follows:where a is the slope, b is the y-intercept, DD is dynamic deflection (m) and IS is the Impact Severity (kJ) computed via the expression as follows:where m is the test inertial mass of impacting vehicle (tonnes), v is the impact speed of the impacting vehicle (m/s) and θ is the impact angle of the impacting vehicle. As explained by Burbridge and Troutbeck [19]: