System and method for controlling wire electric discharge machine

Abstract

Embodiments of the present disclosure provide a wire electrical discharge machine (EDM) including a delivery system in contact with one or a combination of a wire electrode and a workpiece for delivering the wire electrode and the workpiece to a vicinity of the counterpart, and an energy source for inducing an electrical discharge between the wire electrode and the workpiece. The line EDM includes a line electrode position measuring unit including a light source irradiating a line electrode with a coded irradiation pattern and a camera for acquiring a set of images of the line electrode irradiated by the coded irradiation pattern. The line EDM includes a processor that reconstructs a position of a segment of the line electrode at a reconstruction rate greater than an acquisition rate of the camera by utilizing compressive sensing using a sparse reconstruction technique, and a controller that controls the delivery system and the energy source based on the reconstructed position.

Description

Technical Field

[0001] The present invention generally relates to a wire electrical discharge machine (EDM), and more particularly to a method of controlling a wire EDM for machining a workpiece. Background Art

[0002] Electrical discharge machining (EDM) is a metal manufacturing process that uses electrical discharges (or sparks) to obtain the desired shape of a metal workpiece. Material is removed from a metal workpiece by a series of rapidly recurring electrical discharges between two electrodes separated by a dielectric fluid and to which a voltage is applied. One of the electrodes is the tool electrode or tool and the other is the workpiece electrode or workpiece. The manufacturing process depends on the tool and workpiece not coming into physical contact.

[0003] Wire EDM (wire EDM) is a precision cutting device that uses the EDM manufacturing process to process workpieces. The tool electrode in wire EDM is the wire, and the workpiece acts as the second electrode. When the voltage between the wire and the workpiece increases, the intensity of the electric field in the volume between the wire and the workpiece becomes larger, causing dielectric breakdown of the dielectric fluid, which results in the generation of an arc. As a result, material is removed from the electrodes (i.e., the wire and the workpiece).

[0004] Normally, to avoid the wire from corroding and breaking it, the wire is wound between two reels so that the active part of the wire is constantly changing. However, the occurrence of discharges and the relatively small diameter of the wire cause the wire to vibrate while it is damped on two supports that limit the length of the wire vibration.

[0005] Typically, wire EDM is provided with arrangements for one or two types of machining or cutting, such as rough cutting and skim cutting. Rough cutting involves roughly and quickly machining a workpiece, while skim cutting involves an additional operation in which the wire retraces the same path after the rough cutting is completed. Therefore, skim cutting requires higher precision than rough cutting to obtain a finer accurate cut with surface integrity. In particular, although rough cutting and skim cutting have different goals, the accuracy of both types of cutting depends on the vibration of the wire.

[0006] Typically, vibration estimation with desired accuracy is challenging due to the presence of interference and different forces acting on the wire. Furthermore, one or more conventional methods utilize optics to focus the reflection of light to a one-dimensional sensor that detects the oscillation of the wire in one direction as the position of the image forming point of the one-dimensional sensor changes. This arrangement makes it possible to detect small vibrations of the wire, however, the result of estimating the vibration is inaccurate for controlling wire EDM for precision machining processes.

[0007] To this end, in order to solve the aforementioned problems, there exists a need for a method of estimating the vibration of the wire with an accuracy suitable for maintaining the accuracy of the wire EDM during the rough cutting process and the finish cutting process. Summary of the invention

[0008] The present invention provides a wire electrical discharge machine (EDM) and a method for controlling the wire EDM to process a workpiece.

[0009] Some embodiments are based on the understanding that detecting the position changes of the image forming points of the one-dimensional sensor of the camera makes it possible to reconstruct the vibration of the wire electrode in the frequency domain. However, for this reconstruction, some assumptions need to be made. For example, one assumption is that the frequency of the timing of the position changes on a line is indicative of the vibration of the entire wire electrode. However, this assumption may not be correct in the context of wire EDM, because the discharge and the electrolyte ripples caused by the machining of the workpiece disturb the wire electrode harmonics at multiple unknown frequencies.

[0010] Therefore, controlling the machining of a workpiece based only on vibration feedback determined on one line may provide insufficient information for control. The wire electrode is a soft continuum that deforms significantly during machining. The deformation is transmitted to the machined surface (such as the workpiece), which reduces machinability. Therefore, it is difficult to predict the behavior of the wire electrode because the wire electrode is affected by a complex physical phenomenon in which various factors (such as explosions due to discharges and water pressure due to processing fluids) are involved. Therefore, it is necessary to estimate the physical behavior of the wire electrode to improve the accuracy of controlling the wire EDM.

[0011] Some embodiments are based on the recognition that the physical behavior of a wire electrode can be represented by the position and / or shape of the wire electrode at different times. This representation indicates both the wire displacement and the frequency and amplitude of the vibration, which is beneficial to the accuracy of the control. Therefore, the purpose of some embodiments is to estimate the different positions and / or shapes of at least one segment of the wire electrode at different times. Additionally or alternatively, the purpose of some embodiments is to estimate the frequency and amplitude of the vibration of different segments of the wire.

[0012] Some embodiments are further based on the recognition that a camera that observes the wire electrode with at least a two-dimensional 2D field of view (FoV) can be used to reconstruct the position of the wire electrode at different times. However, this solution encounters several problems. For example, the vibration frequency of the wire electrode in the wire EDM is generally in the range of about 1 kilohertz (kHz), which would require a camera with an acquisition rate of at least 2000 frames per second (fps) to accurately locate the wire electrode. Such a high-speed camera may add significant cost to the assembly of the wire EDM. In addition, the discharge causes a wide white blur that interferes with the 2D image acquisition. In addition, bubbles or other transient objects may also cast shadows that interfere with the 2D image acquisition. Therefore, an object of some embodiments is to utilize compressed sensing using sparse reconstruction techniques so that the use of possibly expensive high-speed cameras with high fps can be eliminated, thereby reducing the cost of using the wire EDM.

[0013] To this end, some embodiments are based on the recognition of a wire EDM for machining a workpiece. The wire EDM includes a conveying system, such as a pulley, which contacts one of the wire electrode and the workpiece or a combination thereof for conveying the wire electrode and the workpiece to the vicinity of each other. The wire EDM further includes an energy source configured to induce a discharge between the wire electrode and the workpiece. The EDM further includes a wire electrode position measurement system, the wire electrode position measurement system including a light source and a camera, the light source being configured to illuminate the wire electrode with a coded illumination pattern, the camera having an image sensor, and the image sensor being arranged to acquire a set of images indicating the wire electrode illuminated by the coded illumination pattern at different positions. The wire EDM further includes a processor, the processor being configured to reconstruct the position of at least one segment of the wire electrode at a reconstruction rate greater than the acquisition rate of the camera by utilizing compressed sensing using a sparse reconstruction technique. The wire EDM further includes a controller, the controller being configured to control at least one of the conveying system and the energy source based on the position of at least the segment of the wire electrode reconstructed at the reconstruction rate.

[0014] Some embodiments are based on the recognition that the energy source is further configured to generate a waveform consisting of a sequence of on-time voltage pulses and off-time voltage pulses. The processing energy is reduced by shortening the duration of the on-time voltage pulse or by extending the duration of the off-time, and the processing energy is increased by extending the duration of the on-time voltage pulse or by shortening the duration of the off-time voltage pulse. The processing energy is kept constant and a voltage feedback control is applied to control the processing speed of the workpiece. The control of the processing speed of the workpiece enables the machining accuracy of the workpiece to be achieved.

[0015] Some embodiments are based on the recognition that the coded illumination pattern of the light source is configured to generate a pseudo-random sequence of on and off light pulses. The duration of each pulse of the pseudo-random sequence of on and off light pulses is less than or equal to the Nyquist sampling rate of the vibration frequency of the wire electrode. The total duration of the pseudo-random sequence of on and off light pulses is less than or equal to the duration of a frame exposure of the camera. The duration of each pulse of the sequence of on and off light pulses is less than or equal to the Nyquist sampling rate of the vibration frequency of the wire electrode, which enables the cost of the camera to be reduced.

[0016] Some embodiments are based on the recognition that the light source and the camera of the wire electrode position measurement unit are arranged on opposite sides of the wire electrode. The image sensor of the camera is configured to collect an image set of the sum of the shadows of the wire electrode encoded by the illumination pattern as the wire electrode moves over the image sensor of the camera. The collection of the image set of the sum of the shadows enables the determination of the movement of the vibration of the wire electrode.

[0017] Some embodiments are based on the recognition that compressed sensing using sparse reconstruction techniques includes buffering a set of images acquired from a camera. Compressed sensing using sparse reconstruction techniques further includes removing shadows of bubbles from shadows of a wire electrode moving on an image sensor captured in the set of images acquired from the camera to generate a set of bubble-free images of the wire electrode encoded by a coded illumination pattern. The generation of bubble-free images enables the elimination of contamination of the spectrum of a purely vibrating wire electrode from the set of images. Compressed sensing using sparse reconstruction techniques further includes compressing the pixel dimensions of the set of bubble-free images by multiplying the pixel dimensions of the set of bubble-free images by a Gaussian random matrix to output a set of compressed images. Compressed sensing using sparse reconstruction techniques further includes solving a group-one norm sparse recovery problem to calculate a spectrum matrix of the wire electrode from the set of compressed images. The wire electrode is accompanied by vibrations as it moves on the image sensor. Compressed sensing using sparse reconstruction techniques further includes identifying a reduced set of frequency intervals corresponding to the locations of rows of the spectrum matrix including the maximum Euclidean norm. Compressed sensing using sparse reconstruction techniques further includes solving a least squares reconstruction problem using a reduced set of frequency bins to reconstruct a set of high temporal resolution images of the motion of the wire electrode with a spatial resolution equal to the spatial resolution of the image sensor of the camera. Compressed sensing using sparse reconstruction techniques further includes outputting the position of at least the segment of the wire electrode from the reconstructed set of high temporal resolution images of the motion of the wire electrode. The use of compressed sensing using sparse reconstruction techniques enables the reconstruction of a set of high temporal resolution images without the need for an expensive camera with a high fps.

[0018] Some embodiments are based on the recognition that removing shadows of bubbles from a set of images acquired by a camera to generate a set of bubble-free images is performed by solving a robust principal component analysis problem. The robust principal component analysis problem includes modeling the set of images as consisting of low-rank matrix components and sparse matrix components. The low-rank matrix components correspond to vibrating wire electrodes without bubbles, and the sparse components correspond to bubbles. The robust principal component analysis problem further includes outputting the low-rank matrix components as a set of bubble-free images.

[0019] Some embodiments are based on the recognition that solving the group-one-norm sparse recovery problem includes minimizing the difference between a set of compressed images and a synthesized set of compressed images, the synthesized set of compressed images being formed by the product of a spectrum matrix of a vibrating wire electrode and a Fourier transform applied in an upsampled time domain. Solving the group-one-norm sparse recovery problem further includes regularizing the minimization of the difference by the sum of the Euclidean norms of the rows of the spectrum matrix of the vibrating wire electrode, and outputting in the upsampled time domain a spectrum matrix that is sparse in frequency bins by having a small number of non-zero row norms.

[0020] Some embodiments are based on the recognition that the controller is further configured to determine at least the vibration frequency of the wire electrode by converting the reduced set of frequency intervals into physical frequency values. The controller is further configured to determine at least the vibration amplitude of the wire electrode by converting the positions of the segments of the wire electrode on the sensor array into the physical positions of the wire electrode according to the geometric structure of the components of the wire electrode position measurement unit. The determined vibration frequency of the wire electrode and the vibration amplitude of the wire electrode are used to control the wire EDM to perform precise machining of the workpiece.

[0021] Some embodiments are based on the recognition that the controller is further configured to reduce the likelihood of wire electrode breakage during rough cutting by performing control actions based on: analyzing the determined vibration frequency and amplitude of the wire electrode for significant changes; based on detecting one or more significant changes, reducing the processing energy input to the wire electrode; and based on detecting one or more significant changes, reducing the processing speed of the workpiece and the conveying system. The reduction in the input processing energy and the reduction in the processing speed of the workpiece and the conveying system enable safe operation of the wire EDM.

[0022] Some embodiments are based on the recognition that the controller is further configured to control the straightness and dimensional error of the cut during the finishing cut by performing control actions based on: analyzing the amplitude of the wire vibration to detect that the amplitude is greater than a threshold; when the shape of the wire electrode is estimated to be a convex shape, reducing the processing speed of the workpiece and the conveying system to reduce the vibration amplitude in the wire electrode; when the shape of the wire electrode is estimated to be a concave shape, increasing the processing speed of the workpiece and the conveying system to increase the vibration amplitude in the wire electrode; when the wire electrode is far away from the workpiece, increasing the machining energy; when the wire electrode is closer to the workpiece, reducing the machining energy. Such control enables improving the accuracy of the finishing cut.

[0023] Some embodiments are based on the recognition that the controller is further configured to control the slashes cut during the finishing cut by performing control actions based on: analyzing the vibration amplitude to detect vibration fluctuations of the wire electrode; when the shape of the wire electrode is estimated to be a convex shape, reducing the processing speed of the workpiece and the conveying system to reduce the vibration amplitude in the wire electrode; when the shape of the wire electrode is estimated to be a concave shape, increasing the processing speed of the workpiece and the conveying system to increase the vibration amplitude in the wire electrode; when the wire electrode is far away from the workpiece, increasing the processing energy; when the wire electrode is closer to the workpiece, reducing the processing energy. Such control of the slashes cut during the finishing cut enables the accuracy of the finishing cut to be improved.

[0024] Thus, some embodiments disclose a method for machining a workpiece. The method includes delivering a wire electrode to the vicinity of the workpiece. The method further includes inducing a discharge between the wire electrode and the workpiece. The method further includes irradiating the wire electrode with a coded illumination pattern. The method further includes acquiring a set of images of the wire electrode illuminated by the coded illumination pattern at different positions. The method further includes reconstructing the position of at least one segment of the wire electrode at a reconstruction rate greater than the acquisition rate of a camera that acquires the set of images by utilizing compressed sensing using a sparse reconstruction technique. The method further includes controlling at least one of the following based on the position of at least the segment of the wire electrode reconstructed at the reconstruction rate: a conveying system that delivers the wire electrode to the vicinity of the workpiece, and an energy source that induces the discharge.

[0025] Therefore, some embodiments disclose a non-transitory computer-readable medium storing computer-executable instructions for processing a workpiece. The computer-executable instructions are configured to deliver a wire electrode to the vicinity of the workpiece. The computer-executable instructions are further configured to induce a discharge between the wire electrode and the workpiece. The computer-executable instructions are further configured to illuminate the wire electrode with a coded illumination pattern. The computer-executable instructions are further configured to acquire a set of images indicating the wire electrode illuminated by the coded illumination pattern at different positions. The computer-executable instructions are further configured to reconstruct the position of at least one segment of the wire electrode at a reconstruction rate greater than the acquisition rate of a camera that acquires the image set by utilizing compressed sensing using a sparse reconstruction technique. The computer-executable instructions are further configured to control at least one of the following based on the position of at least the segment of the wire electrode reconstructed at the reconstruction rate: a delivery system that delivers the wire electrode to the vicinity of the workpiece, and an energy source that induces the discharge.

[0026] In the following detailed description, the present disclosure is further described by way of non-limiting examples of exemplary embodiments of the present disclosure with reference to the annotated multiple accompanying drawings in which like reference numerals represent similar parts throughout the several views of the drawings. The drawings shown are not necessarily to scale, with emphasis instead generally being placed upon illustrating the principles of the presently disclosed embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1A A schematic diagram illustrating basic components of a wire electrical discharge machine (EDM) according to some embodiments of the present disclosure.

[0028] Figure 1B A schematic diagram illustrating wire EDM for machining a workpiece according to some embodiments of the present disclosure.

[0029] Figure 2 Inaccuracies that affect the cut quality of a workpiece in conventional wire EDM are illustrated according to some embodiments of the present disclosure.

[0030] Figure 3A Illustrated is a schematic diagram depicting exemplary positions of different components of a wire electrode position measurement unit relative to a wire electrode embedded in a machining fluid according to some embodiments of the present disclosure.

[0031] Figure 3B A schematic diagram illustrating an image of an image set captured by a camera of a wire electrode position measurement unit according to some embodiments of the present disclosure.

[0032] Figure 4A A block diagram illustrating control of a camera for determining timing of triggering and control of a light source for producing an illumination pattern, according to some embodiments of the present disclosure.

[0033] Figure 4B The illustrations depict diagrams of constant illumination patterns produced by light sources according to some embodiments of the present disclosure.

[0034] Figure 4C The illustrations depict a diagram of a pseudo-random sequence of on and off light pulses produced by a light source according to some embodiments of the present disclosure.

[0035] Figure 5 A diagram illustrating the position of a segment of a wire electrode over time and corresponding sensor measurements observed with a camera according to some embodiments of the present disclosure.

[0036] Fig. 6A The illustration depicts a diagram of a measurement operator "A" corresponding to an illumination pattern having a pseudo-random sequence of on and off light pulses that begins at the same time as the camera begins exposure, according to some embodiments of the present disclosure.

[0037] Figure 6B The illustration depicts a diagram of a measurement operator "A" corresponding to an illumination pattern having a pseudo-random sequence of on and off light pulses starting at random moments within the exposure duration of the camera, according to some embodiments of the present disclosure.

[0038] Figure 7 The illustration depicts a diagram of a set of images of a moving wire electrode captured by a camera according to some embodiments of the present disclosure.

[0039] Figure 8 The illustrations depict diagrams depicting a comparison between continuous motion of a wire electrode and a sequence of image sets acquired by a camera, according to some embodiments of the present disclosure.

[0040] Fig. 9 An exemplary block diagram illustrating steps for reconstructing the position of at least one segment of a wire electrode in compressed sensing using sparse reconstruction techniques according to some embodiments of the present disclosure.

[0041] Fig.10 The illustration depicts a diagram illustrating the presence of bubbles in a machining fluid surrounding a wire electrode of a wire EDM, according to some embodiments of the present disclosure.

[0042] Fig.11 The illustration shows a diagram of generating a bubble-free image set from an image set acquired by a camera according to some embodiments of the present disclosure.

[0043] Fig.12 An exemplary block diagram is illustrated for determining at least a vibration frequency and an amplitude of a wire electrode according to some embodiments of the present disclosure.

[0044] Fig.13 An exemplary block diagram illustrating a method for reducing the likelihood of wire electrode breakage during rough cutting according to some embodiments of the present disclosure is illustrated.

[0045] Fig.14 An exemplary block diagram illustrating a method for controlling straightness and dimensional error of a cut during a finishing cut according to some embodiments of the present disclosure is illustrated.

[0046] Fig.15 An exemplary block diagram is illustrated for controlling slashes cut during finish cutting according to an embodiment of the present disclosure.

[0047] Fig.16 Waveforms generated by energy sources according to some embodiments of the present disclosure are illustrated.

[0048] Fig.17 The illustration depicts a flow chart of a method for machining a workpiece according to some embodiments of the present disclosure. DETAILED DESCRIPTION

[0049] (Detailed description)

[0050] In the following description, for the purpose of illustration, many specific details are set forth in order to provide a thorough understanding of the present disclosure. However, it will be clear to those skilled in the art that the present disclosure can be implemented without these specific details. In other cases, the devices and methods are shown only in block diagrams in order to avoid obscuring the present disclosure. It is contemplated that various changes can be made to the functions and arrangements of the elements without departing from the spirit and scope of the disclosed subject matter as set forth in the appended claims.

[0051] As used in this specification and claims, the terms "for example," "for example," and "such as," and the verbs "include," "have," "comprises," and their other verb forms, when used in conjunction with a list of one or more components or other items, are each to be interpreted as open-ended, meaning that the list is not to be considered to exclude other, additional components or items. The term "based on" means based at least in part on. In addition, it will be understood that the phraseology and terminology employed herein are for descriptive purposes and should not be considered limiting. Any headings used within this description are for convenience only and have no legal or limiting effect.

[0052] Specific details are provided in the following description to provide a thorough understanding of the embodiments. However, it will be appreciated by those skilled in the art that embodiments may be implemented without these specific details. For example, the systems, processes and other elements in the disclosed subject matter may be shown as parts in block diagram form, so as not to obscure the embodiments in unnecessary details. In other cases, known processes, structures and techniques may be shown without unnecessary details, so as to avoid obscuring the embodiments. In addition, similar reference numerals and names in the various drawings indicate similar elements.

[0053] (System Overview)

[0054] Figure 1A Schematic diagram 100A of a portion of a wire electrical discharge machine (EDM) according to some embodiments of the present disclosure is illustrated. Schematic diagram 100A includes a workpiece 102, a wire electrode 104, a wire guide 106, and an energy source 108. Schematic diagram 100A further depicts a direction of motion 110 of the workpiece 102 and a direction of motion 112 of the wire electrode 104. In various implementations, the EDM is configured to move one or a combination of the workpiece and the wire electrode itself. Thus, in some embodiments, the machining speed is a relative speed between the wire and the workpiece. Schematic diagram 100A further depicts an electrical discharge 114.

[0055] The workpiece 102 may be a metal piece that needs to be manufactured into a desired shape. The wire electrode 104 may be a wire piece that can be used to manufacture the workpiece 102. Wire EDM utilizes discharge 114 or sparks to remove material from the workpiece 102 to obtain the desired shape of the workpiece 102. The wire electrode 104 acts as a first electrode, and the workpiece 102 acts as a second electrode. The wire electrode 104 and the workpiece 102 are separated by a dielectric fluid, and a series of rapidly repetitive current discharges or electrical discharges 114 are generated between two electrodes (such as the wire electrode 104 and the workpiece 102) by applying a voltage from an energy source 108 to remove material from the workpiece 102.

[0056] An energy source 108, such as a voltage source, is used to provide a voltage between the two electrodes. The workpiece 102 moves along a motion direction 110 during machining of the workpiece 102, and the movement speed of the workpiece 102 is the processing speed. The wire electrode 104 moves along a motion direction 112 for machining the workpiece 102, and the movement speed of the wire electrode 104 is the feed rate of the wire electrode 104. The movement of the wire electrode 104 can be controlled via a wire guide 106. Moreover, the occurrence of the discharge 114 and the relatively small diameter of the wire electrode 104 cause the wire electrode 104 to vibrate while it is damped on two supports that limit the length of the wire vibration. Details of the wire EDM of the present disclosure and components associated therewith are described, for example, in Figure 1B Further provided in.

[0057] Figure 1BA schematic block diagram 100B of a wire EDM 116 for machining a workpiece 102 according to some embodiments of the present disclosure is shown. The wire EDM 116 may include a wire electrode 104, an energy source 108, a delivery system 118, a machining fluid 120, and a wire electrode position measurement system 122. In some implementations, the delivery system 118 is a wire drum configured to control wire feed. Additionally or alternatively, in some embodiments, the wire feed rate is controlled from the wire drum, and the position of the wire itself is controlled by a workpiece motor 132. The wire electrode position measurement system 122 further includes a light source 124 and a camera 126, the camera 126 having an image sensor, such as a wire sensor, and / or a two-dimensional (2D) sensor. The wire sensor can reconstruct the vibration of a point of the wire. In some implementations, the image sensor is 2D to reconstruct a segment of the wire including multiple points. This implementation provides more accurate results. The wire EDM 116 may further include a processor 128 and a controller 130. In an embodiment, the processor 128 and the controller 130 may be part of a control unit. The wire EDM 116 may further include a workpiece motor 132 , a set of electrode supports 134 , a set of power supplies 136 , and a scrap bin 138 .

[0058] The conveying system 118 may include a pulley (also referred to as a wire drum) that contacts one or a combination of the wire electrode 104 and the workpiece 102 for conveying the wire electrode 104 and the workpiece 102 to the vicinity of each other. The conveying system 118 is configured to convey the wire electrode 104 to the vicinity of the workpiece 102. The conveying system 118 may include a roller of the wire electrode 104 so that a portion of the wire electrode 104 from the roller is conveyed to the vicinity of the workpiece 102 as needed. The wire electrode 104 and the workpiece 102 may be embedded in a machining fluid 120. In an embodiment, the machining fluid 120 may be composed of either water or oil.

[0059] The energy source 108 is configured to cause an electrical discharge 114 between the wire electrode 104 and the workpiece 102. When the voltage between the two electrodes (that is, the wire electrode 104 and the workpiece 102) increases, the strength of the electric field in the volume between the electrodes becomes greater, causing dielectric breakdown of the dielectric fluid (such as the machining fluid 120), and generating an arc or discharge 114. As a result, material is removed from the electrodes. Once the current stops, new liquid dielectric is transferred to the inter-electrode volume so that solid particles (or debris) are transported away and the insulating properties of the dielectric fluid are restored. In addition, new liquid dielectric is added to the inter-electrode volume, which is called flushing. After the current flows, the voltage between the electrodes is restored to before the dielectric breakdown so that new liquid dielectric breakdown can occur to repeat the cycle.

[0060] The wire electrode position measurement system 122 includes a light source 124 configured to illuminate the wire electrode 104 with a coded illumination pattern. In an embodiment, the light source 124 is a light emitting diode (LED). In one or more embodiments, the wire electrode position measurement system 122 may further include a lens 124A, which is arranged in the line of sight of the light source 124 to converge the light from the light source 124 toward the first click 104. The wire electrode position measurement system 122 further includes a camera 126, which has an image sensor. The camera 126 can be arranged to collect an image set indicating the wire electrode 104 illuminated by the coded illumination pattern at different positions. For example, the camera 126 can be placed in the opposite direction of the direction of the light source 124 so that the segment of the wire electrode 104 is located between the light source 124 and the image sensor of the camera 126 to capture the image set. In an embodiment, the discharge 114 can cause white blur. The coded illumination pattern can be generated inconsistently with the white blur to reduce the impact of the white blur in the collected image set.

[0061] The processor 128 is configured to reconstruct at least a segmented position of the wire electrode 104 at a reconstruction rate greater than the acquisition rate of the camera 126 by utilizing compressed sensing using sparse reconstruction technology. The reconstruction rate can be defined as the speed at which the processor 128 reconstructs at least a segmented position of the wire electrode 104. Moreover, the acquisition rate can be defined as the speed at which the camera 126 acquires a set of images. Compressed sensing using sparse reconstruction technology processes the acquired image set using the following computational techniques, which can enable the position of the wire electrode 104 to be temporally upsampled to identify the exact position of the wire electrode 104 with a temporal sampling rate (or reconstruction rate) that matches or exceeds the Nyquist rate. The Nyquist rate can be associated with a sampling rate that can be equal to the bandwidth of a frame (such as an image set) acquired by the camera 126 or twice the bandwidth. In this way, an image set can be acquired at a low rate (i.e., a rate lower than the Nyquist rate). This low-rate acquisition of an image set can enable the cost of the camera 126 to be reduced because the need for a high frame rate camera that may be expensive is eliminated. In addition, using compressed sensing with sparse reconstruction to model the video of the vibrating wire electrode 104 as a frequency sparse signal, the controller 130 can be configured to formulate a joint sparse recovery problem to determine the vibration frequency of the wire electrode 104 and reconstruct the high frame rate video. This solution can account for disturbances caused by bubbles and / or ripples in the machining fluid 120 that have frequencies inconsistent with the sparsity of the vibration of the wire electrode 104. Details of compressed sensing with sparse reconstruction are described, for example, in Fig.10 Further provided in.

[0062] Back to Figure 1BThe controller 130 is configured to control at least one of the conveyor system 118 and the energy source 108 based on the position of at least a segment of the wire electrode 104 reconstructed at the reconstruction rate. The controller 130 can determine a processing speed and an amount of potential (or voltage) of the workpiece 102 that can be applied during processing to ensure a clean or smooth cut of the workpiece 102. The controller 130 can receive information about the position of the wire electrode 104 from the wire position measurement system 122. However, due to certain inaccuracies in the overall operation of the wire EDM 116, the cut quality of the workpiece 102 may be deteriorated.

[0063] Figure 2 Inaccuracies that affect the cut quality of the workpiece 102 in the wire EDM 116 are shown. The wire EDM 116 can be configured to perform two types of cutting techniques, a rough cutting technique and a finishing cutting technique. The rough cutting technique can involve roughly machining the workpiece 102. The finishing cutting technique can include an additional operation in which the wire electrode 104 can retrace the same path after the rough cutting is completed. Therefore, finishing cutting requires higher precision than rough cutting to obtain a finer accurate cut with surface integrity.

[0064] However, the quality of the cut of the workpiece 102 may be affected by various factors, such as a large amount of vibration in the wire electrode 104 of the wire EDM 112. For example, the straightness 202 in the cut in the workpiece 102 may be affected, making the cut inconsistent. In addition, due to the vibration in the wire electrode 104, streaks 204 may form in the workpiece 102. In addition, due to dimensional errors 206 in the wire electrode 104, the finished dimensions of the workpiece 102 may be undesirable due to the vibration. Moreover, due to wear and tear of the wire electrode 104 caused by the vibration, wire breaks 208 may be observed in the wire electrode 104. The wire EDM 116 of the present disclosure overcomes the listed inaccuracies by minimizing the vibration induced in the wire electrode 104 using the wire position measurement system 122. Details of the wire EDM 116 capable of controlling the vibration of the wire electrode 104 are described, for example, from Figures 3A to 17 Further provided.

[0065] Figure 3AA schematic diagram 300A depicting exemplary positions of different components of a wire electrode position measurement system 122 relative to a wire electrode 104 embedded in a machining fluid 120 according to some embodiments of the present disclosure is illustrated. A light source 124 and a camera 126 of the wire electrode position measurement system 122 are arranged on opposite sides of the wire electrode 104. An image sensor 126A of the camera 126 is configured to collect a set of images of a sum of shadows of the wire electrode 104 encoded by an illumination pattern as the wire electrode 104 moves across the image sensor 126A of the camera 126. Illumination from the light source 124 may be focused using a lens 124A arranged in a field of view of the light source 124. The light source 124 may be arranged so that a segment cutting illumination of the wire electrode 104 is obtained. The position of the segment cutting illumination of the wire electrode 104 may be collected as a sum of shadows of the wire electrode 104 encoded by the illumination pattern.

[0066] Figure 3B Schematic diagram 300B shows an image 302 of a collection of images captured by camera 126 of wire electrode position measurement system 122 according to some embodiments of the present disclosure. Camera 126 records shadow 304 of wire electrode 104 on a sensor plane (such as the depicted Y axis). Shadow 304 may be formed by an illumination pattern incident on wire electrode 104. Similarly, a sum of shadows (such as shadow 304) is captured corresponding to a collection of images (such as image 302).

[0067] Figure 4A A block diagram 400A illustrating control of a camera 126 for determining timing of triggering and controlling a light source 124 for generating a coded illumination pattern according to some embodiments of the present disclosure is illustrated. A controller 130 may be connected to the light source 124. In an embodiment, the controller 130 may be connected to the light source 124 via an LED control unit 402. The controller 130 may be configured to trigger a coded illumination pattern of the light source 124. The controller 130 may communicate with the LED control unit 402 to trigger a coded illumination pattern of the light source 124.

[0068] The controller 130 may be connected to the camera 126. The controller 130 may determine the trigger timing of the camera 126. The trigger timing of the camera 126 may initiate the exposure of the camera 126 and the triggering of the illumination pattern of the light source 124 to coincide with the duration of the exposure of the camera 126. The LED control unit 402 may be programmed to generate a constant coded illumination pattern or a pseudo-random sequence of ON light pulses and OFF light pulses.

[0069] Figure 4BThe illustration depicts a diagram 400B depicting a constant coded illumination pattern 404 generated by the light source 124 according to some embodiments of the present disclosure. The constant coded illumination pattern 404 can be triggered for the duration when the camera 126 is triggered (i.e., during the exposure time of the camera 126). For example, the constant illumination pattern 404 can include an off light pulse with a duration of 0 msec to 0.5 msec and an on light pulse with a duration of 0.5 msec to 1 msec.

[0070] Additionally, diagram 400B illustrates a graph 406 depicting an exposure time of camera 126. In an embodiment, the exposure time may be 1 millisecond (1 msec). Light source 124 may be triggered based on a trigger of camera 126.

[0071] Figure 4C The illustration depicts a diagram of a pseudo-random sequence of on and off light pulses 408 generated by a light source 124 according to some embodiments of the present disclosure. In some embodiments, the coded illumination pattern of the light source 124 is configured to generate a pseudo-random sequence of on and off light pulses 408.

[0072] Diagram 400C includes a graph 406 depicting the exposure time of the camera 126. The pseudo-random sequence of on light pulses and off light pulses 408 may be generated over the duration when the camera 126 is triggered (i.e., during the exposure time of the camera 126). The duration of each pulse of the sequence of on light pulses and off light pulses is less than or equal to the Nyquist sampling rate of the vibration frequency of the wire electrode 104. In an example, the duration of each off light pulse may be 0.1 msec, and the duration of each on light pulse may be 0.1 msec. In addition, the total duration of the pseudo-random sequence of on light pulses and off light pulses 408 is less than or equal to the duration of the frame exposure or exposure time of the camera 126. The frame exposure or exposure time of the camera 126 may be, for example, 1 msec. The total duration of the pseudo-random sequence of on light pulses and off light pulses 408 may be less than 1 msec.

[0073] Figure 5A diagram 500 is shown of a time-varying position 502 of a segment of a wire electrode 104 and a corresponding sensor measurement 504 observed with a camera 126 according to some embodiments of the present disclosure. The position 502 of a segment of the wire electrode 104 changes over time due to vibrations in the wire electrode 104. The observed sensor measurements 504 may depict a plurality of frames or a set of images acquired by the camera 126. The set of images depicts the shadows of the segments of the wire electrode 104 as the wire electrode 104 moves in the field of view of the image sensor of the camera 126. For example, a first image 504A depicts the position of the segment of the wire electrode 104 at a first moment in time, a second image 504B depicts the position of the segment of the wire electrode 104 at a second moment in time, a third image 504C depicts the position of the segment of the wire electrode 104 at a third moment in time, and so on. Examples of illumination patterns generated based on the sensor measurements 504 observed with the camera 126 are shown, for example, in FIG. Fig. 6A and Figure 6B Further described in .

[0074] Fig. 6A A diagram 600A is shown depicting a measurement operator "A" corresponding to an illumination pattern having a pseudo-random sequence of on and off light pulses that begins at the same time as camera 126 begins exposure according to some embodiments of the present disclosure. An example of a measurement operator "A" is shown in FIG. Fig. 6A 602. The x-axis of the measurement operator 602 is denoted by "m". Let m be a number of video frames or image sets captured by the camera 126 in one second, and the corresponding duration of each frame is The y-axis of measurement operator 602 is denoted by "N". It can be assumed that the duration of each frame is the duration t s Therefore, for every m video frames captured by the camera 126, the target super-resolution video may have N=cnm time samples.

[0075] Diagram 600A further includes exposure duration 604 of camera 126. Measurement operator 602 represents a sampling process performed by combining the illumination pattern of light source 124 and the exposure duration 604 of the image sensor of camera 126. The number of rows of measurement operator A 602 may indicate the number of image sets acquired. The illumination pattern having a pseudo-random sequence of on light pulses and off light pulses is generated at the same time as the exposure duration 604 of camera 126.

[0076] Figure 6BA diagram 600B depicting a measurement operator "A" corresponding to an illumination pattern having a pseudo-random sequence of on light pulses and off light pulses beginning at a random moment within an exposure duration 604 of the camera 126 according to some embodiments of the present disclosure is shown. An example of the measurement operator "A" is shown in FIG. Figure 6B Shown as measurement operator 606.

[0077] The measurement operator 606 represents the sampling process performed by combining the illumination pattern of the light source 124 and the exposure duration 604 of the image sensor of the camera 126. The number of rows of the measurement operator 606 can indicate the number of image sets collected. The illumination pattern with a pseudo-random sequence of on light pulses and off light pulses begins at a random moment within the exposure duration 604 of the camera 126.

[0078] Such an illumination pattern (such as Fig. 6A The illumination pattern and Figure 6B The generation of the illumination pattern in the wire electrode 104 is necessary to determine the vibration of the wire electrode 104. Knowledge of the exact position and shape of the wire electrode 104 or cutting wire is important to determine the vibration or tension in the wire electrode 104 and the quality of the cut. Typically, the vibration frequency of the wire electrode 104 is in the range of about 1 kilohertz (KHz), which would require a camera with an acquisition rate of at least 2000fps to accurately locate the wire electrode 104. Because such a high-speed camera would add significant cost to the equipment, the wire EDM 116 utilizes a camera 126 with a standard frame rate along with time-coded illumination or aperture and calculations to recover the vibration frequency and exact position of the wire electrode 104.

[0079] The position of the vibrating wire electrode 104 can be estimated from a low frame rate video or image set acquired by the camera 126 as a temporal super-resolution problem. A coded illumination pattern a can be used. i ∈{0, 1} n , where i∈{1…m}, occupancy duration s <t f A time period of seconds.

[0080] The duration of the coded illumination pattern may correspond to the exposure or acquisition interval of a low-rate camera, such as camera 126, on which the coded illumination pattern may be applied. Typically, in practice, the exposure or acquisition interval may be much lower than the duration of each frame, t f , because the camera 126 may need some time to send data as a reset.

[0081] In addition, the irradiation pattern a i Acting during the acquisition interval, the strobe is applied at a uniform rate according to the code, i.e., each coefficient of the illumination pattern is illuminated at the time interval The time interval t sIt can further correspond to the target temporal resolution time step of the super-resolution video. It can be assumed that the acquired video or image set can be approximately constant during the time interval. The duration of each frame is the duration t s Therefore, for every m video frames captured by the camera 126, the target super-resolution video may have N=cnm time samples, so that, that is, a super-resolution of cn×time upsampling may be obtained.

[0082] A collection of images or a video sequence acquired with a spatial resolution of H×W pixels capturing the vibration of the wire electrode 104 may be considered during a one second duration. Represents a stack of m rows of measured video frames from one second of video, each row consisting of H×W pixels vectorized into one row. Temporal super-resolution video volume Where N=cnm, and parameters c and n need to be restored.

[0083] It can be noted that during the duration of the frame exposure period, the coded illumination pattern a i to capture each video frame with index i or the i-th row of Y. The measurement operator can be formed This operator can relate the target high frame rate video U to the measured video frame Y using the following linear system:

[0084] Y=AU (1)

[0085] Fig. 6A and Figure 6B Two examples of measurement operators A corresponding to the acquisition of 5 video frames or image sets are shown, where m=5, c=5, and n=100. Fig. 6A In , the white lines in the illumination pattern can indicate the moment when the stroboscopic illumination is turned on. In this example, each frame can be observed with a different pseudo-random illumination pattern. Figure 6B In the case of irradiation pattern a i is shown as a white line. In this example, each frame exposure of the camera 126 is divided into five segments, where the first segment includes the illumination pattern. The remaining four segments may correspond to the downtime of the camera exposure. Furthermore, Figure 7 and Figure 8 To sense the influence of the measurement operator A on the sequence of vibrating wire electrodes 104 .

[0086] Figure 7 The diagram 700 illustrates a set of images 702 of the moving wire electrode 104 captured by the camera 126 according to some embodiments of the present disclosure. For example, the set of images 702 or video frames of the moving wire electrode 104 is captured using Fig. 6A702 is acquired by the measurement operator A depicted in . The image set 702 depicts the blur formed by each image of the wire electrode 104 as the wire electrode 104 moves in space while being illuminated using the time-coded illumination pattern. The image set 702 may include a first image 702A, a second image 702B, a third image 702C, a fourth image 702D, and a fifth image 702E. In an embodiment, the image set 702 may be the same as the sensor measurement 504 of the camera 126.

[0087] The image set 702 (such as the first image 702A, the second image 702B, the third image 702C, the fourth image 702D, and the fifth image 702E) is collected from the vibrating wire electrode 104, where the measurements correspond to m=5, n=5, n=100. Each frame or image of the image set 702 may consist of 10×151 pixels. The image set 702 illustrates the blurring effect caused by observing the vibrating wire electrode 104 through the measurement operator A. The diagram 700 further includes a graph 704 that depicts the average of five observed frames (such as the image set 702).

[0088] Figure 8 The illustration depicts a comparison between the continuous motion of the wire electrode 104 and the sequence of the image set 702 captured by the camera according to some embodiments of the present disclosure. The illustration 800 includes a vibration sequence U 802 (captured as a high frame rate video) of the wire electrode 104 compared to a measured sequence Y 804 observed by a measurement operator A. The last row 806 of the measured sequence Y 804 can correspond to the mean of the five observed frames depicted by the graph 704. A set of five video frames captured by operator A of the example vibration sequence U is shown. In the case where the wire electrode 104 is moving, the measurement operator A results in blurring artifacts. The mean of the observed video frames can be attached to the measurement as part of the measurement operator A to help speed up the reconstruction of the direct current (DC) component of the captured vibration video.

[0089] It is seen in equation (1) that the measurement operator A can act in the same way on each pixel of a video (such as a vibration sequence U). It can be noted that the problem in equation (1) may be severely ill-posed, since an infinite number of solutions to the vibration sequence U may be possible for the system. However, since the wire electrode 104 is moving or oscillating within a narrow frequency band, an accurate reconstruction of the true matrix of the vibration sequence U can be obtained by exploiting the sparsity in the frequency domain.

[0090] set up is the N-dimensional inverse Fourier transform operator, Represent the frequency coefficient matrix of the vibration sequence U such that U=FX.

[0091] Because the intensity fluctuations in the acquired image set or video are driven by the vibrations in the wire electrode 104, the locations of the significant non-zero coefficients in the columns of the matrix X may fall within the same frequency interval. Therefore, a joint sparsity structure may be utilized in the matrix X, which may allow the support of the row norm of the matrix X to be recovered using multiple measurement vectors (such as the columns of the measured sequence Y given by different pixels in the observed video).

[0092] In an embodiment, the technique of using a joint sparsity prior on the matrix X is to use l 2,1 norm penalty function and solve the following optimal problem:

[0093]

[0094] in X(r,:) represents the r-th row of matrix Y.

[0095] In the context of sparse signal recovery, a k-sparse vector of length N requires at least 2k+1 measurements to guarantee recovery. However, when multiple measurements are available, the number of required measurements can be reduced to 2k+1-rank(Y). Specifically, if the measurement matrix is not rank-deficient, the number of measurements required can be reduced by min{m,M}. Therefore, solving the joint sparsity problem does not benefit much from having multiple measurements M that can be greater than m. In addition, the use of l 2,1 Monte Carlo simulations were performed on the minimized joint sparsity reconstruction, and it was observed that the simulations support the conjecture made in the present disclosure, that is, when M>m, the reconstruction quality does not improve much. On the other hand, as M increases, the computational complexity increases significantly because the dimension of the optimal variable is N×M.

[0096] Fig. 9 An exemplary block diagram 900 illustrates steps for reconstructing the position of at least one segment of the wire electrode 104 in compressed sensing using sparse reconstruction techniques according to an embodiment of the present disclosure. The block diagram 900 includes steps 902 to 916.

[0097] At step 902 , a set of images or videos may be buffered into a matrix Y by collecting the images or videos together as shown in the measured sequence Y 804 . The set of images 702 may be acquired from the camera 126 .

[0098] At step 904, outliers caused by bubbles in the machining fluid 120 may be removed. In an embodiment, shadows of bubbles may be removed from shadows of the wire electrode 104 moving on the image sensor captured in the image set 702 acquired from the camera 126 to generate a bubble-free image set of the wire electrode 104 encoded by the coded illumination pattern. Details of generating the bubble-free image set are described in, for example, Fig.10 and Fig.11 Available in.

[0099] In step 906, the pixel dimension of the bubble-free image set obtained in step 904 may be compressed to be equal to the number of images in the image set 702 by multiplying the pixel dimension by a Gaussian random matrix to output a compressed image set. For example, the dimension of the problem in equation (2) may be compressed.

[0100] It can be noted that one of the drawbacks of equation (2) is that it does not scale well with the number of pixels in each video frame, since the optimal variable X is N × HW. However, there is no benefit in increasing the number of measurement vectors beyond the rank of Y. Therefore, the measurement Y can be right-multiplied by the random matrix To reduce or compress the dimensionality of the problem posed by equation (2) to obtain a compressed data matrix corresponding to the compressed image set.

[0101]

[0102] At step 908, a group one-norm sparse recovery problem may be solved to calculate the spectrum matrix of the wire electrode 104 from the compressed image set. For example, a group one-norm sparse recovery problem or a sparse least squares problem may be solved to calculate the compressed spectrum matrix. The wire electrode 104 is accompanied by vibration when it moves on the image sensor of the camera 126.

[0103] It can be noted that The support of the row norm of can be the same as the support of the row norm of X. Using the compressed observation model in equation (3), the equivalent l can be written as follows 2,1 The minimization problem is set up as equation (2):

[0104]

[0105] This helps in finding the optimal variables with significantly reduced dimensionality. The operation is performed by identifying the supports of the compressed spectrum matrix X.

[0106] Further details on solving the group-one norm sparse recovery problem are given in Fig.12 Available in.

[0107] At step 910, the compressed spectrum matrix X may be extracted. To solve equation (3), a modified FISTA algorithm specifically for recovering row norm sparse signals is used. The modified FISTA algorithm for calculating the compressed spectrum matrix X is as follows:

[0108] Algorithm 1: Modified FISTA algorithm

[0109]

[0110] In the modified FISTA algorithm, the variables Calculating Quasi-Newton Estimates Then relative to the valuation The weight vector used in the algorithm is The weighted 2,1 Norm calculation neighbor mapping function Weight vector Where w = F H A T The choice of 1 is designed to suppress non-zero coefficients in the rows of X that match the sampling structure of the measurement operator A.

[0111] The neighbor mapping function is applied row by row, and for each row with index r the neighbor mapping function is defined as follows:

[0112]

[0113] At step 912, a reduced set of frequency bins corresponding to the locations of the rows of the spectral matrix that include the maximum Euclidean norm are identified. The compressed spectral matrix can be used to identify the support of the joint sparse signal X.

[0114] When using Algorithm 1 to calculate the variables Afterwards, the support S of X can be estimated as The row norm vector of The set of indices of , that is, the set of row indices with non-zero l2 norm:

[0115] in where e represents the element-wise Hadamard product, for The element-wise complex conjugate of , where 1 is a vector of all 1s.

[0116] At step 914, a least squares reconstruction problem may be solved using the reduced set of frequency bins to reconstruct a set of high temporal resolution images of the motion of the wire electrode with a spatial resolution equal to the spatial resolution of the image sensor of the camera 126. The coefficients of X restricted to the identified support may be solved in turn to reconstruct the temporal super-resolution video sequence. Once the support S is identified, the high frame rate video U = F may be reconstructed by calculating the coefficients of X restricted to the support S. S X S Matrix F S is a subset of the columns of the inverse Fourier matrix indexed by S. This matrix is ​​realized by solving the following constrained least squares equation:

[0117] The constraint condition is F S X S ≥0. (7)

[0118] Constraint F S X S ≥0 can ensure Each pixel in has a real non-negative feasible pixel value. Equation (7) can be solved using the accelerated projected gradient (APG) descent routine depicted in Algorithm 2.

[0119] Algorithm 2: Accelerated Projected Gradient (APG) for calculating high frame rate video U:

[0120]

[0121] The constraint that U is in the positive quadrant is obtained by the element-wise projection operator It is guaranteed that the projection operator The imaginary component of each element of U may be discarded, and any negative real components may be set to zero.

[0122] At step 916, at least segmented positions of the wire electrode 104 may be output from the reconstructed high temporal resolution image set 702 of the motion of the wire electrode 104. The outputted at least segmented positions of the wire electrode 104, such as positions 918, depict vibrations of the wire electrode 104 over time.

[0123] Fig.10The illustration depicts a diagram depicting the presence of bubbles in a machining fluid 120 surrounding a wire electrode 104 of a wire EDM 116 in accordance with an embodiment of the present disclosure. In an actual wire EDM 116 scenario, the wire electrode 104 may vibrate within the machining fluid 120, which may help lubricate and cool machine components. The presence of the machining fluid 120 and the wire vibrations often result in the appearance of bubbles 1002, such as air bubbles that pass through the machining fluid 120. Such bubbles 1002 may be captured by a camera, such as the camera 126, motion inducing spectral components that contaminate the spectrum of the purely vibrating wire electrode 104. Fortunately, the motion of the bubbles 1002 is not periodic, and the appearance of the bubbles 1002 in the captured video is typically transient.

[0124] Given the properties of bubble 1002, the presence of bubble 1002 can be modeled as a sparse outlier in the measurement model. represents a sparse matrix of outliers corresponding to bubble 1002. The new forward model taking into account the presence of bubble 1002 can be given by the following equation:

[0125] Y=AFX+O. (8)

[0126] In order to recover X and its supports, mechanisms need to be developed for handling the presence of sparse outlier matrices O.

[0127] Fig.11 The illustration shows a diagram 1100 of generating a bubble-free image set 1102 from an image set 702 acquired by the camera 126 according to an embodiment of the present disclosure.

[0128] In an embodiment, removing the shadows of the bubbles 1002 from the image set 702 acquired by the camera 126 to generate the bubble-free image set 1102 is performed by solving a robust principal component analysis (PCA) problem. A further robust principal component analysis problem may include modeling the image set 702 as consisting of a low-rank matrix component and a sparse matrix component 1104. The low-rank matrix component corresponds to the vibrating wire electrode 104 without the bubbles 1002 (such as the bubble-free image set 1102), and the sparse matrix component 1104 corresponds to the bubbles. The low-rank matrix component may be output as the bubble-free image set 1102.

[0129] The sparsity of the row norm of X causes the matrix L:=AFX to have a low rank. The technique used to separate the sum of low-rank components and sparse components is robust principal component analysis (PCA). The robust PCA problem can be summarized as follows:

[0130] Constraint Y = L + O, (9)

[0131] where ||L|| *represents the nuclear norm (the sum of singular values) of the matrix L, and ||O||1 is the l1 norm of the vectorized matrix O.

[0132] In the PCA method, the robust PCA problem may be first solved to calculate the low-rank matrix L. Furthermore, support estimation may be performed, and the video reconstruction step may be performed after replacing the matrix Y with the low-rank matrix L.

[0133] In another embodiment, bubble separation can be performed by using forward modeling. As an alternative to the robust PCA approach, the bubble separation stage can be incorporated directly from the compression measurements into the support identification step as follows:

[0134]

[0135] where B is a random matrix with reduced dimension.

[0136] In some embodiments, it may be necessary to solve a group-one norm sparse recovery problem to calculate the spectrum matrix X of the wire electrode 104 from the compressed image set. For example, the difference between the compressed image set and a synthesized compressed image set formed by the product of the spectrum matrix of the vibrating wire electrode 104 and the Fourier transform in the time domain applied to the upsampling may be minimized. Fig. 9 The minimization is described using equation (4) illustrated at step 908 of .

[0137] Furthermore, the minimization of the difference can be regularized by the sum of the Euclidean norms of the rows of the spectrum matrix of the vibrating wire electrode 104. The details of the minimization of the difference are given in Fig. 9 is further provided in Algorithm 1 at step 910 .

[0138] Furthermore, a spectrum matrix that may be sparse in frequency bins by having a small number of non-zero row norms can be output in the upsampled time domain. Details of the output of the spectrum matrix are given in, for example, Fig. 9 is further provided in Algorithm 1 at step 910 .

[0139] Fig.12 An exemplary block diagram 1200 is illustrated for determining at least the vibration frequency and amplitude of the wire electrode 104 according to an embodiment of the present disclosure. The design of the illumination pattern and the corresponding sensing matrix A plays an important role in determining the reconstruction quality of the super-resolution video captured by the camera 126. In particular, the instantiation and length of the encoded illumination pattern within the exposure duration of the video frame can affect the ability to determine accurate signal support.

[0140] When the coded illumination pattern a iWhen triggered at evenly spaced intervals, the measurement operator A may exhibit a sparse spectrum in the frequency domain that may not be distinguishable from the support of the reconstructed signal U. Alternatively, we can allow the strobe sequence to occupy random starting positions in the frame exposure interval. This approach can help break the periodicity of the sampling operator and result in a relatively flat spectrum that may not exhibit high-valued coefficients at harmonic frequencies.

[0141] In some embodiments, the controller 130 may be further configured to determine a vibration frequency 1202 of the wire electrode 104 by converting the reduced set of frequency intervals into a physical frequency value. The controller 130 may receive as input a position 918 of at least a segment of the wire electrode 104. The controller 130 may divide the segment of the wire electrode 104 into one or more time blocks 1204. The vibration frequency 1202 of the wire electrode 104 may be determined based on the number of oscillations or peaks 1206 of the wire electrode 104 in each of the one or more time blocks 1204. For example, the determined frequency may be equal to the number of oscillations of the wire electrode 104.

[0142] The controller 130 may be further configured to determine a vibration amplitude 1208 of the wire electrode 104 by converting the position of the segment of the wire electrode 104 on the sensor array to the physical position of the wire electrode 104 according to the geometry of the components of the wire electrode position measurement system 122. The amplitude 1208 may be determined based on a calculation of the length 1210 of the segment of the wire electrode 104.

[0143] In an embodiment, the controller 130 may be further configured to determine a curvature 1212 of the vibration of the wire electrode 104. The curvature 1212 may be determined based on the location of the peak 1206 of the wire electrode 104 in each of the one or more time blocks 1204. The exact frequency 1202, amplitude 1208, and curvature 1212 of the wire electrode 104 are determined from the reconstructed high temporal resolution video of the wire electrode 104 to control the cutting quality.

[0144] Fig.13 An exemplary block diagram 1300 is illustrated for reducing the possibility of wire electrode 104 breakage during rough cutting according to an embodiment of the present disclosure. Wire breakage is the most common problem in rough cutting technology. When the amplitude of wire vibration increases or the vibration frequency fluctuates greatly during the process, the process is considered unstable and the possibility of wire breakage may increase.

[0145] In some embodiments, the controller 130 may be further configured to reduce the likelihood of wire electrode breakage during rough cutting by performing control actions.

[0146] At step 1302, the controller 130 may assess the stability of the wire electrode 104. The control action may be based on an analysis of the frequency 1202 and amplitude 1208 of the determined vibrations of the wire electrode 104 for significant changes.

[0147] At step 1304, the control action may be based on a reduction in treatment energy input to the wire electrode 104 based on detecting one or more significant changes, such as based on the frequency 1202 and amplitude 1208 of the determined vibrations of the wire electrode 104. At step 1306, the controller 130 outputs the reduced treatment energy.

[0148] At step 1308, the control action may be based on a reduction in the processing speed of the workpiece 102 and the conveying system 118 based on detecting one or more significant changes, such as based on the frequency 1202 and amplitude 1208 of the determined vibrations of the wire electrode 104. At step 1310, the controller 130 may output the reduced processing speed of the workpiece 102 and the conveying system 118. In addition, the machining energy is controlled by controlling the machining current and the dwell time.

[0149] Fig.14 An exemplary block diagram 1400 is illustrated for controlling the straightness and size error of a cut during a finishing cut according to an embodiment of the present disclosure. In some embodiments, the controller 130 may be further configured to control the straightness and size error of a cut during a finishing cut by performing control actions.

[0150] Regarding finishing cutting, the processing energy is less than that of rough cutting, so the possibility of wire breakage is reduced, but on the other hand, degradation of straightness, streaks, and dimensional errors may cause concerns. The controller 130 can use frequency 1202, curvature 1212, and amplitude 1208 to control processing power and processing speed.

[0151] It can be noted that straightness refers to the straightness of the machined surface, such as the straightness of the workpiece 102 in the vertical direction, and streaks refer to streaks produced on the machined surface. The straightness can be predicted by the amplitude 1208 of the wire vibration, because the shape causes the amplitude 1208 of the wire vibration to be transmitted to the workpiece 102. When the amplitude 1208 of the wire vibration is small, the straightness is better, and when the vibration is large, the straightness is worse. Due to this physical phenomenon, the straightness can be controlled by the processing speed and electrical conditions.

[0152] At step 1402, a control action can be based on an analysis to detect that the amplitude 1208 of the wire vibration is greater than a threshold amplitude 1208. For example, the threshold can be defined based on acceptable limits for vibrations in the wire electrode 104. A determination that the amplitude 1208 is greater than the threshold can determine that the vibrations in the wire electrode 104 may be significant and, therefore, may cause inaccurate cutting. In an embodiment, the controller 130 can receive the frequency 1202, the curvature 1212, and the amplitude 1208 as inputs to control the straightness and dimensional error of the cut during the finishing cut.

[0153] At step 1406, the control action may be based on control of the processing power. In an embodiment, the control action may be based on increasing the processing energy when the wire electrode 104 is away from the workpiece 102 and decreasing the processing energy when the wire electrode 104 is closer to the workpiece 102. The accuracy of the dimensional error may be improved by controlling the processing energy. At step 1406, the controller 130 may output the controlled processing power.

[0154] At step 1408, the control action may be based on the control of the processing speed of the workpiece 102 and the conveying system 118. In an embodiment, the action may be based on reducing the processing speed of the workpiece 102 and the conveying system 118 to reduce the vibration amplitude 1208 in the wire electrode 104 when the shape of the wire electrode 104 is estimated to be a convex shape. When the processing speed is slowed down, the explosive force caused by the discharge becomes weaker as the discharge frequency decreases, and the electrostatic attraction force generated between the wire electrode 104 and the workpiece 102 may become dominant, causing the wire electrode 104 to deflect in a direction close to the workpiece 102, resulting in concave straightness of the machined surface. In another embodiment, the action may be based on increasing the processing speed of the workpiece 102 and the conveying system 118 to increase the vibration amplitude 1208 in the wire electrode 104 when the shape of the wire electrode 104 is estimated to be a concave shape. When the processing speed is increased, the discharge frequency increases, and the explosive force caused by the discharge greatly acts on the wire electrode 104, causing the wire electrode 104 to bend in a direction away from the workpiece 102, and the machined surface has convex straightness accuracy. In step 1410 , the controller 130 may output a controlled processing speed.

[0155] Therefore, straightness accuracy can be improved to control process speed and electrical conditions based on aspects of wire vibration. Accuracy of dimensional error can be improved through the same processing control as straightness. In addition, with respect to dimensional error, the processing trajectory itself can be changed, for example to match the desired shape based on the measured wire position.

[0156] Fig.15An exemplary block diagram 1500 is illustrated for controlling the slash of cutting during finishing cutting according to an embodiment of the present disclosure. In some embodiments, the controller 130 may be further configured to control the slash of cutting during finishing cutting by performing a control action.

[0157] At step 1502, the control action may be based on the vibration amplitude 1208 analysis to detect fluctuations in the vibration of the wire electrode 104. In order to control the streaks, it may be necessary to suppress the vibration component of the wire electrode 104. In order to suppress the vibration component of the wire electrode 104, process control may be considered as described in subsequent steps, such as suppressing fluctuations in processing speed or increasing the tension of the wire. In an embodiment, the controller 130 may receive the frequency 1202, the curvature 1212, and the amplitude 1208 as inputs to control the streaks.

[0158] At step 1504, the control action may be based on the control of machining energy. In an embodiment, the control action may be based on increasing machining energy when the wire electrode 104 is away from the workpiece 102 and decreasing machining energy when the wire electrode 104 is closer to the workpiece 102. At step 1506, the controller 130 may output the controlled machining energy.

[0159] At step 1508, the control action may be based on control of the processing speed of the workpiece 102 and the conveying system 118. In an embodiment, the control action may be based on reducing the processing speed of the workpiece 102 and the conveying system 118 to reduce the vibration amplitude 1208 in the wire electrode 104 when the shape of the wire electrode 104 is estimated to be a convex shape. In another embodiment, the control action may be based on increasing the processing speed of the workpiece 102 and the conveying system 118 to increase the vibration amplitude 1208 in the wire electrode 104 when the shape of the wire electrode 104 is estimated to be a concave shape.

[0160] In addition, the controller 130 controls the energy source 108 based on the position of at least a segment of the wire electrode 104 reconstructed at the reconstruction rate, for example, Fig.16 Available in.

[0161] Fig.16 A waveform 1600 generated by the energy source 108 according to some embodiments of the present disclosure is shown. The energy source 108 is further configured to generate the waveform 1600 consisting of a sequence of on-time voltage pulses and off-time voltage pulses. The generated waveform 1600 may depict voltage on the X-axis and time on the Y-axis. The sequence of on-time voltage pulses and off-time voltage pulses includes alternating on-time voltage pulses 1602 and off-time voltage pulses 1604.

[0162] The processing energy is reduced by shortening the duration of the on-time voltage pulse or by lengthening the duration of the off-time voltage pulse. When the pause time is lengthened or the duration of the on-time voltage pulse is shortened, the on-time per unit time is shortened, which can result in a reduction in processing energy.

[0163] The processing energy is increased by extending the duration of the on-time voltage pulse or by shortening the duration of the off-time voltage pulse. When the duration of the off-time voltage pulse is shortened, the off-time per unit time is shortened, which may result in an increase in processing energy.

[0164] The processing energy is kept constant, and voltage feedback control is applied to control the processing speed of the workpiece 102. Voltage feedback control is used to control the speed so that the processing voltage is kept constant. In addition, the processing speed can be controlled so that: when the target value of the processing voltage decreases, the processing speed becomes faster, and when the processing voltage increases, the processing speed becomes slower. In addition, in order to control the processing energy, the current can be controlled.

[0165] Fig.17 A flow chart 1700 depicting a method for machining a workpiece 102 according to some embodiments of the present disclosure is shown.

[0166] At step 1702, the method for processing the workpiece 102 may include delivering the wire electrode 104 to the vicinity of the workpiece 102. The wire electrode 104 may be used to process the workpiece 102. The details of delivering the wire electrode 104 to the vicinity of the workpiece 102 are as follows. Figure 1B Available in.

[0167] In step 1704, the method for machining the workpiece 102 may include inducing an electrical discharge between the wire electrode 104 and the workpiece 102. The electrical discharge may be necessary to remove metal from the workpiece 102. Details of inducing the electrical discharge between the wire electrode 104 and the workpiece 102 are described in detail. Figure 1B Available in.

[0168] In step 1706, the method for processing the workpiece 102 may include irradiating the wire electrode 104 with a coded illumination pattern. The coded illumination pattern may generate a constant illumination pattern or a pseudo-random sequence of on and off light pulses. Details of generating the constant illumination pattern or the pseudo-random sequence of on and off light pulses are described, for example, in Figure 1B , Figure 4B and Figure 4C Available in.

[0169] In step 1708, the method for processing the workpiece 102 may include acquiring a set of images 702 indicating the wire electrode illuminated by the coded illumination pattern at different positions. The set of images 702 may be captured by the camera 126. The details of the acquired set of images 702 are, for example, Figure 1B Available in.

[0170] In step 1710, the method for processing the workpiece 102 may include reconstructing the position of at least a segment of the wire electrode 104 at a reconstruction rate greater than the acquisition rate of the camera 126 that acquires the image set 702 by utilizing compressed sensing using a sparse reconstruction technique. The details of the position of at least a segment of the wire electrode 104 are reconstructed, for example, Figure 1B and Fig. 9 Available in.

[0171] In step 1712, the method for processing the workpiece 102 may include controlling at least one of a delivery system 118 and an energy source 108 based on the position of at least a segment of the wire electrode 104 reconstructed at the reconstruction rate, the delivery system 118 delivering the wire electrode 104 to the vicinity of the workpiece 102, and the energy source 108 causing the discharge. Details of controlling the delivery system 118 and the energy source 108 are described in, for example, Figure 1B , Fig.14 , Fig.15 and Fig.16 Available in.

[0172] Those skilled in the art to which the present invention belongs will benefit from the teachings presented in the foregoing description and the associated drawings, and will think of many modifications and other embodiments of these inventions set forth herein. It will be understood that the invention is not limited to the specific embodiments disclosed, and modifications and other embodiments are intended to be included within the scope of the appended claims. Moreover, although the foregoing description and the associated drawings describe example embodiments in the context of certain example combinations of elements and / or functions, it should be appreciated that different combinations of elements and / or functions may be provided by alternative embodiments without departing from the scope of the appended claims. In this regard, for example, elements and / or functional combinations different from those explicitly described above are also contemplated as being likely to be set forth in some of the appended claims. Although specific terms are employed herein, they are only used in a general descriptive sense, not for the purpose of limitation.

Claims

1. A wire electrical discharge machine (EDM) for machining a workpiece, the wire EDM comprising: a conveying system in contact with one or a combination of the wire electrode and the workpiece for conveying the wire electrode and the workpiece to the vicinity of each other; an energy source configured to induce an electrical discharge between the wire electrode and the workpiece; A line electrode position measurement system, the line electrode position measurement system comprising: a light source configured to illuminate the wire electrode with a coded illumination pattern; and a camera having an image sensor arranged to acquire a set of images at different positions indicative of the wire electrode illuminated by the coded illumination pattern; a processor configured to reconstruct a position of at least one segment of the wire electrode at a reconstruction rate greater than an acquisition rate of the camera by utilizing compressed sensing using sparse reconstruction; and A controller is configured to control at least one of the delivery system and the energy source based on the position of at least the segment of the wire electrode reconstructed at the reconstruction rate.

2. The wire EDM of claim 1, wherein the energy source is further configured to generate a waveform consisting of a sequence of on-time voltage pulses and off-time voltage pulses, and wherein reducing the processing energy by shortening the duration of the on-time voltage pulse or by lengthening the duration of the off-time voltage pulse; increasing the processing energy by extending the duration of the on-time voltage pulse or by shortening the duration of the off-time voltage pulse; and The process energy is kept constant and voltage feedback control is applied to control the processing speed of the workpiece.

3. The line EDM of claim 1 , wherein the image sensor is a segmented two-dimensional (2D) sensor comprising a plurality of points capturing the line, wherein the coded illumination pattern of the light source is configured to produce a pseudo-random sequence of on light pulses and off light pulses, and wherein The duration of each pulse of the pseudo-random sequence of on-light pulses and off-light pulses is less than or equal to the Nyquist sampling rate of the vibration frequency of the wire electrode; and The total duration of the pseudo-random sequence of on light pulses and off light pulses is less than or equal to the duration of the frame exposure of the camera.

4. The wire EDM according to claim 1, wherein the light source and the camera of the wire electrode position measurement unit are arranged on opposite sides of the wire electrode, and wherein the image sensor of the camera is configured to collect an image set of the sum of the shadows of the wire electrode encoded by the illumination pattern as the wire electrode moves on the 2D sensor of the camera.

5. The wire EDM of claim 1 , wherein the compressive sensing using sparse reconstruction comprises: buffering the set of images acquired from the camera; removing a shadow of the bubble from a shadow of the wire electrode moving on the image sensor captured in the set of images acquired from the camera to generate a set of bubble-free images of the wire electrode encoded by the coded illumination pattern; compressing the pixel dimensions of the bubble-free image set to be equal to the number of images in the image set by multiplying the pixel dimensions of the bubble-free image set by a Gaussian random matrix to output a compressed image set; solving a group-one norm sparse recovery problem to compute a frequency spectrum matrix of the wire electrode from the set of compressed images, wherein the wire electrode moves on the image sensor with vibration; identifying a reduced set of frequency bins corresponding to the location of the row of the spectral matrix comprising a maximum Euclidean norm; solving a least squares reconstruction problem using the reduced set of frequency bins to reconstruct a set of high temporal resolution images of the motion of the wire electrode with a spatial resolution equal to the spatial resolution of the image sensor of the camera; as well as The position of at least the segment of the wire electrode is output from a set of reconstructed high temporal resolution images of the motion of the wire electrode.

6. The wire EDM of claim 5, wherein removing shadows of bubbles from the image set acquired from the camera to generate the bubble-free image set is performed by solving a robust principal component analysis problem, further comprising: The image set is modeled as a low-rank matrix component and a sparse matrix component composition, wherein the low-rank matrix component corresponds to a vibrating wire electrode without bubbles, and the sparse component corresponds to the bubbles; as well as The low-rank matrix components are output as the bubble-free image set.

7. The line EDM of claim 5, wherein solving the group-one norm sparse recovery problem comprises: minimizing the difference between the set of compressed images and a synthesized set of compressed images formed by the product of the spectrum matrix of the vibrated wire electrode and a Fourier transform applied in the upsampled time domain; regularizing the minimization of the difference by the sum of the Euclidean norms of the rows of the spectral matrix of the vibrating wire electrode; and A spectrum matrix that is sparse in the frequency bin by having a small number of non-zero row norms is output in the upsampled time domain.

8. The wire EDM of claim 1 , wherein the controller is further configured to determine at least one of: determining a vibration frequency of the wire electrode by converting a reduced set of frequency intervals into physical frequency values; and The vibration amplitude of the wire electrode is determined by converting the positions of the segments of the wire electrode on the sensor array into the physical positions of the wire electrode according to the geometry of the components of the wire electrode position measurement unit.

9. The wire EDM of claim 8, wherein the controller is further configured to reduce the likelihood of the wire electrode breaking during rough cutting by performing one or more control actions based on: analyzing the determined vibration frequency and amplitude of the wire electrode for significant changes; reducing a treatment energy input to the wire electrode based on detecting one or more significant changes; as well as Based on detecting the one or more significant changes, a processing speed of the workpiece and the conveying system is reduced.

10. The wire EDM of claim 8, wherein the controller is further configured to control the straightness and dimensional error of the cut during the finishing cut by executing control actions based on: analyzing an amplitude of the wire vibration to detect that the amplitude is greater than a threshold; when the shape of the wire electrode is estimated to be a convex shape, reducing a processing speed of the workpiece and the conveying system to reduce a vibration amplitude in the wire electrode; when the shape of the wire electrode is estimated to be a concave shape, increasing the processing speed of the workpiece and the conveying system to increase the vibration amplitude in the wire electrode; as well as Machining energy is changed according to the distance between the wire electrode and the workpiece.

11. The wire EDM of claim 8, wherein the controller is further configured to control the slash cut during the finishing cut by performing a control action based on: analyzing the vibration amplitude to detect vibration fluctuations of the wire electrode; when the shape of the wire electrode is estimated to be a convex shape, reducing a processing speed of the workpiece and the conveying system to reduce a vibration amplitude in the wire electrode; when the shape of the wire electrode is estimated to be a concave shape, increasing the processing speed of the workpiece and the conveying system to increase the vibration amplitude in the wire electrode; as well as Machining energy is changed according to the distance between the wire electrode and the workpiece.

12. A method for processing a workpiece, comprising: conveying a wire electrode to the vicinity of the workpiece; causing an electric discharge between the wire electrode and the workpiece; irradiating the wire electrode with a coded illumination pattern; acquiring a set of images at different positions indicative of the wire electrode illuminated by the coded illumination pattern; reconstructing a position of at least one segment of the wire electrode by utilizing compressed sensing using sparse reconstruction at a reconstruction rate greater than an acquisition rate of a camera acquiring the set of images; as well as At least one of: a conveying system that conveys the wire electrode to the vicinity of the workpiece, and an energy source that causes discharge is controlled based on the position of at least the segment of the wire electrode reconstructed at the reconstruction rate.

13. The method of claim 12, further comprising generating a waveform consisting of a sequence of on-time voltage pulses and off-time voltage pulses, wherein reducing the processing energy by shortening the duration of the on-time voltage pulse or by lengthening the duration of the off-time voltage pulse; increasing the processing energy by extending the duration of the on-time voltage pulse or by shortening the duration of the off-time voltage pulse; and The process energy is kept constant and voltage feedback control is applied to control the processing speed of the workpiece.

14. The method of claim 12, further comprising generating a pseudo-random sequence of on light pulses and off light pulses, wherein The duration of each pulse of the pseudo-random sequence of on-light pulses and off-light pulses is less than or equal to the Nyquist sampling rate of the vibration frequency of the wire electrode; and The total duration of the pseudo-random sequence of on light pulses and off light pulses is less than or equal to the duration of the frame exposure of the camera.

15. The method according to claim 12, further comprising collecting an image set of a sum of shadows of the wire electrode encoded by the illumination pattern as the wire electrode moves on an image sensor of the camera, wherein the light source and the camera of the wire electrode position measurement unit are arranged on opposite sides of the wire electrode.

16. The method of claim 12, wherein the compressive sensing using sparse reconstruction comprises: buffering the set of images acquired from the camera; removing a shadow of the bubble from a shadow of the wire electrode moving on an image sensor captured in the set of images acquired from the camera to generate a set of bubble-free images of the wire electrode encoded by the coded illumination pattern; compressing the pixel dimensions of the bubble-free image set to be equal to the number of images in the image set by multiplying the pixel dimensions of the bubble-free image set by a Gaussian random matrix to output a compressed image set; solving a group-one norm sparse recovery problem to compute a frequency spectrum matrix of the wire electrode from the set of compressed images, wherein the wire electrode moves on the 2D sensor with vibration; identifying a reduced set of frequency bins corresponding to the location of the row of the spectral matrix comprising a maximum Euclidean norm; solving a least squares reconstruction problem using the reduced set of frequency bins to reconstruct a set of high temporal resolution images of the motion of the wire electrode with a spatial resolution equal to the spatial resolution of the image sensor of the camera; as well as The position of at least the segment of the wire electrode is output from a set of reconstructed high temporal resolution images of the motion of the wire electrode.

17. The method of claim 16, wherein removing shadows of bubbles from the image set to generate the bubble-free image set further comprises solving a robust principal component analysis problem, the solving further comprising: The image set is modeled as a low-rank matrix component and a sparse matrix component composition, wherein the low-rank matrix component corresponds to a vibrating wire electrode without bubbles, and the sparse component corresponds to the bubbles; as well as The low-rank matrix components are output as the bubble-free image set.

18. The method of claim 16, wherein solving the group-one norm sparse recovery problem comprises: minimizing the difference between the set of compressed images and a synthesized set of compressed images formed by the product of the spectrum matrix of the vibrated wire electrode and a Fourier transform applied in the upsampled time domain; regularizing the minimization of the difference by the sum of the Euclidean norms of the rows of the spectral matrix of the vibrating wire electrode; and A spectrum matrix that is sparse in the frequency bin by having a small number of non-zero row norms is output in the upsampled time domain.

19. The method of claim 12, further comprising determining at least one of: determining a vibration frequency of the wire electrode by converting a reduced set of frequency intervals into physical frequency values; and The vibration amplitude of the wire electrode is determined by converting the positions of the segments of the wire electrode on the sensor array into the physical positions of the wire electrode according to the geometry of the components of the wire electrode position measurement unit.

20. A non-transitory computer-readable medium storing computer-executable instructions for processing a workpiece, the computer-executable instructions being configured to: The wire electrode is conveyed to the vicinity of the workpiece; causing an electric discharge between the wire electrode and the workpiece; irradiating the wire electrode with a coded illumination pattern; acquiring a set of images at different positions indicative of the wire electrode illuminated by the coded illumination pattern; reconstructing the position of at least one segment of the wire electrode by utilizing compressed sensing using sparse reconstruction at a reconstruction rate greater than an acquisition rate of a camera acquiring the set of images; and At least one of: a conveying system that conveys the wire electrode to the vicinity of the workpiece, and an energy source that causes discharge is controlled based on the position of at least the segment of the wire electrode reconstructed at the reconstruction rate.

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