WO2013167342A1

WO2013167342A1 - A method for computer-aided processing of models of a technical system

Info

Publication number: WO2013167342A1
Application number: PCT/EP2013/057675
Authority: WO
Inventors: Victoria KUSHERBAEVA; Alexander Pyayt
Original assignee: Siemens Aktiengesellschaft
Priority date: 2012-05-07
Filing date: 2013-04-12
Publication date: 2013-11-14

Abstract

The invention refers to a method for computer-aided processing of models (M1, M2, M3, M4) of a technical system, each model (M1, M2, M3, M4) being based on a computer- implemented process for predicting sensor measurements. The method comprises the step of providing several quality criteria (C1, C2, …, C6) for the models (M1, M2, M3, M4) and a weight (w1, w2, …, w6) for each quality criterion (C1, C2, …, C6), each weight (w1, w2, …, w6) representing a contribution of the respective quality criterion (C1, C2, …, C6) to an overall quality of the models (M1, M2, M3, M4), where the weights (w1, w2, …, w6) are determined based on pairwise comparisons of the quality criteria (C1, C2, …, C6) using intensities of importance according to an Analytic Hierarchy Process. Furthermore, a quality measure of the respective model (M1, M2, M3, M4) with respect to the corresponding criterion (C1, C2, …, C6) is determined for each model (M1, M2, M3, M4) and for each quality criterion (C1, C2, …, C6), where a priority value (p11, p12, …, p46) is assigned to the respective model (M1, M2, M3, M4) based on the quality measure for each quality criterion (C1, C2, …, C6). Moreover, a sum (s1, s2, s3, s4) over all quality criteria (C1, C2, …, C6) for each model (M1, M2, M3, M4) is determined, where the summand for a respective quality criterion (C1, C2, …, C6) is the product of the weight (w1, w2, …, w6) for the respective quality criterion (C1, C2, …, C6) and the priority value (p11, p12, …, p46) for the respective model (M1, M2, M3, M4) and quality criterion (C1, C2, …, C6), the sum (s1, s2, s3, s4) representing the overall quality of the respective model (M1, M2, M3, M4). Finally, an output is generated including the model (M1, M2, M3, M4) with the highest overall quality.

Description

A method for computer-aided processing of models of a technical system

The invention refers to a method for computer-aided

processing of models of a technical system as well as to a corresponding computer program product and a corresponding computer program.

It is well-known from the prior art to describe the behavior of a technical system by using models which are based on computer- implemented processes for predicting sensor

measurements of one or more parameters of the technical system. A corresponding model may be used for abnormal behavior detection of the technical system in condition monitoring. To do so, predicted sensor measurements are compared with real sensor measurements and, in case of a high deviation, an anomaly is detected.

As the models for describing a technical system are generally high sophisticated, it is difficult to select the appropriate model that reflects best the behavior of the technical system. The task of such a selection is complicated because there are multiple quality criteria which can be of

quantitative and qualitative nature in order to describe the quality of the model.

Prior art methods do not disclose an approach on how to choose a model which is appropriate for describing a

technical system. In document [1] , a system is developed to select manually parameters of neural networks to simulate the flood level dynamics in a river basin. Documents [2] to [4] refer to a comparison of performances of several mainly non- linear models for dam monitoring and flood forecasting. Those documents do not suggest any formal or informal procedure for choosing an appropriate model or its parameters in a

particular case. It is an object of the invention to provide a computer-aided processing of models of a technical system enabling the determination of the best model for the technical system according to several quality criteria.

This object is solved by the independent patent claims.

Preferred embodiments of the invention are defined in the dependent claims.

The method according to the invention processes several models of a technical system by the use of a computer. Each model is based on a computer- implemented process for

predicting sensor measurements of one or more parameters of the technical system. Particularly, each model predicts one or more sensor measurements based on a time series of previous sensor measurements. Depending on the type of the models, one or more of the models may be trained based on training data comprising one or more time series of sensor measurements. This is e.g. the case for models based on neural networks .

In a step a) of the method of the invention, several quality criteria for the models of the technical system and a weight for each quality criterion are provided. Each weight

represents a contribution of the respective quality criterion to an overall quality of the models, where the weights are determined based on pairwise comparisons of the quality criteria using intensities of importance according to an Analytic Hierarchy Process. Preferably, the weights are determined on-line during performing the method. However, it may also be possible to determine the weights beforehand and store them in a storage where the method can access the storage to read out the weights.

The Analytic Hierarchy Process is well-known from the prior art. E.g., a description of this process can be found in document [5] . The Analytic Hierarchy Process is a method to support decisions, and the above mentioned pairwise

comparisons using intensities of importance is a substantial step of the Analytic Hierarchy Process in case of qualitative comparisons. As a result of this step, corresponding

priorities for alternatives compared in the Analytic

Hierarchy Process are obtained. In step a) of the method according to the invention, those alternatives are the quality criteria. A detailed description of the pairwise comparisons can be found in section 4 of document [5] . The intensities of importance used therein are chosen between 1 and 9 and represent the so-called Saaty scale. However, other scales may also be used for representing the intensities of importance. Based on the pairwise comparisons, it is

determined which one of the quality criteria of a

corresponding pair of the criteria is regarded as more important. As a consequence, a corresponding matrix is built, and the components of the eigenvector of the matrix refer to the weights as defined in step a) of claim 1. As the pairwise comparisons using intensities of importance are well-known from the prior art, these comparisons are not described in detail. However, the detailed description of the application discloses a concrete process of such pairwise comparisons.

In a step b) of the method of the invention, a quality measure of the respective model with respect to the

corresponding criterion for each model and for each quality criterion is determined, where a priority value is assigned to the respective model based on the quality measure for each quality criterion, the priority value increasing with a higher quality according to the quality measure. In some embodiments, the priority may correspond directly to the quality measure, i.e. to the quality value is the quality measure. Depending on the model, the corresponding quality measure can be defined differently. Below, several examples of quality measures for models are given.

In a step c) of the method according to the invention, a sum over all quality criteria for each model is determined, where the summand for a respective quality criterion is the product of the weight for the respective quality criterion and the priority value for the respective model and quality

criterion. The sum represents the overall quality of the respective model such that a higher sum corresponds to a higher overall quality.

Eventually in a step d) , an output including the model with the highest overall quality, i.e. with the highest value of the sum, is generated by the method of the invention.

The method of the invention is based on the finding that the pairwise comparisons defined in an Analytic Hierarchy Process may be used in an efficient manner in order to define the contributions of different quality criteria with respect to an overall quality of a model. In combination with

corresponding quality measures evaluated for each model and each criterion, the best model based on all criteria can be derived. Hence, the method of the invention provides a formal process for choosing an appropriate model for describing a technical system.

The method of the invention can be used for models of any technical systems. In a particularly preferred embodiment, the technical system which is described by the models is a structure, preferably a building and/or bridge and/or dam, where the sensor measurements are determined by sensors installed at the structure. In a preferred variant of the invention, the sensor

measurements are determined by one or more pore pressure sensors and/or inclination sensors and/or displacement sensors installed in a technical system. Pore pressure sensors are particularly used in case that the structure is a dam.

The models processed by the method of the invention

preferably comprise one or more of the following models: an autoregressive process;

a moving average process;

an autoregressive moving average process,

an autoregressive integrated moving average process;

an integrated moving average process;

an autoregressive fractionally integrated moving average process ;

an exponential modes process;

at least one neural network, particularly a feed-forward neural network and/or a recurrent neural network.

All the above mentioned models are well-known for a skilled person and, thus, are not described in detail.

In another embodiment of the invention, the quality criteria comprise one or more of the following criteria:

an error criterion with the quality measure being an error between one or more sensor measurements predicted by the respective model and one or more real sensor measurements, the priority value increasing with a decreasing error, where the error is preferably the root mean squared error and/or the mean absolute error and/or the mean percentage error;

a coefficient of determination criterion with the quality measure being the coefficient of determination (also referred to as R2) for the respective model, the priority value increasing with a decreasing coefficient of

determination;

an AIC criterion with the quality measure being the Akaike information criterion for the respective model, the priority value increasing with a decreasing Akaike information criterion;

an anomaly detection criterion with the quality measure being the success rate or failure rate for correctly determining anomalies based on deviations between one or more sensor measurements predicted by the respective model and one or more real sensor measurements, the priority value increasing with an increasing success rate or decreasing failure rate;

a duration of validity criterion with the quality measure being the duration of validity of predictions of the respective model, the priority value increasing with an increasing duration of validity;

a computational complexity criterion with the quality measure being the computational complexity of the

respective model, the priority value increasing with the decreasing computational complexity.

In another embodiment of the invention, one or more quality criteria from said several quality criteria are quantitative criteria with quality measures which are calculated without using expert knowledge. With respect to the above examples of quality criteria, the error criterion, the coefficient of determination criterion, the AIC criterion, the anomaly detection criterion and the duration of validity criterion are usually quantitative criteria where predetermined formulas exist in order to calculate the quality measures.

Furthermore, one or more quality criteria from said several quality criteria may also be qualitative criteria with quality measures which are determined using expert knowledge. E.g., the above computational complexity criterion is usually a qualitative criterion.

In another embodiment of the invention, the quality measures for one or more predetermined criteria from said several criteria, and particularly from the above mentioned

qualitative criteria, are the priority values which are determined based on pairwise comparisons for the models using intensities of importance according to an Analytic Hierarchy Process. In this embodiment, the well-known pairwise

comparisons of an Analytic Hierarchy Process are once again used for determining priority values. The pairwise

comparisons are performed analogously to the comparisons as defined with respect to step a) of claim 1. However, the alternatives are now the models and not the quality criteria. In case that the predetermined criteria are qualitative criteria, the intensities of importance are based on expert knowledge. As described below, this expert knowledge may be specified by a user via a user interface, i.e. a user can determine the corresponding intensities of importance for the models. This may also be the case for the pairwise

comparisons defined in step a) . I.e., in this step a) of claim 1, also a user may specify the corresponding

intensities of importance for the quality criteria via a user interface .

In a particularly preferred embodiment, the method generates a user interface for enabling a user to at least partially define the models and/or the quality criteria and/or the intensities of importance of the Analytic Hierarchy Process for the quality criteria and/or the intensities of importance of the Analytic Hierarchy Process for the models. Hence, the selection of the appropriate model can be adjusted based on user preferences.

In another embodiment of the invention, the output generated in step d) includes the overall quality for the model with the highest sum and/or a ranking of the models with respect to their overall quality, where the ranking preferably includes the overall qualities for each model. According to this variant, more information despite the model with the highest quality is generated. The output generated in step d) can be stored in a

corresponding storage to be read out later. In a particularly preferred embodiment, the output is provided on a

corresponding user interface (e.g. a monitor) so that a user obtains the information which model is the best for the technical system.

In another preferred embodiment of the invention, the method determines for pairwise comparisons performed in step a) of claim 1 and/or performed for the above described predetermined criteria an inconsistency measure, the

inconsistency measure being preferably output in case that it exceeds a predetermined threshold. The determination of such an inconsistency measure is known from the prior art and e.g. described in section 6 of document [5] .

In another embodiment of the invention, the method calculates a sensitivity measure for the model which is output in step d) by varying the intensities of importance of the Analytic Hierarchy Process as defined in claim 1 and/or the intensity of importance of the Analytic Hierarchy Process used for the above defined predetermined criteria. The definition of such a sensitivity measure lies within the knowledge of a skilled person. Preferably, the sensitivity measure is presented to a user via a user interface.

Besides the above method, the invention also refers to a computer program product directly loadable into the internal memory of a digital computer, comprising software code portions for performing the method of the invention or one or more preferred embodiments of the method of the invention when the product is run on a computer. Moreover, the invention refers to a computer program for controlling a computer to perform the method of the invention or one or more preferred embodiments of the method of the invention . In the following, embodiments of the invention will be described in detail with respect to Fig. 1 showing a

schematic illustration of a variant of the method according to the invention. The invention as described in the following uses techniques from the so-called Analytic Hierarchy Process which is well- known from the prior art in order to support decisions. A description of this process can be found e.g. in document [5] . This Analytic Hierarchy Process is used in order to determine a computer- implemented model out of a plurality of models which is the best model for describing a technical system based on certain quality criteria.

As shown in Fig. 1, the Analytic Hierarchy Process defines a goal G in a first uppermost hierarchy HI, the goal being the choice of the best alternative in general. According to the invention, the corresponding alternatives are different models Ml, M2 , M3 , M4 which are arranged in the lowest hierarchy level H3 of the hierarchical structure of Fig. 1. Each model describes a technical system by a computer- implemented process which predicts sensor measurements of one or more parameters of the technical system. In a preferred embodiment, the technical system is a structure, particularly a bridge, building or dam, where the sensor measurements refer to signals of sensors installed at the structure. E.g., those sensors may be pore pressure sensors (e.g. installed in a dam) and/or inclination sensors and/or displacement sensors.

In the embodiment described herein, the models are used for anomaly detection in the technical system. To do so, sensor measurements predicted by the models based on previous measured parameters and compared with the actual real sensor measurements occurring in the corresponding structure. If there is a high deviation in the model output and the real sensor measurements, an anomaly will be detected by the model. Hence, the corresponding model will be used in an on- line monitoring of the technical system and provides an alarm in case that an anomaly is detected.

In the embodiment as shown in Fig. 1, four models Ml to M4 are compared. Model Ml refers to an autoregressive model, model M2 to an autoregressive moving average model, model M3 to a feed- forward neural network and model M4 to a recurrent neural network. All those models are well-known from the prior art. Evidently, a different number of models and other models may also be used in the method of the invention.

For determining the best model, six quality criteria CI, C2, C3, C4, C5 and C6 are defined in an intermediate hierarchy level H2 between hierarchy levels HI and H3. Criterion CI refers to the duration of validity, criterion C2 to the Akaike information criterion (see document [6] ) , criteria C3 to success/failure in finding anomalies during previous time, criterion C4 to the root mean squared error between predicted and real sensor measurements, criterion C5 to the coefficient of determination, and criterion C6 to the computational complexity. Each criterion expresses a quality which can be determined for each of the models Ml to M4. Particularly, the quality of a respective model is higher when the duration of validity is longer, the Akaike information criterion is smaller, the success rate in finding anomalies is higher or the failure rate is lower, the root mean squared error is lower, the coefficient of determination is lower and the computational complexity is lower. The criteria CI to C6 have already been explained before and, thus, will not be

described in detail once again. However, the invention is not restricted to those criteria and less or more criteria and different criteria reflecting the quality of respective models may be used.

Each of the criteria CI to C6 is associated with a

corresponding weight wl, w2, w6 expressing the

contribution of the respective quality criterion to an overall quality of the model taking into account all the criteria. In order to determine the weights wl to w6, a pairwise comparison of the criteria is performed based on an Analytic Hierarchy Process. This pairwise comparison is well- known from the prior art and e.g. described in section 4 of above mentioned document [5] . When performing this

comparison, intensities of importance on a predetermined scale, in the following between 1 and 9, are assigned to each pair of criteria expressing which criterion of the pair is regarded as more important. If a criterion is compared with itself, the intensity of importance "1" is assigned to this pair. In case that the first criterion of a pair is more important than the second criterion, a value higher than 1 is assigned to this pair. For the reciprocal pair where the first and second criteria are interchanged, the reciprocal value of the intensity of importance is assigned to this pair . Based on the above assignment, a matrix is built where the rows refer to the first criteria of the pairs and the columns to the second criteria of the pairs. Based on this matrix, the (principal) eigenvector of the matrix is determined. A component of the eigenvector represents a priority value with respect to the criterion of the row in the matrix

corresponding to the position of the component. In the embodiment described herein, the weights wl, w2, w6 refer to those eigenvector components/priority values determined by the pairwise comparisons according to the Analytic Hierarchy Process. In order to determine the corresponding intensities of importance, a user interface is generated in the

embodiment of Fig. 1 enabling a user and particularly an expert to define corresponding intensities of importance. This can be done in a qualitative manner, i.e. the user needs not specify the corresponding intensities of importance but only has to judge in a qualitative manner which criterion out of a pair he regards as more important, e.g. by defining a position in a bar visualized on a monitor of a corresponding user interface.

In a next step, each of the models Ml to M4 is evaluated with respect to each of the quality criteria CI to C6. To do so, corresponding quality measures of the criteria are determined for each model. For criterion CI, the quality measure is the duration of validity. For criterion C2, the quality measure is the Akaike information criterion represented by a

corresponding number. For criterion C3 , the quality measure is the success rate or failure rate of anomaly detection. For criterion C4 , the quality measure is the root mean squared error. For criterion C5, the quality measure is the

coefficient of determination. For criterion C6, the quality measure is the computational complexity. The criteria CI to C5 are quantitative criteria for which a corresponding quality measure can be calculated straight forward without using any expert knowledge. Contrary to that, the criterion C6 referring to the computational complexity is a qualitative criterion which needs expert knowledge to be determined.

For evaluating criterion C6, once again pairwise comparisons according to an Analytic Hierarchy Process are used to obtain the quality measure of the computational complexity for each method. In other words, pairwise comparisons of the models are made and corresponding intensities of importance are assigned to each compared pair of models. A higher intensity of importance shall reflect that the first model of the corresponding pair is more important (i.e. has a lower computational complexity) than the second model of the pair. Once again, the intensities of importance are determined by a user via a user interface provided by the method. As a result of the Analytical Hierarchy Process for the criterion C6, a priority value is determined which can be regarded as a quality measure of the criterion C6. As described before, the priority value corresponds to a component of the eigenvector of the matrix of the pairwise comparisons.

For determining the intensities of importance for the above Analytic Hierarchy Process as well as for the Analytic

Hierarchy Process determining the weights of the criteria, the following notions may be used: "equal importance", "more important", "much more important", "very much more

important", "absolutely more important", etc. Those terms may be presented to the user for a selection. The corresponding judgments of the user may then be transferred in numerical representations of the intensities of importance using the scale inherent to the Analytic Hierarchy Process. In the above described reference [5] , a scale between 1 and 9 is used. This scale is also referred to as the Saaty scale.

However, other known scales may also be used, e.g. the Bruck scale, the Logistic scale or the Lootsma scale.

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In a next step, the model with the highest value of the sum is output by the method, e.g. visualized on a monitor of a corresponding user interface. This model refers to the model 35 with the highest overall quality and, thus, gives the user the information which model he shall use. In a preferred embodiment, the other models with the respective values of the sums are also output via the user interface or a ranking of the models according to the values of the sums is shown on the user interface. Furthermore, it may also be possible to determine inconsistencies in the judgments of the users when defining the intensities of importance. The technique of determining such inconsistencies are well-known from the prior art and e.g. described in section 6 of document [5] . The consistency ratio explained in this section can be regarded as a corresponding measure of inconsistency. In case that the inconsistency (i.e. the consistency ratio) is high, e.g. if the inconsistency exceeds a threshold of 10%, the user may be requested to once again define intensities of importance for the pairwise comparisons. In another variant of the invention, also the stability of the decisions based on the intensities of importance input by the user may be determined, e.g. by slightly varying the intensities of importance chosen by the user and evaluating if a high change in the final result occurs. In case that a high change occurs, this can be regarded as an instable decision and a corresponding information may be given to the user by the user interface. Moreover, a corresponding measure of the stability can be shown on the user interface by all means, i.e. irrespective if the decisions are regarded as stable or unstable. In document [5], a sensitivity analysis for evaluating the stability of decisions is described (see section 9.8).

The invention as described in the foregoing is based on both qualitative criteria and quantitative criteria. However, the invention may also be implemented by only using either quantitative criteria or qualitative criteria. Furthermore, the corresponding intensities of importance need not be determined on-line by a user via a user interface.

Particularly, those intensities of importance may be

determined beforehand and stored in a storage which is accessed by the method in order to determine the weights for all criteria and the priorities for the methods with respect to the qualitative criteria.

The invention as described in the foregoing has a number of advantages. Particularly, the invention combines the Analytic Hierarchy Process with models of a technical system in order to select the best model for describing the technical system. In a particularly preferred embodiment, the models describe structures and are used for structural health monitoring where anomalies can be detected based on deviations between predicted sensor measurements and real sensor measurements .

By using the Analytic Hierarchy Process, the problem of determining the best model is decomposed in subtasks of several quality criteria, where each quality criterion is analyzed separately. The method of the invention enables to work with qualitative expert knowledge based on the

evaluation of the priorities of the criteria. Moreover, the method processes quantitative information obtained from numerical experiments with the models. In preferred

embodiments, the invention also estimates inconsistencies in the judgments of a user and provides information with respect to the stability of the decisions made by the user. The method of the invention solves a decision-making problem of choosing the best model for a technical system that fits several predefined criteria. The decision-making process is adaptive depending on the preference of criteria and results of data experiments.

List of References :

[1] Muhammad Aqil et al . : "Decision Support System for Flood Crisis Management using Artificial Neural Network", World Academy of Science, Engineering and Technology 15, 2006.

[2] F. Laio et al.: "A comparison of non-linear flood

forecasting methods", water resources research, Vol. 39, No. 5, 2003, 4 p.

[3] Nianwu Deng et al.: "Introduction and analysis of

commonly used non-parametric models of dam deformation in China", Proc . of the 13th FIG Symposium on deformation measurement and analysis, 2008, 9 p.

[4] Armineh Garabedian et al . : "Monitoring dam behaviour

using innovative approaches based on linear and nonlinear techniques", 2006, 7 p. [5] Thomas L. Saaty: "Relative Measurement and its

Generalization in Decision Making. Why Pairwise

Comparisons are Central in Mathematics for the

Measurement of Intangible Factors, the Analytic

Hierarch/Network Process", Statistics and Operations Research, Vol. 102 (2), 2008, pp. 251-318.

[6] H. Akaike, 1974: "A new look at the statistical model identification", IEEE Transactions on Automatic Control, T. 19: 716-723.

Claims

Patent Claims

1. A method for computer-aided processing of models (Ml, M2, M3, M4) of a technical system, each model (Ml, M2 , M3 , M4) being based on a computer- implemented process for predicting sensor measurements of one or more parameters of the

technical system, the method comprising the steps of:

a) providing several quality criteria (CI, C2 , C6) for the models (Ml, M2 , M3 , M4) of the technical system and a weight (wl, w2 , w6) for each quality criterion (CI, C2,

C6) , each weight (wl, w2 , w6) representing a contribution of the respective quality criterion (CI, C2,

C6) to an overall quality of the models (Ml, M2 , M3 , M4 ) , where the weights (wl, w2, w6) are determined based on pairwise comparisons of the quality criteria (CI,

C2 , C6) using intensities of importance according to an Analytic Hierarchy Process;

b) determining for each model (Ml, M2, M3 , M4 ) and for each quality criterion (CI, C2, C6) a quality measure of the respective model (Ml, M2 , M3 , M4) with respect to the corresponding criterion (CI, C2, C6), where a priority value (pll, pl2, p46) is assigned to the respective model (Ml, M2 , M3 , M4) based on the quality measure for each quality criterion (CI, C2, C6), the priority value (pll, pl2, p46) increasing with a higher quality according to the quality measure;

c) determining a sum (si, s2, s3, s4) over all quality

criteria (CI, C2, C6) for each model (Ml, M2, M3 , M4 ) , where the summand for a respective quality criterion (CI, C2 , C6) is the product of the weight (wl, w2, w6) for the respective quality criterion (CI, C2, C6) and the priority value (pll, pl2, p46) for the respective model (Ml, M2 , M3 , M4) and quality criterion (CI, C2, C6), the sum (si, s2, s3, s4) representing the overall quality of the respective model (Ml, M2, M3 , M4) such that a higher sum (si, s2, s3, s4) corresponds to a higher overall quality; d) generating an output including the model (Ml, M2 , M3 , M4) with the highest overall quality.

2. The method according to claim 1, wherein the technical system is a structure, preferably a building and/or bridge and/or dam, where the sensor measurements are determined by sensors installed at the structure.

3. The method according to claim 1 or 2, wherein the sensor measurements are determined by one or more pore pressure sensors and/or inclination sensors and/or displacement sensors installed at the technical system.

4. The method according to one of the preceding claims, wherein the models (Ml, M2 , M3 , M4) comprise one or more of the following models:

an autoregressive process;

a moving average process;

an autoregressive moving average process;

an autoregressive integrated moving average process;

an integrated moving average process;

an autoregressive fractionally integrated moving average process ;

an exponential modes process;

5. The method according to one of the preceding claims, wherein the quality criteria (CI, C2, C6) comprise one or more of the following criteria:

an error criterion with the quality measure being an error between one or more sensor measurements predicted by the respective model (Ml, M2 , M3 , M4) and one or more real sensor measurements, the priority value (pll, pl2, p46) increasing with a decreasing error, where the error is preferably the root mean squared error and/or the mean absolute error and/or the mean percentage error; a coefficient of determination criterion with the quality measure being the coefficient of determination for the respective model (Ml, M2, M3 , M4 ) , the priority value (pll, pl2, p46) increasing with a decreasing coefficient of determination;

an AIC criterion with the quality measure being the Akaike Information Criterion for the respective model (Ml, M2, M3, M4) , the priority value (pll, pl2, p46) increasing with a decreasing Akaike Information

Criterion ;

an anomaly detection criterion with the quality measure being the success rate or failure rate for correctly determining anomalies based on deviations between one or more sensor measurements predicted by the respective model (Ml, M2 , M3 , M4) and one or more real sensor measurements, the priority value (pll, pl2, p46) increasing with an increasing success rate or decreasing failure rate;

a duration of validity criterion with the quality measure being the duration of validity of predictions of the respective model (Ml, M2, M3 , M4), the priority value increasing with an increasing duration of

validity;

a computational complexity criterion with the quality measure being the computational complexity of the respective model (Ml, M2 , M3 , M4), the priority value (pll, pl2, p46) increasing with a decreasing

computational complexity.

6. The method according to one of the preceding claims, wherein one or more quality criteria from said several quality criteria (CI, C2, C6) are quantitative criteria with quality measures which are calculated without using expert knowledge .

7 . The method according to one of the preceding claims, wherein one or more quality criteria from said several quality criteria (CI, C2, C6) are qualitative criteria with quality measures which are determined using expert knowledge .

8. The method according to one of the preceding claims, wherein the quality measures for one or more predetermined criteria from said several criteria (CI, C2, C6) are the priority values (pll, pl2, p46) which are determined based on pairwise comparisons of the models (Ml, M2, M3 , M4 ) using intensities of importance according to an Analytic Hierarchy Process.

9. The method according to claim 6 and 7, wherein said one or more predetermined criteria (CI, C2 , C6) are qualitative criteria, where the intensities of importance are based on expert knowledge.

10. The method according to one of the preceding claims, wherein the method generates a user interface for enabling a user to at least partially define the models (Ml, M2, M3 , M4) and/or the quality criteria (CI, C2 , C6) and/or the intensities of importance of the Analytic Hierarchy Process of claim 1 and/or the intensities of importance of the

Analytic Hierarchy Process of clam 8.

11. The method according to one of the preceding claims, wherein the output generated in step d) includes the overall quality for the model with the highest sum (si, s2, s3, s4) and/or a ranking of the models (Ml, M2 , M3 , M4) with respect to their overall quality, where the ranking preferably includes the overall qualities for each model.

12. The method according to one of the preceding claims, wherein the method determines for pairwise comparisons performed in step a) of claim 1 and/or performed according to claim 8 an inconsistency measure, the inconsistency measure being preferably output in case that it exceeds a

predetermined threshold.

13. The method according to one of the preceding claims, wherein the method calculates a sensitivity measure for the model (Ml, M2 , M3 , M4) which is output in step d) by varying the intensities of importance of the Analytic Hierarchy Process of claim 1 and/or the intensities of importance of the Analytic Hierarchy Process of clam 8.

14. A computer program product directly loadable into the internal memory of a digital computer, comprising software code portions for performing the method according to one of claims 1 to 13 when said product is run on a computer.

15. A computer program for controlling a computer to perform a method according to one of claims 1 to 13.