The designer describes parameters and its
limits too. Unlike scanning, the numerical experiments are calculated for
several key points in parameter space. Values of objective function in other
points are calculated with the help of methods based on quadratic approximation.
So this tool leads to extremely low calculation efforts especially for
multi-dimensional problems and gives response surface. However there are
restrictions on using this approach. Response surface should be smooth and
should be represented well with the help of quadratic functions. In fact, these
restrictions are not so strong for real technical objects because they normally
have smooth and nearly quadratic response surface. Response surfaces calculated
as result of scanning and approximation are shown. Maximal relative error is at
most 3 % in that example. Practice of modeling shows that, as a rule, maximal
relative errors are less than 10-15 %, but time efforts are decreased in several
times. However the optimal solution obtained with the help of this approach can
be far enough from the true optimum. Generally, this tool is not intended for
searching optimum of objective function. It is rather intended for first, fast
and actually not so deep overview of dynamical properties of a mechanical
system.
The analytic hierarchy process was developed by Saaty. Detailed information is
available in [1]. The method is based on principle of hierarchization, where the
main, most common goal consists of several more detailed sub-goals, each
sub-goal of the first level consists of the corresponding sub-goals of level two
and so on. Every sub-goal has only one upper goal. Different sub-goals affect
the upper goal with a different weight.
Further, the analytic hierarchy process involves the method to determine the weight with which the various elements in one level influence the elements on the next higher level, so that we may compute the relative weight of the impacts of the elements of the lowest level on the overall objectives. The method can be described as follows. Given one goal, and its sub-goals of the next level lower, compare the sub-goals pairwise in their weight of influence on upper level. Let us arrange the agreed upon numbers reflecting the comparison in a matrix and find the eigenvector with the largest eigenvalue. The eigenvector provides the priority ordering, and the eigenvalue is a measure of the consistency of the judgment.
To insert the agreed upon numbers the designer has to compare every pair of sub-goals and give an answer for the question "how stronger the influence of sub-goal B on the upper goal than the influence of sub-goal C on it", this number will be included in the (B, C) matrix element. If B and C are equally important then the number is 1, if B is weakly more important than C then the number is 3 and so on up to number 9 when the B is absolutely more important than C.
[1]. Saaty, T. The Analytic Hierarchy Process, McGraw-Hill, 1980.
Further, the analytic hierarchy process involves the method to determine the weight with which the various elements in one level influence the elements on the next higher level, so that we may compute the relative weight of the impacts of the elements of the lowest level on the overall objectives. The method can be described as follows. Given one goal, and its sub-goals of the next level lower, compare the sub-goals pairwise in their weight of influence on upper level. Let us arrange the agreed upon numbers reflecting the comparison in a matrix and find the eigenvector with the largest eigenvalue. The eigenvector provides the priority ordering, and the eigenvalue is a measure of the consistency of the judgment.
To insert the agreed upon numbers the designer has to compare every pair of sub-goals and give an answer for the question "how stronger the influence of sub-goal B on the upper goal than the influence of sub-goal C on it", this number will be included in the (B, C) matrix element. If B and C are equally important then the number is 1, if B is weakly more important than C then the number is 3 and so on up to number 9 when the B is absolutely more important than C.
[1]. Saaty, T. The Analytic Hierarchy Process, McGraw-Hill, 1980.
The service is based on TCP/IP protocol. It allows using any computer reachable
by TCP/IP under Windows 98/NT/2000/XP for parallel numerical experiments.
Service of distributed calculations consists of two parts: server and client
ones. The server part works on the head computer and controls the execution,
sends jobs and receives results back. The client part is run on the peripheral
computers, gets and fulfils jobs and sends results to the server.






Designer describes parameters to scan (as a rule, it
is geometrical, inertia, stiffness and damping parameters), limits and step
size for each parameter and starts series of numerical experiments. Scanning
saves time history of all selected dynamical performances on a hard disk. These
performances are available after the execution of the project. There are special
possibilities for scanning dynamical behavior of railway vehicles: with various
rail and wheel profiles, various tracks (tangent tracks and curves), various
railway track irregularities. Scanning gives us full information about the
response surface and the global optimum. It is usually enough to solve an
optimization problem. On the other hand, scanning is very time-consuming process
so as it is not practically used for problems with dimension more than 4-5.
Scanning supports
This tool is based on a number of classical
optimization methods: Hook-Jeevse's, Nealder-Mead's, Pawell's etc. The advantage
of this tool is quite low computational efforts. On the other hand the tool has
some disadvantages. Firstly, there is always a possibility that the method stops
in one of the local optimums and does not find the global one. Secondly, all
what the designer has after this kind of optimization does not give the shape of
the objective function, it gives just several points on it. So the designer
cannot get general overview of the dynamical behavior of the system. However it
is well-known that objective functions of real mechanical systems are quite
smooth, otherwise it would be high parameter sensitivity of the system that
should not take place in real systems.