Methods and systems of processing sensing signals

Abstract

A method, comprising applying signal processing (200, 202, 204, 206, 208, 210, 212, 220, 222, 230) to a set of time-varying sensing signals (URXSIN, URXCOS) sensed via a sensor (such as an inductive position sensor, IPS) (14, 20) configured to be coupled to an actuating device (10) having a first part (12) movable relative to a second part (11) The IPS (14, 20) comprises a target object (14) comprising a reflective planar surface configured to backscatter electromagnetic waves impinging thereon, and a transceiver circuit (20) comprising at least one transmitting antenna circuit (TX) configured to transmit an electromagnetic wave towards the reflective planar surface of the target object (14), and at least one receiver antenna (RXSIN, RXCOS) comprising a first receiver antenna circuit (RXSIN) and a second receiver antenna circuit (RXCOS) configured to have the set of time- varying sensing signals (URXSIN, URXCOS) induced therein based on electromagnetic waves backscattered from the reflective planar surface of the target object (14). Applying signal processing (200, 202, 204, 206, 208, 210, 212, 220, 222, 230) to the set of time-varying sensing signals (URXSIN, URXCOS) comprises: applying (210, 222) transformation processing to time-varying sensing signals in the set of time-varying sensing signals (URXSIN, URXCOS); applying pattern recognition processing (212, 230) to the transformed time-varying sensing signals, and providing a set of indicator signals (D; D1, D2) indicative of the operational condition of the actuating device (10) to a user circuit (A).

Description

[0001]“Methods and systems of processing sensing signals” Technical field The description relates to sensing signal processing methods and corresponding signal sensing systems, such as an inductive position sensor (briefly, IPS). One or more embodiments may be equipped on-board industrial manufacturing machines, for instance to detect the working conditions of mechanical or electro-mechanical devices and components thereof, such as rotating and / or linear actuators. Background In industrial contexts it is useful to be able to detect variations in the working conditions of the industrial machinery, particularly of electric motors that drive the machinery to perform manufacturing processes. The performance of mechanical or electro-mechanical devices and components may be affected by a variety of errors, malfunctioning or performance degradation, such as short drifts (e.g., those with a duration lower than a revolution of the motor shaft, such as the so-called “chattering” in computer numerical control - CNC machines) or slow drifts that accumulate over time (e.g., years, due for example to the slow loosening of a shaft coupling or other shaft-motor misalignments that change over time). Maintenance of the motors and other mechanical devices and components may be costly as it may involve lengthy downtimes of the production lines. Conventional approaches to detecting errors and perform a condition monitoring in electric motors involve various kinds of sensors. For instance, vibration sensors may be placed on the case of an electric motor or bearing housing thereof in order to detect its vibrations, e.g., starting from tens of Hz. The vibration sensors could be used to detect short drifts but may fail to detect slow drifts. In general, vibration sensors (as well as sound sensors or accelerometers) are considered hardly suitable for use with low-rpm machines or with machines with sliding bearings (as those conventionally used in large industrial applications). Another approach comprises (e.g., linear) proximity sensors, which measure inductance variations based on eddy currents. For instance, document Prost, Josef et al.: “Semi-Supervised Classification of the State of Operation in Self-Lubricating Journal Bearings Using a Random Forest Classifier”, Lubricants 9 (2021): 50, DOI: 10.3390 / LUBRICANTS9050050 discusses a semi-supervised machine learning method for the classification of the state of operation for a tribological experiment involving a steel shaft sliding in a self-lubricating bronze bearing, comprising a Random Forest classifier trained on individual cycles from the lateral force data from four distinct experimental runs in order to distinguish between four states of operation. The proximity sensors are expensive, and their positioning may be difficult, especially for small diameter shafts, so that their measurements could be affected by electromagnetic interference due to the reduced distance between the pair of sensors. A variant scenario may involve temperature sensors, such as a thermal camera, to monitor the motor component or device. While such a solution may provide feedback on the presence of a malfunctioning of the motor, its costs are non-negligible and it can hardly provide any way to track the drift over time in order to prevent it, thereby being hardly suitable for predictive maintenance. US 2020 / 116532 A1 discusses a method of correcting for errors in a rotational position sensor having a sine signal and a cosine signal which includes compiling data from the sine signal and the cosine signal over a period of rotation of a motor shaft; determining offset correction parameters from the data; correcting the data with the offset correction parameters; determining amplitude difference parameters from the data; correcting the data with the amplitude difference parameters; determining phase difference parameters from the data; correcting the data with the phase difference parameters; and using the offset correction parameters, the amplitude difference parameters, and the phase difference parameters to correct the sine signal and the cosine signal. US 2022 / 187387 A1 discusses methods and apparatus for determining a mechanical angle of a target from sine and cosine signals generated by inductive sensing elements by applying harmonic compensation on the sine and cosine signals using possible mechanical angles and analyzing results of the applied harmonic compensation. US 2022 / 314963 A1 discusses methods, apparatus, systems, and computer program products for estimating error in an electric motor position sensor. In a particular embodiment, an electronic control unit (ECU) for an electric motor receives, during a first state of operation of the electric motor, a first plurality of time samples of a first output signal from a position sensor, the first output signal indicative of a rotational position of the electric motor during the first state. Object and summary An object of one or more embodiments is to contribute to overcoming the aforementioned drawbacks of existing solutions. Document US 2020 / 116532 A1 discusses that a method of investigating the error of a sensor system can be costly to deploy on every unit produced and to use during normal operation of the sensor system. One or more embodiments aim to overcome the existing limitations in online monitoring of the motor conditions. According to one or more embodiments, that object can be achieved via a method having the features set forth in the claims that follow. One or more embodiments may relate to a corresponding sensor, such as an inductive position sensor. One or more embodiments may relate to a corresponding system. One or more embodiments may relate to a method, e.g., as a computer-implemented method. To that effect, one or more embodiments may comprise a computer program product loadable in the memory of at least one processing circuit (e.g., a computer) and comprising software code portions for executing the steps of the method when the product is run on at least one processing circuit. As used herein, reference to such a computer program product is understood as being equivalent to reference to computer-readable medium containing instructions for controlling the processing device / system in order to co-ordinate implementation of the method according to one or more embodiments. Reference to “at least one computer” is intended to highlight the possibility for one or more embodiments to be implemented in modular and / or distributed form. One or more embodiments may be suitable for loading in the memory of at least one processing circuit (e.g., a micro-controller) and comprise software code portions for executing the steps of the method when the product is run on at least one processing circuit. As used herein, reference to an artificial neural network is understood as being equivalent to reference to an electronic circuit and / or computer-readable medium containing instructions for controlling the processing system in order to co-ordinate implementation of the method according to one or more embodiments. The claims are an integral part of the technical teaching provided herein with reference to the embodiments. One or more embodiments facilitate providing a compact sensor to monitor the working conditions of mechanical or electro-mechanical devices or components. One or more embodiments facilitate detecting whether the moving shaft of the motor being monitored are moving in a substantially regular manner of whether their trajectories are changing appreciably. One or more embodiments advantageously exploit relatively simple means (e.g., look-up tables) to provide a diagnostic tool for predictive maintenance. One or more embodiments advantageously exploit relatively simple means (e.g., look-up tables) to provide an online analysis tool for predictive maintenance during operation of a motor shaft. One or more embodiments may exploit one or more machine learning tools, such as artificial neural networks (briefly, ANNs), to output an estimation of the kind of non-idealities (such as misalignments) that affect the device or component under monitoring. One or more embodiments facilitate a fast and robust training of a machine learning tool using a model of the device and component under monitoring in alternative or in addition to measurements. One or more embodiments provide a method for detecting a distance of the sensed trajectory from an ideal one. For instance, in case of a servo motor spiraling out of control, it may be possible to detect the irregular motion even before completion of a single rotation period. One or more embodiments may employ a combined sensor that combines information regarding an absolute position and an incremental or relative position of the motor, providing a combined signal. For instance, it may be possible to apply pattern recognition to the combined signal even in the absence of data from a full period rotation of the motor. Brief description of the several views of the drawings One or more embodiments will now be described, by way of non- limiting example only, with reference to the annexed Figures, wherein: Figure 1 is a diagram exemplary of an apparatus as per the present disclosure; Figure 2 is a diagram exemplary of a method as per the present disclosure; Figure 3 is a diagram exemplary of further operations of a method as per the present disclosure; Figures 4 to 8 are diagrams exemplary of imperfections in a device which may be detected using the method exemplified in Figures 2 and 3; Figures 9 and 10 are diagrams exemplary of training signals for use in the method as per the present disclosure; Figures 11 and 12 are diagrams exemplary of a simulation method for producing the training signals exemplified in Figures 9 and 10; Figure 13 is a top view of a device as per the present disclosure; Figure 14 is a diagram of a measurement method for producing the training signals exemplified in Figures 9 and 10; Figure 15 is a view of an alternative sensor example as per the present disclosure, and Figure 16 is a diagram exemplary of further training signals for use in a method as per the present disclosure. Corresponding numerals and symbols in the different figures generally refer to corresponding parts unless otherwise indicated. The figures are drawn to clearly illustrate the relevant aspects of the embodiments and are not necessarily drawn to scale. Detailed description In the ensuing description, one or more specific details are illustrated, aimed at providing an in-depth understanding of examples of embodiments of this description. The embodiments may be obtained without one or more of the specific details, or with other methods, components, materials, etc. In other cases, known structures, materials, or operations are not illustrated or described in detail so that certain aspects of embodiments will not be obscured. Reference to “an embodiment” or “one embodiment” in the framework of the present description is intended to indicate that a particular configuration, structure, or characteristic described in relation to the embodiment is comprised in at least one embodiment. Hence, phrases such as “in an embodiment” or “in one embodiment” that may be present in one or more points of the present description do not necessarily refer to one and the same embodiment. Moreover, particular conformations, structures, or characteristics may be combined in any adequate way in one or more embodiments. The references used herein are provided merely for convenience and hence do not define the extent of protection or the scope of the embodiments. For the sake of simplicity, in the following detailed description a same reference symbol may be used to designate both a node / line in a circuit and a signal which may occur at that node or line. Also, throughout this description, the wording “neural network (processing)” as used, for instance, in expressions like artificial neural network (briefly, ANN) processing, regression processing or convolutional neural network (briefly, CNN) processing, is intended to designate machine- implemented processing of signals performed via hardware (briefly, HW) and / or software (briefly, SW) tools.Figure 1 is a diagram exemplary of an apparatus 100 (such as an industrial machine apparatus, or a vehicle) comprising an actuating device 10 (such as a conventional electric motor, for instance a brushless motor) comprising a first part, such as a housing 11 and a second part 12 (such as a shaft protruding from the housing) which are movable (in a manner per se known) relatively to one another about an axis of movement (e.g., rotation) Z. Preferably, the actuating device 10 comprises a rotary or linearly extendable electric motor. As exemplified in Figure 1, a shaft-part 12 of the device 10 is coupled to a (e.g., rotary) inductive position sensor (briefly, IPS) device comprising: a target object 14, e.g., having the shape of a disk, coupled to the shaft 12 and comprising a reflective area, configured to backscatter electromagnetic waves, e.g., a half-disk area comprising a metallic / conductive surface; sensing circuity 20 comprising: a transmitting antenna TX comprising a set of transmitting circuit patterns (also denoted as coils or windings) configured to transmit an electromagnetic wave towards the target object 14, and a receiving antenna comprising a set of receiving circuit patterns (also denoted as coils or windings) RXSIN, RXCOS configured to receive respective echo signals backscattered by the reflective surface of the target object 14 when illuminated by the transmitted electromagnetic wave; a processing device 30 (such as a microprocessor or an integrated circuit, for instance) coupled to the transmitter antenna TX to drive the transmitter antenna TX to emit the electromagnetic wave and coupled to the set of receiver coils RXSIN, RXCOS of the receiving antenna configured to receive the sensed echo signal from the at least one receiver antenna coil RXSIN, RXCOS. For the sake of simplicity, one or more embodiments are discussed in the following mainly with reference to rotary IPS devices with a half-disk conductive surface, being otherwise understood that such a kind of IPS is purely exemplary and in no way limiting. One or more embodiments may also apply to linear IPS for detecting linear displacements, arc IPS for detecting rotary displacements, arc IPS, redundant IPS configurations, double IPS configurations, and / or use notionally to any shape for the target and its reflective area (e.g., multi- lobed, multi-lobed with an inner ring, planar, square, and so on). One or more embodiments may, additionally or alternatively, employ a combined IPS sensor comprising a first inductive absolute position sensor and a second inductive sensor of incremental or relative position, the first and the second sensor being adjacent one another on a same circuit, for instance sharing a common center, as exemplified in Figures 15 and 16. For instance, the processing device 30 is configured to apply signal processing to the sensed echo signal as discussed in the following (with reference to Figures 2 and 2A, for instance), providing a set of indicator signals D to user circuits A, for instance to apply a feedback control to the motor 10. For instance, a motor driver circuit A may vary the operation of the motor 10 based on the received set of indicator signals D. This facilitates preventing damages to the motor 10 during its operation, thereby sparing the costs of otherwise expensive replacements and extending the life of the component. In various embodiments, portions of the system of the present invention may be implemented in a Field Programmable Gate Array (briefly, FPGA) or Application Specific Integrated Circuit (briefly, ASIC). As appreciable by the person skilled in the art, various functions of circuit elements may also be implemented as processing steps in a software program. Such software may be employed in, for example, a digital signal processor, micro-controller, or general-purpose computer. In various embodiments, the transceiver coils RXSIN, RXCOS, TX are formed by etching or printing conductive traces on a top layer of a circuit board. Voltage sensing circuit and / or sinusoidal alternating current source may be implemented in one or more semiconductors die that is soldered to the circuit board upon which the transceiver coils are formed to electrically couple the coil assembly to the one or more integrated circuit die. Vias and interconnects between the one or more semiconductor die may extend within other conductive layers of the circuit board, in a manner per se known. As exemplified in Figure 1, the ensemble of the components of the IPS device may be integrated on-board a PCB circuit 20. Such a possibility makes IPS devices very compact and cost-effective. As exemplified in Figure 1, the assembly of the motor 10 and the PCB with the IPS device and the microprocessor 30 mounted thereon may be comprised in an apparatus 100, such as an industrial machine apparatus (e.g., a CNC machine) or a vehicle. IPS devices are also currently referred to as “ratiometric” devices since a position of the target object 14 (and therefore of the motor shaft 12 attached therewith) can be determined based on a ratio of the voltage across two receiving coils RXSIN, RXCOS of the receiver antenna. IPS devices are known, e.g., from document US 4737698 A which discusses a sensor having a drive winding for establishing a forward field and an electrically conductive screen displaceable relative to a sense winding, wherein, in the presence of the drive field, eddy currents are generated in the screen to establish a counter-field opposing the forward field, so that the sense winding is shaded by the screen to a varying extent during relative displacement of screen and sense winding and the voltage induced in the sense winding is accordingly correspondingly varied. Application of a high frequency input to the drive winding results in a modulated output from the sense winding which may be demodulated to provide a signal indicative of screen position relative to sense winding. The position signal may be further processed to provide a speed signal. The sensor may assume a multiplicity of linear or planar, rotational, and axial or solenoidal configurations. The literature discussing to some extend the technology of IPS devices comprise documents: WO2019 / 089095 which discusses a coil design system and a method of providing an optimized position locating sensor coil design, which includes receiving a coil design; simulating position determination with the coil design to form a simulated performance; comparing the simulated response with the specification to provide a comparison; and modifying the coil design based on a comparison between the simulated performance and a performance specification to arrive at an updated coil design; Hoxha A, Passarotto M, Qama G, Specogna R.: “Design Optimization of PCB-Based Rotary-Inductive Position Sensors”, Sensors. 2022; 22(13):4683, doi: 10.3390 / s22134683 which discusses a methodology to optimize the design of a ratiometric rotary inductive position sensor (IPS) fabricated in printed circuit board (PCB) technology, where the optimization aims at reducing the linearity error of the sensor and amplitude mismatch between the voltages on the two receiving (RX) coils; US7319319B2 discusses a sensor comprising an excitation winding, a signal generator operable to generate an excitation signal and arranged to apply the generated excitation signal to the excitation winding, a sensor winding electromagnetically coupled to the excitation winding and a signal processor operable to process a periodic electric signal generated in the sensor winding when the excitation signal is applied to the excitation winding by the signal generator to determine a value of a sensed parameter, wherein the excitation signal comprises a periodic carrier signal having a first frequency modulated by a periodic modulation signal having a second frequency, the first frequency being greater than the second frequency; Lin Ye, Ming Yang, Liang Xu, Chao Guo, Ling Li, Dengquan Wang: “Optimization of inductive angle sensor using response surface methodology and finite element method”, Measurement, Volume 48, 2014, Pages 252-262, ISSN 0263-2241, doi: 10.1016 / j.measurement.2013.11.017 discusses an optimal design method for the inductive angle sensor obtained through selecting the key parameters of the sensor and setting initial search domain of the key parameters; Ye L, Yang M, Xu L, Zhuang X, Dong Z, Li S.: “Nonlinearity analysis and parameters optimization for an inductive angle sensor”, Sensors (Basel), 2014 Feb 28;14(3):4111-25, doi: 10.3390 / s140304111; PMID: 24590353; PMCID: PMC4003933 discusses a nonlinearity analysis based on parameter optimization to design an inductive angle senso, where the finite element method and particle swarm optimization are combined for the sensor design to get the minimal nonlinearity error; and Golby, J. (2010), “Advances in inductive position sensor technology”, Sensor Review, Vol. 30 No. 2, pp. 142-147. doi: 10.1108 / 02602281011022742 discusses outline the basic principles of inductive position sensors, presenting one company’s advances in inductive position technology in detail, together with some of the applications for which they are now suitable. It is shown that concentrating on high volume applications in market sectors such as automotive, user interfaces, and utility metering, where the low cost of these sensors and their moderate accuracy (typically<1 percent of full scale) offers an attractive price / performance ratio. As appreciable to those of skill in the art, when the target object 14 performs a movement (e.g., a revolution) over the receiver coils RXSIN, RXCOS, the respective voltages URXSIN, URXCOS induced by the echo signals as the target position changes may be expressed as: where ^ is a position of the shaft 12. Therefore, it is possible to compute the (e.g., angular) position ^ based on an inverse tangent function of the ratio of the received voltages URXSIN, URXCOS, which may be expressed as: U ^=atan (RXSIN(^)) URXCOS(^) As appreciable to those of skill in the art, the CORDIC technique known, e.g., from document Volder, J.E.: “The CORDIC trigonometric computing technique”, IRE Trans. Electron. Comput. 1959, 8, 330–334 may be suitable for use to obtain the angular position ^. Figure 2 is exemplary of a signal processing method which, based on the induced voltages URXCOS, URXSIN detected via the receiver coils RXSIN, RXCOS, facilitates providing the set of indicators D of an operating condition of the motor 10. For instance, the method provides an indication of the type(s) of error(s) or performance degradation(s) that affect the motor 10. In the exemplary case discussed in the following, the main source of error discussed comprises misalignments, in particular linear ones, of the motor shaft 12. As exemplified in Figure 2, the method comprises: block 200: receiving the (e.g., demodulated) set of time-varying electrical (e.g., voltage or current) signals URXCOS, URXSIN from the receiver coils RXSIN, RXCOS of the IPS device 14, 20; block 210: analyzing the evolution over time of the sensing voltage signals URXSIN, URXCOS in search for irregular patterns of movement; for instance, the method comprises applying a coordinate transformation to the received demodulated induced signals URXSIN, URXCOS, by defining bidimensional coordinates x, y of a Cartesian plane as equal to the values of the signals URXCOS, URXSIN (e.g., voltages at N sampled consecutive time instants, with N a positive integer), respectively, which therefore become parameters of a parametric equation of a trajectory curve; this approach proves useful in case of servo motors having an angular velocity which is highly variable, e.g. even the direction changes frequently; as exemplified in portion b) of Figure 2, block 212: providing a reference trajectory curve TJR in the parametric coordinate space, computing a difference (e.g., a norm) between the sensed signals and the reference trajectory curve TJR and comparing the difference with a threshold distance value ΔTHJ, providing a set of indicators D0 as a result of the computed difference exceeding or failing to exceed the threshold distance value ΔTHJ; for instance, the reference trajectory TJR can be obtained as the signal of a complete period of revolution sampled when the device is aligned or in normal operating conditions or it can be a “theoretical” circumferential curve. The operations exemplified in Figure 2 by blocks 210 and 212 may also be indicated as pattern recognition operations insofar as they facilitate detecting irregular patterns of movement of the target object 14 and / or motor shaft 12. As exemplified in Figure 2, alternatively, block 212 comprises applying artificial neural network processing to the parametric curve defined over time as a function of the sensing signals URXSIN, URXCOS, producing as a result the first set of indicator signals D0 indicative of faults detected in the electric motor based on the sensing signals URXSIN, URXCOS from the sensing device 14, 20. For instance, a suitable neural network for use in block 212 comprises recurrent neural networks (RNN), LSTM (Long Short Term Memory) and GRU (Gated Recurrent Unit) networks which may be trained in an unsupervised manner using one or more reference trajectories TJR. As appreciable to those of skill in the art, these kind of neural network topologies can be suitable for processing time-varying signals. The use of unsupervised training methods may facilitate to skip a step of defining a model to use; clustering techniques may be used to try to classifying the signals due to misalignments or faults. A cluster-than-label approach may be used to relate a cluster with a known problem (e.g., tilting, deviating from the trajectory) of the device 14, 20. It is noted that one or more embodiments are discussed in the following mainly with reference to Fourier transform processing of signals as exemplary transformation processing for the sake of simplicity, being otherwise understood that such an exemplary transformation processing is purely exemplary and in no way limiting. As exemplified in Figure 2, the method further comprises: block 202: identifying a (time) period T of each induced voltage signal in the set of induced voltage signals URXCOS, URXSIN; as exemplified in portion c) of Figure 2, any of the induced voltage signals U comprises a periodic wave whose period T may be identified, e.g., via zero crossing detection, in a manner per se known; block 204: computing the (e.g., angular) position ^ based on the ratio of the extracted periods of the induced voltage signals URXSIN, URXCOS, (e.g., ^=arctan(URXSIN, URXCOS)), computing a (e.g., angular) velocity ω(ρ) as the ratio of the position ^ and the time period T as well as computing a mean velocity value ωM, as exemplified in portion d) of Figure 2; for the sake of simplicity, in the following the reference sign for indicating the velocity ω(ρ) is simplified by using an implicit notation of the dependence from the (geometrical) radius ρ; block 206: optionally, applying normalization processing to the velocity ω, dividing the signal by a reference (e.g., angular) velocity ω0 (whose value may be stored in a memory of a processing device configured to execute the instructions of the method, and / or which may be varied by the user based on the application, for instance), and computing a (e.g., angular) velocity variation Δω, for instance by computing a norm (e.g., applying a known L-infinity norm operator thereto, providing the largest magnitude among each element of a vector) of the difference between the velocity ω and the mean velocity ωM; block 208: performing a comparison of the velocity variation Δω and a threshold value ε (whose value may be stored in a memory of a processing device configured to execute the instructions of the method, and / or which may be varied by the user based on the application, for instance), in order to evaluate whether the variation of velocity Δω is appreciable (e.g., in case the difference Δω exceeds the threshold value ^) or whether it can be considered substantially constant (e.g., at least in a revolution, in case the difference Δω exceeds the threshold value ^); block 220: in case the comparison performed in block 208 yields that the angular velocity variation ω fails to exceed the threshold velocity value ε, implying angular velocity ω may be treated as substantially constant during a revolution, providing difference signals ΔVsin(ψ), ΔVcos(ψ) as a result of computing a difference between each received voltage signal URXSIN, URXCOS and a reference voltage signal UREF (whose value may be stored in a memory of a processing device configured to execute the instructions of the method, and / or which may be varied by the user based on the application, for instance); for the sake of simplicity, in the following an implicit notation is used to denote the dependence of the difference electric (e.g., voltage or current) signals ΔVsin, ΔVcos from the position angle ψ; block 222: applying Fourier transform processing (e.g., fast Fourier transform, FFT), for instance using a fixed time window, to the received difference signals ΔVsin, ΔVcos, and block 230: applying a further classification and / or pattern recognition processing pipeline to the difference signals ΔVsin, ΔVcos, for instance via artificial neural network processing (e.g., trained as discussed in the following) or using a look-up table, providing further indicator signals D1, D2 indicative of faults and / or vibrations which may be present in the electric motor, as discussed in the following. An operation of computing a mean velocity value ωM, as exemplified in portion d) of Figure 2 and discussed with respect to block 204 comprises, for instance, computing the mean velocity value ωM over one or more time periods T of one or more induced voltage signal in the set of induced voltage signals URXCOS, URXSIN. As exemplified in Figure 3, the further processing pipeline 230 comprises: block 231: apply a first (e.g., low band) filtering processing to the difference signals ΔVsin, ΔVcos in order to extract the frequency components of the signals relative to the imperfections (e.g., misalignments) of the sensing device, providing a first set of filtered signals LB; block 232: apply a second (e.g., high band) filtering processing to the difference signals ΔVsin, ΔVcos in order to extract the frequency components of the signals relative to the vibrations of the motor, providing a second set of filtered signals HB; block 234: apply a regression processing, e.g., via a look-up table or an artificial neural network processing stage, to the first set of filtered signals LB, producing as a result a second set of indicator signals D1 indicative of a kind of imperfections detected based on the sensing signal from the sensing device; block 236: apply a second classification processing to the second set of filtered signals HB, e.g., via a look-up table or an artificial neural network processing stage, producing as a result a third set of indicator signals D2 indicative of a type of faults detected in the electric motor based on the sensing signal from the sensing device. As exemplified herein, the artificial neural network (briefly, ANN) processing stage suitable for use in block 234 comprises a feedforward neural network (briefly, FNN) with 5 or 6 layers, 256 or 128 inputs, 9 outputs, Rectified Linear Unit (briefly, ReLU) activation functions for the input layers and linear for the output layer, Root Mean Square (briefly, RMS) loss function and coupled to an Adamax optimizer (known per se). Preferably, a supervised machine learning that performs a regression is preferred for training such an ANN. As exemplified herein, an ANN processing stage suitable for use in block 236 comprises a cluster-than-label approach to perform clustering of signals and to relate the clusters with possible problems of the device. For instance, an unsupervised machine learning method may be preferred, as it may be difficult to find models that accurately represent short drifts problems. Figures 4 to 8 are diagrams exemplary of the types of imperfections that may be detected as a result of applying regression processing 233 to the first set of filtered signals LB. As exemplified in Figure 4, the set of imperfections comprises a skew error defined as the angle between the rotational axis of the shaft 12 and the azimuthal axis perpendicular to the bottom surface of the moving target object 14. As exemplified in portions a) and b) of Figure 4; the skew can be measured via a first skew angle ψ_skew indicative of inclination and a second skew angle φ_skew indicative of the azimuth of the skew. For instance, the inclination ψ_skew measures the amount of skew rotation, whereas azimuth φ_skew specifies in which direction the skew rotation is applied. For example, a value of φ_skew=0° indicates that the skew rotation ψ_skew is applied by rotating on the Y axis, while a value of φ_skew =90° indicates that the skew rotation ψ_skew is applied by rotating on the X axis. It is noted that the rotation along the Y axis is used as an example; alternatively, the rotation along the X and Z axes can be used to define the error. As exemplified in Figure 5, the set of imperfections comprises a “wobble” imperfection defined as the lateral displacement W of a geometrical center of the target object 14 with respect to the point where the rotational axis of the shaft 12 crosses the target object 14. In other words, the wobble W measures the eccentricity of the target object 14 with respect to the rotational axis of the shaft 12, which can have a horizontal component Wx along the X axis and a vertical component along the Y axis. As exemplified in Figure 6, the set of imperfections comprises a tilt of the target object 14 which is defined as the angle between the rotational axis of the shaft 12 and the axis Z normal to the surface of the receiving coils and passing through the center O of the receiving coils RXSIN, RXCOS on the PCB 20. Similarly to the skew imperfection, the tilt imperfection is defined via a first tilt angle ψ_tilt (exemplified in portion a of Figure 6) formed by the actual position of the shaft 12 and the ideal azimuthal axis Z orthogonal to the surface of the receiving circuit coils on the PCB 20, and a second tilt angle φ_tilt (exemplified in portion b of Figure 6) formed by the presence of a non-ideal position of the target object 14 with respect to the vertical shaft 12. For instance, the first tilt angle ψ_tilt is indicative of an inclination of the target object 14 while the second tilt angle φ_tilt is indicative of the azimuth of the inclination. In other words, the inclination is the amount of tilt whereas azimuth specifies in which direction the tilt is applied. It is noted that the rotation along the Y axis is used as an example; alternatively, the rotation along the X and Z axes can be used to define the error. As exemplified in Figure 7, the set of imperfections comprises an off- axis error O_A due to a misalignment between the ideal orthogonal axis Z passing through the center O of the receiving coils RXSIN, RXCOS on the PCB circuit 20 and the position of the shaft 12. For instance, the off-axis error has two components O_Ax and O_Ay for each of the plana axes X, Y which are defined as the distance between the rotational axis of the shaft 12 and a crossing point between a symmetry axis of the PCB 20 and the target object 14. As exemplified in Figure 8, the set of imperfections comprises an “air- gap” error defined as the distance AG along the azimuthal direction between the coils and the crossing point between the rotational axis of the shaft 12 and the target object 14. Note that the crossing point matches the bottom surface of the target only in the absence of wobble. The Inventor has observed that a plot of the filtered signals in the first set of signals, provided as a result of applying the first filtering 231 to the difference signals ΔVsin, ΔVcos, varies in ways peculiar to the specific type of imperfection that affects the sensing arrangement 12, 14, 20. For instance: - as exemplified in portion a) of Figure 9, the presence of an off-axis O_A appears as a liver-shaped (or bean-shaped) curve; it may also be possible to distinguish between an off-axis error along the x direction, which appears in the bottom-left part of the plot of ΔVsin, ΔVcos and an off-axis along the y direction appears in the top-right part of the plot ΔVsin, ΔVcos; - as exemplified in portion b) of Figure 9, the presence of a wobble W is characterized by a rhomboidal shaped curve; it may be possible to distinguish between a wobble error along the x direction, which appears smaller and almost square in the plot of ΔVsin, ΔVcos and a wobble along the y direction, which is bigger and more rhomboidal in the plot ΔVsin, ΔVcos; - as exemplified in portion a) of Figure 10, the presence of a first tilt error ψ_tilt is visible as a double ellipse curve; it may be possible to distinguish between a tilt error angle ψ_tilt at the second angle φ=0, which appears closer to the origin in the plot of ΔVsin, ΔVcos and a first tilt error angle ψ_tilt at the second angle φ=90°, which is more distant from the origin in the plot ΔVsin, ΔVcos; - as exemplified in portion b) of Figure 10, the presence of a first skew error ψ_skew is visible as a circular curve; it may be possible to distinguish between a first skew error angle ψ_skew at the second angle φ=0, which appears with a wider diameter in the plot of ΔVsin, ΔVcos and a first skew error angle ψ_skew at the second angle φ=90°, which is far from the origin in the plot ΔVsin, ΔVcos. Therefore, it may be possible to generate a look-up table for use in block 233 of the method exemplified in Figure 3 for detecting the kind of imperfection that affects the sensing device. The Inventor has noted that the recognition of the various patterns of the different misalignments may be automated for use as a look-up table or by training an artificial neural network, such as a convolutional neural network (briefly, CNN) trained (e.g., in a supervised manner) to classify the errors based on a training dataset produced by measuring a number of errors or simulating their expected effects on the sensor. Figures 11 and 12 are exemplary of a (e.g., computer-implemented) virtual prototyping or simulation tool 1000 for sampling values of signals and generating the look-up table and / or the training data to use to train the ANN processing stages (e.g., block 234 and / or 236 in Figure 3) of the method to recognize the patterns associated to different kind of imperfections in the set of imperfections. As exemplified in Figures 11 and 12, obtaining / providing the sampled signal values via the simulation tool 1000 comprises: block 1010: providing a (e.g., Gerber or any parametric CAD) file describing the electromagnetic parameters of transmitting circuits TX1 of the IPS device 14, 20 under analysis, block 1012: providing a (e.g., Gerber or any parametric CAD) file describing the electromagnetic parameters of receiving circuits RX1 of the IPS device 14, 20 under analysis, block 1014: providing a (e.g., Gerber or any parametric CAD) file describing the electromagnetic parameters of the target object 14 of the IPS device 14, 20 under analysis. block 1100: setting a number of geometrical parameters for the IPS device 14, 20 regarding a receiving coil RX1 among the receiving circuits, a transmitting coil TX1 among the transmitting circuits and the target object 14 as well as the PCB device 20; for instance, these parameters comprise: number of turns of receiving coil RX1, minimum radius D of the receiving coil RX1, thickness T of the printed circuit traces on the PCB 20, trace width, clearance, vias pad, vias hole diameters, and other parameters appreciable to the person skilled in the art. It is noted that Figures 11 and 12 encompass the simulation of a half- disk reflective area of the target object for the sake of simplicity, being otherwise understood that this is purely exemplary and in no way limiting. One or more embodiments may exploit symmetry to retrieve the mechanical behavior of the remaining half of the target or in other scenarios it may be possible to simulate the target object in its entirety. The digital version of the target object input to the simulation tool 1000 may be considered as a “digital twin” of the target object 14 itself, advantageously simplifying the collection of signals in the digitized domain. As exemplified in Figure 12, the simulated imperfection (e.g., air-gap AG) may be specified by varying the value of the corresponding parameters in a dedicated part (such as block 1200) of the simulation tool 1000. For instance, applying the various kinds of imperfection to the simulated IPS device RX1, TX1, 14, 20 comprises: initializing the target object 14 position, for instance placed at an ideal air-gap (e.g., AG = 0 mm) and having an ideal lack of skew and tilt (that is, ψ_skew=0° and ψ_tilt=0°), and / or skewing the target object 14, introducing a skew inclination value ψ_skew at a random skew azimuth value φ_skew, and / or displacing the target along the X and Y directions with respect to the ideal rotational axis, applying a “wobble” imperfection value W as a result, and / or tilting the target object 14 with respect to a plane parallel to the PCB 20, introducing a tilt inclination value ψ_tilt at a random tilt azimuth value φ_tilt. As exemplified in Figure 12, the values of the voltages ΔVsin, ΔVcos detected at the receiving coils RX1 in the presence of the applied imperfections are collected as a result of simulating a mechanical sweep (again via part 1200 of the tool 1000) of the “imperfected” target object 14 over the simulated receiving coils RX1. For instance, the parameters of the mechanical sweep 1200 may be customized and may comprise number of target positions at which to perform sampling of the detected sensing signals URXSIN, URXCOS. For instance, the tool 1000 may be configured to simulate the selected specific combination of imperfections to use for training the neural network(s) during the simulation of the mechanical sweep of the target object 14. For instance, introducing the air-gap imperfection AG comprises: initializing the moving target object of the simulated IPS device in ideal conditions (that is, no imperfections); applying a first rotation step to the moving target object 14; displacing the target object 14 along the azimuthal axis, introducing the air-gap AG; displacing the target object 14 along the horizontal X axis by a fixed step, e.g., linearly interpolated between start and end coordinates for the mechanical sweep (e.g., stored in registers sweep_start_x and sweep_end_x, respectively, from the origin to the number of target positions); for each target position, the target object 14 is translated in Y and Z axes by a value linearly interpolated between start and end coordinates (e.g., stored in register sweep_start_y and sweep_end_y) in the Y axis and between start and end coordinates (e.g., stored in registers sweep_start_z and sweep_end_z) in the Z axis. As exemplified in Figures 11 and 12, it may be possible to visualize the position of the simulated target object 14 at every step of the mechanical sweep, for instance by moving a cursor over a bar 1400 of a control bar for graphically reproducing the mechanical sweep simulation 1200 performed via the tool 1000. As exemplified in Figures 11 and 12, the tool 100 comprises further sections which may perform further operations such as: setting the mechanical features of the target (e.g., shape, diameter), the electromagnetic properties of the reflective surface (e.g., reflectivity coefficient, conductivity) and the kind of IPS target (e.g., rotary, linear); setting stackup parameters, in a manner per se known; setting excitation parameters for the transmission coil (e.g., frequency, intensity, waveform). The sampled signal values collected via the simulation tool 1000, in addition or in alternative to being used to train the ANN processing stage(s), may also be stored in a database together with information regarding the kind of imperfection simulated to generate the sampled signal values. This way, it may be possible to use the database as a look-up table to recognize the kind of misalignment that corresponds to a certain value of the difference signals ΔVsin, ΔVcos computed based on the received sensing signals URXSIN, URXCOS. As discussed in the following, it may be possible to use experimental signals in addition or in alternative to simulated signals for the look-up table and / or for training the ANN processing stage(s). Figures 13 and 14 are exemplary of an alternative or additional method of acquiring sample signals for training the ANN processing stage(s) or for use as look-up tables. Figure 13 is exemplary of a (e.g., “dummy”) IPS device 14, 20 suitable to perform measurements of the experimental signals, wherein the target object has the reflective surface 140 and with the PCB 20 incorporating the receiving coils RXSIN, RXCOS, the transmitter coils TX and the circuitry 300 to couple the processing device 30 (such as a microcontroller, for instance) thereto. As exemplified in Figure 14, the target object 14 may be coupled to an end 12 of an actuated rotatable arm 120 with the PCB 20 attached to a measurement bench and coupled to an external controller 50 configured to drive the actuated rotatable arm 120 to apply the various imperfections to the target object 14 and configured to generate transmission signals for the transmitting coils TX1 and to receive the voltages ΔVsin, ΔVcos via the receiver coils RXSIN, RXCOS. The Inventor has noted that performing automatic simulations of the imperfections advantageously facilitates providing a fast way of generating a massive amount of training data for the ANN without substantially reducing an accuracy of the classification capabilities of the network with respect to the use of measurements which would otherwise involve relatively lengthy data collection procedures. As mentioned, what discussed in the foregoing mainly with respect to a rotary IPS device 14, 20 may be applied also to a linear IPS device configured to interact with a linearly moving shaft. This kind of devices (per se known) may be affected by the same or similar misalignments with respect to the rotating IPS devices 14, 20 discussed in the foregoing. For instance, (at least) the air-gap and tilt misalignments may apply to both kinds (e.g., linear and rotary) of IPS devices. A method as exemplified herein, comprises applying signal processing 200, 202, 204, 206, 208, 210, 212, 220, 222, 230 to a set of time-varying sensing signals URXSIN, URXCOS sensed via a sensor 14, 20 coupled to an actuating device 10 having a first part 12 movable relative to a second part 11. As exemplified herein, the sensor 14, 20 comprises an inductive position sensor, IPS. For instance, the sensor comprises: a target object 14 comprising a reflective area 140 configured to backscatter electromagnetic waves impinging thereon, and a transceiver 20, comprising a transmitting antenna TX configured to transmit electromagnetic waves towards the reflective area 140 of the target object, and a receiver antenna RXSIN, RXCOS comprising a first set of receiver antenna circuits RXSIN and a second set of receiver antenna circuits RXCOS. In the exemplary scenario considered, the set of time-varying sensing signals URXSIN, URXCOS comprises a first time-varying sensing signal URXSIN induced in the first set of receiver windings RXSIN based on electromagnetic waves backscattered from the reflective area of the target object and a second time-varying sensing signal URXCOS in quadrature with the first time-varying sensing signal URXSIN. Still in the exemplary scenario considered, applying the signal processing to the set of time-varying sensing signals comprises: applying pattern recognition processing 210, 212, 230 to the set of time-varying sensing signals ΔVsin, ΔVcos, in order to classify a condition of the actuating device 10 with respect to a reference condition thereof, providing an indication of the kind of irregularity detected with respect to a set of reference irregularity types W, AG, ψ_tilt, ψ_skew, O_A, and as a result of the pattern recognition processing 210, 212, 230, providing a set of indicator signals D; D0, D1, D2 to a user circuit A, the set of indicator signals indicative of the classified condition of the actuating device. As exemplified herein, e.g., in situations in which space constraints can be relaxed, it is possible to employ a combined (e.g., rotary) IPS sensor device, as discussed in the following mainly with respect to Figures 15 and 16. Figures 15 is a diagram exemplary of a combined (IPS) sensor device 20’ comprising an absolute position sensing circuit 1202 and a relative position sensing circuit 1204 which may be employed in one or more embodiments. As appreciable to those of skill in the art, the receiving coils 1202 of an absolute position IPS sensor 1202 may be considered as a single period of a spatial pattern comprising a plurality of receiving coils 1204, thereby providing the incremental position sensor. Combined sensor devices 20’ with adjacently arranged position inductive sensors are per se known. As exemplified in Figure 15, a rotary combined sensor 20’ comprises: - an inner sense receiver or winding 1202 having a number of pickup coils configured to detect N1=1 period of the motor shaft 12, and - an outer sense receiver 1204, for instance concentric with the inner sense receiver 1202, having a number of pickup coils configured to detect N2=16 periods of the motor shaft 12. It is noted that the values indicated above for the number of period pickup coils N1, N2 are purely exemplary and in no way limiting as notionally any number of pickup coils may be used in one or more embodiments. For instance, there is one turn of pick-up coils in every portion of the sensor and there are M=4 turns of excitation coils in every transmitter group TX. In one or more embodiments, using combined sensor 20’ exemplified in Figures 15 in the method as per the present disclosure provides an increased precision in detecting imperfections (such as misalignments) as it is possible to combine the precision of a multiperiod sensor (up to 0.02°) with the data collected by an absolute encoder. Without being bound to any specific model, the Inventor has observed that, while an absolute position sensor (also currently referred to as encoder) is sensitive to misalignments, the incremental position sensor is rather robust against the same. A method as per the present disclosure may be applied to the signals received both from the absolute encoder and from the relative encoder, in particular when data from a mechanical rotation of a full period T of the motor 10 is performed. Applying signal and / or pattern recognition processing 200, 202, 204, 206, 208, 210, 212, 220, 222, 230 to both signals may provide further insights into the behavior of the motor shaft 12 coupled to the target 14. For instance, the method employing combined sensor 20’ comprises: based on electromagnetic waves backscattered from the reflective area 140 of the target object 14, detecting a first set of time-varying sensing signal URXSIN URXCOS induced in a first portion 1202 of the combined sensor 20’ and a second set of time-varying sensing signals URXA, URXB induced in a second portion 1204 of the combined sensor 20’; applying signal processing 200, 202, 204, 206,to the first set of time- varying sensing signals URXSIN, URXCOS as well as to the second set of time-varying sensing signals URXA, URXB, and applying pattern recognition processing 210, 220, 212, 222, 230 to the first set of processed time-varying sensing signals URXSIN, URXCOS and to the second set of processed time-varying sensing signals URXA, URXB in order to classify an (error or misalignment) condition of the actuating device 10 associated to the combined sensor 20’ with respect to a reference (aligned) condition thereof, and as a result of the pattern recognition processing 210, 212, 230, providing a set of indicator signals D; D0, D1, D2 to a user circuit A, the set of indicator signals D; D0, D1, D2 indicative of the classified (error or misalignment) condition of the actuating device 10 (associated to the combined sensor 20’). Using a device as exemplified in Figure 15further provides the advantage of facilitating reconstructing an evolution over time of the position of the target 14 even when it rotates with a speed that varies (that is, non- uniform speed) across a full period T of the motor 10. In the alternative scenario in which the combined sensor 20’ is used in place of the sensor 20 the training (and corresponding inference signals) for the pattern recognition processing stages may be also expanded to comprise further signals such as those exemplified in Figure 16. The Inventor has observed that a plot of the filtered signals in the first URXSIN, URXCOS and second URXA, URXB sets of time-varying signals, provided as a result of applying the first filtering 231 to the difference signals ΔVsin, ΔVcos, varies in ways peculiar to the specific type of imperfection that affect the motor shaft 12 coupled to the respective sensing arrangement 14, 20’. For instance, as exemplified in Figure 16, the signal from the relative position sensor 1204 (visible about the center area of the plot) provides an additional information with respect to that provided by the double-circle curves obtained as a result of the detection with the absolute position sensor 1202. As exemplified in Figure 16, a first tilt error ψ_tilt is visible as a double curve; it may be possible to distinguish between a tilt error angle ψ_tilt (e.g., at angle φ=0) and a further tilt error angle ψ_tilt (e.g., at φ=90°). A method as exemplified herein comprises applying signal processing 200, 202, 204, 206, 208, 210, 212, 220, 222, 230 to a set of time-varying sensing signals URXSIN, URXCOS; URXA, URXB sensed via a sensor 14, 20; 20’ coupled to an actuating device 10 having a first part 12 movable relative to a second part 11. As exemplified herein, the sensor device 14, 20; 20’ comprises: a target object 14 comprising a reflective area 140 configured to backscatter electromagnetic waves impinging thereon, and a transceiver 20; 20’, comprising at least one transmitting antenna TX configured to transmit electromagnetic waves towards the reflective area 140 of the target object 14, and at least one receiver antenna RXSIN, RXCOS; 1202, 1204 comprising a first set of receiver winding RXSIN; 1202 and a second set of receiver windings RXCOS; 1204. For instance, the set of time-varying sensing signals comprises at least one first time-varying sensing signal induced in the first set of receiver windings based on electromagnetic waves backscattered from the reflective area of the target object and at least one second time-varying sensing signal in quadrature with the at least one first time-varying sensing signal. For instance, applying signal processing to the set of time-varying sensing signals comprises: applying pattern recognition processing 210, 212, 230 to the set of time-varying sensing signals in order to classify a condition of the actuating device with respect to a reference condition thereof, and as a result of the pattern recognition processing, providing a set of indicator signals D; D0, D1, D2 to a user circuit A, the set of indicator signals being indicative of the classified condition of the actuating device. Preferably, the classified condition of the actuating device comprises an alignment error condition of the actuating device with respect to a reference alignment condition thereof. As exemplified in Figures 15 and 16, the at least one receiver 1202, 1204 of the sensor 20’ comprises a first receiver 1202 and a second receiver 1204. For instance, the set of time-varying sensing signals comprises a first set of time-varying sensing signals URXSIN, URXCOS induced in the first receiver 1202 based on electromagnetic waves backscattered from the reflective area of the target object and a second set of time-varying sensing signals URXA, URXB induced in the second receiver 1204 based on electromagnetic waves backscattered from the reflective area of the target object. In the scenario exemplified in Figures 15 and 16, applying said signal processing to the set of time-varying sensing signals comprises: applying pattern recognition processing 210, 212, 230 to the time varying sensing signals in said first set of time varying sensing signals and in said second set of time varying sensing signal in order to classify a condition of the actuating device with respect to the reference alignment condition thereof, and as a result of the pattern recognition processing, providing a set of indicator signals to a user circuit, the set of indicator signals indicative of the classified (error or misalignment) condition of the actuating device. As exemplified herein, the method of using the combined sensor 20’ further comprises: measuring 200 at least a portion of periodically time-varying sensing signals in the first set of time-varying sensing signals URXSIN, URXCOS as well as in the second set of time-varying sensing signals URXA, URXB, extracting 202 a phase of the sensing signals second set of time- varying sensing signals URXA, URXB based on time-varying sensing signals in the first URXSIN, URXCOS and second URXA, URXB; computing 204 a first position of the first part 12 of the actuating device 10 based on a ratio of the portions of the sensing signals in the first set of time-varying sensing signals URXSIN, URXCOS; computing 204 a second position of the first part 12 of the actuating device 10 based on a ratio of the portions of the sensing signals in the second set of time-varying sensing signals URXA, URXB; combining the first (e.g., absolute) position data and the second (e.g., relative, incremental) position data to determine the angular phase ^ of the first signal detected with the absolute sensor 1202 by analyzing the sample detected at the same time by the relative encoder 1204. In a scenario that employs a combined sensor 20’ comprising an absolute position sensor 1202 and an incremental position sensor 1204 as exemplified Figure 15, the operations in block 208 of computing a mean velocity value ωM and the comparison performed is rendered optional. This is the result of the robustness of the incremental sensor 1204 with respect to target misalignments. Therefore, the incremental sensor 1204 can be used as a way to detect the position of the target 14, for example by detecting the real mechanical angle of the shaft 12 therewith. In alternative scenarios it may be possible to use an optical encoder (per se known) in place of the incremental sensor, for instance in order to find the mechanical angle of the shaft 12. In the scenario discussed above, the method thus comprises: measuring 200 a period T of a sensing signal U in the set of time- varying sensing signals, extracting 202 respective period-length portions of the time-varying sensing signals in the set of time-varying sensing signals based on the measured period; computing 204 a position ^ of the first part 12 of the actuating device based on a ratio of the period-length portions of the first time-varying sensing signal and of the second time-varying sensing signal; computing a (e.g., angular) velocity ω of the first part (e.g., a rotating shaft) of the actuating device (e.g., an electric motor) as the ratio of the position and of the measured period; subtracting 210, 220 a reference signal UREF from the first set of sensing signals and the second set of sensing signals in the set of time- varying sensing signals, providing a set of difference signals ΔVsin, ΔVcos as a result; applying 222 transformation processing to the set of difference signals ΔVsin, ΔVcos, providing a set of transformed difference signals as a result; applying pattern recognition processing 230 to the transformed set of difference signals, providing as a result a set of indicator signals D; D1, D2 indicative of an error condition of the actuating device. As exemplified herein, the method comprises: measuring 200 a period T of a sensing signal U in the set of time- varying sensing signals, extracting 202 respective period-length portions of the time-varying sensing signals in the set of time-varying sensing signals based on the measured period; computing 204 a position ^ of the first part 12 of the actuating device based on a ratio of the period-length portions of the first time-varying sensing signal and of the second time-varying sensing signal; computing a (e.g., angular) velocity ω of the first part (e.g., a rotating shaft) of the actuating device (e.g., an electric motor) as the ratio of the position and of the measured period; computing an average value ωM of the velocity; computing a velocity variation Δω based on a difference between the average angular velocity value and the angular velocity ω, preferably as a norm of the difference, and performing a comparison 208 of the computed velocity variation Δω with a threshold value ε, and as a result of the comparison indicating that the velocity variation Δω fails to exceed the threshold value ε, performing operations comprising: subtracting 210, 220 a reference signal UREF from the first sensing signal and the second sensing signal in the set of time-varying sensing signals, providing a set of difference signals ΔVsin, ΔVcos as a result; applying 222 transformation processing to the set of difference signals ΔVsin, ΔVcos, providing a set of transformed difference signals as a result; applying pattern recognition processing 230 to the transformed set of difference signals, providing as a result a set of indicator signals D; D1, D2 indicative of an error condition of the actuating device. As exemplified herein, the method comprises: applying 1200, 1300, 1400 a set of misalignments W, AG, ψ_tilt, ψ_skew, O_A to an assembly of the target object 14 and the actuating device 10, the set of misalignments W, AG, ψ_tilt, ψ_skew, O_A comprising different types of misalignments; collecting 1000 a set of reference difference signals indicative of the set of misalignments applied to the assembly of the target object and the actuating device; providing the collected set of reference difference signals to a user circuit. For instance, as exemplified in Figures 11 and 12, the method comprises: providing a simulation environment 1000 for numerical simulation of the electro-mechanical properties of the assembly of the target object and the actuating device, providing a digital version of the assembly of the target object and the actuating device in the simulation environment, applying 1200, 1300, 1400 a set of misalignments W, AG, ψ_tilt, ψ_skew, O_A to the digital version of the assembly of the target object and the actuating device, the set of misalignments W, AG, ψ_tilt, ψ_skew, O_A comprising different types of misalignments; performing, in the simulation environment, a simulation of the electro- mechanical properties of the digital version of the assembly of the target object and of the actuating device; as a result of the simulation performed, collecting a set of reference difference signals indicative of the set of misalignments applied to the assembly of the target object and the actuating device; providing the collected set of reference difference signals to a user circuit. As exemplified herein, the method comprises: training a pattern recognition processing stage 212, 230 to recognize patterns in the set of reference difference signals ΔVsin, ΔVcos associated to the different types of imperfections in the set of applied imperfections W, AG, ψ_tilt, ψ_skew, O_A, applying pattern recognition processing 212, 230 to the transformed difference signals ΔVsin, ΔVcos using the pattern recognition stage trained to recognize different types of imperfections using the collected set of reference difference signals. As exemplified herein, the method comprises applying low pass filtering 231 or high pass filtering 232 to the set of difference signals ΔVsin, ΔVcos prior to applying pattern recognition processing thereto. As exemplified herein, the method comprises applying normalization processing 206 to the computed velocity, dividing the computed angular velocity by a reference angular velocity ω0. A sensor as exemplified herein may comprise: a target object 14 configured to be coupled to an actuating device 10 and comprising a reflective area 140 configured to backscatter electromagnetic waves impinging thereon, and a transceiver circuit 20 comprising a transmitting antenna TX configured to be driven to transmit an electromagnetic wave towards the reflective planar surface 140 of the target object 14, and a receiver antenna RXSIN, RXCOS comprising a first receiver antenna circuit RXSIN and a second receiver antenna circuit RXCOS, the set of receiver antenna circuits RXSIN, RXCOS configured to receive a set of time-varying sensing signals URXCOS, URXSIN comprising a first time-varying sensing signal URXSIN and a second time-varying sensing signal URXCOS in quadrature with the first sensing signal, the set of time-varying sensing signals being induced in the set of receiver antenna circuits based on electromagnetic waves backscattered from the reflective planar surface of the target object, wherein the sensor further comprises processing circuitry 30 configured to drive transmission of the electromagnetic waves towards the reflective planar surface 140 of the target object 14 and to receive the induced set of time-varying sensing signals, the processing circuitry configured to apply signal processing to the set of time-varying sensing signals according to the method of any of the previous claims (e.g., when the inductive position sensor 14, 20 is coupled to an actuating device 10 having a first part 12 movable relative to a second part 11 along a movement trajectory). As exemplified herein, an apparatus 100 for industrial manufacturing, comprises: an actuating device having a first part movable relative to a second part, preferably a brushless electric motor, and a sensor as per the present disclosure, control circuitry A coupled to the actuating device and to the sensor and configured to drive the first part of the actuating device based on the set of indicator signals. It will be otherwise understood that the various individual implementing options exemplified throughout the figures accompanying this description are not necessarily intended to be adopted in the same combinations exemplified in the figures. One or more embodiments may thus adopt these (otherwise non-mandatory) options individually and / or in different combinations with respect to the combination exemplified in the accompanying figures. Without prejudice to the underlying principles, the details and embodiments may vary, even significantly, with respect to what has been described by way of example only, without departing from the extent of protection. The extent of protection is defined by the annexed claims.

Claims

CLAIMS 1. A method, comprising: applying signal processing (200, 202, 204, 206, 210, 212, 220, 222, 230) to a set of time-varying sensing signals (URXSIN, URXCOS; URXA, URXB) sensed via a sensor (14, 20; 20’) coupled to an actuating device (10) having a first part (12) movable relative to a second part (11), wherein the sensor (14, 20; 20’) comprises: a target object (14) comprising a reflective area (140) configured to backscatter electromagnetic waves impinging thereon, and a transceiver (20; 20’), comprising: at least one transmitting antenna (TX) configured to transmit electromagnetic waves towards the reflective area (140) of the target object (14), and at least one receiver antenna (RXSIN, RXCOS; 1202, 1204) comprising a first set of receiver antenna circuits (RXSIN; 1202) and a second set of receiver antenna circuits (RXCOS; 1204), wherein: the set of time-varying sensing signals (URXSIN, URXCOS; URXA, URXB) comprises at least one first time-varying sensing signal (URXSIN; URXA) induced in the first set of receiver windings (RXSIN; 1202) based on electromagnetic waves backscattered from the reflective area (140) of the target object (14) and at least one second time-varying sensing signal (URXCOS; URXB) in quadrature with the first time-varying sensing signal (URXSIN; URXA), and applying said signal processing (200, 202, 204, 206, 210, 212, 220, 222, 230) to the set of time-varying sensing signals (URXSIN, URXCOS; URXA, URXB) comprises: applying pattern recognition processing (210, 212, 230) to the set of time-varying sensing signals (URXSIN, URXCOS; URXA, URXB) in order to classify a condition of the actuating device (10) with respect to a reference condition thereof, and as a result of the pattern recognition processing (210, 212, 230), providing a set of indicator signals (D; D0, D1, D2) to a user circuit (A), the set of indicator signals (D; D0, D1, D2) indicative of the classifiedcondition of the actuating device (10), preferably wherein the method classified condition of the actuating device (10) comprises an alignment error condition of the actuating device (10) with respect to a reference alignment condition thereof.

2. The method of claim 1, comprising: measuring (200) a period (T) of a sensing signal (U) in the set of time- varying sensing signals (URXSIN, URXCOS), extracting (202) respective period-length portions of the time-varying sensing signals in the set of time-varying sensing signals (URXSIN, URXCOS) based on the measured period portion (T); computing (204) a position (^) of the first part (12) of the actuating device (10) based on a ratio of the period-length portions of the first time- varying sensing signal (URXSIN) and of the second time-varying sensing signal (URXCOS); computing a velocity (ω) of the first part (12) of the actuating device (10) as the ratio of the position (^) and of the measured period portion (T); computing an average value (ωM) of the velocity (ω) over said measured period portion (T); computing a velocity variation (Δω) based on a difference between the average angular velocity value (ωM) and the angular velocity (ω), preferably as a norm of said difference, and performing a comparison (208) of the computed velocity variation (Δω) with a threshold value (ε), and as a result of the comparison (208) indicating that the velocity variation (Δω) fails to exceed said threshold value (ε), performing operations comprising: subtracting (210, 220) a reference signal (UREF) from the first sensing signal (URXSIN) and the second sensing signal (URXCOS) in the set of time-varying sensing signals (URXSIN, URXCOS), providing a set of difference signals (ΔVsin, ΔVcos) as a result; applying (222) transformation processing, preferably fast Fourier transform, FFT processing, to the set of difference signals (ΔVsin, ΔVcos), providing a set of transformed difference signals as a result; applying pattern recognition processing (230) to the transformed set of difference signals, providing as a result a set of indicatorsignals (D; D1, D2) indicative of an error condition of the actuating device (10).

3. The method of claim 1 or claim 2, comprising: applying (1200, 1300, 1400) a set of misalignments (W, AG, ψ_tilt, ψ_skew, O_A) to an assembly of the target object (14) and the actuating device (10), the set of misalignments (W, AG, ψ_tilt, ψ_skew, O_A) comprising different types of misalignments; collecting (1000) a set of reference difference signals indicative of the set of misalignments applied to the assembly of the target object (14) and the actuating device (10); providing the collected set of reference difference signals to a user circuit (212, 230).

4. The method of claim 1 or claim 2, comprising: providing a simulation tool (1000) for numerical simulation of the electro-mechanical properties of the assembly of the target object (14) and the actuating device (10), setting a digital version of the assembly of the target object (14) and the actuating device (10) in said simulation tool (1000), applying (1200, 1300, 1400) a set of misalignments (W, AG, ψ_tilt, ψ_skew, O_A) to said digital version of the assembly of the target object (14) and the actuating device (10), the set of misalignments (W, AG, ψ_tilt, ψ_skew, O_A) comprising different types of misalignments; performing, in the simulation tool (1000), a simulation of the electro- mechanical properties of said digital version of the assembly of the target object (14) and of the actuating device (10); as a result of the simulation performed, collecting (1000) a set of reference difference signals indicative of the set of misalignments applied to the assembly of the target object (14) and the actuating device (10); providing the collected set of reference difference signals to a user circuit (212, 230).

5. The method of claim 3 or claim 4, comprising: training a pattern recognition processing stage (230) to recognizepatterns in the set of reference difference signals (ΔVsin, ΔVcos) associated to the different types of imperfections in the set of applied imperfections (W, AG, ψ_tilt, ψ_skew, O_A), applying pattern recognition processing to the transformed difference signals (ΔVsin, ΔVcos) using the trained pattern recognition stage (230) to recognize different types of imperfections using the collected set of reference difference signals (ΔVsin, ΔVcos).

6. The method of claim 4 or claim 5, comprising: applying low pass filtering (231) to the set of reference difference signals, and applying pattern recognition processing (230, 234) to the low pass filtered transformed difference signals (ΔVsin, ΔVcos), wherein applying pattern recognition processing (230, 234) comprises applying regression processing (234).

7. The method of claim 4 or claim 5, comprising: applying high pass filtering (232) to the set of reference difference signals, and applying pattern recognition processing (230, 236) to the high pass filtered set of reference difference signals (ΔVsin, ΔVcos), wherein applying pattern recognition processing (230, 236) comprises applying artificial neural network processing (236).

8. The method of any one of claims 2 to 7, comprising applying normalization processing (206) to the computed velocity (ω), dividing the computed angular velocity (ω) by a reference angular velocity (ω0).

9. The method of any one of the previous claims, wherein applying pattern recognition processing (210, 212, 230) to the set of time-varying sensing signals (ΔVsin, ΔVcos) comprises: applying (210) a coordinate transformation to the time-varying sensing signals (URXSIN, URXCOS), associating a set of parametric coordinates to the values of samples of the time-varying sensing signals (URXCOS, URXSIN), determining a parametric equation of a trajectorycurve of the target object (14); providing (212) a reference trajectory curve (TJR) in the defined parametric coordinate space; computing a norm between the transformed signals and the reference trajectory curve (TJR); performing a comparison between the difference of the computed norm and a threshold distance value (ΔTHJ), and providing a set of indicators (D0) as a result of the comparison.

10. The method of any one of the previous claims, wherein: - the at least one receiver (RXSIN, RXCOS; 1202, 1204) of the sensor (20’) comprises a first receiver (1202) and a second receiver (1204), and - the set of time-varying sensing signals (URXSIN, URXCOS; URXA, URXB) comprises a first set of time-varying sensing signals (URXSIN, URXCOS) induced in the first receiver (RXSIN, RXCOS; 1202) based on electromagnetic waves backscattered from the reflective area (140) of the target object (14) and a second set of time-varying sensing signals (URXA, URXB) induced in the second receiver (1204) based on electromagnetic waves backscattered from the reflective area (140) of the target object (14).

11. The method of claim 10, comprising: measuring (200) at least one portion of a period (T) oftime-varying sensing signals in the first set of time-varying sensing signals (URXSIN, URXCOS), as well as in the second set of time-varying sensing signals (URXA, URXB); extracting (202) a phase of the sensing signals in the second set of time-varying sensing signals (URXA, URXB) based on time-varying sensing signals in the first (URXSIN, URXCOS) and second (URXA, URXB) time- varying sensing signals; computing (204) a first position of the first part (12) of the actuating device (10) based on a ratio of the portions of the sensing signals in the first set of time-varying sensing signals (URXSIN, URXCOS); computing (204) a second position of the first part (12) of the actuating device (10) based on a ratio of the portions of the sensing signalsin the second set of time-varying sensing signals (URXA, URXB); combining the first position data and the second position to determine the angular phase (^) of the first signal detected with the first receiver(1202) by analyzing the sample detected at the same time by the second receiver (1204), applying pattern recognition processing (210, 212, 230) to the combined sensing signals in the set of combined sensing signals in order to classify a condition of the actuating device (10) with respect to the reference alignment condition thereof, and as a result of the pattern recognition processing (210, 212, 230), providing a set of indicator signals (D; D0, D1, D2) to a user circuit (A), the set of indicator signals (D; D0, D1, D2) indicative of the classified condition of the actuating device (10).

12. The method of anyone of the previous claims, wherein applying said signal processing (200, 202, 204, 206, 210, 212, 220, 222, 230) to the set of time-varying sensing signals (URXSIN, URXCOS; URXA, URXB) comprises: measuring (200) at least one portion of a period (T) of a sensing signal (U) in the set of time-varying sensing signals (URXSIN, URXCOS; URXA, URXB); extracting (202) respective period-length portions of the time-varying sensing signals in the set of time-varying sensing signals (URXSIN, URXCOS; URXA, URXB) based on the measured period portion (T); computing (204) a position (^) of the first part (12) of the actuating device (10) based on a ratio of the period-length portions of the at least one first time-varying sensing signal (URXSIN; URXA) and of the at least one second time-varying sensing signal (URXCOS; URXB); computing a velocity (ω) of the first part (12) of the actuating device (10) as the ratio of the position (^) and of the measured period portion (T); subtracting (210, 220) a reference signal (UREF) from the at least one first sensing signal (URXSIN; URXA) and the at least one second sensing signal (URXCOS; URXB) in the set of time-varying sensing signals (URXSIN, URXCOS; URXA, URXB), providing a set of difference signals (ΔVsin, ΔVcos) as a result;applying (222) transformation processing, preferably fast Fourier transform, FFT processing, to the set of difference signals (ΔVsin, ΔVcos), providing a set of transformed difference signals as a result; applying pattern recognition processing (230) to the transformed set of difference signals, providing as a result a set of indicator signals (D; D1, D2) indicative of an error condition of the actuating device (10).

13. A sensor (14, 20; 20’) comprising: a target object (14) configured to be coupled to an actuating device (10) and comprising a reflective area (140) configured to backscatter electromagnetic waves impinging thereon, and a transceiver circuit (20; 20’) comprising at least one transmitting antenna (TX) configured to be driven to transmit an electromagnetic wave towards the reflective planar surface (140) of the target object (14), and at least one receiver antenna (RXSIN, RXCOS; 1202, 1204) comprising a first receiver antenna circuit (RXSIN; 1202) and a second receiver antenna circuit (RXCOS; 1204), the set of receiver antenna circuits (RXSIN, RXCOS; 1202, 1204) configured to receive a set of time- varying sensing signals (URXCOS, URXSIN; URXA, URXB) comprising at least one first time-varying sensing signals (URXSIN; URXA) and at least one second time-varying sensing signals (URXCOS; URXB) in quadrature with the at least one first sensing signal (URXSIN; URXA), the set of time- varying sensing signals (URXSIN, URXCOS; URXA, URXB) being induced in the set of receiver antenna circuits (RXSIN, RXCOS; 1202, 1204) based on electromagnetic waves backscattered from the reflective planar surface (140) of the target object (14), wherein the sensor (14, 20; 20’) further comprises processing circuitry (30) configured to drive transmission of the electromagnetic waves towards the reflective planar surface (140) of the target object (14) and to receive the induced set of time-varying sensing signals (URXSIN, URXCOS; URXA, URXB), the processing circuitry (30) configured to apply signal processing to the set of time-varying sensing signals (URXSIN, URXCOS; URXA, URXB) according to the method of any one of the previous claims.

14. The sensor (14, 20; 20’) of claim 13, comprising; a first receiver antenna (1202) and a second receiver antenna (1204) arranged adjacent therebetween, - the second receiver antenna (1204) comprises a plurality of antenna circuit patterns comprising replicas of an antenna circuit pattern of said first receiver antenna (1202), and wherein the processing circuitry (30) is configured to drive transmission of the electromagnetic waves towards the reflective planar surface (140) of the target object (14) and to receive the first set of time- varying sensing signals (URXSIN, URXCOS) induced in said first receiver (200) and the second set of time-varying sensing signals (URXA, URXB) induced in said second receiver antenna (1204).

15. Apparatus (100) for industrial manufacturing, comprising: an actuating device (10) having a first part (12) movable relative to a second part (11), preferably a brushless electric motor, and a sensor (14, 20; 20’) according to claim 13 or claim 14, the sensor (14, 20; 20’) being coupled to the actuating device (10), control circuitry (A) coupled to the actuating device (10) and to the sensor (14, 20; 20’) and configured to drive the first part (12) of the actuating device (10) based on said set of indicator signals (D; D0, D1, D2).

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