MODFIT solves parameter estimation (data fitting, system identification,
nonlinear regression) problems, where
parameters in explicit model functions, Laplace transforms, steady-state systems,
systems of ordinary differential equations, or systems of differential
algebraic equations are to be identified.
The problem may possess additional equality or inequality constraints. A statistical analysis provides confidence intervals for
estimated parameters, correlation and covariance matrix, identification of
significance levels for estimated parameters, and optimum experimental design.
As a by-product, curve and surface fits are available.
Numerical Method:
The algorithm creates a nonlinear least squares problem
and solves it by a couple of alternative parameter estimation methods, e.g. DFNLP.
Differential equations are integrated by seven available ODE-solvers,
e.g. the Hairer and Wanner codes for stiff and non-stiff systems, or
an explicit Runge-Futta code with internal numerical differentiation.
The back-transformation of Laplace functions is done by the
formula of Stehfest.
Steady-State-Systems are solved by Newton's method.
Gradients are evaluated either by numerical approximation, hand-coded Fortran statements of
the user, automatic differentiation, or
by internal numerical differentiation of a Runge-Kutta scheme.
Program Organization:
MODFIT are a double precision FORTRAN subroutine and
all parameters
are passed through arguments. An additional main program takes over
some organizational ballast and reads in all problem data. A user
provided subroutine is required to define initial values, constraints,
the right-hand side of a differential equation, or a fitting criterion.
Special Features:
alternative norms (min-max, sum of absolute values)
dynamic constraints depending on the state variables
switching points for non-continuous alterations of the dynamic system,
constant or variable
differential algebraic equations up to index 3
computation of consistent initial values for index-1-formulations
exploiting band structure
multiple shooting for unstable equations
arbitrary number of fitting criteria and experimental data sets
additional independent model variable (e.g. concentration)
various scaling options (individual or automatic)
confidence intervals for
estimated parameters, correlation and covariance matrix
identification
of significance levels for estimated parameters
computation
of optimal
experimental designs (A-criterion)
alternative direct search algorithms for parameter estimation,
e.g. for problems with bad starting values
generation of plot data and TEX-reports
full documentation
FORTRAN source code
Applications:
MODFIT is in practical use to solve mechanical, chemical and
pharmaceutical parameter estimation problems, e.g. for robot design,
multibody systems, linear and nonlinear pharmacokinetics, distillation
columns, or chemical reactors.
Customers include Boehringer Ingelheim KG,
BASF AG, Bayer Inc., Eurocopter GmbH, and various academic institutions.
Reference:
K. Schittkowski, MODFIT: A FORTRAN code for constrained parameter
estimation in differential equations and explicit model functions,
Report, Department of Mathematics, University of Bayreuth (1994)