New!3D regression analysis
This calculation allows obtaining approximation of 3D data
using generalized Pade (rational) functions. Coefficients of these functions are derived from
the Least Residual Sum of Squares (RSS) condition. Traditional form of RSS leads to a system of nonlinear equations
in the case of rational functions and therefore it is rather costly. The new form of RSS which leads to linear equations was suggested for 2D regression
analysis in paper 'On regression analysis with Pade approximants'
(August, 2022, DOI: 10.48550/arXiv.2208.09945)
by G.Yevkin and O.Yevkin. In this calculation we have expanded this approach to the case of 3D regression analysis.
2D Data fitting
This calculation allows
obtaining approximation of data using generalized Pade (rational) functions.
The accuracy of approximation can be managed by user changing values of
three main parameters: number of coefficients of Pade function;
given accuracy, and correlation coefficient of data fitting.
We suppose that this calculation will be useful for researchers and engineers looking
for good approximation of data with simple formula.
New! Free!Non-parametric estimation
This calculation allows the user to analyze probability of events without any assumption
about an underlying parametric distribution function. The observed event times are converted to the corresponding probability values.
The following rank-regression models can be selected by user: Benard, Hazen, Mean and Kaplan-Meier. The confidence bounds are also calculated.
New! Free!Weibull prediction
This calculation allows to analyze and predict probability of events selecting
an underlying distribution function: Exponential, Weibull, Normal or Log-Normal. Two method are provided:
Maximum Likelihood and Rank Regression method. If the Rank Regression method is selected, the observed event times are converted
to the corresponding probability values first. For this purpose the following models can be selected by user: Benard, Hazen and Mean.
The confidence bounds can also be calculated using the Fisher Matrix or the Likelihood Ratio method.
New!Imperfect repair
This calculation allows analyzing Number of recurrent events,
Frequency of events and probability that a component is down.
Imperfect repair is described by Kijima models (I and II) with the following underlying lifetime distributions: Weibull, Normal and Log-Normal.
Time to repair can be represented as a deterministic or random process with exponential distribution function.
An efficient advanced Monte Carlo method is used.
New!Recurrent event prediction with Kijima model
The recurrent process is considered
using Kijima model with the following underlying lifetime distributions: Weibull, Normal and Log-Normal.
Having event times of several components, the calculation allows to estimate parameters of the underlying lifetime distribution
and the restoration factor of imperfect repair. Time to repair can be also introduced into the calculation.
The Maximum likelihood and an efficient advanced Monte Carlo method are used. Confidence bounds can also be estimated
using the Fisher information matrix.
New!Recurrent event prediction with Pade functions
The recurrent process (for example, failure-repair) is analyzed.First, non-parametric estimation of expected number of events is performed, then regression analysis with Pade fuctions is applied to obtained data for recurrent event prediction . The obtained result is thus represented as a relatively simple formula.
New! Optimal maintenance
Calculation allows to define optimal replacement policy (time) under Kijima’s imperfect repair model with the underlying
Weibull distribution function. The generalized renewal process includes minimal and perfect repair models.
The advanced Monte Carlo method is used to calculate the optimal replacement strategy with minimal cost per unit time.
The online calculation takes several seconds.
Cantilever beams & simply supported beams
Calculates reactions, bending moments, shear forces and deflections of
statically determined beams.
The result is represented as diagrams of these components of the beam.
Calculation is helpful not only for structural engineers,
but also for students because all main steps (formulas) of the solution are provided.
Bending of statically indeterminate (continuous ) beams
Calculates reactions, bending moments, shear forces and deflections of
statically indeterminate (continuous ) beams. The result is represented as diagrams of these components of the beam.
All main steps (formulas) of the solution are provided.
Trusses
The purpose of this model is calculation
of reactions and internal forces of tension or compression in truss members
of statically determinate 2D trusses. It is helpful not only for structural
engineers, but also for students because all main steps of the solution are provided.
Bending of isotropic and orthotropic rectangular plate
Calculates deflections and stresses of simply supported orthotropic rectangular plate under uniformly distributed load applied to rectangular area. The approximation formula for deflection function is provided.
Buckling of isotropic and orthotropic rectangular plates.
Calculates the critical load of simply supported rectangular plate uniformly compressed in two directions.
Free!Shock absorber
Calculates the main characteristics of a novel shock (energy) absorber: load-displacement diagram, maximum stresses and absorption energy for a cycle of loading. The shock absorber contains spring and thin elastic reversing shell of revolution with nonlinear behavior. The methodology of calculation is based on the application of new asymptotic formulae, obtained for the Reissner's equations describing axially symmetric deformation of the orthotropic thin shells of revolution by large deflections. The accuracy of the asymptotic formulae corresponds to the accuracy of the initial equations of thin shell theory.
Free!Orthotropic spherical shell under concentrated force
Calculates the nonlinear load-displacement diagram, maximum stresses by large deflections of the orthotropic clamped spherical thin shell under concentrated force. The methodology of calculation is based on the application of new asymptotic formulae, obtained for the Reissner's equations describing axially symmetric deformation of the orthotropic thin shells of revolution by large deflections. The accuracy of the asymptotic formulae corresponds to the accuracy of the initial equations of thin shell theory.
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