Abstract:
A method for indirectly monitoring tire pressure or for detecting damage to a wheel suspension, wherein a pressure loss detection variable (DVE) is determined using an analysis of a vibratory behavior of a wheel of a motor vehicle, and a pressure loss in the tire of the wheel or damage to the wheel suspension is detected by comparing a momentarily determined pressure loss detection variable (DVE akt ) to a learned pressure loss detection variable (DVE soil ), wherein at least two dimensional variables are determined from a wheel speed signal (w) of the wheel, each representing a dimension for the extent of a frequency or a frequency range in the vibratory behavior of the wheel, and that the pressure loss detection variable (DVE) is derived from the two dimensional variables (e 1 , e 2 , e 3 ), particularly from a ratio of the two dimensional variables (e 2 /e 3 ), and a tire pressure monitoring system.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is the U.S. national phase application of PCT International Application No. PCT/EP2008/066299, filed Nov. 27, 2008, which claims priority to German Patent Application No. 10 2007 059 648.2, filed Dec. 10, 2007, and German Patent Application No. 10 2008 056 664.0, filed Nov. 11, 2008, the contents of such applications being incorporated by reference herein. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The invention relates to a method for indirectly monitoring tire pressure or for detecting damage to a wheel suspension system and to a tire pressure monitoring system in which a wheel speed (ω) of at least one wheel or a variable which is associated with the wheel speed (ω) of the wheel is obtained and is evaluated for the detection of a tire pressure loss. 
       BACKGROUND OF THE INVENTION 
       [0003]    Various tire pressure monitoring systems are known which operate either on the basis of directly measuring sensors or detect an abnormal tire pressure by evaluating rotational speed properties or oscillation properties of the vehicle wheels. 
         [0004]    DE 100 58 140 A1, which is incorporated by reference, discloses what is referred to as an indirectly measuring tire pressure monitoring system which detects a tire pressure loss by evaluating the rotational movement of the wheel (DDS: Deflation Detection System). 
         [0005]    EP 0 578 826 B1, which is incorporated by reference, discloses a tire pressure gauge which determines a pressure loss in a tire on the basis of tire oscillations, wherein at least one resonant frequency component is extracted from the tire oscillations. 
         [0006]    A method for indirectly monitoring tire pressure which, by taking into account the natural torsional frequency of the tires, improves an indirectly measuring tire pressure monitoring system which is based on the evaluation of the rotational movement of the wheel is disclosed in patent application DE 10 2005 004 910 A1, which is incorporated by reference. 
         [0007]    A tire monitoring system with combined evaluation of wheel speed information and analysis of the axial frequency in which the vertical acceleration of the wheels is measured and taken into account by means of sensors is described in WO 03/031990 A1, which is incorporated by reference. 
         [0008]    Indirect systems for detecting loss of tire pressure which are known from the prior art resort to the wheel speed information in order to calculate an indicator variable for a tire pressure loss (pressure loss detection variable), wherein the change in the natural frequency or resonant frequency of the torsional oscillation between the rim and the belt in the event of a pressure loss is used as an indicator variable which can be observed in a frequency spectrum of the wheel speed signal. This change is based on the reduction in the torsional spring constant between the belt and the rim when there is reduced pressure in the tire. The displacement/change in the resonant frequency of a current frequency spectrum of the wheel speed compared to a resonant frequency learnt in the case of correct tire air pressure is then used to detect the pressure loss. 
       SUMMARY OF THE INVENTION 
       [0009]    An object of the invention is to make available an alternative method for indirectly monitoring tire pressure or a method for detecting damage to a wheel suspension system in which the oscillation behavior of at least one wheel is evaluated. 
         [0010]    The term “wheel speed” is understood according to aspects of the invention as a generalization of the term. For example, the term is also understood to refer to all other wheel rotational movement variables which are directly logically linked to the wheel speed, for example rotation time, angular speed or rotational speed. 
         [0011]    The invention relates to the idea of detecting a pressure loss at a wheel and/or damage to a wheel suspension system by comparing a currently determined pressure loss detection variable with a learnt pressure loss detection variable, wherein the pressure loss detection variable is determined from at least two dimensional variables which are determined from the wheel speed signal of the wheel and which each represent a measure of the value of a frequency or of a frequency range in the oscillation behavior of the wheel. 
         [0012]    The frequencies are advantageously different resonant frequencies of a wheel torsional oscillation and/or a wheel vertical oscillation, and the frequency ranges are advantageously different frequency ranges about the resonant frequencies of a wheel torsional oscillation and/or a wheel vertical oscillation. These resonant frequencies reflect the torsional spring constant between the tire belt and rim and the spring/shock absorber effect of the tire in respect of a vertical movement, and therefore depend on the tire pressure. 
         [0013]    The pressure loss detection variable is preferably formed from a ratio between the two dimensional variables. As a result, influences due to the excitation of the road are minimized and incorrect warnings are therefore avoided. 
         [0014]    During the calculation of the pressure loss detection variable, the vehicle velocity is preferably additionally included in order to take into account its influence on the pressure loss detection variable directly. 
         [0015]    In order to determine a dimensional variable, the wheel speed signal is preferably filtered with a bandpass filter with cutoff frequencies about the corresponding natural frequency. The variance of the filtered signal is particularly preferably used as a measure of the energy in this range. In order to determine the dimensional variables, it is then not necessary to determine a frequency spectrum of the wheel speed signal so that there is also no corresponding need for storage space to calculate a frequency spectrum. 
         [0016]    According to one preferred embodiment of the invention, dimensional variables are determined for three different frequencies and/or frequency ranges and are used for pressure loss detection and/or damage detection in order to take into account the widest possible range of wheel oscillations during the monitoring process. Two resonant frequencies or resonant frequency ranges of wheel torsional oscillations and a resonant frequency or a resonant frequency range of a wheel vertical oscillation are particularly preferably evaluated since these resonant frequencies exhibit different behavior in terms of their value in the event of a loss of tire pressure and/or when different interference variables, for example road excitations, occur. 
         [0017]    In order to take into account the influence of road excitations and other interference effects as comprehensively as possible, the pressure loss detection variable is preferably formed from a ratio between two dimensional variables, and the pressure loss detection variable is additionally learnt as a function of the third dimensional variable. In order also to minimize the influences due to road excitations in terms of the third dimensional variable, the pressure loss detection variable is particularly preferably learnt as a function of a ratio between two dimensional variables, which ratio contains the third dimensional variable. 
         [0018]    In order to take into account directly the vehicle velocity, which is a measure of the wheel excitation, the pressure loss detection variable is preferably calculated from a ratio between two dimensional variables and the vehicle velocity. The vehicle velocity is usually available within the scope of a slip control system or is measured with a sensor. 
         [0019]    For reliable monitoring it is advantageous if at least two of the frequencies and/or frequency ranges considered are selected in such a way that the corresponding dimensional variables exhibit a different change in terms of their values or an opposing behavior in terms of their change in the event of a tire pressure loss/wheel suspension damage. 
         [0020]    In order to keep the expenditure on evaluation and therefore the costs of implementation low, a dimensional variable is preferably determined by means of bandpass filtering of the wheel speed signal, wherein the variance of the filtered signal is used as a dimensional variable. The cutoff frequencies of the respective bandpass filter correspond to the frequency range which is considered. In order to eliminate statistical fluctuations, mean value formation or mean value filtering of the variance is particularly preferably carried out. 
         [0021]    According to one preferred embodiment of the method according to aspects of the invention, a dimensional variable is obtained as an amplitude value of the frequency spectrum of the wheel speed signal at a predefined or specific frequency. As a result, apart from the calculation of the frequency spectrum, the evaluation can be implemented in a simple and therefore cost-effective way. This is advantageous in particular if the frequency spectrum has to be calculated within the scope of another method. 
         [0022]    According to another preferred embodiment of the method according to aspects of the invention, a dimensional variable is determined by integrating or averaging the amplitude values of the frequency spectrum of the wheel speed signal in a predefined or specific frequency range. Although more evaluation steps, for example the buffering of values, are necessary for this type of evaluation, the dimensional variable which is determined then depends on a large number of amplitude values, with the result that a possibly incorrectly determined amplitude value makes a smaller contribution to the falsification of the dimensional variable. 
         [0023]    For simple and cost-effective evaluation, the frequencies and/or frequency ranges for determining the dimensional variables are preferably predefined. 
         [0024]    In order to adapt the determination of the dimensional variables to the respective vehicle and therefore achieve more reliable pressure loss detection/damage detection, the resonant frequency or the frequency ranges in which a resonant frequency is located are preferably determined from an obtained frequency spectrum of the wheel speed signal. If only the resonant frequencies are determined from the obtained frequency spectrum, corresponding frequency ranges can be determined from the obtained resonant frequency and predefined frequency interval. 
         [0025]    It is likewise preferred to obtain the resonant frequencies or frequency ranges from model parameters of at least one model or at least one model-based equation, wherein the model parameters are determined by parameter estimation with evaluation of the wheel speed signal. This is advantageous in particular in cases in which the method according to aspects of the invention is carried out in addition to a tire pressure monitoring system whose pressure loss detection is based on such a model or model-based equation since in these cases the model parameters are already available. 
         [0026]    During the learning phase, a dependence between one dimensional variable (or a ratio between dimensional variables) and another dimensional variable (or one (other) ratio between dimensional variables) is preferably learnt. The learnt dependence is then used in the comparison phase or pressure loss monitoring phase for compensating the corresponding variable (dimensional variable or ratio between dimensional variables) in terms of the other variable (dimensional variable or ratio between dimensional variables). As a result the detection is improved since alternating dependencies can be taken into account/compensated. The pressure loss detection variable, which is determined from a ratio between dimensional variables, is particularly preferably learnt as a function of another ratio between dimensional variables. In the comparison phase, the current pressure loss detection variable is then compensated by means of the learnt dependence, and the compensated current pressure loss detection variable is used for comparison with the learnt pressure loss detection variable. As a result, nonlinearities in the components of the wheel suspension system are taken into account. 
         [0027]    The dependence of a dimensional variable (or of a ratio between dimensional variables) on the vehicle velocity and/or of a dimensional variable (or of a ratio between dimensional variables) on a temperature is likewise preferably learnt in the learning phase and taken into account in the comparison phase since both the speed and the temperature have an influence on the wheel oscillation. 
         [0028]    The dependence between one variable and another variable is preferably predefined in the form of a functional relationship with parameter variables, wherein the parameter variables are determined during the learning phase. For this purpose, value pairs of the variables are stored, and the parameter variables are determined using the value pairs. 
         [0029]    In a less computationally costly method, the dependence between a first variable and a second variable is determined by the first variable being learnt in value intervals of the second variable. A comparison between a current first variable then takes place with the corresponding, learnt value of the first variable for the same value of the second variable. 
         [0030]    According to one development of the invention, the method according to aspects of the invention is combined with another method for indirectly monitoring tire pressure. A more reliable pressure loss detection therefore becomes possible. A combination with a method whose pressure loss detection variable is a resonant frequency is particularly advantageous. In this context, a large number of the variables which are necessary for detection, for example the frequency spectrum, then only have to be determined once, and can then be used by both methods. 
         [0031]    Since tire pressure monitoring methods often only provide reliable pressure loss detection under specific conditions, it is preferred to carry out the pressure loss detection as a function of the vehicle velocity and/or the values of the dimensional variables by means of the one or other method for indirectly monitoring tire pressure, or to carry out the warning through a weighted combination of the results of the two methods, wherein the weighting is changed as a function of the vehicle velocity and/or the values of the dimensional variables. 
         [0032]    One advantage of the method according to aspects of the invention is that, compared to other methods, more reliable warning is possible since different frequency ranges of oscillations and/or types of oscillations of the wheels are included in the monitoring. As a result, it is also possible to compensate various interference effects. A further advantage of the method according to aspects of the invention is that the consideration of a ratio between dimensional variables allows the interference influence of the excitation of the road to be at least partially compensated in an easy fashion. 
         [0033]    The invention also relates to a tire pressure monitoring system in which a method as described above is carried out. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0034]    The invention is best understood from the following detailed description when read in connection wit the accompanying drawings. Included in the drawings is the following features: 
           [0035]      FIG. 1  shows a flowchart of a first exemplary embodiment of a method according to aspects of the invention, 
           [0036]      FIG. 2  shows a flowchart for determining dimensional variables according to a second exemplary embodiment of a method according to aspects of the invention, and 
           [0037]      FIG. 3  shows a flowchart of a fourth exemplary embodiment of a method according to aspects of the invention, 
           [0038]      FIG. 4  shows a first model of a wheel, 
           [0039]      FIG. 5  shows an exemplary relationship between a transfer function and a frequency for various tire pressures, 
           [0040]      FIG. 6  shows a second model of a wheel, 
           [0041]      FIG. 7  shows an exemplary relationship between the transfer function and frequency for various values of α/v, and 
           [0042]      FIG. 8  shows exemplary dependencies between the torque and the slip. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0043]      FIG. 1  is a schematic view of a flowchart of a first exemplary embodiment of a method according to aspects of the invention. In block  1 , at least two, for example three, dimensional variables e 1 , e 2  and e 3  are determined from a wheel speed signal ω of a wheel by means of an energy evaluation method. Each dimensional variable constitutes a measure of the value of a frequency or of a frequency range in the oscillation behavior of the wheel. In block  2 , the oscillation behavior of the tire in the case of a correct or predefined air pressure is obtained and the dimensional variables and/or a pressure loss detection variable DVE which is determined from dimensional variables are learnt in a learning phase. After the learning, evaluation of the dimensional variables and/or of the pressure loss detection variable DVE which is determined from dimensional variables takes place in block  3 . By comparing a currently determined pressure loss detection variable DVE curr  with a learnt pressure loss detection variable DVE setp , pressure loss at the tire of the wheel or damage to the wheel suspension system is detected. If the deviation from current pressure loss detection variable DVE curr  and learnt pressure loss detection variable DVE setp  exceeds a detection threshold, a warning is output to the driver in block  4 . 
         [0044]    For example, a ratio between dimensional variables, for example the ratio e 2 /e 3  between the two dimensional variables e 2  and e 3  is used as the pressure loss detection variable DVE: 
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         [0045]    The invention is therefore based on the fact that a change in the torsional and/or radial spring constant of the tire in the event of a pressure loss results in a change and/or redistribution of the energies in the oscillation spectrum of the wheel speed. For example the signal amplitudes of the associated natural frequency or resonant frequency (i.e. the level of the maximum/the amplitude in a frequency spectrum at the natural frequency or resonant frequency) change. 
         [0046]    For example the spectral energies or signal amplitudes (i.e. the value of the natural frequency, in particular the energy content of the frequency spectrum of the wheel speed in the region of a natural frequency) are therefore evaluated in order to determine a tire air pressure or tire air pressure loss or to detect damage to the wheel suspension system. 
         [0047]    A dimensional variable can be determined, for example, by integration of the spectrum over a limited frequency range. 
         [0048]    However, since the spectral energies depend not only on the air pressure but also on further (interference) variables, the influences of these interference variables should be taken into account. Failure to consider these influences can lead to incorrect warnings or else to authorized warnings not occurring. 
         [0049]    Significant interference variables which are taken into account are, for example:
       (a) road influences/coefficient of friction,   (b) speed, and   (c) load.       
 
         [0053]    For example, monitoring of the tire air pressure is carried out with three dimensional variables e 1 , e 2 , e 3  which describe the resonant amplitudes or values of three relevant oscillations in the wheel speed signal. The resonant amplitudes can also be considered to be signal energies. 
         [0054]    The three abovementioned oscillations are, for example,
       (a) a wheel vertical oscillation,   (b) a first wheel torsional oscillation, and   (c) a second wheel torsional oscillation.       
 
         [0058]    According to one exemplary embodiment, the respective frequency ranges from which the dimensional variables e 1 , e 2 , e 3  are determined are predefined. For example, a resonant range of approximately 10 to 20 Hz is set for the wheel vertical oscillation, a resonant range of approximately 30 to 60 Hz is set for the first wheel torsional oscillation, and a resonant range of approximately 70 to 110 Hz is set for the second wheel torsional oscillation. 
         [0059]    According to another exemplary embodiment, the relevant frequency ranges for the respective vehicle are determined individually. For this purpose, various methods can be used. For more precise determination as to which frequency intervals are used for calculating the dimensional variables, for example the actual resonant frequencies f nat1 , f nat2 , f nat3  are first obtained for the corresponding vehicle and then used to define the frequency intervals. The relevant frequency ranges are selected, for example, as ranges of one or more different predefined frequency bands Δf nati  about the specific resonant frequencies f nati  (f nati ±Δf nati /2 where i=1, 2 or 3). 
         [0060]    Predefined frequency bands (for example Δf nat1  about f nat1 ) can, however, also firstly be assumed to be starting values for the frequency ranges. Starting from the starting values, the frequency ranges can then also be adapted to the present vehicle, i.e. to the specific frequency spectrums. In this way, vehicle-specific evaluation is possible. 
         [0061]    The resonant frequencies f nat1 , f nat2 , f nat3  of the three oscillations are, for example, obtained by means of parameter estimation of the corresponding transfer functions (for example equation (4) and (9) further below) in the respective frequency range. For this purpose, the wheel speed signal ω and its derivative/derivatives are used. The resonant frequency is determined from the estimated model parameters (see for example equation (5) and (6)). 
         [0062]    Alternatively, the resonant frequencies f nat1 , f nat2 /f nat3  can be found by means of a spectral analysis of the wheel speed signal ω as maximum values in the respective frequency ranges. 
         [0063]      FIG. 2  is a schematic illustration, in the form of a flowchart, of determination of the dimensional variables e 1 , e 2 , e 3  according to a second exemplary embodiment of a method according to aspects of the invention. The wheel speed signal ω is filtered in the predefined or specific frequency ranges with a bandpass filter BP in each case. For example, the frequency range 10-20 Hz is filtered out in block  5 , the frequency range 30-60 Hz is filtered out in block  6  and the frequency range 70-110 Hz is filtered out in block  7 . In blocks  8 , in each case the variance Var of the signal is determined and subsequently filtered in the blocks  9  with a mean value filter. This method for determining the dimensional variables e 1 , e 2 , e 3  is advantageous since it is not necessary to obtain a frequency spectrum and the expenditure of an evaluation is thus relatively low. 
         [0064]    The frequency band of each bandpass filter is to be selected here, for example, in such a way that in each case the amplitude maximum (resonant frequency f nati ) is included. This is important, in particular, in the event of unreliable determination of the relevant frequency range. 
         [0065]    According to a third exemplary embodiment (not illustrated) of a method according to aspects of the invention, the dimensional variables e 1 , e 2 , e 3  are obtained by means of a specific frequency spectrum of the wheel speed signal ω. The frequency spectrum is preferably calculated by means of a discrete Fourier transformation. This determination of the dimensional variables is advantageous in particular when the method according to aspects of the invention is combined with another indirect tire pressure loss method which is based on the evaluation/displacement of a resonant frequency which is obtained from a frequency spectrum. In this case, the frequency spectrum is already obtained within the scope of the other indirect method and only has to be then correspondingly evaluated. 
         [0066]    For example, an unfiltered frequency spectrum is firstly determined from the speed signal ω of a wheel, for example by frequency analysis by means of a Fourier transformation. Such a spectrum is obtained, for example, with a 1 second clock cycle (therefore corresponds to a frequency resolution of 1 Hz). For example, averaging of the individual spectrums to form an overall spectrum is then carried out. 
         [0067]    If the spectrum of the wheel speed signal ω is therefore available, the variables e 1 , e 2 , e 3  can then be obtained directly from the spectrum. In this context, either the amplitude (for example G(f nat1 )) can be determined directly at the obtained resonant frequency or a mean value about the resonant frequency is obtained (averaging of G(f) for frequency range f lower ≦f≦f upper , in which case, for example, f lower  can=f nat1 −Δf 1 /2 and f upper  can=f nat1 +Δf 1 /2 with a predetermined interval width Δf 1 ). Alternatively, the energy content of the spectrum can also be used in a frequency range, i.e. the integral over the transfer function G in a frequency range (for example f nat1 −Δf 1 /2 to f nat1 +Δf 1 /2) about the respective natural frequency 
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         [0068]    As already mentioned above, different road excitations lead to different spectral densities in the individual frequency ranges of the frequency spectrum, as a result of which reliable pressure loss detection by means of the dimensional variables e 1 , e 2 , e 3  can be disrupted. In order to compensate for this, in addition to or instead of the dimensional variables e 1 , e 2 , e 3  themselves, their quotients (ratio between dimensional variables) are considered. A possible selection of ratios is e 1 /e 2 , e 1 /e 3  and e 2 /e 3  (alternatively, other ratios between the dimensional variables can also be formed). By means of the formation of quotients, displacements of the spectral density due to, for example, road excitations are compensated. 
         [0069]    The pressure loss detection variable DVE is preferably formed from a ratio between two dimensional variables and at least one dimensional variable itself is additionally used to control the tire pressure monitoring method and/or to compensate the pressure loss detection variable DVE. 
         [0070]    According to one exemplary embodiment, the tire pressure monitoring method is deactivated if a dimensional variable, for example e 3 , becomes greater than a first predefined threshold value or smaller than a second predefined threshold value. 
         [0071]    Additionally or alternatively, a dimensional variable, for example e 1 , is used to compensate the pressure loss detection variable DVE (see also description below). 
         [0072]    Increases or reductions in individual regions in the frequency spectrum are averaged out, for example, by filtering the dimensional variables (over time). 
         [0073]    The vehicle velocity v influences, as a model parameter and as an excitation component, the dimensional variables e 1 , e 2 , e 3 . For this reason, according to one exemplary embodiment the dependencies of the dimensional variables and/or of the pressure loss detection variable DVE on the velocity are taken into account. For this purpose, a velocity dependence can be predefined as a functional relationship and taken into account directly in an explicit fashion (see equation (2)) or the velocity dependence is learnt and subsequently used for the compensation. 
         [0074]    According to one exemplary embodiment, a pressure loss detection variable DVE is determined from the ratio e 2 /e 3  between the two dimensional variables e 2  and e 3  and the vehicle velocity v in accordance with the following equation: 
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         [0075]    This pressure loss detection variable DVE corresponds to a velocity-compensated ratio between dimensional variables. With the formation of quotient e 2 /e 3 , a large degree of independence from the route is achieved and the greater part of the velocity dependence of the pressure loss detection variable DVE is taken into account explicitly by means of the functional relationship v 3/2 . 
         [0076]    As an alternative to taking into account the vehicle velocity v described in equation (2) by means of a predefined relationship, the dependence on the vehicle velocity v can also be taken into account by learning the pressure loss detection variable DVE (for example 
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         [0000]    according to equation (1)) in velocity intervals. 
         [0077]    Furthermore, a more precise velocity dependence, for example on the basis of equation (2) (or see further below), can also be subsequently learnt. 
         [0078]    According to another exemplary embodiment, instead of the quotient e 2 /e 3  which was used in the exemplary embodiments described above the quotient e 2 /e 1  is used to form a pressure loss detection variable DVE. 
         [0079]    Nonlinearities, for example in the behavior of individual components of the wheel suspension systems (see also below), lead to excitation-dependent influencing of the dimensional variables. For this reason, the dependencies of the dimensional variables on one another and/or the dependencies of the ratios of dimensional variables on one another are advantageously learnt and subsequently used for compensation. 
         [0080]    According to a further exemplary embodiment, the pressure loss detection variable DVE, for example according to equation (1) or (2), is learnt as a function of the energy ratio e 1 /e 3 . As a result, possible still remaining dependencies on the route are better taken into account. For this purpose, the pressure loss detection variable DVE is learnt in value intervals of e 1 /e 3  and compared later. 
         [0081]    The temperature T also influences the dimensional variables e 1 , e 2 , e 3 , for example via the tire damping (see the model parameters further below). For this reason, the dependencies of the dimensional variables or of the ratios of dimensional variables or of the pressure loss detection variable DVE on the temperature are advantageously learnt and subsequently used for the compensation. The temperature is obtained, for example, by means of sensors or a temperature model. 
         [0082]    As an alternative to compensation, the temperature during the learning process can, in particular, be stored together with the learnt dimensional variables e 1 , e 2 , e 3  or the pressure loss detection variable DVE and then compared with the (current) temperature during the pressure loss monitoring process/damage detection process. If these temperatures differ greatly, the run-in time of the filters can be increased or the system prevents a warning. 
         [0083]      FIG. 3  is a schematic illustration of a flowchart of a fourth exemplary embodiment of a method according to aspects of the invention. In addition to the dimensional variables e 1 , e 2 , e 3  obtained and the ratios e 1 /e 2 , e 2 /e 3 , e 1 /e 3  formed therefrom, the vehicle velocity v and the temperature T are also included as input variables in the pressure loss detection and/or damage detection. When the monitoring system is initialized or recalibrated, for example after a reset switch has been activated by the driver in block  13  (in this context the tire pressure/the tire pressures should correspond to the setpoint value or values thereof), the dependencies of the dimensional variables e 1 , e 2 , e 3  and/or their ratios, for example the pressure loss detection variable DVE, between one another and/or on the vehicle velocity v and/or the temperature T are learnt in block  10 . The relationships between the variables can be modeled by a linear or nonlinear parametric model of the input variables or by a black box system such as a neural network. Dependencies can also be learnt by mean values in specific intervals of input variables. After the learning phase, at least one setpoint value DVE setp  of the pressure loss detection variable DVE is available for the monitoring of pressure loss. It is also possible for a plurality of setpoint values of the pressure loss detection variable DVE to be available if the pressure loss detection variable DVE is learnt, for example, in intervals of values of one variable (for example velocity v, temperature T and/or ratio e 1 /e 3 ). The pressure loss detection variable DVE depends here essentially only now on the tire pressure. In order to monitor the pressure loss, the current input variables are used in block  11  together with the learnt dependencies to obtain a current, compensated value DVE curr  of the pressure loss detection variable DVE. A pressure loss warning takes place in block  12  if the current pressure loss detection variable DVE curr  exceeds the corresponding, learnt value DVE setp  (for example with the same/similar value of the ratio e 1 /e 3 ) by a threshold value S: 
         [0000]      | DVE   curr   −DVE   setp   |&gt;S   (3)
 
         [0084]    The threshold value S may be permanently predefined or may have been determined from vehicle information. 
         [0085]    For example, the learning phase in block  10  is started by confirmation of a reset switch by the driver, but other starting conditions for a learning process are also conceivable. 
         [0086]    In the text which follows, an example of a method for compensating a variable, for example the pressure loss detection variable DVE (for example according to equation (1) or (2)), in terms of another variable Y, for example the temperature T or the ratio e 1 /e 3 , is described. In this context, a functional relationship g (for example a linear relationship), specifically the parameters of the assumed functional relationship g, is learnt by means of specific (X, Y) value pairs, which relationship g describes the changing of the variable X from a setpoint value X 0  and the interference influence Y and possible further variables: 
         [0000]        X=g ( X 0 ,Y , . . . ) 
         [0087]    For example, a linear relationship is set on the basis of the simple determinability by regression: 
         [0000]        X=X 0 +a*Y,    
         [0000]    wherein the parameters X 0  and a of the straight-line equation are determined, for example by fitting on the (X, Y) value pairs, in the learning phase  10 . The parameter X 0  then corresponds to the learnt comparison value (for example DVE setp ). 
         [0088]    For the purpose of compensation (for example in the comparison phase  11 ), the currently obtained variable X is compensated by the inverse function g −1 . For this purpose, for example the currently obtained variable X current  is compensated according to) X comp =X current −a*Y current  by means of the current variable Y current  and the learnt parameter a. 
         [0089]    According to a further exemplary embodiment of the method according to aspects of the invention, what is referred to as a basic compensation of the pressure loss detection variable DVE is predefined, and is stored, for example, in a control unit in the form of a predefined functional relationship between pressure loss detection variable DVE and influencing variables (for example temperature T, velocity v, one or more dimensional variables e 1 , e 2 , e 3 ) and corresponding predefined parameters of the functional relationship. This basic compensation is then optimized/improved in the learning phase. 
         [0090]    For example, the basic compensation (predefined parameters) is read in after a reset. In the subsequent learning phase, optimized values for the parameters of the functional relationship are learnt by fitting the functional relationship to obtained value combinations (for example (DVE, T, v, e 1 ) value combination). These optimized parameters are then used to compensate the pressure loss detection variable DVE in the comparison phase. 
         [0091]    According to one example, a functional relationship 
         [0000]        DVE   comp   =DVE   current   +a*T+b*v+c*v   2   +d*e 1 
         [0000]    is set, wherein the influencing variables temperature T, velocity v and dimensional variable e 1  are taken into account, and “starting values” are predefined for the parameters a, b, c and d. However, it is also conceivable to use a different functional relationship and/or to take into account a greater or lesser number of influencing variables. Improved values for the parameters a, b, c and d are then adapted in the learning phase. 
         [0092]    Instead of the ratios ei/ej specified in the examples, it is also possible in each case to consider the reciprocal value ej/ei. 
         [0093]    The method according to aspects of the invention permits wheel-specific detection of the tire pressure loss. 
         [0094]    The described method for evaluating dimensional variables is also suitable for detecting damage to the wheel suspension system. When the components of the wheel suspension system change, the energy ratios also change, which can be detected by means of the dimensional variables e 1 , e 2 , e 3  and/or their ratios. 
         [0095]    In order to detect pressure loss it is also optionally possible to carry out an evaluation of the position of one or more resonances, i.e. the values of the resonant frequencies f nat1 , f nat2 , f nat3 . For this purpose, for example the positions of the resonant frequency of the wheel vertical frequency and wheel torsional frequency are evaluated together. An air pressure loss is detected or a pressure loss detection of another pressure loss detection method is supported if both resonant frequencies are lower than their respective learnt setpoint values. 
         [0096]    According to a fifth exemplary embodiment, a method according to aspects of the invention based on a pressure loss detection variable DVE composed of two dimensional variables e 1 , e 2 , e 3  (for example DVE according to equation (1) or (2)) is combined with a pressure loss detection method based on the displacement of at least one resonant frequency (for example a pressure loss detection variable DVE corresponds to a resonant frequency). In this context, the pressure loss detection is carried out, in terms of its focus, by means of the pressure loss detection variable DVE of one or other method as a function of the vehicle velocity v and/or a value of a dimensional variables (or of a ratio between two dimensional variables). Since the frequency shift, in particular at relatively low velocities v, and the method according to aspects of the invention at relatively high velocities v supply reliable results, for example corresponding weighting of the individual methods and the results thereof as a function of the velocities v is performed and combined to form an overall result. 
         [0097]    In the text which follows, exemplary models are presented in order to describe and explain the torsional oscillation and the vertical dynamics of the tire, separately from one another. A separate consideration is possible since the two systems operate in different frequency ranges. 
         [0098]    In the text which follows, a model which describes the torsional oscillation is described first, said model giving rise to an exemplary movement equation.  FIG. 4  is a schematic illustration of a model of the wheel. The wheel is described by the moment of inertia of the rim J rim  and the moment of inertia of the tire belt J belt . The torsional spring constant between the belt and the rim is denoted by c. The rotational speed of the belt, which corresponds to the rotational speed of the circumference of the wheel, is described by the angular speed ω 2  and the rotational speed of the rim, which is measured, for example, with a wheel speed sensor, is described by the angular speed ω. The radius of the tire is denoted by R. 
         [0099]    The excitation moment M excitation  which acts on the belt is described according to the model by means of the following slip equation: 
         [0000]    
       
         
           
             
               M 
               excitation 
             
             = 
             
               a 
               · 
               R 
               · 
               
                 
                   v 
                   - 
                   
                     
                       ω 
                       2 
                     
                     · 
                     R 
                   
                 
                 v 
               
             
           
         
       
     
         [0100]    Here, α represents the increase in the wheel torque as a function of the change in the wheel slip. 
         [0101]    After the differential equations have been drawn up, the slip equation inserted and after transfer into the frequency range (Laplace transformation with the Laplace variable s), the following transfer function G is obtained between an excitation moment M excitation  which acts on the belt and an angular speed ω which can be measured by a wheel speed sensor (equation (4)): 
         [0000]    
       
         
           
             
               
                 
                   G 
                   = 
                   
                     ω 
                     
                       M 
                       excitation 
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     1 
                     
                       
                         
                           
                             
                               J 
                               rim 
                             
                             · 
                             
                               J 
                               belt 
                             
                           
                           c 
                         
                         · 
                         
                           s 
                           2 
                         
                       
                       + 
                       
                         
                           
                             
                               J 
                               rim 
                             
                             · 
                             
                               R 
                               2 
                             
                           
                           c 
                         
                          
                         
                           
                             α 
                             v 
                           
                           · 
                           
                             s 
                             2 
                           
                         
                       
                       + 
                       
                         
                           ( 
                           
                             
                               J 
                               rim 
                             
                             + 
                             
                               J 
                               belt 
                             
                           
                           ) 
                         
                         · 
                         s 
                       
                       + 
                       
                         
                           
                             R 
                             2 
                           
                            
                           α 
                         
                         v 
                       
                     
                   
                 
               
             
           
         
       
     
         [0102]    The moment of inertia of the rim J rim , of the belt J belt , the tire radius R and the spring constant c can be assumed to be constant for a vehicle without a change of tire and without a change in the tire pressure. The velocity v and the gradient of the torque/slip relationship α are variable during the journey. 
         [0103]    The values of s 3 , s 2  and s are obtained from the time derivatives of relatively high order of the angular speed ω, and can therefore be determined from the measured angular speed ω. 
         [0104]    The absolute value of the transfer function |G| of the system changes as a function of the frequency f (the torsional oscillation) with the varying quotient α/v. Depending on the quotient α/v, either a resonant frequency f nat2  occurs in the region of approximately 45 Hz, or else a resonant frequency f nat3  occurs in the region of approximately 75 Hz. 
         [0105]    In the boundary case α/v toward zero (i.e. high velocities v and/or smooth underlying surface), the following natural frequency of the system (high natural frequency f nat3 ) occurs: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     
                       nat 
                        
                       
                           
                       
                        
                       3 
                     
                   
                   = 
                   
                     
                       
                         
                           c 
                            
                           
                             ( 
                             
                               
                                 J 
                                 rim 
                               
                               + 
                               
                                 J 
                                 belt 
                               
                             
                             ) 
                           
                         
                         
                           
                             J 
                             rim 
                           
                           · 
                           
                             J 
                             belt 
                           
                         
                       
                     
                     
                       2 
                        
                       
                           
                       
                        
                       π 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0106]    For the other boundary case α/v toward the infinite, the natural frequency of the system is obtained as (relatively low natural frequency f nat2 ): 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     
                       nat 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   = 
                   
                     
                       
                         c 
                         
                           J 
                           rim 
                         
                       
                     
                     
                       2 
                        
                       
                           
                       
                        
                       π 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0107]    For small α/v, the high natural frequency f nat3  (approximately 75-80 Hz) occurs, and as α/v increases further the system enters a transition region before the lower resonant frequency f nat2  occurs as α/v rises even further (see also  FIG. 7  and associated description). 
         [0108]    For the consideration of the resonant amplitude for the relatively low natural frequency (f nat2 ), equation (4) is simplified for the boundary case α/v toward the infinite. This boundary case describes the customary driving situation for a high coefficient of friction and moderate velocities v. The transfer function G obtained is: 
         [0000]    
       
         
           
             
               
                 
                   
                     ω 
                     
                       M 
                       excitation 
                     
                   
                   = 
                   
                     
                       
                         c 
                         · 
                         v 
                       
                       
                         
                           J 
                           rim 
                         
                         · 
                         
                           R 
                           2 
                         
                       
                     
                     · 
                     
                       1 
                       
                         
                           s 
                           2 
                         
                         + 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     J 
                                     rim 
                                   
                                   + 
                                   
                                     J 
                                     belt 
                                   
                                 
                                 ) 
                               
                               · 
                               c 
                               · 
                               v 
                             
                             
                               
                                 J 
                                 rim 
                               
                               · 
                               
                                 R 
                                 2 
                               
                               · 
                               α 
                             
                           
                           · 
                           s 
                         
                         + 
                         
                           c 
                           
                             J 
                             rim 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0109]    The resonant amplitude A 2   max  is obtained with (equation (7) selected in accordance with k and d): 
         [0000]    
       
         
           
             
               
                 
                   
                     ω 
                     
                       M 
                       excitation 
                     
                   
                   = 
                   
                     
                       k 
                       · 
                       
                         1 
                         
                           
                             
                               
                                 J 
                                 rim 
                               
                               · 
                               
                                 s 
                                 2 
                               
                             
                             + 
                             
                               d 
                               · 
                               c 
                               · 
                               s 
                             
                             + 
                             c 
                           
                            
                         
                       
                     
                      
                     
                         
                     
                      
                     as 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     A 
                     max 
                     2 
                   
                   = 
                   
                     
                       2 
                       · 
                       
                         J 
                         rim 
                       
                     
                     
                       
                         c 
                         
                           3 
                           / 
                           2 
                         
                       
                       · 
                       d 
                       · 
                       
                         
                           
                             4 
                              
                             
                                 
                             
                              
                             m 
                           
                           - 
                           
                             
                               d 
                               2 
                             
                             · 
                             c 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0110]    When the tire pressure drops (pressure loss), the spring constant c is reduced and the resonant amplitude A 2   max  therefore becomes larger. This is illustrated schematically in the frequency range of f nat2  (approximately 40-60 Hz) in  FIG. 5 . 
         [0111]    In the text which follows, a model for describing and explaining the vertical dynamics of the tire, which gives rise to exemplary movement equations of the vertical oscillation, will be described with reference to  FIG. 6 . In the frequency spectrum of the wheel speed signal, a further resonant frequency f nat1  (approximately 15-20 Hz) can be seen, which resonant frequency can be explained by the vertical dynamics of the tire. For the considered frequency range of the wheel dynamics it is sufficient to consider the wheel mass m R  and the spring/shock absorber effect of the tire c R /d R . In the model used, the movement equation of the wheel (instantaneous deflection z R ) in the case of unevennesses of the road z s  is as follows, with the force F z  acting on the tire: 
         [0000]        m   R   {umlaut over (z)}   R   =c   R ( z   s   −z   R )+ d   R ( ż   s   −ż   R )  (10)
 
         [0000]        F   z   =c   R ( z   S   −z   R )  (11)
 
         [0112]    According to the physical law “force F z  times lever arm n”, the forces acting on the tire, which act on the tire via the rolling behavior and the geometry (for example of the wheel suspension system) of the section of road, give rise to a torque (J R : moment of wheel inertia): 
         [0000]    
       
      
       J 
       R 
       ·ω=F 
       z 
       ·n  
      
     
         [0113]    The following is obtained 
         [0000]    
       
         
           
             
               
                 
                   ω 
                   = 
                   
                     
                       
                         
                           m 
                           R 
                         
                         · 
                         
                           c 
                           R 
                         
                         · 
                         n 
                         · 
                         
                           J 
                           R 
                           
                             - 
                             1 
                           
                         
                         · 
                         s 
                       
                       
                         
                           
                             m 
                             R 
                           
                            
                           
                             s 
                             2 
                           
                         
                         + 
                         
                           
                             d 
                             R 
                           
                            
                           s 
                         
                         + 
                         
                           c 
                           R 
                         
                       
                     
                     · 
                     
                       z 
                       s 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0000]    and the resonant amplitude A 1   max : 
         [0000]    
       
         
           
             
               
                 
                   
                     A 
                     max 
                     1 
                   
                   = 
                   
                     
                       
                         m 
                         R 
                       
                       · 
                       
                         c 
                         R 
                       
                       · 
                       n 
                       · 
                       
                         J 
                         R 
                         
                           - 
                           1 
                         
                       
                     
                     
                       d 
                       R 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0114]    When the air pressure drops, c R  is reduced and the resonant amplitude A 1   max  therefore becomes smaller. 
         [0115]    It is clearly possible to state that the oscillation of the tire in the vertical direction (caused, for example, by the excitation of the road) is superimposed on the wheel speed ω owing to the lever arm (wheel castern). The vertical oscillation can therefore be observed in the wheel speed signal ω, to be more precise in the frequency spectrum of the wheel speed. 
         [0116]    In  FIG. 5 , exemplary frequency spectrums (absolute value of the transfer function G as a function of the frequency f) of a wheel speed signal are plotted for various tire pressures (a decrease in pressure is indicated by the arrows).  FIG. 5  verifies once more the relationship described above according to which when there is a pressure loss the resonant amplitude of the (vertical) wheel oscillation at f nat1  becomes smaller (and therefore the dimensional variable e 1 ), while the resonant amplitude of the torsional oscillation at f nat2  becomes larger (and therefore the dimensional variable e 2 ). 
         [0117]    An interference effect during an evaluation of the frequency spectrum is the dependence on the road excitation. The road excitation can be understood to be a further frequency spectrum which is superimposed on the system behavior. Two influences on the resonant amplitudes A 1   max , A 2   max , A 3   max  of the three natural frequencies follow from this:
       (a) The total level of the resonant amplitudes varies with the type of road.   (b) Unevennesses in a road can lead to increases or reductions in individual regions in the frequency spectrum.       
 
         [0120]    This leads to a dependence of the resonant amplitudes on the excitation. 
         [0121]    A further interference effect is the dependence on nonlinearities. The individual components of the wheel suspension system, such as a tire, shock absorber, spring or rubber bearing, typically have a nonlinear behavior. This means that they have a system behavior which is dependent on the working point. In particular, individual components can therefore assume different parameters during operation as a result of different road excitations. This leads to a further dependence of the resonant amplitudes on the excitation. 
         [0122]    A further interference effect is the dependence on the temperature. The properties individual components of the wheel suspension system are heavily dependent on the temperature. These include, in particular, the damping of the wheel and shock absorber, which are included directly in the equations of the resonant amplitudes. 
         [0123]    Furthermore, the dependence on the coefficient of friction (of the road), the loading (of the vehicle) and the velocity (of the vehicle) are to be taken into account. Changes in the coefficient of friction, loading and velocity directly influence the quotient α/v from equation (4). This changes the values of the resonant frequencies, in particular in the case of f nat2  and f nat3 , as already mentioned above. 
         [0124]    Exemplary changes in the resonant amplitudes A 1   max , A 2   max , A 3   max  of the three considered natural frequencies f nat1 , f nat2 , f nat3  in the event of a change in α/v are illustrated in  FIG. 7 . The uppermost curve  20  corresponds to a small value of α/v, and the bottom curve  21  corresponds to a large value of α/v. As can be seen, the resonant amplitude A 1   max  of the vertical oscillations at approximately 18 Hz (f nat1 ) is influenced only to a small degree, and the resonant amplitude A 2   max  of the torsional oscillations at 50 Hz (f nat2 ) is not influenced or is hardly influenced. However, the third resonance at approximately 80 Hz (f nat3 ) occurs with a greater or smaller resonant amplitude A 3   max  as a function of α/v. 
         [0125]    The torque/slip curve of a tire is dependent on the coefficient of friction μ and the wheel load Fz. Exemplary curves  40 ,  41 ,  42  of the torque M are shown schematically as a function of the slip Λ with a varying coefficient of friction μ and wheel load Fz in  FIG. 8 . The variable α represents the increase in the torque M as a function of the change in the slip Λ (Λ=(v−ω 2 R)/v), i.e. the variable α can be considered to be the gradient of a torque/slip curve at a (working) point (the dashed line  43  indicates a gradient α for curve  41 ). 
         [0126]    All the variables which change α have an influence on the transmission function G and the resonant frequencies which occur. 
         [0127]    A small coefficient of friction μ generally gives rise to a relatively small α (curve  40  in  FIG. 8 ). 
         [0128]    α changes as a function of the current working point (drive torque/braking torque) on the torque/slip curve. α generally drops at relatively high slip values Λ or torques M. 
         [0129]    An increased wheel load F z  (indicated by an arrow in  FIG. 8 ), for example due to a load, gives rise to an increasing α. 
         [0130]    The vehicle velocity v is included directly in a reciprocal fashion in α/v. 
         [0131]    It is apparent that a tire pressure loss can be detected by monitoring dimensional variables which are based on the resonant amplitude (for example spectral energy density or energy content). Furthermore, the various influences should preferably be compensated.