DE102021201878A1 - Optimization of test procedures - Google Patents

Abstract

The invention relates to a computer-implemented method for numerically optimizing the selection and distribution of test points within a parameter space for executing a test in a test device, the test being described by a model with at least two input parameters and a state vector as the output parameter, the parameter space being described by the at least two Input parameters of the model of the test is spanned and the parameter space includes boundary conditions that exclude certain combinations of input parameters and previously known information about the parameter space is available, so that at least one fixed test point can be generated. The optimization of the selection and distribution of the test points within the parameter space is generated by the following steps: initialization, movement, friction, force calculation, acceleration, convergence check and modification.

Description

The invention relates to a computer-implemented method for numerically optimizing the selection and distribution of test points within a parameter space for executing a test in a test device.

Parameter spaces are also used in particular for training artificial intelligence and for testing the behavior of electronic and/or mechanical components. The selection of points within a parameter space and the optimization of the points are important criteria in order to run the training and test procedures efficiently and in a way that conserves resources.

In the optimization of physical parameters of electrical or mechanical components or complex regulation and control systems, methods are often used that require the parameter space to be initially covered by test points before the actual optimization process can be started. Efficient coverage of the parameter space on the one hand prevents function evaluation at non-informative points and on the other hand has a decisive influence on the convergence speed of the optimization.

Latin-Hypercube Sampling (LHS) has been the accepted state of the art for almost 40 years to generate space-filling samples even in high-dimensional spaces and has been proven to be clearly superior to random sampling. LHS random samples can be optimized according to various criteria, e.g. the max-min criterion, in which the minimum distance between two points in space is maximized. Furthermore, it can be specified that the density distribution should follow a specified distribution in each individual dimension.

In practice, many optimization problems are subject to boundary conditions that exclude certain combinations of parameters a priori.
LHS samples can only satisfy such boundary conditions in the case of simple inequality conditions. More complex interdependencies between parameters cannot be taken into account. Explicit previous knowledge about function values for given values, which may be available, for example, through expert knowledge or experiments that have already been carried out, cannot be taken into account when creating LHS samples. The explicit selection of points of interest destroys the space-filling properties of the experimental design.

It would be desirable to overcome these disadvantages.

1. a) der Test wird durch ein Modell mit zumindest zwei Eingangsparametern und einem Zustandsvektor als Ausgabeparameter beschrieben;
2. b) der Parameterraum wird von den zumindest zwei Eingangsparametern des Models des Tests aufgespannt und wobei der Parameterraum Randbedingungen umfasst, die gewisse Kombinationen von Eingangsparametern ausschließen;
3. c) Vorbekannte Informationen über den Parameterraum vorliegen, so dass zumindest ein fixer Testpunkt erzeugt werden kann; und wobei die Optimierung der Auswahl und Verteilung der Testpunkte innerhalb des Parameterraums durch folgende Schritte erzeugt wird:
   1. 1) Erstellen von n zufällig im Parameterraum verteilten beweglichen Testpunkten, die die Randbedingungen erfüllen und zuweisen von einem zufälligen Geschwindigkeitsvektor und einer Masse an die zufällig im Parameterraum verteilten beweglichen Testpunkten; und Zuweisen von m fixen Testpunkten, deren Position im Parameterraum durch die vorbekannten Informationen bestimmt sind und zuweisen von einem Geschwindigkeitsvektor und einer Masse, wobei der Geschwindigkeitsvektor der Nullvektor ist;
   2. 2) Ausführen eines zeitlichen Integrationsschritt, wobei sich alle Testpunkte gemäß ihrer Geschwindigkeit unter der Berücksichtigung periodischer Randbedingungen an den Grenzen des Parameterraums fortbewegen und wobei sich Testpunkte, deren neue Position die Randbedingungen verletzen würden, sich nicht weiterbewegen;
   3. 3) Setzen der Geschwindigkeitsvektoren aller Testpunkte auf null;
   4. 4) Berechnen von abstoßenden Kräften für alle N=n+m Testpunkte proportional zu den Massen der Testpunkte nach einem inversen Quadratgesetz, wobei die Berechnung der abstoßenden Kräfte den Randbedingungen des Parameterraums gehorcht;
   5. 5) Zuweisen eines neuen Geschwindigkeitsvektors an die n beweglichen Testpunkte basierend auf den berechneten abstoßenden Kräften;
   6. 6) Überprüfen eines Konvergenzkriteriums und wiederholen der Schritte 2 bis 5, wenn das Konvergenzkriteriums nicht erfüllt ist;
   7. 7) Modifikation der erzeugten Testpunkteverteilung im Parameterraum unter Verwendung von vorbekannten Informationen, wobei gegebenenfalls weitere fixe Testpunkte hinzugefügt und bewegliche Testpunkte entfernt oder umpositioniert werden können;
   8. 8) Wiederholen der Schritte 2 bis 7, bis erneut Konvergenz erreicht ist und keine weiteren Modifikationen in Schritt 7 durchgeführt werden.

A computer-implemented method according to the invention includes that

1. a) the test is described by a model with at least two input parameters and a state vector as the output parameter;
2. b) the parameter space is spanned by the at least two input parameters of the model of the test and the parameter space includes boundary conditions that exclude certain combinations of input parameters;
3. c) Previously known information about the parameter space is available, so that at least one fixed test point can be generated; and wherein the optimization of the selection and distribution of the test points within the parameter space is generated by the following steps:
   1. 1) creating n randomly distributed in parameter space moving test points that satisfy the boundary conditions and assigning a random velocity vector and a mass to the randomly distributed in parameter space moving test points; and assigning m fixed test points whose position in the parameter space is determined by the previously known information and assigning a velocity vector and a mass, the velocity vector being the zero vector;
   2. 2) performing a time integration step, where all test points move according to their speed considering periodic constraints at the boundaries of the parameter space and where test points whose new position would violate the constraints do not move any further;
   3. 3) set the velocity vectors of all test points to zero;
   4. 4) calculating repulsive forces for all N=n+m test points proportional to the masses of the test points according to an inverse square law, the calculation of the repulsive forces obeying the boundary conditions of the parameter space;
   5. 5) assigning a new velocity vector to the n moving test points based on the calculated repulsive forces;
   6. 6) checking a convergence criterion and repeating steps 2 to 5 if the convergence criterion is not met;
   7. 7) modification of the generated test point distribution in the parameter space using previously known information, it being possible for further fixed test points to be added and movable test points to be removed or repositioned;
   8. 8) Repeat steps 2 through 7 until convergence is again achieved and no further modifications are made in step 7.

Furthermore, the test device can be configured to be connected to an electrical component, or the test device can be configured to be connected to a mechanical component, or the test device can be configured to be connected to an electromechanical component to be brought, or the test device can be designed to train an artificial intelligence.

In addition, the masses associated with the test points can be unit masses.

In the modification in step 7, an area that is intended to have a higher density of test points is preferably assigned a fixed test point whose mass is smaller than the masses of the surrounding test points.

A test system according to the invention comprises a component to be tested, a recording unit for the component to be tested, a computer unit and a control unit.

1. 1. Vordefinierten Randbedingungen gehorchen können
2. 2. Vorwissen, das auf evtl. nicht raumfüllenden Verteilungen gewonnen wurde, optimal integrieren
3. 3. Vielfältig justierbar sind.

The procedure described generates space-filling distributions that correspond to the max-min criterion, unless the desired deviation is made by changing the particle mass, but which

1. 1. Being able to obey predefined boundary conditions
2. 2. Optimally integrate prior knowledge gained from distributions that may not fill space
3. 3. Can be adjusted in many ways.

The method described is superior to the prior art, in which, for example, boundary conditions are observed by discarding randomly drawn points that violate them, because these methods do not generate space-filling distributions, but instead contain points with low information content.

• 1: ein Ablaufdiagramm eines erfindungsgemäßen Verfahrens;
• 2: eine beispielhafte Punktverteilung in einem Parameterraum;
• 3: eine beispielhafte Konvergenz des erfindungsgemäßen Verfahrens;
• 4: eine beispielhafte Punktverteilung nach Erreichen der Konvergenz;
• 5: eine beispielhafte Punktverteilung im Parameterraum nach zusätzlicher Modifikation; und
• 6: eine beispielhafte Punktverteilung nach Modifikation und erneuter Konvergenz.

Further features, properties and advantages of the present invention result from the following description with reference to the enclosed figures. It shows schematically:

• 1 : a flowchart of a method according to the invention;
• 2 : an exemplary point distribution in a parameter space;
• 3 : an exemplary convergence of the method according to the invention;
• 4 : an example point distribution after reaching convergence;
• 5 : an exemplary point distribution in the parameter space after additional modification; and
• 6 : an exemplary point distribution after modification and re-convergence.

A specific embodiment of the method according to the invention has the steps of initialization S1, movement S2, friction S3, force calculation S4, acceleration S5, convergence check S6 and modification S7, as in 1 pictured.

The parameter space is to be generated by a function with two parameters x1 and x2, with the parameters here being scaled to the unit interval [0,1] as an example. There are boundary conditions that prohibit the combination of some parameter values. These prohibited areas are shown hatched in the figures. The limited budget and the high costs of function evaluation make it necessary to specify a maximum number of test runs (here e.g. N = 20) for which the best possible points in the parameter space must be found.

In the first step initialization S1, n randomly distributed positions in the allowed parameter space are selected and points (round points) are assigned, as in 2 pictured. Random velocity vectors are assigned to the n randomly distributed positions. Furthermore, there is a previously known point in the parameter space (represented as a rhombus in the figures), which is considered to be particularly interesting for the parameter evaluation and should therefore be taken into account in the experimental design. This is given as (n+1). position fixed. These types of points remain fixed throughout the optimization process. All (n+1) points also receive a mass parameter, here for example mi = 1, where mi describes the mass parameter m for the ith point. However, the weighting of the mass parameters can also depend on the position or other information that is already available. The result of this step is exemplary for n = 19 in 2 shown.

1. 1. Bewegungen, die einen Punkt in einen nicht erlaubten Bereich des Parameterraums führen würden, werden nicht ausgeführt. Der Punkt verbleibt an seinem Ort.
2. 2. Periodische Randbedingungen werden beachtet, d.h. allen neuen Ortsvektorkomponenten xi wird der Wert xi mod 1 zugewiesen, wobei mod die Modulo-Funktion darstellt.

In the second step Movement S2, all moving points are now moved for a fixed time dt based on their velocity vectors. The time dt is either already available as information or can also be determined using optimizations. The following conditions are observed:

1. 1. Movements that would lead a point into a non-permissible area of the parameter space are not executed. The point stays in place.
2. 2. Periodic boundary conditions are observed, ie all new position vector components xi are assigned the value xi mod 1, where mod represents the modulo function.

In step S3, all speeds are set to zero.

, analog zum Newotnschen Gravitationsgesetz mit Gravitationskonstante von 1 und den vorher bereits definierten Massenparametern mi.In step S4, repulsive forces are calculated for all points using an algorithm. Here, for example, the force Fi acting on a point i is set as a function of the direction and the distance rij=xi-xj to the other points j: $fi={\displaystyle {\sum }_{j=\mathrm{1,}j\ne i}^N\frac{\text{wed}\ast \text{my}}{{\text{rij}}^3}\ast \mathrm{right}ij}$

, analogous to Newotn's law of gravitation with a gravitational constant of 1 and the previously defined mass parameters mi.

1. 1. diese Kräfte auch als Gradient des Potentials der Dichteverteilung der Masse berechnet werden können;
2. 2. das Potential über eine Poissongleichung mit der Dichteverteilung verbunden ist;
3. 3. Poissongleichungen sich numerisch effizient über Fourier Transformationen lösen lassen.

You can take advantage of that

1. 1. these forces can also be calculated as the gradient of the potential of the density distribution of the mass;
2. 2. the potential is related to the density distribution by a Poisson equation;
3. 3. Poisson equations can be solved numerically efficiently using Fourier transformations.

In practice, the density distribution is generated on a regular grid by assigning grid points to the point masses. The Fourier transform of the density distribution discretized in this way is calculated by a fast Fourier transform (FFT). This algorithm naturally creates periodic boundary conditions. The Fourier transform of the potential is obtained from the connection with the Poisson equation. The potential is then calculated by an inverse FFT. The force field is now obtained by calculating the gradient of the potential as a finite difference, taking into account the periodic boundary conditions. Forces are now assigned to the points using the same discretization scheme that was used to generate the density distribution.

In step S5, a new velocity vector is obtained from the forces acting on all points resulting in acceleration, which acts exclusively on the n moving points for a fixed period of time dt.

In step S6, convergence criterion, it is checked whether convergence has been achieved. For example, the convergence criterion can be that the mean point speed no longer decreases. In 3 shows the mean absolute speed of the points as a function of the number of iterations of the method (steps S2 to S6). in the in 3 In the example shown, a stable equilibrium is reached after a few hundred iterations. If convergence is reached, the method continues with step S7. If no convergence is achieved, the method continues with step S2. The distribution of the points based on the in 2 and the description defined conditions and parameters in 4 shown.

If further information about an advantageous distribution of the points is known or the distances between individual points are too small, further fixed points can be replaced in exchange for other points or individual points can be relocated. This is carried out in step S7 modification and is exemplified in 5 shown where two more fixed points were set and two other points were deleted in their place. This can be necessary, for example, if problems occur during implementation at or around certain points in the parameter space, but there are more advantageous points nearby, ie points that can be implemented more easily.

If a changed distribution results in step S7, fine-tuning is carried out by continuing to carry out the method starting with step S2 until convergence is achieved again in step S6 and no modifications are carried out in step S7. An example is the final distribution after modification and following steps S2 to S6 again until convergence in 6 pictured. Otherwise the procedure ends.

The position of the points now corresponds to the points in the parameter space in order to run the training and test procedures efficiently and in a way that conserves resources.

• • Motorbetriebene bewegliche Elemente wie Heckklappen, Schiebetüren und -dächer, Fenster oder Sitze
• • Antriebsaggregate und Einspritzsysteme
• • Abgas Regulationssysteme
• • Getriebe
• • Herstellungs- oder Produktionsprozesse
• • Darüber hinaus lässt sich das beschriebene Verfahren auch zur Initialisierung evolutionärer Algorithmen einsetzen, sowie für destruktivere Versuche (Material- und CrashTests), die sich nicht beliebig oft wiederholen lassen und mit beschränkter Versuchszahl den Parameterraum optimal abdecken müssen.

The optimization of functions that are difficult to evaluate is a broad field. Common problems in the automotive sector that are tested on test systems are:

• • Motorized moving elements such as tailgates, sliding doors and roofs, windows or seats
• • Power units and injection systems
• • Exhaust gas regulation systems
• • Transmission
• • Manufacturing or production processes
• • In addition, the method described can also be used to initialize evolutionary algorithms, as well as for more destructive tests (material and crash tests) that cannot be repeated any number of times and must optimally cover the parameter space with a limited number of tests.

Although the invention has been illustrated and described in detail by the preferred embodiments, the invention is not limited by the disclosed examples. Variations may be devised by those skilled in the art without departing from the scope of the invention as defined by the following claims.

Claims (4)

A computer-implemented method for numerically optimizing the selection and distribution of test points within a parameter space for executing a test in a test fixture, where a) the test is described by a model with at least two input parameters and a state vector as the output parameter; b) the parameter space is spanned by the at least two input parameters of the model of the test and the parameter space includes boundary conditions that exclude certain combinations of input parameters; c) Previously known information about the parameter space is available, so that at least one fixed test point can be generated; and the optimization of the selection and distribution of the test points within the parameter space is generated by the following steps: 1) creating n randomly distributed in parameter space moving test points that satisfy the boundary conditions and assigning a random velocity vector and a mass to the randomly distributed in parameter space moving test points; and assigning m fixed test points whose position in the parameter space is determined by the previously known information and assigning a velocity vector and a mass, the velocity vector being the zero vector; 2) performing a time integration step, where all test points move according to their velocity considering periodic constraints at the boundaries of the parameter space and where test points whose new position would violate the constraints do not move any further; 3) set the velocity vectors of all test points to zero; 4) calculating repulsive forces for all N=n+m test points proportional to the masses of the test points according to an inverse square law, the calculation of the repulsive forces obeying the boundary conditions of the parameter space; 5) assigning a new velocity vector to the n moving test points based on the calculated repulsive forces; 6) checking a convergence criterion and repeating steps 2 to 5 if the convergence criterion is not met; 7) modification of the generated test point distribution in the parameter space using previously known information, it being possible for further fixed test points to be added and movable test points to be removed or repositioned; 8) Repeat steps 2 through 7 until convergence is again achieved and no further modifications are made in step 7. Computer-implemented method claim 1 , characterized in that the test device is designed to be connected to an electrical component, or the test device is designed to be connected to a mechanical component, or the test device is designed to be connected to an electromechanical component in To be connected, or the test device is designed to train an artificial intelligence. Computer-implemented method claim 1 or 2 , characterized in that the masses assigned to the test points are unit masses. Computer-implemented method according to one of the preceding claims, characterized in that in the modification in step 7 an area which is to have a higher density of test points is assigned a fixed test point whose mass is smaller than the masses of the surrounding test points.

Images