EP3504633A1

EP3504633A1 - Method and device for estimating force

Info

Publication number: EP3504633A1
Application number: EP17768178.0A
Authority: EP
Inventors: John-Jairo MARTINEZ-MOLINA
Original assignee: Institut Polytechnique de Grenoble
Current assignee: Institut Polytechnique de Grenoble
Priority date: 2016-08-25
Filing date: 2017-08-24
Publication date: 2019-07-03
Also published as: JP2019534997A; US11572122B2; JP6978490B2; WO2018037191A1; FR3055440B1; US20190188235A1; FR3055440A1

Abstract

The invention relates to a method for estimating a periodic or substantially periodic force present in a mechanical or electromechanical system, the method comprising: estimating, by a processing device, one or more harmonic frequencies of an acceleration signal representing an acceleration in the system, the substantially periodic force contributing to said acceleration; and estimating, by the processing device, the force on the basis of a dynamic model of the system, the dynamic model being defined by said one or more estimated harmonic frequencies.

Description

FORCE ESTIMATING METHOD AND DEVICE

The present patent application claims the priority of the French patent application FR16 / 57939 which will be considered as an integral part of the present description.

Field of the invention

The present description relates to the field of force estimation methods and devices, and in particular to methods and devices for estimating a force in a mechanical or electromechanical system.

Presentation of the prior art

In some areas it would be desirable to be able to estimate one or more variable forces that influence the system. For example, in the case of a motor-assisted bicycle, it might be desirable to be able to estimate the force exerted by the cyclist. Similarly, in the case of a wind turbine, it may be desirable to be able to estimate the force generated by the wind.

In the case of motor-assisted bicycles, it has been proposed to use a torque or power sensor to detect the force exerted by each foot of the cyclist. Such torque or power detectors are based on the detection of a mechanical deformation, for example the torsion of the shaft in the pedal shaft. It has also been proposed to provide force detectors in the pedals of the bicycle. However, a disadvantage of such solutions is that their accuracy is generally affected by temperature variations and aging of the materials used, which means that frequent calibration is usually necessary. In addition, such detectors add weight to the structure and are relatively expensive to install.

There is therefore a need in the art for a force estimation method and device that solves some or all of the aforementioned disadvantages.

summary

An object of embodiments of the present description is to at least partially meet one or more needs of the prior art.

According to one aspect, there is provided a method for estimating a periodic or substantially periodic force present in a mechanical or electromechanical system, the method comprising: estimating, by a processing device, one or more harmonic frequencies of a signal of acceleration representing an acceleration in the system, the substantially periodic force contributing to said acceleration; and estimating, by the processing device, the force based on a dynamic model of the system, the dynamic model being defined by said one or more estimated harmonic frequencies.

According to one embodiment, the dynamic model is updated based on an error signal representing the difference between a captured velocity signal and an estimated velocity signal.

According to one embodiment, the method further comprises generating an acceleration signal based on a time differential calculation for two or more values of a speed signal representing an angular or linear velocity in the system. According to one embodiment, the estimation of said one or more harmonic frequencies of the acceleration signal involves the calculation of an error signal equal to:

where r (k) is a current acceleration value, and is a

estimation of vector-based acceleration representing the harmonic frequencies and a vector φ representing one or more preceding acceleration values.

According to one embodiment, the mechanical or electromechanical system is a motor-assisted bicycle, and the periodic or substantially periodic force is the pedaling force generated by the cyclist, and the dynamic model comprises one or more of the estimates. where each of these estimates is defined as follows:

where Ts is the sampling period, M is the mass of the cyclist and the bicycle, F _M is the force generated by the engine, and represent one of the harmonic frequencies, is the estimate of the force exerted by the cyclist, and is an estimate of other forces in the system.

According to one embodiment, the mechanical or electromechanical system is a wind turbine, and the periodic or substantially periodic force is a periodic component of the wind force on the blades of the wind turbine, and the dynamic model includes one or more of the estimates. and where each of these estimates is defined as follows:

where Ts is the sampling period, represent one of the harmonic frequencies, is the estimate of the force exerted by the wind, and is an estimate of other forces in the system, where ω _τ is the speed of the turbine, and is an estimate of the speed of the turbine, I is the inertia of the turbine, is the torque applied by the generator, equal for example to where Ke is the constant

engine speed and is the current generated by the generator, and represents the total torque generated by the wind, representing a cyclical component of this couple.

According to one embodiment, the one or more harmonic frequencies comprise at least one of the fundamental frequency, the first harmonic frequency, the second harmonic frequency and the third harmonic frequency.

According to another aspect, there is provided a processing device arranged to estimate a periodic or substantially periodic force present in a mechanical or electromechanical system, the processing device being arranged to: estimate one or more harmonic frequencies of an acceleration signal representing an acceleration in the system, the substantially periodic force contributing to the acceleration; and estimating the force based on a dynamic model of the system, the dynamic model being defined by said one or more estimated harmonic frequencies.

Brief description of the drawings

The foregoing and other objects and advantages will become apparent with the following detailed description of embodiments, given by way of illustration and not by way of illustration. limitation, with reference to the accompanying drawings, in which:

Figure 1 illustrates a bicycle assisted by a motor according to an embodiment of the present description;

FIG. 2 diagrammatically represents a force estimation system according to an exemplary embodiment;

FIG. 3 is a flowchart illustrating steps in a force estimation method in a mechanical or electromechanical system according to an exemplary embodiment;

FIG. 4 is a graph showing frequency components of an acceleration signal according to an exemplary embodiment;

FIG. 5 schematically illustrates a force estimation method in a mechanical or electromechanical system according to an exemplary embodiment;

Figure 6 schematically illustrates a part of the method of Figure 6 in more detail according to an exemplary embodiment;

Fig. 7 is a flowchart showing in more detail steps in the method of Fig. 3 according to an example embodiment;

Fig. 8A is a graph illustrating an acceleration signal and a resultant force according to an exemplary embodiment;

Fig. 8B is a graph illustrating an acceleration signal and a dynamic constraint according to an exemplary embodiment;

Figure 9 schematically illustrates a computing device according to an exemplary embodiment; and

FIG. 10 illustrates a wind turbine according to an exemplary embodiment.

detailed description

The embodiments described herein relate to a method and apparatus for estimating a periodic force. or substantially periodically in a mechanical or electromechanical system. The term "periodic force" is used herein to refer to a force that is, at least within certain limits, of a cyclic nature. For example, the force exerted by a cyclist on the pedals of a bicycle is periodic since the force will generally result from the downward thrust applied by the cyclist's foot when each pedal reaches a certain range of angular position in its cycle. rotation. There are other mechanical or electromechanical systems in which a periodic or substantially periodic force is present and can be estimated by the techniques described herein. For example, the present inventor has discovered that the force exerted by the wind on the blades of a wind turbine generally has a periodic or substantially periodic component which can be estimated, as will be described in more detail below. Those skilled in the art will know other applications in which a periodic or substantially periodic force could be estimated according to the techniques described here, such as the force exerted on a train by a rower, or waves on a boat.

Figure 1 illustrates a bicycle 100 assisted by a motor according to an exemplary embodiment. The bicycle 100 comprises, for example, an electric motor 102. In the example of FIG. 1, the motor 102 is for example a roller motor pressing on the tire mounted near the bottom axle 103, so that the motor apply a force directly to the tire of the rear wheel. In alternative embodiments, the motor 102 could apply a force to the crank axle 103, or could be mounted elsewhere, such as on the hub of the front or rear wheel. The motor 102 is for example an electric motor powered by a battery 104, which is for example mounted on a luggage rack disposed above the rear wheel of the bicycle. In alternative embodiments, the battery 104 could be mounted elsewhere on the bicycle. The motor is for example controlled by a computer 106, which is for example mounted on the handlebars of the bicycle, although here again it could be mounted elsewhere. The computer 106 allows for example the cyclist to select the level of assistance provided by the engine.

The computer 106 is for example adapted to estimate the useful force exerted by the cyclist. The useful force is, for example, the force that leads to an acceleration of the bicycle, and excludes, for example, certain components of the force that are lost due to friction, etc. The useful force will generally correspond to the torque applied to the pedal axle 103 from the pedal cranks. In some embodiments, the computer 106 includes a display, and is adapted to display an indication of the estimated force.

In addition or instead, the computer 106 is for example adapted to control the motor 102 on the basis of the estimated force. For example, the level of assistance provided by the motor 102 is controlled so that the overall acceleration of the bicycle remains relatively constant, for example in a range of 10% around the average value. In other words, the engine is for example controlled to provide greater assistance between the cyclist's pedal strokes. Alternatively, the computer 106 may be adapted to control the motor 102 in a different manner on the basis of the estimated force, for example to provide a level of assistance that is proportional or inversely proportional to the estimated force.

FIG. 2 schematically illustrates a force estimation system 200 according to an exemplary embodiment. The system 200 is for example partially implemented by the computer 106, and partially implemented by detectors and sensors described in more detail below.

The system 200 comprises, for example, a motor force detector (MOTOR FORCE DETECTOR) 202, which for example provides a signal F _M indicating the force applied by the motor at a given instant. The system 200 also comprises, for example, a pedaling sensor (PEDALLING SENSOR) 204, which provides a signal <Bp indicating the angular velocity of the pedal cranks. This signal can for example be used to determine the speed In addition to or instead of the pedaling sensor, a wheel speed sensor (WHEEL SPEED SENSOR) 206 is for example provided and generates a signal <* ¾ indicating the speed of the bicycle. of the invention, the signal <* ¾ indicating the speed of the bicycle could be provided directly by the motor, in which case the wheel speed sensor could be omitted, the signal <* ¾ is for example composed of digital samples and comprises minus five samples for each complete rotation of a pedal crank, and preferably at least seven samples for each complete rotation of a pedal crank.

The system of 200 further comprises an estimator of unknown forces (UNKNON FORCE ESTIMATOR) 208, implemented for example by the computer 106, and adapted to estimate an unknown force F in the system, this force corresponding to the useful force exerted by the cyclist. The estimator 208 receives, for example, the signal F _M and an indication of the mass (MASS) of the bicycle and the cyclist. In some embodiments, the mass is provided by a mass estimator (MASS ESTIMATOR) 210, which for example receives the force of the motor F _M from the motor force sensor 202, and also the speed of the bicycle ¾, and estimates the mass based on these parameters while the cyclist is not pedaling. Alternatively, the mass can be obtained by an information input provided by the user.

In some embodiments, the unknown force estimator also receives a pedaling speed signal a> p from the pedal sensor 204 and / or a bicycle speed signal <* ¾ from a speed sensor. wheel. The estimator 208 also receives, for example, a biased cyclist force F _C from a previous force calculation, which is used as the basis for calculating a next force value during a next iteration, as described further in detail below. The unknown force estimator 208 provides, for example, an estimate F of the effective force generated by the cyclist in the system, which contributes to the acceleration of the bicycle.

A generator of cinematic constraints (KINEMATIC

CONSTRAINTS) 212 receives, for example, the estimated forces F and the pedaling speed <¾>, and generates a biased cyclist force F _C , which is supplied on a feedback path to the unknown force estimator 208. The force signal For example, a bias cyclist F _C is also supplied to a cyclist power estimator (CYCLIST POWER ESTIMATOR) 214, which also receives, for example, the speed of the bicycle <* ¾, and generates the estimated power of the cyclist. In particular, it will appear

clearly to those skilled in the art that, while in the described embodiments a cyclist force is estimated, in some embodiments this force could be expressed as a power value, equal to the multiplied force by the distance in time. For example, in some embodiments the wattage can be obtained by the following equation:

where v (k) is the speed of the bicycle, and is the estimated useful strength of the cyclist.

Alternatively, rather than being expressed as a linear force, the force exerted by the cyclist could be expressed as a torque. For example, the torque in Nm can be obtained by the following equation:

In yet another example, the acceleration in m / s ² generated by the cyclist could be obtained by the following equation: where M is the mass of the cyclist and the bicycle.

Of course, in some embodiments, the engine could be shut down, so that the force of the motor F _M remains zero.

FIG. 3 is a flowchart illustrating steps in a method of determining the strength of a cyclist on an engine-assisted bicycle, such as bicycle 100 of FIG. 1. The method is for example implemented by the computer 106.

In a step 301, a reading of the speed v (k) of the bicycle is for example obtained. In some embodiments, this rate may be generated based on the signal <* ¾ from a wheel speed sensor or other input. Alternatively, the speed v (k) can be calculated on the basis of a reading of the engine speed C0MOTOR 'in radiants per second, and on the basis of the engine radius Rm, with for example

In a step 302, an acceleration value a (k) is calculated on the basis of the speed value, for example by a differential calculation on the speed signal over time.

In a step 303, the frequency of one or more harmonics of the acceleration signal a (t) is for example determined. The term "harmonic" is used to designate a fundamental frequency and / or the first, second, third, etc., harmonic frequencies. In an embodiment described in more detail below, the harmonic frequencies are determined on the basis of an iterative algorithm.

Fig. 4 is a graph illustrating an example of the amplitudes of frequency components of the acceleration signal. The frequency axis has, for example, the normalized frequency in the form of fractions of the sampling frequency 1 / Ts, where Ts is the sampling period. In one embodiment, the sampling frequency is 20 Hz, and so the sampling period Ts is 50 ms. More generally, the sampling frequency is for example between 10 and 50 Hz.

In the example of FIG. 4, the harmonic frequencies correspond to peaks of the frequency distribution curve, referenced 402, 404 and 406, which are, for example, respectively approximately 3, 5 and 9 Hz. There is also by for example a DC component, DC, of the acceleration signal represented by a peak 408 at 0 Hz. The step 303 of FIG. 3 involves, for example, the estimation of the frequency of one or more of the harmonics 402, 404 , 406.

Referring again to FIG. 3, in a step 304, a pattern is generated for the forces present in the bicycle system, based on the harmonic frequencies. This model includes a strength component .

In a step 305, the force component is extracted from the model to obtain the estimate of the useful force exerted by the cyclist.

In some embodiments, another step 306 involves determining an ERROR error value associated with the estimated force. .

Fig. 5 is a block diagram showing the steps

302 to 305 of Figure 3 in more detail.

Block 502 in FIG. 5 represents the implementation of steps 302 and 303 of FIG. 3. Block 502 receives the speed value v (k), and calculates, on the basis of a model of a transfer function. harmonics updated on the basis of the speed value v (k).

A block 504 in FIG. 5 represents the implementation of the steps 304, 305 and 306 of FIG. 3. The block 504 receives the speed value v (k), the harmonics generated by the block

502, and the force of the motor The force of the motor F _M can for example be determined on the basis of the speed constant of the motor Ke and a measurement of the current I supplied to the motor. In particular, the force of the motor is for example generated on the basis of the engine torque ¾, equal for example to Ke * I, where Ke is the motor speed constant and I is the current. The force of the motor F _M is, for example, equal to ¾ / Rm, where Rm is the radius of the motor, in the case of a roller motor on a tire, like the motor 102 of FIG. 1. The block 504 generates by example an estimate of the useful force exerted by the cyclist. In

In some embodiments, block 504 further generates an error value ERROR indicating a margin of error of the force estimate.

Figure 6 illustrates the block 504 of Figure 5 in more detail according to an exemplary embodiment.

A dynamic model (DY AMIC MODEL) 606 receives, for example, the force of the motor Fj ^ k), the harmonic frequencies and an error value obtained by subtracting from the speed value v (k) an estimate speed. Block 606 for example provides an updated dynamic model Xe (k). Block 608 represents the extraction from the dynamic model Xe (k) of the force estimate .

Another block 610 represents the determination of the error associated with the force estimation.

Fig. 7 is a flowchart showing the method of Fig. 3 in more detail according to an example embodiment.

After step 301 in which the speed value v (k) is read, step 302 involves for example the calculation of the acceleration value a (k) as a value ώ _Ρ (k) based on the pedal speed value. For example, the value

pedal acceleration is calculated by the following equation:

where is a previous value of the pedal speed, and

Ts is the sampling period, for example equal to the time period between samples of the

pedal speed. Course, rather than being based on pedal speed in alternative embodiments the value

acceleration a (k) could be calculated on the basis of another speed signal.

Steps 703 to 705 of FIG. 7 implement step 303 of FIG. 3, involving finding one or more harmonics of the acceleration signal.

Step 703 involves for example the calculation of a vector φ in the form [r (k-1); r (k-2)], where and

Step 704 involves for example the calculation of an error value ei (k) and a parameter L (k).

The error value ei (k) is for example based on the following formula:

or is for example a vector representing an estimate of the harmonic frequencies and which is initialized to zero, and is an estimate of the acceleration.

The parameter L (k) is for example based on the following formula:

where FF is a forgetting factor, for example equal to 0.95, and P (k) is a matrix which is for example initialized to a certain value, for example to a value of:

and is recalculated for each new iteration by the following formula:

In a step 705, a harmonic vector is for example generated on the basis of the following formula:

For example, in the case of a single harmonic, harmonic vector for example the following form

where is the frequency of the harmonic, for example in the form f being the frequency of the harmonic, and represents the quality factor of the harmonic, which is for example close to 1.

Step 304 involves, for example, substeps 706 and 707. In these steps, a dynamic model Xe representing the bicycle system is, for example, modified on the basis of the last speed value v (k). For example, the dynamic model is based on the following equation for the driving force of the bicycle:

where represents the strength exerted by the cyclist and represents other forces contributing to overall strength on the bicycle, such as wind, terrain, etc. On the basis of this equation, the dynamic model following Xe can for example be defined as being a vector having the following components:

where are defined in the way

The matrix Ad (k) is for example calculated on the basis of the following formula:

where Ts is the sampling period, and M is the mass of the bicycle and the cyclist.

The vector Ld (k) is for example calculated on the basis of the following formula:

where Cd is for example the vector [1 0 0 0], and Vd is a constant representing the expected covariance of the speed measurements.

The vector P2 (k + 1) is for example calculated on the basis of the following formula:

where Wd is a constant matrix representing the expected covariance of process perturbations, ie the covariance of exogenous forces.

In a step 707, the vector Xe (k + 1) is for example calculated on the basis of the following formula:

where e _{2 (} kk) is an error value equal to is

an estimate of the speed v (k).

In a step 305, the force exerted by the cyclist is extracted, corresponding for example to the third element Xe (3) of the vector Xe. Additionally, other forces can be extracted, these corresponding for example to the second element Xe (2) of the vector Xe.

Step 306 involves, for example, determining an error value associated with the estimated force, as shown by block 610 in Figure 6. The error value is for example determined on the basis of the following equation for an error vector ERROR of the vector Xe:

The error value is, for example, extracted as the third ERROR element (3) from the ERROR vector. In some embodiments, the magnitude of the error value is then compared to a permissible level, to decide if the force estimate is accurate enough to be useful. For example, the following operation is implemented:

where ε is the allowable level, for example equal to a value between 2 and 10 percent, and in some embodiments between 2 and 5 percent.

Optionally, in a step 708, the motor of the bicycle is controlled on the basis of the estimated force, if for example the estimated force is determined in step 306 as permissible.

Fig. 8A is a graph including a curve 802 showing an example of the estimated acceleration produced by the cyclist before considering the constraints. Dotted lines 804 and 806 respectively represent the maximum and minimum accelerations produced by gravity, assuming a road gradient of not more than 20 percent. Curves 808 and 810 represent other constraints, calculated for example by the module 212 of Figure 2 in real time. In particular, the curve 808 represents the maximum acceleration produced by the weight of the cyclist on the pedals, this signal falling for example to zero during periods in which the cyclist stops pedaling. Curve 810 represents, for example, the maximum acceleration in the presence of aerodynamic losses.

Fig. 8B is another graph illustrating the constraints 804, 806, 808 and 810 of Fig. 8A, and illustrating in addition, a curve 812 representing the forced force F _C after having taken into account the constraints. In particular, curves 804, 808 and 810 represent maximum stress values Cmax (t), while curve 806 represents a minimum stress value Cmin (t).

The force F _C is for example equal to the force of the estimated non-stressed cyclist F if none of the constraints is exceeded, for example since Cmin (t) <= F <= Cmax (t). Alternatively, if F <Cmin (t), F _C is for example equal to Cmin (t), and if F> Cmax (t), F _C is for example equal to Cmax (t).

FIG. 9 schematically illustrates a computer 900 arranged to implement the method of FIG. 3 and / or FIG. 7 to calculate a cyclist force, and which corresponds, for example, to the computer 106 of FIG.

The computer 900 comprises, for example, a processing device (P) 902 comprising one or more processors under the control of instructions stored in an instruction memory (Instruction Memory) 904. An input interface (I / O INTERFACE) 906 makes it possible, for example, to introduce into the processing device 902 readings from different measuring devices, for example from the electric motor, and / or from a separate speed sensor. A memory (MEMORY) 908 stores for example the various parameters, vectors and matrices described above for the implementation of the method.

Rather than being used to calculate an estimate of the force exerted by a cyclist, in an alternative embodiment, the methods of FIGS. 3 and 7, and the device of FIG. 9, could be applied to estimate the force exerted by the cyclist. wind on the blades of a wind turbine, as will now be described in more detail with reference to Figure 10.

Figure 10 illustrates an example of a wind turbine 1000, comprising two or more blades 1002 coupled to an axis 1004, which in turn is coupled to an electricity generator 1006. Among the equations 1 to 5 indicated above and representing the dynamic model of the forces on the bicycle, the equations 1, 2 and 5 remain unchanged, for example, whereas the equations 2 and 3 are for example replaced by the following equations 1 ', 2 'and 3':

where ω _τ is the speed of the turbine, and is an estimate of the speed of the turbine, Ts is the sampling period, I is the inertia of the turbine, is the torque applied by the generator, equal for example to where Ke is the engine speed constant and is the current generated by the generator, and represents the total torque generated by the wind, representing a cyclical component of this couple. The speed of the turbine ω _τ is for example detected by a speed sensor located on the main shaft of the turbine and / or by using a generator speed measurement, based for example on rotation encoders.

The speed of the generator depends on both the torque produced by the wind and the torque produced by the generator, which is proportional to the electric current from the generator. In some embodiments, estimating the torque produced by the wind can be used to control the speed of the generator by controlling the current level ^An advantage of controlling the generator torque in this manner is that cyclic fluctuations in the speed of the blades 1002 can be avoided, thus avoiding or reducing the risk of damaging the turbine.

An advantage of the embodiments described herein is that a periodic or substantially periodic force in a mechanical or electromechanical system can be estimated substantially in real time and with relatively high accuracy in a relatively simple manner. With the description thus made of at least one illustrative embodiment, various alterations, modifications and improvements will readily occur to those skilled in the art. For example, although a particular example of a dynamic model is given by the aforementioned equations 1 to 5, it will be apparent to one skilled in the art that modifications could be made to these equations, for example to take account of additional forces present in the system, and that the equations could be adapted to other applications than the bicycle and wind turbine examples described here.

Claims

A method for estimating a periodic or substantially periodic force present in a mechanical or electromechanical system, the method comprising:

estimating, by a processing device, one or more harmonic frequencies of an acceleration signal representing an acceleration in the system, the substantially periodic force contributing to said acceleration; and estimating, by the processing device, the force based on a dynamic model of the system, the dynamic model being defined by said one or more estimated harmonic frequencies.

The method of claim 1, wherein the dynamic model is updated on the basis of an error signal (e2 (k)) representing the difference between a captured velocity signal (v (k)) and a estimated speed signal .

The method of claim 1 or 2, further comprising generating an acceleration signal based on a time differential calculation for two or more values of a speed signal representing an angular velocity or linear in the system.

The method according to any one of claims 1 to 3, wherein estimating said one or more harmonic frequencies of the acceleration signal involves computing an error signal equal to:

where r (k) is a current acceleration value, and is an estimate of vector-based acceleration representing the harmonic frequencies and a vector φ representing one or more preceding acceleration values.

The method of any one of claims 1 to 4, wherein the mechanical or electromechanical system is a motor-assisted bicycle, and the periodic or substantially periodic force is the pedaling force generated by the engine. cyclist, and in which the dynamic model includes one or more estimates where each of

these estimates are defined as follows:

6. A method according to any one of claims 1 to 4, wherein the mechanical or electromechanical system is a wind turbine, and the periodic or substantially periodic force is a periodic component of the force of the wind on the blades of the wind turbine, and wherein the dynamic model includes one or more of the estimates where each of these estimates is defined as follows:

where Ts is the sampling period, represent one of the harmonic frequencies, is the estimate of the force exerted by the wind, and is an estimate of other forces in the system, where ω _τ is the speed of the turbine, and is an estimate of the speed of the turbine, I is the inertia of the turbine, is the torque applied by the generator, equal for example to where Ke is the engine speed constant and is the current generated by the generator, and represents the total torque generated by the wind, representing a cyclical component of this couple.

The method according to any one of claims 1 to 6, wherein the one or more harmonic frequencies comprise at least one of the fundamental frequency, the first harmonic frequency, the second harmonic frequency and the third harmonic frequency.

8. Treatment device arranged to estimate a periodic or substantially periodic force present in a mechanical or electromechanical system, the treatment device being arranged for:

estimating one or more harmonic frequencies of an acceleration signal representing an acceleration in the system, the substantially periodic force contributing to the acceleration; and

estimating the force based on a dynamic model of the system, the dynamic model being defined by said one or more estimated harmonic frequencies.