Field of invention

The present invention relates to a method and to an arrange- ment for estimation of rotor speed, azimuth and rotation di- rection of a rotating rotor of a wind turbine and further re- lates to a wind turbine comprising the arrangement.

Art Background

A wind turbine may comprise a wind turbine tower, a nacelle mounted on top of the wind turbine tower, wherein the nacelle harbors a main rotor shaft at which plural rotor blades are mounted and which is coupled to an electric generator which generates electric energy upon rotation of the main rotor.

The determination of rotor operational characteristics, such as rotor speed, rotor azimuth and rotation direction may be necessary for properly controlling the wind turbine. For de- termination of the rotor operational characteristics one or more sensors may be installed at different locations of the wind turbine. Conventional methods and arrangements for esti- mating rotor operational characteristics often make use of proximity sensors that generate digital pulses when they de- tect a passing target. Methods and arrangements that use proximity sensors encounter various obstacles that compromise their accuracy and robustness. For example, some methods are only capable of producing estimates for one rotor operational characteristic, namely the rotational speed, whereas other characteristics necessary for proper control of the wind tur- bine, such as rotor azimuth and direction of rotation, must be estimated using an alternative method based around differ- ent sensing hardware. Methods using proximity sensors often require parts to be es- pecially fabricated with high precision to serve as targets for detection by the sensors, which can add a non negligible cost to the turbine. Since the pulse trains generated by proximity sensors are directly related to the size and spac- ing of the detection targets, methods that do not account for potential imperfections in the fabrication of the targets have difficulty providing accurate estimates of rotor opera- tional characteristics when machining tolerances have not been met. Moreover, sensors can be placed such that they are misaligned with the targets or, in arrangements that use mul- tiple sensors, misaligned with each other enough to compro- mise the reliability of the measurements. In addition, vibra- tions of the wind turbine and/or the components to which the sensors and targets are mounted can vary the alignment be- tween the sensors and targets enough to produce erroneous pulses or to miss pulses, resulting in inaccurate estimates of the rotor operational characteristics.

Methods normally do not use all the information available from the pulse trains generated by the sensors. In particu- lar, methods are often based around the timing or counting of one of the edges of the pulses (i.e., either the rising or the falling edge) when a second edge is also available for detection and can be employed to algorithmically compensate for uncertainties in sensor properties. Moreover, methods that make use of only a single sensor lack measurement redun- dancy, which can be leveraged to detect sensor faults (e.g., missed pulses or erroneous pulses), increase sampling rates, and reduce sensitivity to vibrations, sensor specifications, sensor placement, target fabrication quality, etc.

Thus, there may be a need for a more robust method and an ar- rangement for estimation of rotor operational characteris- tics, in particular rotor speed, rotor azimuth and rotation direction of a rotating rotor of a wind turbine that uses proximity sensors, and there may be a corresponding need for a wind turbine comprising the arrangement. The need may be satisfied by the subject-matter of the inde- pendent claims. The dependent claims specify particular em- bodiments of the present invention.

Summary of the Invention

According to an embodiment of the present invention, it is provided a method of estimation of rotor operational charac- teristics, in particular rotor speed, rotor azimuth and rota- tion direction, of a rotating rotor of a wind turbine, the method comprising: measuring pulse rising edge time and pulse falling edge time of pulses generated by each of multiple proximity sensors originating from each of multiple detection targets arranged on the rotor; estimating values of parame- ters associated with the sensors and/or targets, in particu- lar parameters associated with the positioning and/or detec- tion range of at least one sensor and/or parameters associat- ed with the positioning and/or size of at least one target, based on the measured pulse rising edge times and pulse fall- ing edge times; estimating rotor operational characteristics, in particular a rotor speed and/or a rotor azimuth and/or a rotation direction, based on the measured pulse rising edge times and pulse falling edge times and the estimated values of parameters associated with the sensors and/or targets.

Estimation of the rotor operational characteristics and un- known parameters associated with the sensors and/or targets may be implemented partly in software and/or hardware. The method may be executed by a wind turbine controller, in par- ticular a module or particular unit of the wind turbine con- troller. Thereby, the controller may receive measurement re- sults as obtained from the multiple proximity sensors. The controller may process the measurement results in order to estimate the rotor operational characteristics.

A proximity sensor may be mounted at any portion of the wind turbine which is stationary relative to the rotating rotor. In particular, multiple proximity sensors may be mounted at different azimuthal positions. Moreover, some of the proximi- ty sensors may have same, some may have different radial po- sitions .

The multiple detection targets may at least partly be formed by holes which are comprised in a conventional rotor or which are at least not especially fabricated. The proximity sensor may also detect the presence of a hole which is surrounded by material, since the hole, i.e. absence of target material, will cause an interruption in the detection of the surround- ing target material. Thus, at least some of detection targets may be formed by missing target material surrounded by target material. The multiple detection targets may be positioned at different azimuthal positions. Some of the targets may have same, some may have different radial positions.

When one of the multiple detection targets approaches one of the proximity sensors, the respective sensor may output a pulse comprising a rising edge and a falling edge. The pulse may be characterized by the point in time when the rising edge occurs, i.e. the pulse rising edge time, and also the point in time when the falling edge occurs, i.e. the pulse falling edge time. The pulse rising edge time and/or the pulse falling edge time of pulses generated by each of the multiple proximity sensors originally originating from multi- ple detection targets arranged on the rotor may depend on the rotor speed, rotor azimuth and rotation direction. Thus, these pulse rising edge times and pulse falling edge times may be suitable to derive therefrom the rotor operational characteristics, in particular rotor speed, rotor azimuth and rotation direction.

According to an embodiment of the present invention, the de- tection targets are not necessarily regularly positioned to a high precision, but may have positional tolerances, for exam- ple within as much as 1% or more of the intended azimuthal and/or radial placement. Generally, the multiple detection targets may be arranged at plural different azimuthal posi- tions around the entire circumference of the rotor. When pre- existing holes or recesses are employed as at least some of the multiple detection targets, these do not need to be ma- chined especially for the purpose of estimation of rotor op- erational characteristics. Thereby, costs of producing or manufacturing the rotor may be reduced.

The method may also be capable of estimating and compensating for inaccuracies or uncertainties in the positionings of the multiple detection targets and/or the multiple proximity sen- sors, and/or in the detection ranges of the sensors. Further- more, the multiple detection targets may not all be arranged or mounted at a same radial position (as measured from a ro- tation axis of the rotor) but may also comprise in the radial direction different radial positions. The same may hold for the multiple proximity sensors. However, approximative posi- tions of the multiple proximity sensors as well as approxima- tive positions of the multiple detection targets may be pre- known and utilized by the method for estimation of the rotor operational characteristics.

When plural proximity sensors are utilized to detect plural detection targets, the reliability of the method may be im- proved. Furthermore, there may be less strict requirements regarding the exact positioning of the detection targets and/or the proximity sensors. Thereby, costs of the arrange- ment and the measurement equipment and the rotor may be re- duced.

Embodiments of the present invention provide a cost- effective, algorithmically sophisticated proximity-based so- lution which is feasible to provide measurements of rotor speed, azimuth, and direction of rotation, that is less sen- sitive to vibrations, sensor specifications, and machining tolerances than conventionally known methods. According to an embodiment of the present invention, the es- timating the rotor speed and/or the rotor azimuth and/or the rotation direction is further based on sensor positioning pa- rameters of at least one sensor and/or a sensor detection range of at least one sensor and/or target positioning param- eters and/or target size parameters of at least one target, in particular based on target diameters and/or target angular size of at least one target, and/or target relative angular spacing of at least one pair of targets, and/or sensor-target radial distance of at least one pair of sensor and target, and/or a sensor detection angular range of at least one sen- sor, and/or sensor relative angular spacing of at least one pair of sensors.

The sensor positioning parameters may comprise parameters re- garding an azimuthal and/or radial and/or axial position of the respective sensor. The sensor detection range of at least one sensor may define a sensor viewing range or area. The target position parameters may comprise parameters regarding the radial and/or azimuthal and/or axial position of the re- spective target. The target size parameters may for example comprise parameters regarding a radial size (radial extension for example) and/or an azimuthal extension (for example given in degrees) of the respective target.

For example, the difference between a pulse rising edge time and a pulse falling edge time of a pulse detected by one sen- sor originating from a particular target may be dependent on the target azimuthal extent as well as on the rotor speed. Furthermore, this difference may be dependent on the sensor detection angular range, i.e. for example the azimuthal range over which the considered sensor is capable to detect a tar- get. At least rough or approximative values of the sensor po- sitional parameters and/or the target positioning parameters and/or the target size parameters may be pre-given or pre- known and may be utilized by the method. According to an embodiment of the present invention, the method further comprises estimating the sensor positioning parameters of at least one sensor and/or a sensor detection range and/or the target positioning parameters and/or the target size parameters of at least one target based on the measured pulse rising edge times and pulse falling edge times, wherein estimating the unknown parameters and/or rotor operational characteristics may be based on a measurement model, in particular a mathematical model relating the meas- ured pulse rising edge times and pulse falling edge times to the rotor operational characteristics and/or the parameters associated with the sensors and/or targets.

As has been stated above, the exact sensor positioning param- eters and/or sensor detection ranges and/or target position- ing parameters and/or target size parameters may be unknown when the method is started. However, the values of these pa- rameters may be estimated based on the redundant measurement of pulses by multiple sensors originating from multiple de- tection targets. For example, a particular detection target may be measured by the multiple proximity sensor in a redun- dant manner, allowing to deduce or derive the values of the sensor positioning parameters and/or sensor detection ranges and/or target positioning parameters and/or target size pa- rameters .

The model may be represented by a set of equations relating the unknown parameters and rotor operational characteristics to the measured rising times and falling times. The set of equations may be solved by the method of least squares, in particular in a recursive manner, in particular by an itera- tion.

According to an embodiment of the present invention, estimat- ing the rotor speed and/or the rotor azimuth and/or the rota- tion direction and/or the values of parameters, in particular specifically for each of the sensors and/or targets, includes applying an adaptive filter to the measurement model relating these quantities to the measured rising times and falling times.

After the values of the parameters have been estimated, the respective parameters may be updated to new sensor position- ing parameters and/or new sensor detection ranges and/or new target positioning parameters and/or new target size parame- ters which may then be utilized in the method further on. Thereby, the estimation of the rotor operational characteris- tics may be compensated for the uncertainties in the arrange- ment of sensors and/or targets. Thereby, the accuracy or re- liability of the estimation of the rotor operational charac- teristics may be improved.

According to an embodiment of the present invention, the es- timation of the rotor speed and/or the rotor azimuth and/or the rotation direction and/or estimating the parameters asso- ciated with the sensors and/or targets is based on at least one of: measured times of pulses being high and times of pulses being low as detected by at least one sensor; measured times between (e.g. rising edges or falling edges of) pulses as detected by at least one pair of sensors.

The time of a pulse being high may be the difference between a pulse falling edge time and a pulse rising edge time of the considered pulse. The time of pulses being low may be the difference between a pulse rising edge time of a next pulse and a pulse falling edge time of a previous immediately adja- cent pulse. The times of pulses being high and time of pulses being low may depend on the rotor speed, angular target ex- tent and azimuthal or angular distance between adjacent tar- gets.

The measured time between pulses may also be regarded as times of pulses being low according to an embodiment of the present invention. The time difference between for example rising edges of pulses as detected by at least one pair of sensors originating from a same detection target may depend on the rotor speed and the angular distance between the prox- imity sensors but may not depend on the angular extent of the considered target. Thereby, the rotor speed may be measured independently from the angular extent of the target. Thereby, the method may still be improved.

According to an embodiment of the present invention, the sen- sors comprise at least one reference (also referred to as ab- solute) sensor and at least one relative sensor. The refer- ence sensor(s) as well as the relative sensor(s) may be of same or similar type or construction or may have different construction and different type. Measurement results of all the sensors may be converted to values relative to a refer- ence sensor. Thus, a reference or absolute sensor may set a particular coordinate system, in particular angular coordi- nate system relative to which measurement results of all the other sensors may be interpreted. The conversion of the meas- urement results of the other different relative sensors may be made using the sensor positioning parameters of the rela- tive sensors and the reference sensors.

According to an embodiment of the present invention, the tar- gets comprise: a reference (also referred to as absolute) target; and at least one relative target, wherein pulses originating from the reference target can only be generated by detections from a reference sensor and can thus be distin- guished from pulses originating from a relative target, which can only be generated by detections from a relative sensor.

The reference or absolute target may have for example a dif- ferent azimuthal and/or radial size and/or a different azi- muthal and/or radial position than the relative target(s).

The reference or absolute target may have been directly mounted at the rotor and may have been especially manufac- tured for the purpose serving as a reference target. The one or more relative targets may substantially all be structured or sized equally or at least approximately equally. However, the relative target(s) may be formed by a pre-existing struc- ture in the rotor thus not being especially manufactured or provided for the purpose of serving as a relative target for estimation of rotor operational characteristics.

According to an embodiment of the present invention, the ref- erence target, a reference sensor (S _Ai ), and a relative sen- sor (S _Ri ) are configured and positioned such that pulses originating from the reference target, as detected by the reference sensor (S _Ai ), overlap in time with pulses originat- ing from a relative target as detected by the relative sensor (S _Ri ), where i denotes the index of each relative sensor which a reference sensor has been configured and positioned to be associated with.

When the pulse as detected by a reference sensor overlaps in time with another pulse as detected by the relative sensor associated with that reference sensor, the direction of rota- tion may be easily detected.

The at least one reference sensor, the at least one relative sensor, the reference target and the at least one relative target may be positioned, in particular regarding a respec- tive radial position, such that: each of the at least one relative target is out of the sensor detection range of the at least one reference sensor; and each of the at least one reference target is out of the sensor detection range of each of the at least one relative sensor.

According to an embodiment of the present invention, estimat- ing the direction of rotation includes: detecting whether the reference sensor (S _Ai ) or its associated relative sensor (S _Ri ) first detects its corresponding target.

Other procedures for estimating or detecting the direction of rotating rotation may be employed, for example not utilizing signals as originating from the reference target but signals or pulses originating from any of the other relative tar- get (s). According to an embodiment of the present invention, a refer- ence azimuth position is detected when the reference sensor detects a pulse originating from the reference target, where- in a mounting position of the reference sensor is determined by calibration using external azimuth measurement.

An external azimuth measurement may be simultaneously or sub- sequently performed during a calibration procedure with the recording of the pulse. Then, a particular point in time in the phase of the pulse being high, may be associated with the azimuth position as measured by the external azimuth measure- ment. Thereby, an accurate calibration of the azimuth estima- tion may be achieved.

According to an embodiment of the present invention, the method further comprises determining a difference between subsequent pulse rising edge times and/or a pulse falling edge times of a first pulse and a subsequent second pulse, the first and second pulses detected by any of the at least one relative sensor and originating from any of the at least one relative target, wherein estimating the rotor azimuth is based on a previously estimated rotor azimuth increased or decreased, depending on estimated rotation direction, by an integral of the estimated rotor speed over the difference.

The two pulses whose respective pulse rising edge times and pulse falling edge times are determined may originate from any combination of sensors and targets. For example, the two pulses may originate from detections of two adjacent targets by the same relative sensor, detections of the same target by two adjacent sensors, or the detections of two adjacent tar- gets by two adjacent sensors. The difference, which may de- pend on the rotor speed, may reflect the time needed for a target to reach the position of its adjacent target, the time needed for a target to travel from one sensor to another sen- sor, or the time between when two adjacent sensors each de- tect two adjacent targets, respectively. Taking into account the estimated rotor speed and in particular integrating the estimated rotor speed over the determined difference may rep- resent an azimuth increment or decrement which may be added to the previously estimated rotor azimuth to obtain the actu- al rotor azimuth.

According to an embodiment of the present invention, the method further comprises validating of at least one of the sensors by making a (one or several) consistency check of measurement results of this sensor and the estimated rotor speed and/or estimated rotor azimuth; and disqualifying of one sensor, if it does not pass the consistency check.

The redundancy of measurement enables the consistency check during the validation. Thereby, one or more sensors may be identified which provide erroneous results due to one or more problems, such as damage, improper function/positioning, or the like. The disqualified sensor may not be utilized in the method any more. In particular, measurement results provided or detected by this sensor may not be utilized for estimation of the rotor operational characteristics.

According to an embodiment of the present invention, the method further comprises, if only one sensor passes the con- sistency check: estimating the rotor speed based on pulse high and pulse low time measurements of only the sensor hav- ing passed the consistency check.

The time range during which a pulse is high, may depend on the rotor speed. Thereby, rotor speed estimation is even pos- sible if only one sensor has been assessed as a proper func- tioning sensor.

It should be understood that features, individually or in any combination, disclosed, explained, described or provided for a method of estimation of rotor speed, azimuth and rotation direction of a rotating rotor of a wind turbine are also, in- dividually or in any combination, applicable to an arrange- ment for estimation of rotor speed, azimuth and rotation di- rection (in general rotor operational characteristics) of a rotating rotor of a wind turbine according to embodiments of the present invention and vice versa.

According to an embodiment of the present invention, it is provided an arrangement for estimation of rotor speed, azi- muth and rotation direction of a rotating rotor of a wind turbine, the arrangement comprising: multiple proximity sen- sors; wherein the arrangement is configured: to measure pulse rising edge time and pulse falling edge time of pulses gener- ated by each of the multiple proximity sensors originating from multiple detection targets arranged on the rotor; and to estimate rotor operational characteristics, in particular a rotor speed and/or a rotor azimuth and/or a rotation direc- tion, based on the measured pulse rising edge times and pulse falling edge times.

The arrangement may for example be comprised or implemented as a hardware and/or software module of a wind turbine con- troller .

Furthermore, according to an embodiment of the present inven- tion, it is provided a wind turbine, comprising: a rotor at which plural rotor blades are mounted; an arrangement accord- ing to the preceding embodiment.

The aspects defined above and further aspects of the present invention are apparent from the examples of embodiment to be described hereinafter and are explained with reference to the examples of embodiment. The invention will be described in more detail hereinafter with reference to examples of embodi- ment but to which the invention is not limited.

Brief Description of the Drawings

Fig. 1 schematically illustrates a portion of a wind tur- bine according to an embodiment of the present in- vention comprising an arrangement for estimation of rotor operational characteristics according to an embodiment of the present invention;

Fig. 2 schematically illustrates a conceptional circuit di- agram of an arrangement for estimation of rotor op- erational characteristics of a rotating rotor of a wind turbine according to an embodiment of the pre- sent invention;

Fig. 3 illustrates the modelled angular distances while Fig. 4 illustrates the corresponding measured time differences associated with sensor pulse traces of several sensors as considered in embodiments of the present invention.

Detailed Description

The portion 3 of a wind turbine according to an embodiment of the present invention schematically illustrated in Fig. 1 in a sectional view along an axial direction 5 (direction of a rotation axis of a rotor) comprises an arrangement 1 for es- timation of rotor operational characteristics of a rotating rotor 7 according to an embodiment of the present invention.

A schematic circuit diagram of the arrangement 1 is also de- picted in Fig. 2 which will be described below.

The arrangement 1 comprises multiple inductive proximity sen- sors S _A1 , S _R1 , S _R2 which are mounted (in particular close to a frontal face of a rotor lock disk) at a not in detail illus- trated stationary portion near to the main bearing of the wind turbine 3. The absolute inductive proximity sensor S _A1 is mounted at a different radial position, in particular fur- ther outwards, from the centre of rotation than the relative sensors S _R1 , S _R2 .

The arrangement 1 is configured to measure pulse rising edge time and pulse falling edge time of pulses (see for example Fig. 4) P1, P2, P3, P4, P5, generated by each of the multiple inductive proximity sensors S _A1 , S _R1 , S _R2 originating from an absolute target T _A and two of multiple relative targets T _R1 ,

T _R2 , ..., T _Rn which are arranged at the rotor 7. The absolute target T _A is mounted at a different radial position than the relative targets T _R1 , T _R2 , ..., T _Rn . The absolute target T _A can only be detected by the absolute sensor (but not any of the relative sensors) and the relative targets T _R1 , T _R2 , ..., T _Rn can only be detected by one of the relative sensors (but not the absolute sensor).

The arrangement 1 is further configured to estimate the rotor operational characteristics based on the measured pulse ris- ing edge times and pulse falling edge times.

Rather than utilize and mount only one proximity sensor to detect targets on a dedicated, precision-machined rotating part, embodiments of the present invention propose to utilize and mount multiple (inductive) proximity sensors to detect targets already pre-existing at a rotating part, and in par- ticular at the rotor 7. In particular, the rotor lock disk near the main bearing of the wind turbine may be a part in- cluding the detection targets T _A , T _R1 , T _R2 , ..., T _Rn which are monitored by the sensors S _A1 , S _R1 , S _R2 . Although only three sensors are depicted in Fig. 1, other embodiments of the pre- sent invention utilize more than three sensors, such as four, five, six or in-between three and 50 or even more.

In particular, the absolute target 'T _A ' (also referred to as reference target) may be realized by a (iron) ferrous piece to be detected by the absolute sensor S _A1 , while the relative targets T _R1 , T _R2 , ..., T _Rn may each be a previously-machined hole around the circumference of the ferrous disk acting as the relative target to be detected by the relative sensors S _R1 , S _R2 . However, any combination of holes, exposed bolt heads, gear teeth, mounted pieces, etc. may be utilized as targets (in particular relative targets) according to embodi- ments of the present invention. By using multiple sensors S _A1 , S _R1 , S _R2 embodiments of the pre- sent invention may have the benefit of being able to simulta- neously estimate the rotor speed, rotor azimuth and also de- termine the direction of the rotation. Further advantages may include measurement redundancy that may allow for improved sensor validation, robustness to vibration or to faults with individual sensors, and the ability to estimate and compen- sate for variations in sensor sensitivity, sensor placement, target size and target spacing. In addition, the total cost of the inductive proximity sensors may be less than alterna- tive solutions, including the cost of precision-machined ded- icated parts used by conventional inductive proximity sensor methods .

In Fig. 1 also relevant sensor positioning parameters, for example designed (or nominal) azimuthal distance between ad- jacent sensors, labelled as Df and misalignment e1,2 between sensors S _R1 and S _R2 are depicted in Fig. 1. Furthermore, tar- get positioning parameters, such as the radial and/or circum- ferential positioning of the absolute target T _A , the radial and/or azimuthal positioning of the relative targets T _R1 , T _R2 are indicated in Fig. 1. Furthermore, target size parameters, such as the relative target diameter d _rel , the azimuthal rela- tive target size q _rel are indicated in Fig. 1. Furthermore, target relative positioning parameters, such as relative tar- get spacing F _rel is indicated in Fig. 1. These positioning and/or size parameters of the sensors and/or targets are uti- lized in the algorithm to determine the direction of rota- tion, rotational speed and rotor azimuth.

Although the embodiment illustrated in the figures demon- strates the use of three sensors, any number of sensors more than two may be used. While q³l sensors (referred to as sen- sors S _A1 , ..., S _Aq , or the "absolute sensors") each detect an absolute target T _A once per revolution of the rotor, the re- maining m³1 sensors (referred to as sensors S _R1 , S _R2 , ..., S _Rm , or the "relative sensors") each detect multiple "relative targets" arranged around the circumference of the part n times per revolution, where m³1 is the number of relative targets used. In the illustrated embodiment the mounted fer- rous piece 'T _A ' assumes the role of the absolute target while the previous-machined holes T _R1 , T _R2 , ..., T _Rn assume the role of the relative targets.

The arrangement 1 comprises a processing section 9 which re- ceives measurement results 11 of all the proximity sensors S _A1 , S _R1 , S _R2 and processes these measurement results 11 in or- der to estimate the rotor operational characteristics based thereon.

Fig. 1 further indicates the sensor sensitivity p (also re- ferred to as azimuthal viewing range of the sensor or angular viewing range of the sensor).

The arrangement 1 is depicted in more detail in Fig. 2 as a schematic circuit diagram including the processing section 9 and the sensor section 10. The conceptional diagram illus- trated in Fig. 2 may be implemented in software and/or hard- ware. The arrangement 1 includes the absolute sensor S _A1 , a first relative sensor S _R1 and a second relative sensor S _R2 . In the block 13 the pulse times of pulses as detected by the sensors S _R1 and S _R2 are measured and determined. The measure- ment results 11 of the absolute sensor S _A1 and the first rel- ative sensor S _R1 are supplied to a block 15 which determines the direction of rotation of the rotor.

In a module 17 a pre-validation of the proximity sensor is carried out, wherein the measurement results for the differ- ent sensors are assessed for consistency.

If it is determined that multiple sensors are valid, it is branched into the branch 19 which leads to a multiple sensor estimator 21. Therein, the measurement results of multiple sensors are utilized. In a calibration step 23, the relevant parameters, such as sensor positioning parameters and/or tar- get positioning parameters and target size parameters are calibrated based on the pulse measurements 11. In a method block 25 the rotor speed and the change in the azimuth is es- timated based on the measurement results after calibrating the parameters.

When the proximity sensor pre-validation (module 17) assesses only one sensor as valid, it is branched into the branch 27 which leads to a single sensor estimation module 29. Also herein, the relevant positioning and/or sizing parameters of the sensors and/or targets are calibrated in a module or method step 31. The calibration of parameters is not always being performed, but only in the case the decision element 33 assesses that the parameters are not yet calibrated. After calibration of the parameters, it is proceeded to the method step 34 where the rotational speed and the change in azimuth is estimated based on the measurement results after calibra- tion or using the calibrated parameters.

The multi-sensor estimator 21 as well as the single-sensor estimator 29 provide their output to a proximity sensor post- validation block 35 in which a post-validation of the proxim- ity sensors is carried out including one or more consistency checks. The block 35 outputs the status 37 of the sensors which is fed-back to the proximity sensor pre-validation mod- ule 17.

Furthermore, the proximity sensor post-validation outputs the estimate 39 of the rotational speed. Furthermore, the proxim- ity sensor post-validation outputs the estimation 41 of the change in the azimuth.

The estimate 39 of the rotational speed as well as the esti- mate 41 of the change in azimuth are both provided to a prox- imity-based azimuth estimator 43, namely to an integrator 45 and a relative azimuth update module 47, respectively. The proximity-based azimuth estimator 43 receives for calibration external azimuth data 49 which is supplied to an azimuth sen- sor calibration module 51. To this module 51 also the meas- urement data 53 as determined by the absolute proximity sen- sor S _A1 are provided.

If the decision block 55 assesses that the azimuth is not calibrated, the azimuth will be calibrated in the calibration module 51. If it is assessed that the azimuth is calibrated, an absolute azimuth update is performed in module 57 and the output is provided to the relative azimuth update module 47. This relative azimuth update module 47 further receives the signal 59 indicating the direction of rotating from the rota- tional direction determination module 15. The estimate 61 of the rotor azimuth is finally output by the integration module 45 and the estimation 59 of the direction rotation is also output by the arrangement 1.

As shown in Figure 2, the algorithm not only estimates the rotor speed, azimuth, and direction of rotation, but also takes steps to calibrate the azimuth and unknown parameters. Moreover, steps are taken to validate both the input and out- put signals of the rotor speed estimation. This includes en- suring that there is no chatter in the sensor pulses and that the pulse time measurements and rotor speed estimates appear consistent over time. These checks on the inputs and outputs of the speed estimation are referred to as the "Pre- Validation" (block 17) and "Post-Validation" (block 35) steps, respectively. Depending on the severity and duration of the detected fault, it can either be ignored, corrected, or used to disqualify the sensor from the rotor speed estima- tion. Each of these responses are made within the "Pre- Validation" step, using the measurements from the sensors and the previous status reported by "Post-Validation" as inputs. In the case when the azimuth sensor is disqualified, the azimuth can continue to be esti- mated by using the incremental azimuth fixes at each relative target (T _R1 , T _R2 , ..., T _Rn) and integrating (block 45) the speed estimate between these targets. An absolute azimuth fix can still be performed by determining the relative target as- sociated with the fix. This can be done by a combination of counting through the known number of relative targets and finding the edge of the target that is closest to the cali- brated absolute azimuth value.

After disqualification of a speed sensor, the rotor speed and azimuth estimations can continue depending on the number of sensors that remain valid. If more than one sensor are valid, each of their pulse times as well as the times between their pulses can be used to estimate rotor speed by the multi- sensor estimator described above.

However, if only one sensor is valid, its pulse times can still be used to estimate rotor speed by a variant of the original algorithm referred to as the single-sensor estimator (block 29). This estimator performs the same function as the multi-sensor estimator (block 21) but using only the high and low time measurements associated with the one valid sensor. Thus, since the number and spacing of sensors S _R1 , S _R2 , ...,

S _Rm are chosen to optimize the update rate of the estimates, improving performance, the performance begins to degrade as the number of relative sensors m reduces to 1. Finally, if no valid sensors remain to be used in the estimation, an alarm must be reported by the functionality to indicate that the rotor speed and rotor azimuth cannot be estimated.

As is evident from the conceptual diagram of the proximity- based speed, azimuth, and direction estimation algorithm il- lustrated in Fig. 2, the algorithm first determines the di- rection of rotation and validates the proximity sensors be- fore updating the rotor speed and rotor azimuth estimates us- ing the pulses and pulse times acquired. The algorithm pro- vides the direction of rotation, estimates of the speed and azimuth, as well as the status of the proximity sensors.

Fig. 3 schematically illustrates pulses as detected by the proximity sensors S _A1 , S _R1 , S _R2 and the combination of sensor S _R1 and sensor S _R2 . Furthermore, the relative positioning pa- rameters of the relative targets F _rel , the relative target size (azimuthal target extent q _rel and the sensor azimuthal viewing range p are indicated as defining for example the an- gular differences between a falling edge and a rising edge between subsequent pulses or a rising edge and a falling edge of one pulse.

Fig. 4 illustrates these same pulses, wherein however the time differences as determined by the arrangement 1 are indi- cated. From the time differences the respective rotor opera- tional characteristics are determined and values of parame- ters associated with the sensors and/or targets are calibrat- ed according to embodiments of the present invention.

As the rotor rotates, the proximity sensors S _A1 , S _R1 , S _R2 out- put binary digital signals 11, 53 indicating whether or not they detect a target. As a function of time the sensor sig- nals resemble pulses (e.g. P1, ..., P5 in Figs. 3, 4 for the case with an absolute target, at least two relative targets (n>1), one absolute sensor (q=1) and two relative sensors (m=2)), whose high and low times depend on the speed of the rotor as well as on the sensitivity and alignment of the sen- sors and on the size and spacing of the targets (see Figure 1). An embodiment of the present invention uses computational hardware to measure the time (e.g. Dtl, Dt2, Dt3, Dt4 in Fig. 4) that each sensor's pulse is high and low, as well as the times between the pulses produced by each pair of successive sensors (e.g. Dt5, Dt6 in Fig. 4). By mapping the angular distances (see Fig. 3) associated with the sensor pulses to each of their corresponding time measurements (see Fig. 4), the rotor speed can be estimated along with the values for the unknown parameters that influence the time measurements.

For example, if any of the sensors are misaligned by various amounts around the circumference of the rotating part with respect to the other sensors, if these sensors have varied sensitivities to ferrous metal, or if the targets vary in size and placement (e.g., due to being poorly machined), an adaptive filter automatically estimates these uncertainties and compensates for them in its estimation of the rotor speed. Depending on the degree of variation between the tar- gets, an additional step may be introduced in which compensa- tion is applied as a function of the targets. In other words, the parameter values may be estimated separately for each in- dividual target and the appropriate set of values would be applied when the corresponding target is encountered.

By integrating multiple proximity sensors in the solution and utilizing existing rotating machined features, embodiments of the invention remove several limitations confronting prior solutions. Since the invention uses multiple proximity sen- sors in the detection of targets, each target is able to be detected more than once. This measurement redundancy allows the uncertainty caused by variations in the sensors and the targets described above to be estimated and prevented from corrupting the rotor speed and azimuth estimates. Thus, the need to precisely machine the targets, and the associated cost of this process, is mitigated. By spacing the multiple proximity sensors out such that they span the distance be- tween two consecutive targets, a sufficiently fast update rate can be achieved with significantly less targets per rev- olution. Misalignments in the sensors and variations in their sensitivity are automatically estimated and compensated for by the algorithm. Moreover, by attaching a unique target to be detected once per revolution by one of the sensors (i.e., the "absolute target"), accurate determination of the rotor azimuth and the direction of rotation can also be achieved.

At least one reference (a.k.a. absolute sensor) may be needed and at least one relative sensor may be needed to estimate rotor speed, azimuth, and rotation direction. Reference sen- sors are only able to detect the reference target and the relative sensors are only able to detect the relative tar- gets. If the reference target was visible to the relative sensors, there would be no need for a reference sensor: di- rection of rotation and absolute azimuth updates could come from the relative sensors by identifying which pulse is dis- tinct from the others and associating it with the reference target. However, this can introduce more complexity to the solution or be more inconvenient (it can be more convenient or appropriate to introduce a reference target of opposite type as the relative targets) than introducing a reference sensor. However, the reference sensor and target may be moved out of range from the relative sensors/targets, otherwise the reference and relative sensors will become functionally equivalent .

There may be two types of targets, e.g. metal and absence of metal (i.e., holes). Often it may be convenient to attach a reference target that is the opposite type as the relative targets. In this case a reference sensor is required to de- tect the reference target type, since the relative sensors have been mounted and positioned to trigger upon detection of the relative target type. In other cases, it is more conven- ient to attach a reference target that is the same type, how- ever as mentioned above, it must be out of range of the rela- tive sensors.

To improve aspects of the solution such as accuracy, robust- ness to individual sensor faults, increased update rate, it may become beneficial to introduce additional reference and/or relative sensors. With more reference sensors, there is simply more robustness to faults with one or more refer- ence sensors. However, with more relative sensors, there is an increase in the update rate of the estimated rotor charac- teristics, increased robustness to individual sensor faults, but also the solution has increased abilities, including the ability to estimate the size of and spacing between the rela- tive targets.

One alternative to using reference targets and reference sen- sors is to leverage the extra ability of estimating the sizes of and spacings between the relative targets: since each real target would be expected to have a slightly different size and spacing, each relative target could be directly identi- fied according to the unique values it has for these parame- ters. However, this would require that the target fabrication be imprecise enough to be detected by the sensitivity and resolution of the hardware/software used in the solution. Again, it may be more feasible to simply use a reference tar- get and reference sensor(s).

The reference target and reference sensor may be placed such that the pulse generated by the reference sensor when detect- ing the reference target will overlap with a pulse generated by the relative sensor when detecting a relative target.

The model according to one embodiment is described in detail below:

When relating the modelled angular distances and measured times associated with the pulses originating from the detec- tion of a target by two relative sensors (m=2), the following equations are obtained:

, where w is the average rotor angular speed as exhibited by the target. In these equations, some variables are known con- stants, some variables are unknown and must be estimated, while some variables are measurements of low and high times obtained by counter modules at the rising edge and falling edge of sensor pulses, respectively. The terms on the left hand side of eq. (1) correspond to the angular distances travelled by each target as it passes sensor S _R1 and sensor S _R2 to produce the pulse traces given in Fig. 3. The differ- ence times on the right hand side of eq. (1) correspond to the time differences measured by sensor S _R1 and sensor S _R2 in Fig. 4.

The variablesF _rel andq _rel are the angular spacing (in degrees) between the relative targets and the angular width (in de- grees) of the relative targets, respectively. Moreover, r ₁ and r2 are angular quantities that represent the error in the width of the pulses (affecting the high times measured) pro- duced by S _R1 and S _R2 , respectively, which is caused by uncer- tainties in the sensitivities of the sensors compared to the specifications given by the sensor manufacturer (e.g., due to variations in temperature, input voltage, wear, etc.). The initial values assumed for r ₁ and r2 can be determined using the specifications found in the datasheets for the sensors. Note that the sign convention taken for r ₁ and r2 is as fol- lows: positive values will tend to expand the pulse widths from the sensors while negative values will tend to reduce the pulse widths. Thus, sensors configured to detect metal targets (e.g., bolt heads, gear teeth, attached pieces, etc.) will tend to have positive values for these parameters while sensors configured to "detect" holes or gaps will tend to have negative values. In addition to these parameters, e _1,2 is an angular quantity that represents the error in the spacing between S _R1 and S _R2 (i.e., the deviation from the ideal spac- ing of F _rel /2, affecting the low times measured). Since the true value of this misalignment should be relatively small in either direction, an initial value of zero is assumed for e _1,2 . Note that the sign convention taken for e _1,2 is as follows: positive values for this parameter will tend to expand the distance and measured time from the falling edge of S _R1 to the rising edge of S _R2 while reducing the distance from the falling edge of S _R2 to the rising edge of S _R1 , with negative values having the reverse effect. In the case of more than two speed sensors, positive values of e _{k- ,} can be thought of as expanding the distance on the left side of the pulse from Sensor ^k while reducing the distance on the right side of this pulse. The measurements of high and low times have subscripts that adhere to a particular convention. Measurements whose sub- scripts begin with 'X2' are obtained by monitoring the pulse trains associated with only one sensor and thus consist of 2 edges (i.e., one rising and one falling) per period. Mean- while, measurements whose subscripts begin with 'X4' are ob- tained by monitoring the pulse trains from all of the availa- ble relative sensors together: in the case where ^{m = 2} , these are the pulse trains that consist of 4 edges (i.e., two per sensor) per target; thus, the subscripts 'X4' are used. While the measurements that end in 'R' are obtained at the rising edge of S _R1 or S _R2 , measurements ending in 'F' are obtained at the falling edge of that sensor. Although six equations are listed in (1), only four of them are independent. With four unknowns to be estimated (i.e., w, r ₁ , r ₂ , and e _1,2 ), this is enough information to complete the estimation. Fortunately, it can be shown that, by dividing both sides of (1) by w the equations can be made linear in the unknowns: Note that formulating (2) involved a transformation of varia- bles: rather than being linear in the original unknowns

(i.e., , r ₁ r ₂ , and e _1,2 , (2) is linear in where Therefore, the procedure to estimate all four original parameters involves first esti- mating the values of calculating the recipro- cal of to obtain the speed estimate, and then multiplying the speed estimate by to yield r ₁ , r ₂ , and e _1,2 re- spectively . To estimate a linear least mean squares (LMS) filter is applied that recursively adjusts their values until their mean-square error is minimized. How- ever, note that only 4 of the 6 measurements are used to per- form the estimation. If both sensors are deemed to be per- forming well, the measurements and are related to the unknowns in the matrix equation

Thus, x is the vector of transformed unknowns, y is the vec- tor of measurements, and H is the matrix of coefficients that map the transformed unknowns onto the measurements. Then, an LMS filter can be used to recursively arrive at an estimated vector of transformed unknowns,

Where is the error between the actual time measurements obtained, and the predicted measurements and f* is a constant scale parameter whose value is chosen to bal- ance speed of responsiveness with stability. Note that the reciprocal of the first element of is the rotor speed esti- mate that we are after and is expected to change significant- ly over time. The remaining three elements of which can be used to peer into the amount of uncertainty (e.g., sensor misalignment, machining error, etc.) affecting the measure- ment system, are expected to approximately constant over time. Note that, the lower the value of ^m , the more time re- quired for the rotor speed estimates to converge. Therefore, a method is introduced to evaluate whether the three estimat- ed parameters have sufficiently converged so that, when con- vergence has occurred, the LMS filter is replaced with direct calculation of rotor speed using an alternative reformulation of the equations in (1):

Each of the equations in (5) represents a calculation of the rotor speed from the converged estimated values of the param- eters and the time measurements obtained from the sensor pulses. Depending on which edge of which sensor pulse has ar- rived (i.e., the falling or rising edge of S _R1 or S _R2 ), the corresponding equation in (5) is used to directly update the rotor speed estimate. However, under certain conditions (e.g., significant changes in temperature, sensor wear, input voltage, etc.), the sensor parameters may need to be re- calibrated using the LMS filter. Therefore, a routine parame- ter check can be scheduled once each day or so by applying the LMS filter, provided that conditions allow for it; other- wise, the solution should run the direct calculations in (5) until conditions change.

If only one sensor is deemed to be performing well, then the above procedure can be applied to the one working sensor by ignoring the pulses and parameters associated with the faulty sensor and applying the relevant equations in (1) and (2).

For example, if S _R2 is determined to be faulty, the measure- ments that depend on the pulses from S _R2 (i.e., as well as the associated param- eters are ignored. The remaining measurements and their associated equations in (2) are used to form the following matrix equation: This equation is used with the LMS filter to estimate w and r ₁ and, upon convergence of r ₁ , the equations are reformulated to directly calculate w at each rising and falling edge of the pulses from S _R1 . The same can be done using only the measurements from S _R2 (i.e., . However, note that as the number of sensors used to estimate the rotor speed reduces, so will the update rate with which the rotor speed estimates can be provided. In general, more than two sensors can be used to obtain a speed estimate. This would be necessary as the spacing be- tween the targets increases sufficiently relative to the sen- sitivities of the sensors, and thus can be covered by more sensors in order to maximize the update rate of the speed es- timates . With ^m sensors, the equations used as the basis of the solution are as follows: which yields the following matrix equation of the form ^{x = y} to be used with the LMS filter:

As sensors are determined to be faulty, the relevant rows and columns of ^H,x , and ^y can be removed above and the process can still be used. When two or one healthy sensors remain, the equations given for ^{m = 2} or ^{m = 1} above are used.

It is known that the recursive least squares (RLS) filter of- ten converges faster than the LMS filter in general, but is more computationally intensive than the LMS. Therefore, LMS is being preferred over the RLS for this application.

Below the relationship between number of sensors/targets, up- date rate, and critical rotor speed is discussed: The primary performance limitation of the proposed solution may be that the update rate of the solution is proportional to the magnitude of the rotor speed. Hence at low rpm, the solution is forced to wait some nontrivial amount of time be- tween target detections, introducing a time lag in the speed and azimuth updates. However, by introducing multiple rela- tive sensors at the optimal spacing (i.e., where F _rel is the spacing between the targets in degrees and ^m is the num- ber of relative sensors), the update rate is reduced by a factor of ^m . Therefore, there is a direct relationship be- tween the number of sensors, number of targets, rotor speed, and amount of time the solution is forced to wait between es- timation updates. The critical rotor speed, can be defined as the rotor speed below which the update rate falls below the requirement (i.e., the amount of time that we are willing to wait for an update), and can be directly calculated as follows where is the required update period from the sensor in seconds, and is the number of relative targets. If this critical rotor speed is reasonable, then the number of sen- sors and targets are appropriate. If the number of targets, update rate requirement, and desired critical rotor speed are known, then the formula can be manipulated to calculate the required number of sensors:

It should be noted that the term "comprising" does not ex- elude other elements or steps and "a" or "an" does not ex- clude a plurality. Also elements described in association with different embodiments may be combined. It should also be noted that reference signs in the claims should not be con- strued as limiting the scope of the claims.