WO2014122208A1

WO2014122208A1 - Method for verifying or identifying a model structure

Info

Publication number: WO2014122208A1
Application number: PCT/EP2014/052314
Authority: WO
Inventors: Riccardo MÖLLER; Björn HAFFKE
Original assignee: Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V.
Priority date: 2013-02-08
Filing date: 2014-02-06
Publication date: 2014-08-14
Also published as: DE102013202155A1; EP2954296A1

Abstract

The invention relates to a computer-aided method for verifying or identifying a model structure of a system to be tested (1), involving the steps of: creating a system of equations (26), which has at least one parameter, for describing the system (1) to be tested or a part thereof, wherein a description model underlies the system of equations (26) as an assumed model of the system (1) and/or a description model structure underlies the system of equations as an assumed model structure of the system (1); restructuring the system of equations (26) into a test model (10), which has no or reduced parameters, which qualitatively describes the system and which describes at least one model output signal on the basis of one or a plurality of model input signals; stimulating the test model (10) with at least one model input signal; capturing at least one model output signal of the test model (10); comparing (32) the at least one model output signal of the test model with at least one corresponding system signal; and/or calculating a quality function on the basis of the at least one model signal and of a system signal; selecting the description model or the selected description model structure as an identified model or as an identified structure of the system (1) if a pre-defined criterion was satisfied during the comparison or by the quality function; or creating a modified system of equations (26), which a modified description model and/or a modified description mode structure underlie; and repeating the method steps if the pre-defined criterion was not satisfied during the comparison (32) or by the quality function; and/or assigning the result of the comparison (32) to the description model as an evaluation of the description model.

Description

Method for checking or identifying a model structure

The present invention relates to a method for checking or identifying a model structure of a system to be examined. Furthermore, the present invention relates to a computer program product for carrying out a method for checking or identifying a model structure. Mathematical models of dynamic systems are used in different areas, for example for simulating real systems or, in particular, for model-based control and monitoring systems. These mathematical models consist of two basic components. The first component represents the structure of the mathematical model, in the form of a mostly symbolic description. The second component is in the form of numerical parameters, which are mostly physically motivated and decisively influence the dynamic behavior. Examples of these parameters are i.a. Masses, spring stiffnesses, electrical resistances, etc. A big challenge in the development and creation of mathematical models lies in the comparison of these models with numerical data in order to check and improve the correspondence with real systems or other mathematical models.

If deviations occur during the checking of the agreement, the assignment of the deviations to a faulty analytical description of the structure on the one hand or to a faulty parameter set on the other hand is often not clearly possible.

Previous strategies used to limit the causes of deviations, in particular numerical deviations, are based primarily on logical plausibility checks, also using prior knowledge and experience, or on suitable transformations of the signals in order to emphasize certain, in particular dynamic properties of the systems more clearly. For example, logical reasoning uses limits that are defined for physical parameters, or special signals that are used for verification and that do not affect some dynamic effects, thereby limiting deviations. Suitable transformations for the confinement of errors are, for example, Fourier transformations with which frequency-dependent effects can be investigated. NEN. Other approaches, for example, from statistics, are also known, but also offer no comprehensive and practical solution. In addition, complex model simplifications are often carried out to limit errors.

In addition, methods are known for identifying parameters, for example by numerical optimization methods, which adapt the parameters in order to minimize a previously defined error criterion, and thus the deviations. However, an identification presupposes that the structure of the mathematical model can in principle represent the measurement data. If this is not possible with the mathematical model, the error after the identification can indeed be smaller, but not completely disappear, whereby deviations inevitably remain. The optimization is typically done for selected input-output measurements. With the model used, the optimized parameter set provides an optimal result even for deviations in the model structure. However, a general validity of this model, consisting of structure and parameter set, is thus not necessarily guaranteed.

A classical control technique for identifying in particular a linear physical system distinguishes between the identification of the system order and the system parameters. Here, an order identification is first made to detect the order of the system. If the system order is known, a generally valid linear system description can be used, of which only the parameters have to be identified.

In reality, there are virtually no linear systems. Nevertheless, such a linear system approach is often used because the linear system theory is well developed and thus, at least in working areas, approximations are possible. The recorded system order is then regularly the one in which the next largest system order does not lead to a significant improvement of the system description. In other words, the underlying system order is increased until it is no longer possible to improve significantly by the system order. The remaining deviations of this linear system with the selected or identified order are then taken into account as much as possible by a corresponding parameter selection, or parameters are identified by means of parameter identification for the assumed linear model such that this model behavior, namely in particular input-output behavior this model, the input-output behavior of the system to be identified as well as possible. This makes it clear that in the case of a faulty structure identification is attempted to compensate for these by the parameters. Such a model usually works satisfactorily, even if the excitation of the system essentially corresponds to the suggestion that was used in the identification. However, if the stimulus is changed significantly, for example because the system is operating in a different workspace than before, the error can be severe. It may also be a serious error, if the parameter identification is repeated for this new work area, but the underlying simplified linear system order for the changed work area no longer has sufficient validity. The problem is therefore that the actual model structure could not be identified and that there is insufficient differentiation between structural influences and parameter influences. In particular, it is problematic that the system to be examined naturally has parameters which also influence the order identification accordingly. If a nonlinear model is used instead of a linear one and the parameters of the system are identified or optimized, there is the additional problem that, in the current state of the art, globally optimal parameterization is difficult to find. The previously known methods search, for example, in a local environment for starting values for possible parameters. Global optimization methods usually require impractically high computation times to test several solutions and thus to iteratively improve the parameters. It can not be clearly demonstrated with existing methods, in these frequently occurring cases, whether parameter influences or structural influences are the cause of deviations. It is also not possible to clearly quantify which model structure and thus which model approach has the highest imaging quality in principle without trying out several models, whereby the previously described problems of non-optimal parameterizability inevitably arise.

The present invention is therefore based on the object to address at least one of the above problems. In particular, a solution should be proposed that can more systematically identify or recognize a structure. In particular, a corruption of the structure identification should be minimized by the influence of concrete parameters. At least an alternative solution should be proposed.

According to the invention, a method according to claim 1 for testing or identifying a model structure of a system to be examined is proposed. Such a system, namely a physical system, can be, for example, a machine, an actuator, tor, a vehicle or even a reactor in which a chemical process takes place. In principle, the description of a dynamic process, such as a growth process, is also considered as a system. In particular, subsystems such as a brake system or a spring damping system of a vehicle can form the system to be examined. The method thus also includes a method for checking or identifying a model structure of a machine, an actuator, a vehicle or even a chemical reactor.

Such a system is based on a structure which, in particular assuming simplifications, forms a model structure. This model structure should be found, ie identified and / or tested. If, therefore, a model structure is used, which emerged, for example, from a system engineering point of view, this model structure can be checked with the proposed method to determine whether it adequately describes the system. The model structure can either be a mathematical model or, linked to it, a description model, or the mathematical model is another description of the description model.

The method comprises the following steps. In the first step, a parameter system having a parameter is set up to describe the system to be examined or a part thereof. This system of equations may be based on a description model as a model of the system which has been initially assumed and / or the system of equations may be based on a description model structure as an assumed model structure of the system. In principle, a description model is assumed which is assigned to the system and is therefore based on this system of equations. However, the method can also be used if this description model is, for example, incomplete or inaccurate with regard to a parameter, as long as the underlying initial description model structure is based on it.

This equation system is then transformed into a parameterless or at least parameter-reduced test model describing the system. The test model describes at least one model output signal as a function of one or more model input signals. The fact that this test model describes the system is to be understood in a mathematical sense, namely that the test model can reproduce the dynamics and behavior of the system. In addition, this test model describes at least one model output signal as a function of one or more model input signals, the at least one model input signal and / or the at least one model output signal not each at least one input signal of the system or a Output signal of the system must correspond. By transforming the equation system into this parameterless or parameter-reduced form, the relationships between system quantities or system signals on the one hand and model sizes or model signals on the other hand can also be different. However, there must be connections and these relationships are recorded and used in this system of equations.

In a next step, the test model thus created is then excited with at least one model input signal. Such an excitation can take place, in particular, in a simulator in which the test model is stored as a simulation model and, if appropriate, the equation system can also be used directly in a computer and subjected to corresponding signals, ie the at least one model input signal.

As one embodiment, the test model may also be excited with both at least one model input and model output of a description model or a mathematical model.

Accordingly, at least one model output signal of the test model is recorded, namely as a result of the described excitation of the test model.

In a next step, the at least one model output signal is compared with at least one corresponding system signal. For example, to illustrate a simplified, plastic example, a system output signal may form the model input signal and the model output signal may correspond to the system input signal, checking how far the model output matches the system input signal. Conveniently, this example could be such that the system is excited with its system input signal and results in a system output signal. The system output signal is then input to the test model and the model output signal is detected and, as stated, compared to the system input signal. How model signals are related to the system signals is essentially also determined by the transformation of the system of equations into a parameterless or at least parameter-reduced system, and the mode of deformation will be described in more detail below.

The evaluation of the comparison is based on a quality criterion. Depending on this criterion, the next step is then carried out. The quality The criterion may, for example, be the amount of a deviation, or it may be, for example, a summary, possibly weighted, of several deviations.

In particular, stimulating the test model is on a computer, analog computer or similar. Device performed. The model output signal is also preferably recorded with a computer, in particular with the same computer, which also performs the stimulation of the test model. Likewise, the comparison of the at least one model output signal and / or the calculation of the quality function is carried out on a computer or similar device comprising a microprocessor or similar computing unit. If the detection of at least one system output signal takes place as a reaction of the system to at least one system input signal stimulating the system with the aid of a simulation model, these variables or signals or a part of these signals, that is to say created by means of a simulation, then also preferably takes place by means of a computer o. ä. Computing device. It is also advantageous that corresponding input variables, output variables and intermediate variables in a computing unit, such as the aforementioned computer or the like. Overall device available and can be exchanged between individual process steps. The implementation of the method is correspondingly efficiently feasible.

According to one embodiment, a quality function is calculated as a function of at least one model signal and one system signal. For this purpose, for example, a model output signal and a system output signal can be used as the basis and a quality function can be calculated from the relationship of these signals to one another. This relationship may be a direct comparison, but other relationships may also be considered. For example. may be formed a product of the two or more signals, or another link. As a further example, a comparison of derivatives and / or integrations of the signals or of a number of signals may be mentioned, weightings also being able to be used. For example. For example, the time derivative of a system signal can be compared with a model signal. A comparison can in principle also be made by subtraction. A difference between two signals can then be evaluated absolutely, e.g. after the largest difference, or a sum of squares over several values can be formed and evaluated, just to name a few examples.

Another possibility according to this invention is to input all test model input and test model output signals into the test model and then to analyze the agreement of the signals with the test model. For example, investigations of the solubility of the equation systems which, for example, are advantageous. can also be represented in matrix form. In this case, the model output signal of the test model could directly output a quality criterion.

If the criterion is fulfilled, e.g. If a difference remains below a predetermined limit, then the description model or the description model structure is accepted as an identified model or identified structure. If the predetermined criterion is not met, a modified system of equations is set up on which a modified description model or a modified description model structure is based. Instead of the description model, the mathematical model can also be used directly. The predetermined criterion may be, for example, an absolute value that may not exceed the magnitude of the difference between the model output signal and the system signal. The quality criterion may also be used for other signals, e.g. Deviations from internal state variables, be designed and applied to it. Thus, if this value remains below this threshold value in absolute value, the initially written description model or the initially set description model structure is used as the identified model. If this amount exceeds the limit, the steps are repeated with the system of equations changed.

According to another embodiment, the criterion may be a percentage value by which the model signal may deviate from the system signal in the comparison. Likewise, as a quality criterion or predetermined criterion, it is possible to form the sum of the squares of all deviations and to set a limit value for them.

In this case, in particular, the transformation of the system of equations into a parameterless test model is as important as possible, and this transformation of the system of equations can accordingly also lead to a transformed system of equations or at least one reshaped equation. Such a parameter-reduced system no longer contains the parameters and thus can no longer completely reproduce the system in its quantity, ie its parameter-determined properties, but it can qualitatively describe the behavior of the system. As a result, however, the parameters need not be completely known or, in the optimal case, not at all known. This solution, namely to test or identify a model structure with the aid of a transformation of a descriptive system of equations into a particularly parameterless system, skilfully uses methods for the elimination of variables, for example described by Ritt, JF "Differential Algebra", Amer. Math. Soc, 1950. Using such algorithms, parameters in non-linear, polynomial differential equations are eliminated giving rise to higher order derivatives.

A simple example of the basic procedure, without directly applying the methods of, for example, riding, is a mass m, which is accelerated by a force F (t) and whose distance x (t) represents a measured variable of the system. This describes the following equation. ^■ m x (t) - F (t) = 0 (Equation 1)

By derivation results:

^• x (f) - F (f)) .. · ,,, _ά ,. .

- ± ^ = m ^■ x (t) - F (t) (Equation 2)

Substituting Equation 1 into Equation 2 so that the parameter m disappears:

F (f) = ^{F (f) 'X (f)} (Equation 3)

x (f)

The resulting differential equations can then be applied to some input and output variables of the system and their derivatives, wherein one or some of the remaining input and output variables and their departments are compared with the output system, as explained in more detail below in connection with FIG.

If the structure of the system, represented by the parameter-free differential equations, can satisfy the comparison system in principle, the deviation will be exactly zero in the ideal case. In reality, however, slight deviations due to measurement noise, a limited resolution of the sensors, necessary filtering of the system and modeling assumptions are to be expected. These deviations must be appropriately assessed and quantified to verify compliance.

The proposal according to the invention thus achieves, in particular, that a review of the structure of models, in particular of mathematical models describing physical systems, is independent of numerical or physical Parameters, although these parameters are present in the underlying physical system.

Similar to the review of modeling approaches and the model reduction, the solution presented here can be used to find out the inner structure of dynamic systems independently of numerical parameters. This makes it possible, for example iteratively, to close the internal structure of a system.

Preferably, at least one system output signal x (t) is detected as a response of the system to at least one system input signal F (t) exciting the system. The at least one model input signal of the description model or of the mathematical model is then determined from the at least one system input signal F (t) with which the system was excited and / or from the at least one detected system output signal x (t). In that regard, this system input signal F (t) is one that actually excites the system. The at least one detected system output signal x (t) is one resulting from this excitation. This can also include internal resulting state variables, insofar as they can be detected.

Each system input signal F (t) and each system output signal x (t) each form a system signal. A system signal is thus the generic term for all signals of the system. For carrying out the method, the system output signal x (t) and also the system input signal F (t) can also be taken into account by a simulation. For example, a complex simulation model with known tools can be set up, which describes the system with very good accuracy, but can not be used for some applications, in particular a later regulatory consideration. This may be due, for example, to the fact that the simulation tool, in particular a special software, can not be integrated into other systems. It may also be because the simulation of this complex, precise model is too slow and can not be done in real time. The simulation model can also be used poorly if, for example, analytical descriptions of the dynamics are needed for a later controller design.

In any case, such a simulation model can be used for checking or identifying the model structure of the description model or of the mathematical model. Instead of exciting the system with the system input signal F (t), the simulation model can be excited with it and the simulation model can then output the at least one system output signal x (t). Based on these signals, the at least one model input signal can then be determined. It needs The system input signal F (t) may not necessarily be transmitted from the system input or the simulation model input to the test model input but, if present as a clearly defined signal, may also be redetermined there to determine the model input signal. According to one embodiment, it is thus proposed that when comparing the at least one model output signal of the test model with at least one corresponding system signal, the system signal is a measured, a predetermined and / or an expected signal. In particular, if here the system signal is the system input signal, or can be easily derived analytically from the signal input signal, the measured system signal need not be used here. Insofar as a measured signal is used or alternatively a result of a complex simulation model, this can be used directly or the system signal to be compared can still be subjected to a further calculation step in order to obtain from it, for example, another expected signal. For example, if the speed of a wheel is measured in a vehicle, the position of a point of the wheel can be uniquely determined by integration of this speed, as far as the initial values are known or zero, and vice versa, for example, when detecting the position, the speed can be determined uniquely. This integrative or differential relationship is clear and thus independent of further details, in particular further parameters of the system under investigation.

These examples and proposed embodiments are intended to explain in particular that it is crucial to reshape the system of equations set up initially in such a way that it becomes as parameterless as possible. This results in descriptive model signals that can correspond to system signals in very different ways. The comparisons are then carried out in accordance with this respective relationship. In particular, differentiations are usually carried out during the transformation into the parameterless form. Accordingly, even when comparing the behavior of the test model with the system under test, system signals can be derived in order to compare corresponding derivatives of the system signals with corresponding signals of the test model.

In particular, a model output signal of the test model is thus a measure of the structural conformity of the test model and thus of the description model with the system. Accordingly, according to one embodiment, it is proposed that the model input signals comprise at least one system signal derived at least once in a time.

According to an advantageous embodiment, it is proposed that at least one non-linear model description is integrated or incorporated when setting up the equation system, and / or that when setting up the changed equation system at least one non-linear model description is exchanged for another, in particular integrating, incorporating or exchanging a non-linear model description is taken from a model collection comprising several non-linear model descriptions.

For example, a non-linear model description is a clipping or saturation function. This exemplary saturation function is frequently encountered in technical processes and can be described by an input / output characteristic which, in the normalized case, has a straight line with the slope 1 in the range from -1 to +1 on the abscissa, ie the points (-1 ; -1) and (1; 1) connects. For input values less than -1 it has a constant value of -1 and for input values greater than 1 it has a constant output value of 1. Such a function is non-linear because its input / output behavior depends on the amplitude of the input signal. Such a nonlinear model description, namely a non-linear partial model description, is therefore integrated in setting up the system of equations in the underlying system to be examined, for example instead of a linear transmission element which satisfies the equation f (x) = x.

Preferably, when setting up the changed system of equations, at least one non-linear model description is exchanged for another one. For the example mentioned, the normalized saturation function, in which the person skilled in the art assumes the term saturation function anyway from a normalization to 1, could be exchanged for a tangent hyperbolic function (tanh). Basically, such a hyperbolic tangent function, like the saturation function, has a limit of -1 and +1, respectively, and has a slope of 1 in the origin, where the slope can be adjusted with appropriate parameters and extensions of the function. However, the transitions are without kinks and thus continuously differentiable. In addition, the hyperbolic tangent function is strictly monotonically increasing. By different substitutions and transformations, the hyperbolic tangent function can be transformed into a polynomial form and can be examined by the proposed method. In addition, so in an optionally desired even further exchange step, ie When setting up a system of equations that has been changed again, a saturation function with hysteresis can be used, as is known from the hysteresis curve for a magnet, namely the course of the magnetic induction or magnetic flux density B as a function of the magnetic field strength H. Incidentally, different functions can also be used here Hysteresefunktionen come as a non-linear model description or non-linear partial model description into consideration.

All of these non-linear functions exemplified may describe the underlying system more or less well, and the proposed method provides a way to test or qualify their suitability in the overall system description. Preferably, it is thus proposed to use the result of the comparison of the at least one model output signal with the at least one corresponding system signal to qualify the suitability of the corresponding description model or the non-linear model description used therein. The above-described evaluations of this comparison result for checking with a predetermined criterion can be used analogously for the evaluation. Alternatively, according to the second embodiment, a criterion for the suitability of a model description can be generated directly.

In order to perform the check with different non-linear model descriptions, a model collection comprising several non-linear model descriptions is used. Nonlinear model descriptions including their mathematical description may be included here. Thus, it is easier to use such non-linear model descriptions and in particular to exchange. Preferably, such a model collection, which can also be referred to as a model pool, is constructed successively by including each new non-linear model description in this model collection or model pool. In this case, a classification of the collected nonlinear model descriptions in the model collection or the model pool is preferably carried out. For this purpose, for example, categories or classifications can be assigned to these non-linear model descriptions. For example, the above three examples of the saturation function, hyperbolic tangent function and hysteresis function can be included in the model description and possibly all labeled under the classification saturation.

If, for example, a system knows that a limiting behavior is present, this can be done by successively trying out the stored functions of the category Saturation can be modeled and it can be selected at the end of the most suitable non-linear model description.

According to one embodiment, it is proposed that the system is subdivided as an overall system into several subsystems, each subsystem is identified individually as a physical system, and then an identified overall system is assembled from the subsystems thus identified.

Often, at least in a simplistic perspective, systems can be broken down into multiple subsystems. Such a decomposition can be different in complexity. It is advantageous here, which can also justify a costly decomposition, that the transformation of the equation system into a parameterless or parameter-reduced system is simplified in each case. In some circumstances, this makes it possible to achieve this transformation of the equation system into a parameter-free or parameter-reduced system with appropriate effort.

An example of such a division, for example, be a technical system with actuator. Then, the actuator may be one subsystem and the system on which the actuator acts may be another subsystem. For example, a vehicle with brake can be subdivided into the actuator which activates the brake, for example the brake shoes, including the resulting movement of the brake shoes, and wherein the vehicle can be a further subsystem, in particular with regard to the resulting braking effect. These two subsystems can also be considered separately. For this purpose, on the one hand, it is possible to prepare both subsystems in terms of simulation technology in such a way that the system signals can be generated from this in order to carry out the proposed method. However, it is also possible to use the actual system for examination by recording a corresponding number of system signals, in particular at corresponding points, system signals. In the example, a braking operation can be examined by the input signal of the brake, so basically taken the brake command as the input of the first subsystem and the movement of the brake shoes as the output of this subsystem and used accordingly. The movement of the brake shoes can then simultaneously form the input signal for the second subsystem and the resulting braking effect, so in particular the resulting deceleration of the vehicle can be used as an output signal of the second subsystem, to name only a simplified, plastic example. Once both subsystems have been identified, they can then be recalculated and put together to the required system identification.

Preferably, the subdivision of the overall system is such that at least one input signal is selected so that it only partially excites the entire system, and / or at least one output signal is selected such that it is only affected by the excited subsystem and / or that part of a System behavior is computationally eliminated.

Thus, it is proposed to stimulate only one subsystem or to consider only inputs or outputs of a subsystem. Such partial stimulation may also regularly mean that the system is specifically stimulated for experimental purposes. Such an excitation may be one which would not or would not be made in the proper operation of the system. A partial excitation, ie the excitation of only a part of the overall system, can in particular also take place in the case of a multi-variable system, that is to say in the case of a system which has several input variables and / or several output variables.

The excitation of a subsystem could for example be made in the above-mentioned example of the braked vehicle so that the brake shoes are controlled separately by an external device, namely so that their movement can be specified more specific. Here, only the second subsystem would need to be considered.

For a separate excitation of the first subsystem of this example, so only the brake, comes into consideration to test them at a standstill. A braking effect then does not occur and the second subsystem of this exemplary system remains inactive.

A calculation of a part can be done for the said example system so that the second subsystem is further subdivided or reduced in its system behavior, for example by a braking distance is measured as the output, if the vehicle for this was of course not measured at a standstill, from the mathematically unique can be calculated back to the resulting speed and also clearly to the resulting acceleration. Accordingly, this second subsystem could be reduced by two system orders, which would greatly simplify the transformation into a parameterless or parameter-reduced system. According to one embodiment, it is proposed that a polynomial description is used as a non-linear model description and / or that a nonlinear model description is converted into a polynomial description. Thus, it is proposed to use a polynomial description, ie in particular to describe a nonlinear function by a polynomial or a quotient of two polynomials. If there is another one for the desired nonlinear model description, it may be proposed to convert this into a polynomial description. By such a polynomial description, a nonlinear behavior, namely in particular a nonlinear function, can at least theoretically be approximated mathematically arbitrarily exactly if the order of the polynomial description is high enough. But even for comparatively small orders, a fairly good polynomial description can often be given, which can certainly be sufficient in a relevant area. The polynomial description is then particularly advantageous for the transformation of the equation system into a parameter-free or parameter-reduced test model. When using polynomial differential equations, it is also possible, for example, to describe very strongly nonlinear functions, such as the presented tanh function, without drastically increasing the order,

Preferably, at least one system output x (t) is detected in response to the system responding to at least one system input signal F (t) by exciting the system with the system input signal and measuring at least one system output signal and / or using a simulation model describing the system the system input signal is excited and the at least one system output signal is received as an output signal of the simulation model. Accordingly, it is proposed that system input signal and system output signal be obtained either by operating and measuring the system, or by using a corresponding simulation model.

As a system input signal for exciting the system, an at least once continuously differentiable signal is preferably used and / or a filtered non-continuously differentiable signal, for example a noise signal, is used. This selection of the system signal to excite the system takes into account that when forming the equation system into a parameterless or parameter-reduced system often one or more derivatives occur and also derived system signals are used to stimulate the test model as model input signals. In that regard, it is advantageous to already tune the excitation signal to such requirements. A preferred embodiment proposes that, when setting up the system of equations, a subsystem, in particular a known subsystem of the system, is taken into account as a substitution submodel by a submodel deviating from the subsystem. Therefore, a deviating submodel for a subsystem is deliberately used in order to be able to draw conclusions as to whether a system change can make sense. For example, a passive component in a system when setting up the equation system can be considered as an active component or vice versa. In this way it can be determined whether and how great the influence of this change of the passive component into an active component or vice versa influences the overall system dynamics. Again, the idea is based on the fact that the proposed method as far as possible parameter-independent testing can be made. The proposal of the transformation into the parameterless test model thus eliminates parameter-related influences. The result of the examination thus does not depend or at least less on parameters. If, for example, the examination using a substitution model is negative, ie if too large differences occur in the examination, especially in the comparison, this would not be due to parameter inaccuracies, but it can generally be concluded that the structure under investigation is not correct or not suitable is.

The design of passive components, such as elastomer components or shock absorbers in motor vehicles, usually represents a compromise, since not all desired properties can be achieved in all operating conditions.

Thanks to highly integrated actuators and advances in control technology, passive components can increasingly be replaced by active components whose characteristics can be dynamically adapted during operation. With the help of the methodology presented here, it is already possible in the development process to clearly predict whether an active component can in principle possess the same properties of a passive component. In addition, it is possible to check whether a desired and / or any idealized behavior can be achieved by a passive or active component. In contrast to known analytical approaches, the methodology presented here is capable of taking into account nonlinearities such as manipulated variable constraints. Numerical limit values can be integrated into the overall system without parameters and can thus be taken into account. It is favorable in this case if, when setting up the changed equation system, the substitution submodel is replaced by a modified substitution submodel. This makes it possible to search specifically for a suitable substitution model.

According to one embodiment, the method is characterized in that, in addition to the system of equations of the mathematical model, a different reference equation system is set up, wherein the reference equation system differs from the equation system in that it has a different substitution submodel for a submodel of the equation system, wherein the equation system and the reference equation system are respectively transformed into a parameter-free or parameter-reduced test system or reference test model describing at least one model output signal as a function of one or more model input signals, and wherein the at least one model output signal is compared with at least one corresponding system signal, that the test model and the

Referenzprüfmodell be excited with at least one same signal and at least in each case a model output signal corresponding outputs of the test model and the Referenzprüfmodells be compared with each other. Alternatively, in one embodiment, the system input and system output signals or model input and model output signals of the description model or the mathematical model may represent the model input signals of the test model and the model output signal may provide a quality criterion.

Thus, this proposal deliberately compares two systems of equations that are almost identical, which differ in that one has a substitution sub-model instead of a corresponding sub-model. It is then possible to observe and assess the influence of the substitution submodel as a substitute for the actual submodel by directly comparing both equation systems.

Preferably, the method is performed by a computer program product when executed on a computer system or the like. Further, the invention includes a computer program product having computer implementable instructions, and which is constructed and / or arranged after being loaded and executed in a computer system or the like. Regelein- direction to carry out the steps of the method according to the invention. Thus, the computer program product-loaded and executed on a computer system-serves to test or identify a model structure of a system to be examined. In particular, the computer program product is for testing or identifying a model structure of a machine, an actuator, a vehicle or even a chemical reactor with a computer system or similar control device.

The test model describing the system is to be understood in particular as a model in the mathematical sense, namely a description of the system. Accordingly, such a description in the mathematical sense on a computer system by means of a corresponding computer program product, ie corresponding software, can be implemented. The result of the test leads to an identification or at least an evaluation of the description model. Insofar as this has been identified, this also means that it has been verified as correct.

The invention will now be explained in more detail by way of example with reference to exemplary embodiments with reference to the accompanying figures.

Fig. 1 shows a classical observer structure for observing a system including the possibility of error evaluation of the quality of the system model used.

Fig. 2 shows schematically and by way of example the evaluation of a system model according to an embodiment of the invention.

FIG. 3 symbolically shows the creation and validation of simulation models according to the prior art.

4 shows symbolically the creation and validation of simulation models according to an embodiment of the invention.

5 illustrates the basic problem underlying the selection of modeling approaches.

Fig. 6 illustrates the nature and problems of selecting modeling approaches according to the prior art. Figure 7 illustrates the selection of modeling approaches including the problems of the prior art.

Fig. 8 illustrates the selection of modeling approaches according to an embodiment of the invention.

9 shows schematically and by way of example the evaluation of a system model according to a further embodiment of the invention.

10 illustrates an observer structure with a test model according to an embodiment of the invention.

In a conventional method according to the prior art, parallel to a system 1, an observer 2 is connected in parallel with a model of the system. The system 1 and the observer 2 receive the same system input signal F (t). As a result, the system 1 outputs the system output signal x (t). The observer 2 and hence the contained system model also outputs an output signal x (f), which is ideally identical to the system output signal x (t). Usually, however, this ideal case can not be assumed and a difference between the system output signal x (t) and the model output signal x (f) in the summation point 4 is formed. The result of this difference is called observation error x (f). This observation error is fed back into the observer 2 and, depending on the observation error, the system model is adapted with regard to its states, namely such that the observation error x (f) is minimized as far as possible. This adjustment actually serves to compensate for unknown initial states of the system model. Insofar as a remaining observation error still remains, it must be due to a faulty system model, which can be evaluated in the error evaluation block 6.

The system model contained in the observer 2 must be defined in terms of structure and parameters so that it can be connected in parallel to the system 1 as shown in FIG. Both wrong parameters and wrong structures of the system model lead to a model output x (f) that deviates from the system output x (t). The extent to which a deviation is due to parameters or structures of the system model is difficult or impossible to verify. According to a further embodiment, a structure according to FIG. 2 is proposed. By way of illustration, a concrete example is shown here, to which the above-mentioned equations 1 to 3 are assigned.

This structure is also based on a system 1 which may be identical to the system 1 of FIG. It is also assumed that a system model for describing the system, which is referred to here as a description model. Equation 1 is set up for this description model, namely: m ^■ x (t) -F (t) = 0

This equation system, which is based on a description model, is then transformed into a parameterless test model. In this case, the description model does not need to be additionally presented in a different form, but the representation as a system of equations is sufficient. The test model is then represented by Equation 3 for this example, namely by:

F (t) = ^ ^{{t) '}

x (t) This transformed equation system or equation thus describes the test model 10, which is shown by the block 10 with the above equation 3 included.

This test model 10 thus also contains information about the structure of the description model, but without parameters. As a result of this transformation into the parameterless form which the test model 10 displays in the block 10, information about the structure of the description model has thus been preserved, whereas the parameters and thus the parameter influences have been eliminated.

In this case, the inputs and the output of the test model 10 differ. In principle, one or more input signals and one or more output signals of the test model 10 can be present. These depend on the input and output of the dynamic system 1, which could also have multiple inputs and / or multiple outputs.

In order to check the test model 10, the signal quantities which are to be taken from the transformed equation system or the transformed equation are required, namely The second and third derivatives of the system output signal and the first derivative of the system input signal are input variables of the test model 10. These quantities are generated by the differentiation block 12 from the system input signal F (t) and the system output signal x (t) and then presented to the test model as a model. entered input signals. Instead of a Differentiationsblocks 12 also comes, depending on the system or depending on the underlying description model another calculation block into consideration. Also, instead of or in addition to this system output signal x (t), other system signals may be included and taken into account.

The test model 10 then outputs the system input signal or a signal corresponding to this system input signal F (t) in the example shown, namely as a model output signal. This model output is then compared to the system input signal in the comparison block 16 and the resulting error is evaluated. Thus, only the underlying structure of the description model is included in the evaluation. Parameters are not included and therefore can not affect the error evaluation in the comparison block 16.

FIG. 3 illustrates one way of creating and validating simulation models according to the prior art. For this purpose, a common excitation signal 20 is generated and then acts both on the system to be examined 1, which may also be a test stand, and the excitation signal 20 acts on the simulation model 22. The simulation model 22 includes both system parameters 24 and system equations or at least one system equation 26th The system parameters can be obtained, for example, from data sheets of the system 1 to be examined or by numerical identification. In any case, inaccurate and / or idealized numerical values and scattering are to be expected. The resulting errors or the resulting fundamental error is thus a parameter error.

Furthermore, system equations are needed which indicate the structure of the system and there is the problem that insufficient or incorrect structures of the equations or, in general, a wrong model approach can lead to a structural error.

The simulation model 22 operated and created in this way then outputs a simulated system response 28. This is compared with the measured system response 30, which was measured as the output signal of the system 1. The result 32 of the comparison is shown symbolically as a superimposition of the simulated system response 28 with the measured system response 30. This results in deviations in reality, which can go back both to errors in numerical values of the parameters and thus to parameter errors, as well as to errors in the structure of the simulation model, namely structural errors.

With previous tools, it is difficult to answer whether the error is due to parameter errors and / or structural errors. However, in order to perform such an error evaluation, elaborate manual parameter studies are required to find and minimize the parameter error. The structural error often requires time-consuming manual extensions of the model structure, including the necessary parameter settings, until deviations diminish. 4 shows the creation and validation of simulation models according to an embodiment of the invention. In the manner shown there, description models and / or mathematical models can also be created and validated. Again, the system 1 is excited by an excitation signal 20, resulting in a measured system response 30, wherein the excitation signal 20 and correspondingly also the measured system response to those of FIG. 3 may differ. System equations 26 of the system are also used, which could have an insufficient or incorrect structure as a problem of these equations. These system equations can also have a structural error. However, it is now proposed that these system equations or system equations are transformed into the parameter-free form, which is used here as the test model 10 and can correspond to the test model 10 according to FIG. 2. The test model 10 is accordingly essentially dependent on the underlying system. The test model 10 or the underlying description contained therein can also be referred to as a structural system equation or structural system equations, which leads to a decoupling of numerical parameters.

Both the excitation signal 20 and the measured system response 30 flow into this test model 10. The resulting output model signal of the test model 10, referred to herein as the model output signal 34, is then fed to an error criterion block 36. The result is fed to the evaluation block 38. In the evaluation block 38, a qualitative and quantitative assessment can be made. To simplify matters, the evaluation block 38 distinguishes between two possibilities, namely the possibility 38A that the system equations 26 are correct, the error criterion is therefore satisfied, any deviations are therefore small, or the possibility 38B that the system equations are wrong, the error criterion was not fulfilled. If the system equations are correct, yourself However, in the comparison between system and description model result in serious errors, ie in particular in a comparison as he is finally illustrated in Fig. 3 with the comparison 32, this means that the parameters must be incorrect. So there must be a parameter error. However, if the system equations prove to be wrong, then at least a structural error is present. Although a parameter error can still exist, the system equations can be further improved until the system equations are no longer wrong. This can be done in the scheme of FIG. 4 when the system equations are changed and the process shown is repeated. As a result, it is also possible to achieve a significant increase in efficiency in the isolation process, because it becomes possible first of all to address a structural error independently of the parameters.

FIG. 5 is intended to illustrate the underlying problem by way of example with reference to a concrete example, namely a shock absorber. Fig. 5 shows symbolically such a shock absorber 50, which has a resilient element 52 and a damping element 54, via which the symbolically illustrated wheel 56 is fixed to the vehicle 58. This shock absorber is to be mapped in a simulation. If possible, a best compromise between accuracy and complexity of the model should be found.

By way of example, two model approaches, namely model approach A and model approach B are shown. It is therefore based on a model A or model B, which thus each form a description model A and B respectively. A modeling approach should be selected and the answer to this question is which model is most appropriate.

Both model approaches show a characteristic of the shock absorber, namely the damping force as a function of the speed, whereby both model approaches assume a functional relationship, which is nonlinear in both cases.

The model approach A is probably a good but not perfect representation of the measured results. Model A also uses a few parameters and should be easy to parameterize.

The model approach B is probably a better representation of the measured results, but has many parameters and is highly nonlinear, namely stronger than the model approach A. The model approach B should therefore be difficult to parameterize. Here are On the one hand, there are likely to be numerical problems and, on the other hand, there is a risk that corresponding parameters will not be available.

According to the state of the art, the procedure has hitherto been to start with the model which is as simple as possible, namely model approach A, in order to answer the question as to which model approach is most suitable. This start with model approach A is illustrated in FIG. Accordingly, a system equation or the system equations 26 is set up for this model approach A or corresponding to the model A and parameterized with system parameters 24, which can be done for example by data sheets or numerical identification. Accordingly, these parameters are assigned to the system equations, so that the system equations are then parameterized and can be tested. These system equations include the simple model approach A. This is excited with the excitation signal 20 and the resulting simulation result is compared with a corresponding measurement in the comparison 32. As a result, deviations between measurement and simulation should be present, as indicated by the result block 40.

The advantage of this simple model A is in particular that parameterization of the model by data sheets, numerical system identification and / or numerical optimization of the parameters can often be carried out in a simple manner. This model is relatively simple, has low non-linearities and no redundant parameters.

The result block 40 illustrates that deviations are present, however. The question now arises as to whether a complex model offers advantages that justify the significantly higher effort involved in the creation.

To test this, the more complex model has to be tested, which is shown in FIG. 7. There is also a system equation 26 or system equations 26 set up or select and parameterize by means of the system parameters 24, which can be done by data sheets or numerical identification or optimization of the parameters. The system equation 26 and the system parameters 24 will, however, assume different values here than in FIG. 6, and to clarify the relationships, the same reference numerals have nevertheless been selected here.

An excitation is now also carried out by the measured excitation signal 20, whereby now the complex model approach B is based. When comparing the obtained simulation result with measured values of the system, deviations may still occur. gene between measurement and simulation, which the result block 40 illustrates. The cause of deviations must be searched in the system equation 26 and the parameterization 24. However, it is not clear whether the model approach is still insufficient, or whether there is still an incorrect or inadequate parameterization. Not least of all, this uncertainty lies in the fact that if deviations are detected in result block 40, it can not be ensured that the best possible parameterization actually took place. With this insecurity remains the question of whether the effort has ever paid off. Such a complex approach may have numerical problems in the numerical identification of the parameters; a global optimization of the parameters can be very difficult; This can result in very high costs for model creation with an uncertain result. Ultimately, this complex model approach is also difficult or not clearly identifiable, which can lead to these problems.

A proposed solution according to one embodiment is illustrated in FIG. 8. Accordingly, equation systems for model approach A and model approach B are set up and respectively transformed into parameter-free form and lead in each case to a test model 10 or a corresponding equation system or corresponding equation. FIG. 8 shows two test models 10 which are different from one another but have the same reference number to illustrate their functional similarity. Both test models 10 have structural system equations in which a decoupling of numerical parameters has taken place.

Measurement signals of the real system, namely an excitation signal 20 and the measured system response 30 are used to check the structural system equations of the two test models 10. For example, this excitation signal 20 and the measured system response 30 may be included in the test model 10 in a manner as illustrated in FIG. 2, based on other system equations. For the sake of simplicity, FIG. 8 illustrates that the excitation signal 20 and the measured system response 30 are included in the error criterion 36. In that regard, the illustration of FIG. 8 is shown in simplified form and is merely intended to express that the excitation signal 20 and the measured system response 30 are included in order to check both test models 10 and the subsequent evaluation via the error criterion 36. The result block 42 should make it clear that a clear, fast decision as to which modeling approach should be pursued can be brought about. The parameterless examination and the underlying criterion in the error criterion block 36 makes such a decision possible, at least favors it. The approach used here, namely in the evaluation by means of error criteria can be considered better in the error criteria block 36, as far as the uncertainty that the better result may be due to a better parameterization, is not given. In fact, such a parameter-free examination also makes it possible, or at least better, to base it on an absolute error criterion.

In contrast to previous methods of the prior art, in particular as described in FIGS. 6 and 7, only a real measuring signal is now necessary. In the prior art described, many different measurements are used for validation and model selection. This is the case in particular when a model approach has to be varied several times in order to adapt the parameters as precisely as possible. There is a significant increase in efficiency in the simulation process possible.

Fig. 9 shows a further embodiment of the invention. The illustration corresponds to FIG. 2, to which reference is hereby made and where the same reference numerals are used to illustrate the similarities. However, another test model 10 is based on outputting a quality function or a quality signal G instead of a model output signal which corresponds to a system signal. The signal F (t) now enters the test model 10 as a further input variable and can be used to calculate the quality signal. The quality signal may be a single size or a time function and / or a multivariate signal. In any case, the quality signal, which can also be referred to as a quality function, is already the result of an evaluation or preliminary evaluation in the test model 10. The quality signal G is then input to the block 16 for final evaluation. The block 16 can form a comparison block 16, in which the quality signal is compared with a comparison value, or another evaluation can be carried out in the block 16. FIG. 10 essentially corresponds to the structure of FIG. 1, but the observer 2 has another functionality, namely an integrated test model. The test model can serve to validate the model underlying the observer. It can be shown that in the parameterless description of this exemplary system, the parameter m can be transformed into the initial values of the system. For a faultless description of the structure of the system, the observer error would therefore have to disappear, since the unknown initial values are compensated. An embodiment of this invention can thereby verify the model structure with the aid of observers. Thus, a verification of the structure used in the observer is possible, even if the observer thereby has parameter errors. As a general statement, detached from the embodiments shown, it should be pointed out that simulation models according to the state of the art have a high degree of complexity due, inter alia, to the required quality of results, the breadth of use as models and the available computing power. Nevertheless, in many areas of application, such as real-time simulation, control engineering, system monitoring, etc., reduced models are necessary. For linear systems very good methods for model reduction are available, for nonlinear systems only a few approaches are known.

With the method presented here, the necessary structure of the mathematical models can be reduced to a minimum by adding and / or removing successive elements. It then checks whether the structure can continue to fulfill measurement or simulation data. In addition, the evaluation of the sensitivity of individual elements and thus the control of deviations is possible. Since element sensitivity is evaluated on the basis of the model structure only, decoupled from the parameter set, it does not require complex parameter set optimization, which causes additional numerical problems. The model reduction becomes much more efficient.

The dynamics of complex systems can often be approximated by simplified substitute modes, for example in the form of phenomenological models. In particular, the review of the chosen system structure is difficult. Typically, the free parameters of the system are optimized after determining the system structure with numerical methods. Subsequently, the comparison is made with measured data or with simulation data of other models of the same system. In numerical optimization often insufficient results are achieved. On the one hand, the cause may be that the global minimum for the parameter set to be optimized, for example due to a high number of local minima, can not be identified. On the other hand, there is the possibility that the chosen model structure can not fully satisfy the numerical data at all.

The presented method can be used to check whether a selected model structure can fulfill numerical data and thus whether it is possible to find free parameters for the system with which the numerical data can be fulfilled in principle. This provides a way to review modeling approaches. Especially in the development of safety-relevant algorithms and circuits or in components with very high numbers, such as microprocessors, today (formal) verification procedures are used. This clearly indicates whether algorithms and circuits have the desired behavior in every possible operating state.

The method presented here is also suitable for checking, independent of parameters, whether an algorithm, a circuit or a dynamic system can always have the desired behavior.

By a suitable choice of the excitation signal, additional statements about the behavior in the frequency domain can be made. Finally, an automatic verification of algorithms and circuits, in particular analog circuits, can be proposed.

The proposed methods, at least one of them, also provides the possibility of checking the substitutability of passive by active components, such as elastomeric bearings, by means of appropriately controlled actuators, to name but one example. In this application of the proposed method is to be expected in a considerable efficiency gain in technical development, since the suitability of technical systems, namely already at the idea stage, to achieve a desired input / output behavior can be checked very quickly in advance.

Claims

Computer-aided method for checking or identifying a model structure to be examined (1), comprising the steps:

Establishing a system of equations (26) having at least one parameter for describing the system (1) to be examined or a part thereof, wherein the system of equations (26) has a description model as an assumed model of the system (1) and / or a description model structure as an assumed model structure of the system System (1) is based,

- transforming the equation system (26) into a parameterless or parameter-reduced test system (10) qualitatively describing the system, which describes at least one model output signal as a function of one or more model input signals,

Exciting the test model (10) with at least one model input signal,

Picking up at least one model output signal of the test model (10),

Comparing (32) the at least one model output signal of the test model with at least one corresponding system signal, and / or calculating a quality function depending on the at least one model signal and a system signal,

Selecting the description model or the selected description model structure as an identified model or identified structure of the system (1) if a predetermined criterion has been fulfilled in the comparison or with the quality function, or

Establishing a modified system of equations (26) based on a changed description model and / or a modified description model structure and repeating the method steps if the predetermined criterion was not met in the comparison (32) or with the quality function, and / or - associating the result of the comparison (32) with the description model as evaluation of the description model.

2. Computer-aided method according to claim 1, characterized by the steps

Detecting at least one system output signal x (t) in response to the system (1) to at least one system input signal F (t) and

Determining the at least one model input signal of the test model from the at least one system input signal F (t) with which the system was excited and / or from the at least one detected system output signal x (t), wherein each system input signal F (t) and each system output signal x (t) each form a system signal.

3. Computer-aided method according to claim 1 or 2, characterized in that when comparing (32) of the at least one model output signal of the test model with at least one corresponding system signal, the system signal is a measured, a predetermined and / or expected signal.

4. Computer-aided method according to one of the preceding claims, characterized in that the model input signals comprise at least one, derived at least once in a time system signal.

5. Computer-assisted method according to one of the preceding claims, characterized in that when setting up the equation system (26) at least one non-linear model description (A, B) is integrated or incorporated, and / or that when setting up the modified equation system (26) at least one nonlinear model description (A, B) is exchanged for another (A, B), wherein in integrating, incorporating or exchanging, in particular, a non-linear model description (A, B) is taken from a model collection comprising several non-linear model descriptions (A, B) becomes.

6. Computer-aided method according to one of the preceding claims, characterized in that the system is subdivided as an overall system into several subsystems. each subsystem is identified individually as a physical system, and then an identified overall system is assembled from the subsystems thus identified.

7. A computer-aided method according to claim 6, characterized in that the subdivision of the overall system is such that at least one input signal is selected so that it only partially excites the entire system, and / or at least one output signal is selected so that it only from the excited subsystem is influenced and / or that part of a system behavior is computationally eliminated.

8. Computer-aided method according to one of the preceding claims, characterized in that a polynomial description is used as a non-linear model description (A, B) and / or a non-linear model description (A, B) is converted into a polynomial description.

A computerized method according to any one of the preceding claims, characterized in that the detection of at least one system output signal x (t) in response to the system (1) to at least one system input signal F (t) is effected by exciting the system with the system input signal and the at least one system output signal is measured, and / or a simulation model describing the system is excited with the system input signal and the at least one system output signal is received as an output signal of the simulation model.

10. Computer-aided method according to one of the preceding claims, characterized in that as a system input signal for exciting the system (1) at least once continuously differentiable signal is used and / or a filtered non-continuously differentiable signal is used, and / or at least one model input signal in Test model is filtered.

1 1. Computer-assisted method according to one of the preceding claims, characterized in that when setting up the system of equations (26), a subsystem, in particular a known subsystem of the system (1) is taken into account as a substitution submodel by deviating from the subsystem submodel.

12. A computer-aided method according to claim 1 1, characterized in that when setting up the amended equation system (26), the substitution partial model is replaced by a modified Substitutionsteilmodell.

13. A computer-aided method according to one of the preceding claims, characterized in that in addition to the equation system (26) a different reference equation system is set up, wherein the reference equation system to the equation system (26) differs in that it is a subset of the equation system (26 ), wherein the system of equations (26) and the reference equation system are each transformed into a parameterless or parameter reduced test system (10) or reference test model respectively describing at least one model output signal in response to one or more model input signals; Comparing (32) the at least one model output signal with at least one corresponding system signal takes place in such a way that the test model (10) and the reference test model are excited with at least one identical signal and at least in each case s a model output signal corresponding outputs of the test model (10) and the reference test model are compared with each other and / or that model input and / or model output signals are entered into the test model and the reference test model, respectively at least one quality criterion is generated and the quality criterion of the test model with Quality criterion of the reference test model is compared.

A computer program product with computer-implementable instructions adapted, after loading and executing in a computer system or the like, to perform the steps of a method according to any one of the preceding claims.