Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q10/00—Administration; Management
  • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F30/00—Computer-aided design [CAD]
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F2111/00—Details relating to CAD techniques
  • G06F2111/08—Probabilistic or stochastic CAD

Definitions

• the invention relates to a method for the automatic planning of experiments and a corresponding computer program product and a system for the automatic planning of experiments.
• test planning In the field of statistical test planning, different types of test planning are distinguished in the prior art. In particular, a distinction is made between the classic, full-factorial method and modern Taguchi or Shainin methods.
• Shainin-DOE Design of Experiment
• the Taguchi DOE is based on previous, partial factorial, orthogonal test plans. Because of the drastic savings in trial runs by preselecting the most important influencing factors, this is a quick and relatively economical procedure for trial and process planning.
• test planning are partial factorial test plans ("fractional factorial”), Plackett-Burmann test plans, central composite plans ("central composite”), box-bound test plans, D-optimal plans ("D-optimal designs”), Mixing plans, balanced block plans, Latin squares, Desperado plans (see also http://www.technischsteil.de).
• test points are evenly distributed on a multidimensional spherical surface in order to weight the individual manufacturing parameters evenly.
• the invention is based on the object of creating an improved method for the automatic planning of experiments and a corresponding computer program product and system.
• the present invention makes it possible to carry out test planning for a predetermined number M of experiments by uniformly distributing the experiments in a discretized parameter space which can be restricted by constraints.
• Expert knowledge of the user of the corresponding test planning tool can be incorporated here, namely by defining a measure of similarity between two different experiments and by defining a measure of evaluation for individual experiments.
• the use of the present invention is particularly advantageous for the test planning for data acquisition for the training of neural networks or hybrid neural networks with rigorous model components.
• a uniform distribution of the test planning in the relevant space can be achieved with the invention, so that a neural network or a hybrid neural network can be trained with a relatively small number of test data.
• a particular advantage compared to the test planning program known from the prior art is that, in principle, any boundary conditions for the type of experiments can be specified.
• prior knowledge - for example structural information about a process to be modeled - can already be taken into account when planning the experiment.
• a similarity measure represents a numerical value for the similarity or dissimilarity of two experiments.
• the background to this is that the experiments to be planned should be chosen so that they are as dissimilar as possible. What similarity or dissimilarity for a particular
• Trial means can be defined by the user via the definition of the similarity measure.
• an evaluation measure with regard to the evaluation of individual experiments can be specified by the user.
• criteria can be included in this assessment measure, such as the conditions of the test facility, costs for carrying out an experiment, the time required to carry out an experiment, etc.
• certain parameter combinations such as high pressure and high temperature can damage the Run a test facility so that such "forbidden" parameter combinations are provided with an appropriate evaluation.
• the similarity and evaluation measures defined in this way are incorporated into a quality measure which combines the similarity measure and the evaluation measure with one another. Based on the quality measure, those experiments for which the quality measure takes an extreme value are then determined according to the invention. Depending on the choice of the similarity measure and evaluation measure and the choice of the respective sign, this extreme value is a maximum or a minimum of the quality measure.
• the similarity measure is based on the Euclidean distance between two experiments in a parameter space.
• Each experiment is defined by a vector which contains the parameter values of the various test variables for this specific experiment.
• This parameter space is preferably discretized, ie the parameter values can only assume certain discrete values.
• the distance between two experiments is e.g. as the Euclidean distance of the parameter vectors of the considered experiments.
• a reciprocal Euclidean distance between two experiments is preferably defined as a measure of similarity.
• an exponential function can be defined as a measure of similarity, which has the reciprocal Euclidean distance of two experiments as exponents. Further definitions of similarity measures are possible depending on the respective test scenario.
• the evaluation measure can also be defined in the form of a formula. Alternatively, the evaluation measure can also be defined in the form of a table or the like.
• the similarity measures of all pairings of parameter vectors are calculated and added to calculate the quality measure.
• the evaluation measures are calculated for all the experiments under consideration.
• the summed similarity measures and the summed evaluation measures are then added or subtracted depending on the definition of the similarity and evaluation measures. This addition or subtraction then results in the quality measure which is to be minimized or maximized.
• experiments already carried out are also used for the calculation of the similarity measure and the evaluation measure. For example, if a number N experiments have already been performed, M new experiments are searched in the discrete parameter space. The quality measure is then calculated based on the N experiments already performed and the M new experiments in order to select the M new experiments.
• the extreme value of the quality measure is determined using a Monte Carlo method.
• a genetic algorithm or another suitable numerical optimization method are used.
• test planning program is connected to the system control, so that the test planning program
• Parameter vectors of the experiments found can be transferred to the controller.
• FIG. 1 shows a flow diagram of a first embodiment of the method for the automatic planning of experiments
• FIG. 2 shows a second embodiment based on Monte Carlo optimization
• FIG. 3 is a block diagram of an embodiment of an inventive
• FIG. 1 shows a flow chart for the automatic planning of experiments.
• the experiments are to be planned in a d-dimensional parameter space.
• J mitj e (l..n,) ie (l ..d) are specified for the individual coordinates.
• n denotes the number of possible settings for the coordinate i.
• this d-dimensional parameter space is defined with its discretizations.
• step 2 the number M of experiments to be planned is entered.
• step 3 a similarity measure R of two experiments is entered.
• the similarity measure R is defined such that the more similar two experiments are, the greater the similarity measure.
• One possibility for defining the similarity measure R of two experiments xi and x 2 is given below:
• an evaluation measure S of an individual experiment x is then entered.
• the function S (x) can be stored, for example, in the form of a table. In addition to the boundary conditions specified by the test facility, other criteria, such as, for example, the time and / or cost involved in carrying out a particular experiment, can also be represented using the evaluation measure S.
• the evaluation measure S in the form of a function or table is chosen such that the larger the more desirable an individual experiment is, the more desirable it is.
• step 5 this results in a quality measure Q, which is based on the similarity measure R and the evaluation measure S.
• a minimum of the quality measure Q is determined, that is to say a selection of M experiments from the parameter space, so that Q becomes minimal and thus the quality reaches a maximum.
• test planning problem solved in step 6 is therefore formal:
• step 7 the M experiments determined in step 6 are output.
• test planning it is particularly advantageous in this embodiment of the test planning according to the invention that, on the one hand, the experiments to be carried out and existing differ from one another as much as possible and, on the other hand, that they are each individually desired if possible.
• This structural approach allows complex solving the most delicate test planning problems by formulating the measure for the difference between two experiments in a way that is adapted to the problem and, for example, implementing additional conditions through individual evaluation of experiments. If you have defined the measure for the difference or similarity and the individual evaluation function, ie the evaluation measure, the test planning is reduced to an optimization problem, which can be solved with mathematical aids.
• test planning problems Some examples of different types of test planning problems and their implementation using the method according to the invention are described below:
• the invention not only allows experiments to be planned which differ as much as possible, but also an individual evaluation of experiments is carried out via the evaluation measure S.
• "hard” constraints on experiments to be carried out can be specified. For example, criteria can be specified which must be or must not be fulfilled in all experiments.
• the experiments are evenly distributed in the space restricted in this way. This possibility in particular allows that certain types of experiments are excluded from the outset.
• experiments are planned that allow a model to be created that can distinguish between good and bad operating conditions.
• a sequence of new experiments is planned, which specifically examine the range of desired operating states. This is realized with the help of the evaluation measure S.
• S the evaluation measure
• the model can be improved in the interesting parameter areas and a new series of tests can now be created with more ambitious process quality specifications. This process is repeated until the optimum state of the process has been found with the desired accuracy.
• a possible method for solving the optimization problem that is, for choosing M experiments so that the quality measure Q takes an extreme value, is the Monte Carlo method.
• FIG. 2 shows an embodiment with regard to the implementation of a
• step 8 a number of M experiments are arbitrarily selected from the parameter space. Furthermore, a quality difference ⁇ is initialized. In step 9, an experiment is then arbitrarily selected from these M experiments. In step 10, the quality measure Q is calculated for the test plan with this experiment.
• step 11 a coordinate of this experiment is selected arbitrarily. If the coordinate is ordinal, it is preferably increased or decreased by one step at random; if the coordinate is categorical, it will be chosen at random. This is done in step 12.
• step 13 the quality measure Q 'is calculated for the selected experiment with the varied coordinate.
• step 14 the quality measures Q and
• step 15 the experiment selected in step 9 is replaced by this selected experiment with the varied coordinate.
• the quality difference ⁇ is then reduced. If, on the other hand, the quality has deteriorated significantly, the experiment originally selected in step 9 is retained. In this case too, the quality difference ⁇ can be reduced. Steps 9 to 14 and optionally 15 are repeated until an abort condition is reached.
• the value of ⁇ is continuously reduced to zero.
• a termination condition can be a maximum number of iterations; Another choice of a termination condition is when the quality measure Q no longer changes or does not change significantly. This way and
• a minimum of the quality measure Q and thus the M experiments sought can thus be determined (cf. step 6 of FIG. 1).
• FIG. 3 shows a block diagram of an embodiment of a system according to the invention.
• the system includes a test facility 30 for carrying out the experiments.
• the experimental system 30 is controlled by a controller 31.
• a computer 32 is connected to the controller 31 and has a computer program 33 for carrying out the test planning.
• the computer program 33 contains a function 34 for calculating the similarity measure and a function 35 for calculating the evaluation measure (cf. steps 3 and step 4 of the figure
• the computer program 33 has an adaptation module 44 for adapting the evaluation measure 35 to the results of the experiments 39 carried out.
• the termination module 45 is also provided for the cyclic operation of the system, so that the method ends when a predefined termination criterion is reached.
• the computer program 33 contains a function 36 for calculating the quality measure based on the functions 34 and 35 (cf. step 5 of FIG. 1).
• the computer program 33 also contains an image 37 of the discrete parameter space X (cf. step 1 of FIG. 1).
• the computer program also includes
• the computer 32 also has a memory 39 for storing the parameter vectors from previous experiments. On this memory 39, the
• the computer 32 also has a user interface 40, via which a user can use a screen 41 to enter the functions 34, 35 and / or 36 as well as an adaptation scheme into the adaptation module 44 and an abort criterion into the termination module 45.
• the user can also specify the parameter space 37 via the user interface 40.
• the experiments can be automatically planned by the computer program 33.
• the program module 38 accesses the memory 39 and the function 36 in order to optimize them, that is to say to find a number of M experiments in such a way that the quality measure takes an extreme value.
• the parameter vectors of the M experiments to be carried out are available. These parameter values are transmitted to the controller 31 as a file 42, which has the form of a matrix, for example.
• the controller 31 makes the corresponding settings in the test installation so that the individual M experiments are carried out.
• the controller 31 determines the measurement results of interest from the test system 30 and combines them into a file 43 which is automatically transmitted to the computer 23.
• the user of the computer 32 can open the file 43 and, if necessary, analyze it using further software.
• Memory 39 transferred, so that they are used in a subsequent planning for the evaluation of functions 34, 35 and / or 36.
• the computer program 33 can adapt the evaluation measure 35 with the aid of the adaptation module 44.
• the system plans the new test series and transmits the experiments to the control system 31. This is repeated cyclically until a predefined reduction criterion (termination module 45) is met, or the method is ended through user intervention via user interface 40.

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