Measurement system for detecting bubbles

Abstract

A measurement system (10) for detecting bubbles in a tank (1) comprising: an acoustic sensor (20) configured to detect acoustic waves in the tank (1); a controller (30) configured to receive a signal indicative of the acoustic waves from the acoustic sensor (20), wherein the controller (30) is configured to: sample the signal received from the acoustic sensor (20) over a predetermined time period to generate a sampled signal; extract an envelope of the sampled signal; detect, based on the envelope of the sampled signal, acoustic events above a predetermined threshold value which are indicative of the presence of bubbles in the tank (1).

Description

[0001] Measurement system for detecting bubbles

[0002] Field of the disclosure

[0003] The present disclosure relates to measurement systems. In particular, the present disclosure relates to the detection of bubbles using a measurement system.

[0004] Background

[0005] The manufacture of various liquids including paint, inks, emulsions, suspensions, slurries, and the like typically involves the stirring of the liquid being manufactured. Such stirring processes may be performed in a stirred tank, for example an unbaffled stirred tank. Typically, an unbaffled stirred tank comprises a cylindrical tank having smooth internal walls. A stirrer (e.g. an impeller) is located towards the bottom of the tank which is configured to rotate in order to stir the liquid within the tank.

[0006] Stirring of the tank with the stirrer when a liquid is present generally results in the formation of a vortex above the stirrer. As the rotation speed of the stirrer increases, the vortex extends deeper into the liquid of the tank, towards the stirrer. Under certain conditions where the rotation speed of the stirrer is sufficiently high, the vortex may contact the stirrer, which may lead to air becoming entrained in the liquid. Air may be entrained in the liquid in the form of bubbles.

[0007] For some manufacturing processes, it may be desirable to avoid air becoming entrained in the liquid being stirred (e.g. due to the above mechanism, or any other air entrainment mechanism).

[0008] Against this background, the present disclosure seeks to provide an improved, or at least commercially relevant alternative, measurement system and method.

[0009] Summary

[0010] According to a first aspect of the disclosure, a measurement system for detecting bubbles in a tank is provided. The measurement system comprisesan acoustic sensor configured to detect acoustic waves in the tank and a controller configured to receive a signal indicative of the acoustic waves from the acoustic sensor. The controller is configured to sample the signal received from the acoustic sensor over a predetermined time period to generate a sampled signal, extract an envelope of the sampled signal, and detect, based on the envelope of the sampled signal, acoustic events above a predetermined threshold value which are indicative of the presence of bubbles in the tank.

[0011] As such, the measurement system of the first aspect may use acoustic measurements to detect the presence of bubbles in a liquid provided within a tank, optionally a stirred tank. For many manufacturing processes, it is desirable to stir a liquid without air becoming entrained within the liquid (i.e. to prevent bubbles forming in the liquid). For some manufacturing processes in tank, the presence of bubbles in a tank (e.g. due to a reaction) may be indicative of the progress of the manufacturing process. The measurement system according to the first aspect can detect the formation and / or presence of bubbles within a tank in order to provide improved monitoring and / or control over the manufacturing process. Such a measurement system may be particularly applicable to the manufacture of liquids such as emulsions, suspensions, slurries, inks, paints, washcoats and the like. The measurement system may also be applicable to manufacturing processes involving precipitation stirring and other stirring processes where air entrainment is to be controlled, reduced, or eliminated.

[0012] It will be appreciated that during stirring, stirred tanks in particular generate acoustic signals across a broad range of frequencies. Thus, separating out acoustic events associated with the presence of bubbles simply based on a frequency analysis of acoustic data from a stirred tank is challenging, as it is difficult to distinguish signals associated with bubbles from the background noise. Accordingly, the controller of the first aspect, processes the acoustic data to more accurately identify when bubbles are present in real-time.

[0013] The measurement system of the first aspect provides a controller which is configured to interpret acoustic data from a tank in order to detect acoustic events associated with the presence of bubbles in the tank. In particular, the measurement system may be configured to detect the presence of bubbles in an unbaffled stirred tank or a baffled stirred tank, or any other type of stirred tank. In such embodiments, as the rotation speed of a stirrer in the stirred tank is increased, the likelihood of air becoming entrained (i.e. bubbles being present) increases. In particular, as rotation speed increases, a vortex may form in the stirred tank, wherein the depth of the vortex increases with rotation speed. Where the rotation speed is sufficient for the vortex to reach the stirrer (towards the bottom of the tank), air may become entrained in the stirred liquid. Due the relatively complex nature of the formation of a vortex within a stirred tank, it is challenging to predict in advance the rotation speed at which air entrainment may occur. The measurement system of the first aspect allows a stirred tank to be calibrated for a manufacturing process in a straightforward manner. In a baffled tank, a vortex may also be formed “behind” each of the baffles, as liquid moves past the baffles. Each vortex formed may be capable of introducing bubbles into the liquid.

[0014] In some embodiments, the signal may be sampled at a frequency of at least: 100 Hz, 1 kHz, 10 kHz. Preferably the signal may be sampled at a frequency of at least 40 kHz, more preferably at least 50 kHz, furthermore preferably at least 100 kHz. As such, the signal may be sampled at a frequency sufficiently high to capture acoustic data which may be indicative of the presence of bubbles. For example, in some embodiments, acoustic data indicative of the presence of bubbles may have characteristic frequencies of up to about 20 kHz, and so providing a minimum sampling frequency ensures that the characteristic frequencies are captured in the sampled signal.

[0015] In some embodiments, the signal may be sampled at a frequency of no greater than 200 kHz. Accordingly the amount of data generated by sampling the signal over the predetermined time period may be processed in a computationally efficient manner.

[0016] In some embodiments, in order to extract the envelope of the sampled signal, the controller may be configured to determine a Hilbert transform of the sampled signal. By taking the Hilbert transform of the sampled signal over the predetermined time period, the controller can manipulate the sampled signal in order to more efficiently and accurately detect acoustic events associated with the presence of bubbles.

[0017] In some embodiments, prior to determining the Hilbert transform, the controller may be configured to filter the sampled signal.

[0018] In some embodiments, the controller may be configured to filter the sampled signal using a low pass filter. For example, the controller may be configured to low pass filter the sampled signal with a low pass filter having a cut-off frequency of no greater than 20 kHz, or no greater than 15 kHz. By filtering the sampled signal prior to taking the Hilbert transform, the resulting envelope of the sampled signal may more accurately capture acoustic events associated with bubbles, whilst removing other acoustic events which may not be associated with bubbles.

[0019] In some embodiments, prior to extracting the envelope, the controller may be configured to transform the sampled signal using a discrete wavelet transform (DWT). In some embodiments, the controller may extract the envelope of the sampled signal directly from the transformed signal, while in other embodiments, the controller may subsequently invert the transformed signal using an inverse DWT prior to extracting the envelope.

[0020] In some embodiments, the controller may be configured to filter the sampled signal by determining a discrete wavelet transform (DWT) of the sampled signal. In some embodiments, the controller may apply a threshold to the DWT of the sampled signal and determine the inverse DWT of the thresholded DWT of the sampled signal. By using a DWT, the sampled signal may be filtered in order to more accurately identify acoustic events associated with bubbles. For example, in some embodiments the DWT transformed of the sampled signal may be based on a bubble wavelet. A bubble wavelet may be a wavelet which reflects an acoustic event associated with the presence of bubbles. For example, in some embodiments the bubble wavelet to be used in the DWT may be determined based on a calibration measurement of the tank where bubbles are known to be present (e.g. due to stirring or performing a known reaction which generates bubbles in the tank).

[0021] In some embodiments, the controller may be further configured to determine a time period associated with the detected acoustic events occurring, and to calculate a ratio of the time period to the predetermined time period in order to provide an indication of the amount of bubbles present in the tank. As such, the controller may be configured to normalise the acoustic events detected, wherein the calculated ratio (i.e. the normalised detected events) may be used to determine how likely it is, or the degree to which, bubbles may be present in the liquid contained within the tank.

[0022] In some embodiments, the predetermined time period may be at least 0.2 s. In some embodiments, the predetermined time period may be at least: 0.1 s, 0.5 s, 1 s, 1.5 s, 2 s, 3 s, or 5 s. As such, the measurement system may record data which is indicative of a plurality of revolutions of the stirred tank, following which the measurement system may determine whether bubbles are present in the liquid.

[0023] In some embodiments, the controller may be further configured to output the sampled signal to a cloud-based storage medium. Thus, the sampled signal may be accessed at a later time for further analysis. In some embodiments, the sampled signal may be output in a Hierarchical Data Format version 5 (HDF5) format to the cloud. In some embodiments, the data output to the cloud may comprise sampled signals from a plurality of acoustic sensors of the measurement system. Other intermediate data signals determined by the controller may also be output to the cloud. By outputting the data in an HDF5 format, the data may be compressed during file transfer.

[0024] In some embodiments, the acoustic sensor is configured to detect acoustic waves associated with air entrainment in a stirred tank and / or acoustic waves associated with bubbles generated as a reaction product. In some embodiments, a plurality of acoustic sensors may be provided, wherein each acoustic sensor is configured to detect acoustic waves in the tank. Each acoustic sensor may comprise an interface material which is configured to attach the acoustic sensor to an outer wall of the tank and to provide an acoustic medium to allow acoustic waves to travel from the tank to the acoustic sensor.

[0025] In some embodiments, the tank may be a stirred tank. In such embodiments, the measurement system further comprises a sensor configured to sense a rotational speed of a stirrer of the stirred tank, wherein the controller is configured to receive data indicative of the rotational speed of the stirred tank over the predetermined time period. As such, the controller may be configured to determine a rotational speed of the stirred tank at which air starts to become entrained. It will be appreciated that the rotational speed at which bubbles start to be formed depends on the properties of the liquid being stirred as well as the geometry of the tank and stirrer. As such, for a new stirring manufacturing process (e.g. a property of the liquid is new, or a new stirred tank design) it is challenging to predict in advance an upper rotational speed limit to avoid the entrainment of air. Thus, the measurement system of the first aspect may allow a user to optimise a variety of stirred tank manufacturing processes in a relatively quick and efficient manner.

[0026] In some embodiments, the controller is further configured to control the rotational speed of the stirrer based on the detection of acoustic events above a predetermined threshold value which are indicative of the presence of bubbles in the tank. As such, in some embodiments, the controller may provide feedback to the stirrer of the stirred tank in order to slow down the rotational speed of the stirrer when acoustic events associated with bubbles are detected.

[0027] In some embodiments, the measurement system of the first aspect may be provided as part of a tank, optionally a stirred tank. As such, the controller and the acoustic sensor may be integrated into the design of the tank. In some embodiments, the stirred tank may be an unbaffled stirred tank or a baffled stirred tank.

[0028] In some embodiments, a machine learning process may be used to detect acoustic events which are indicative of the presence of bubbles in the tank. In some embodiments, prior to extracting the envelope of the sampled signal, the controller may be further configured to transform the sampled signal using a discrete wavelet transform, wherein the envelope is extracted from the transformed signal. The controller may then be configured to detect acoustic events which are indicative of the presence of bubbles in the tank based on the envelope of the sampled signal using a trained machine learning model. As such, machine learning techniques may also be used to effectively apply the predetermined threshold used for detecting bubbles.

[0029] In some embodiments, the controller may be configured: to determine a plurality of events from the transformed signal, wherein each event is determined based on an average amplitude of the envelope over an event time period, wherein the controller may be configured to detect acoustic events which are indicative of the presence of bubbles by classifying the plurality of events using the trained machine learning model. As such, the machine learning model may classify a plurality of events determined from the sampled signal.

[0030] In some embodiments, the controller may be configured to classify the plurality of events into a plurality categories comprising two or more categories selected from the group comprising: Machinery Noise with Bubbles, Machinery Noise with No Bubbles, Detached Sensor, Anomalous Sensor Reading, Background Machinery Noise, No Machinery Noise with Bubbles, No Machinery Noise with No Bubbles. As such, a machine learning process may be used to classify the sampled signal into a plurality of different categories. In particular, the machine learning process may detect when the sampled signal is influenced by machinery noise and / or a fault may have occurred with the acoustic sensor.

[0031] In some embodiments, the controller may be configured to transform the sampled signal using a discrete wavelet transform having a plurality of levels to generate a transformed signal comprising details coefficients and approximation coefficients for each of the plurality of levels. As such, in some embodiments, the machine learning process may make use of a plurality of different levels of the DWT for classifying the sampled signal.

[0032] In some embodiments, an envelope may be extracted from the details coefficients of one or more levels of the transformed signal and / or the approximations coefficients of one or more levels of the transformed signal. That is to say, some levels of the transformed signal may have more relevant information for the classification of events than others. As such, not all levels of the details coefficients and / or approximation coefficients may be analysed by the trained machined learning model in order to accurately detect the presence of bubbles and / or other events.

[0033] According to a second aspect of the disclosure, a method of detecting bubbles in a tank, optionally a stirred tank, is provided. The method comprises: detecting acoustic waves in the tank using an acoustic sensor to generate a signal indicative of the acoustic waves: sampling the signal over a predetermined time period to generate a sampled signal; extracting an envelope of the sampled signal; and detecting, based on the envelope of the sampled signal, acoustic events above a predetermined threshold value which are indicative of the presence of bubbles in the tank.

[0034] As such, the method of the second aspect may be performed by the measurement system of the first aspect. It will be appreciated that the method of the second aspect may include any optional features and associated advantages of the first aspect.

[0035] Brief description of the figures

[0036] Embodiments of the disclosure will now be described with reference to the following nonlimiting figures in which: Fig. 1 shows a schematic diagram of a measurement system according to an embodiment of the disclosure;

[0037] Fig. 2 shows a graph of the variation in vortex depth with stirring speed;

[0038] Fig. 3 shows a block diagram of a method according to an embodiment of the disclosure;

[0039] Figs. 4a, 4b, and 4c shows examples of sampled signals obtained by the measurement system of Fig. 1;

[0040] Fig. 5 shows a further example of a sampled signal obtained by the measurement system of Fig. 1;

[0041] Fig. 6 shows examples of the frequency spectrum of some sampled signals obtained by the measurement system of Fig. 1 ;

[0042] Fig. 7 shows a graph of a frequency response of a low pass filter according to an embodiment of the disclosure;

[0043] Fig. 8 shows a graph of a Hilbert transform of the sampled signal;

[0044] Fig. 9 shows a graph of a threshold value used to detect an acoustic event;

[0045] Fig. 10 shows a graph of acoustic events detected for a stirred tank at different impeller speeds;

[0046] Fig. 11 shows a graph of the variation in acoustic events for a stirred tank over the duration of a reaction;

[0047] Fig. 12 shows a schematic diagram of a DWT filter according to an embodiment of the disclosure;

[0048] Fig. 13 shows a graph of the ‘db30’ wavelet filter;

[0049] Fig.14 shows a graph of the ‘db30’ scaling function;

[0050] Fig. 15 shows a graph of the power spectra of the ‘db30’ wavelet function by level;

[0051] Fig. 16 shows a graph of the power spectra of the ‘db30’ scaling function by level;

[0052] Fig. 17 shows an example of values calculated from signal data using a DWT for different levels of the DWT;

[0053] Fig. 18 shows an example of values calculated from signal data after applying a soft wavelet filter on the DWT coefficients;

[0054] Fig. 19 shows an example of reconstructed time series data calculated after applying the DWT for both a) and unfiltered DWT and b) a soft filtered DWT;

[0055] Fig. 20 shows an example of time series data after applying the Hilbert transform to the reconstructed time series data of Fig. 19;

[0056] Fig. 21 shows a graph of the power spectra of the reconstructed time series data of Fig. 20; Fig. 22 shows a graph of acoustic events detected based on the reconstructed time series data of Fig. 20;

[0057] Fig. 23 shows a schematic diagram of a process for detecting acoustic events using a machine learning algorithm.

[0058] Fig. 24 shows a graph of different events extracted from an envelope of a sampled signal for different levels of the DWT ;

[0059] Fig. 25 shows a graph the mean normalised detected events extracted from the sampled signal for different levels of the DWT; and

[0060] Fig. 26 is table showing confidence levels for the classification of different events using a trained machine learning algorithm according to this disclosure.

[0061] Detailed description

[0062] Fig. 1 shows a schematic diagram of a measurement system 10 according to an embodiment of the disclosure. The measurement system 10 is configured to detect bubbles in a stirred tank 1. The measurement system 10 comprises an acoustic sensor 20, a controller 30, and a cloud-based storage medium 40.

[0063] The stirred tank 1 shown in Fig. 1 is an unbaffled stirred tank. The stirred tank 1 comprises cylindrical tank wall 3, and an impeller 5. The cylindrical tank wall 3 defines a tank volume. The internal walls of the unbaffled stirred tank define a smooth internal volume of the stirred tank. As shown in Fig. 1 , the cylindrical tank wall 3 has an internal diameter of T. In some embodiments, the internal diameter T may be at least: 0.1 m, 0.5 m, 0.7 m. 1.0 m, 1.5 m, or 2 m. While the embodiment of Fig. 1 is an unbaffled stirred tank, in other embodiments of the disclosure, other types of stirred tank 1 , for example a baffled stirred tank may be provided. The measurement system 10 may also be used to detect the presence of bubbles in other types of tanks which are not stirred. For example, the measurement system 10 may be used to detect the presence of bubbles in liquid 7 in an unstirred tank, wherein the bubbles are generated as part of a reaction occurring in liquid 7.

[0064] As shown in Fig. 1 , a liquid 7 is provided within the stirred tank 1 which partially fills a tank volume defined by the cylindrical tank wall 3. The impeller 5 is submerged in the liquid 7. As shown in Fig. 1 , the impeller 5 has a diameter D which is less than the internal diameter T of the stirred tank 1. The impeller 5 is rotated in the stirred tank by means of a shaft 9 which may be connected to a motor (not shown in Fig. 1). A rotational speed of the impeller 5 and / or shaft 9 may be detected by a sensor 8. In the embodiment of Fig. 1 , the sensor 8 may be connected to the shaft 9. The sensor 8 is configured to output data indicative of the rotational speed of the impeller 5 to the controller 30.

[0065] As will be appreciated by the skilled person, various manufacturing processes for liquids utilise a stirred tank 1. By way of example only, the measurement system 10 may be particularly applicable for the manufacture of liquids where it is desirable to not entrain air during stirring. For example, the liquid may comprise an ink for use in a hydrogen fuel cell. Air entrainment in inks for hydrogen fuel cells may result in pin hole defects being formed in the ink film when it dries, resulting in defective fuel cells. For the manufacture of inks for hydrogen fuel cells, stirring can also result in a reaction occurring which produces gas bubbles. As such, the monitoring of a stirring process for an ink of a hydrogen fuel cell may allow the identification of air entrainment in the ink. Identifying air entrainment before the ink is used as a coating may prevent the manufacture of parts comprising pinhole defects.

[0066] In another embodiment, the liquid 7 may comprise a washcoat for a catalyst. In such cases, air entrainment in the liquid may impact the cohesion of the washcoat to the substrate and / or catalyst it is to be applied to.

[0067] In other embodiments, the liquid 7 may comprise an emulsion, a suspension, or a slurry.

[0068] In other embodiments, the manufacturing process may involve the precipitation of a solid from a liquid 7. In such cases, it is desirable to achieve maximum speed and torque for the impeller 5 without any power loss occurring due to surface air entrainment.

[0069] In some embodiments, for example the embodiment shown in Fig. 1 , the measurement system 10 may be provided as a portable measurement system. As such, the controller 30 and acoustic sensor 20 may be configured to be transported to, and perform measurements on, a plurality of different stirred tanks 1. In order to allow the measurement system 10 to be portable, the measurement system 10 may comprise an internal power source (e.g. a rechargeable battery not shown in Fig. 1), or be configured to be connected to an external power source (e.g. via an electrical plug). The controller 30 may be provided within a transport housing (not shown in Fig. 1) and be provided with an integrated display (not shown in Fig. 1) in order to allow a user to view the output of the measurement system 10 in situ. The controller 30 may be configured to communicate with the cloud-based storage medium 40 via a wired or a wireless network. Thus data obtained by the measurement system 10 may be accessed by other users not in the same location as the measurement system 10.

[0070] The acoustic sensor 20 is configured to detect acoustic waves in the stirred tank 1. As shown in Fig. 1 , the acoustic sensor 20 is configured to output a signal indicative of the acoustic waves in the stirred tank 1 to the controller 30. In the embodiment of Fig. 1 , the acoustic sensor is configured to be attached to the outer surface of the cylindrical tank wall 3. By attaching the acoustic sensor 20 to the outer surface of the cylindrical tank wall 3, the measurement system 1 may be configured to detect bubbles on a variety of stirred tanks 1 without interfering with the stirring process within the stirred tank 1.

[0071] The acoustic sensor 20 may be any suitable acoustic sensor for detecting acoustic waves in the frequency range of interest. For example, a Physical Acoustics R.45I low frequency acoustic sensor having a resonant frequency of about 18.55 kHz may be used. The acoustic sensor 20 may be connected to the outer wall of the stirred tank 1 using silicon grease or any other medium which may improve the contact between the acoustic sensor 20 and the cylindrical tank wall 3.

[0072] In the embodiment of Fig. 1, the acoustic sensor 20 is connected to the controller 30 by a wired connection.

[0073] The impeller 5 is configured to stir the liquid 7 within the stirred tank. The impeller 5 may be arranged to rotate about a central axis of the cylindrical tank wall 3. The impeller stirs the liquid such that it forms a vortex. A Rankine vortex model of the vortex formed in the stirred tank is shown in Fig. 2. As shown in Fig. 2, as the rotational speed of the impeller 5 increases, the vortex extends from the surface of the liquid 7 towards the impeller and the floor of the stirred tank 1. At the point where the vortex contacts the impeller 5, air (in the form of bubbles) may become entrained in the liquid 7. While a Rankine vortex model may be used to predict the rotational speeds at which air becomes entrained, the model may struggle to accurately reflect real-world conditions of the stirred tank 1. It may also be computationally expensive and time consuming to generate models for each stirred tank / manufacturing process. Accordingly, the measurement system 10 provides a straightforward system to allow for the detection of bubbles in a stirred tank 1. The controller 30 is configured to receive the signal from the acoustic sensor 20 as part of measurement system 10. The controller 30 is configured to process the signal in order to detect the presence of bubbles in liquid 7. The processing steps performed by the controller 30 will be discussed in more detail below. The controller 30 may be any suitable equipment for processing the signal from the acoustic sensor. For example, in some embodiments, the controller 30 may comprise an oscilloscope, or other signal processing device which receives the signal from the acoustic sensor 20. In some embodiments, the controller 30 may comprise a microprocessor or other computing device which is configured to process the signal. In some embodiments, the controller 30 may comprise a plurality of processing devices. For example, the controller 30 may comprise an oscilloscope which is configured to sample the signal received from the acoustic sensor. The oscilloscope may then be configured to transmit the sampled signal to a further processing device (e.g. a microprocessor) for further analysis. Various other combinations of devices for analysing the signal according to this disclosure will be apparent to the skilled person.

[0074] Next, according to another embodiment of the disclosure, a method 100 of detecting bubbles in a stirred tank will be described. The method 100 is performed by the measurement system 10 connected to the stirred tank 1 of Fig. 1. A block diagram of the method is shown in Fig. 3.

[0075] In step 101 of the method, acoustic waves present in the tank are detected using the acoustic sensor 20 to generate a signal indicative of the acoustic waves. The signal is transmitted from the acoustic sensor 20 to the controller 30.

[0076] In step 102, the controller 30 samples the signal over a predetermined time period to generate a sampled signal. In some embodiments, the predetermined time period may be at least 0.2 s. In some embodiments, the predetermined time period may be at least 3 s. In some embodiments of this disclosure, the predetermined time period is at least 5 s. For stirred tanks having a rotational speed in the order of 100-1000 rpm, it is preferable to sample the signal for at least 0.2 s in order to capture acoustic data of at least 20 rotations of the impeller 5. Such a predetermined time period should then capture any acoustic events associated with bubbles if they are occurring, on average, over the predetermined time period. In some embodiments, the predetermined time period may be no greater than 30 s, in order to allow the (data) size of the of the sampled signal to be relatively straightforward to process with the controller 30. Larger sampled signals may be more computationally expensive to processes according to method 100.

[0077] Fig. 4a, 4b, and 4c shows examples of sampled signals generated by the controller for the stirred tank 1 of Fig. 1 at different rotational speeds of the impeller 5. It will be appreciated from Figs. 4a, 4b, and 4c that the amplitude of the sampled signal increases as the rotational speed is increased, at least in part due to the increase in the velocity of the liquid 7 with rotational speed of the impeller. In the example of Fig. 4a (rpm 40), no bubbles are present in the liquid (i.e. the vortex does not extend to the impeller 5). In the example of Fig. 4b (rpm 460), a relatively small amount of bubbles are present, as the vortex now extends close to the impeller 5. That is to say, an rpm of 460 is the rotational speed at which the onset of air entrainment in the liquid 7 occurs. In the example of Fig. 4c (rpm 600), the vortex overlaps the impeller and air is entrained in the liquid 7 (i.e. bubbles are present in the liquid 7).

[0078] Fig. 5 shows a further example of the sampled signal for a sub-section of the predetermined time period. It will be appreciated from the detailed view of Fig.5 that acoustic events associated with bubbles are difficult to detect from mere inspection of the sampled signal in the time domain alone. As such, the method 100 further processes the sampled signal in order to improve the accuracy of acoustic event detection.

[0079] Fig. 6 shows a further graph of a frequency domain of a sampled signal (different from the signals of Figs 4 and 5) obtained from measurement of a stirred tank 1 at different rotational speeds. One data plot is a sampled signal obtained at 1200 revolution per minute (rpm), while the other sampled signal was obtained as 2400 rpm. It will be appreciated from the frequency domain data that the majority of the signal power for each of the two signals is present at frequencies below about 10 kHz. Furthermore, it will be appreciated that it is difficult to identify acoustic events associated with bubbles from the frequency data alone.

[0080] In view of this, the controller 30 may be configured to sample the signal with a sampling frequency of at least 40 kHz. While a Nyquist frequency of about at least 20 kHz would allow the sampled signal to capture much of the spectral power present in the signal of e.g. Fig. 6, a higher sampling frequency may be provided to allow the measurement system to be adaptable to different stirred tanks which may have different spectral characteristics. In some embodiments, the sampling frequency of the controller 30 may preferably be at least 50 kHz, or more preferably at least 100 kHz. As such, the signal may be sampled at a frequency sufficiently high to capture acoustic data which may be indicative of the presence of bubbles. For example, in some embodiments, acoustic data indicative of the presence of bubbles may have characteristic frequencies of up to about 20 kHz.

[0081] In some embodiments, the controller 30 may be configured to sample the signal at a frequency of no greater than 200 kHz. Accordingly the amount of data generated by sampling the signal over the predetermined time period may be processed in a computationally efficient manner.

[0082] In some embodiments, following the sampling of the signal, and prior to performing step 104, the controller 30 may optionally perform step 103 of filtering the sampled signal.

[0083] According to embodiments of the disclosure, the controller 30 may filter the sampled signal in a variety of manners. For example, the controller 30 may filter the sampled signal by applying a low pass filter, or a discrete wavelet transform (DWT) filter, as further discussed below. Each filter is configured to remove background noise from the sampled signal and to improve the signal to noise ratio of acoustic events associated with bubbles. Other filters which achieve substantially the same effects as the filters discussed herein known to the skilled person may also be used to filter the sampled signal according to this disclosure.

[0084] Fig. 7 shows a frequency response of a low pass filter which may be applied to the sampled signal. The low pass filter has a generally flat response up to a cut off frequency of about 20 kHz. By applying a low pass filter with a cut off frequency of 20 kHz, relatively high frequencies which may not be associated with acoustic events resulting from bubbles may be removed or supressed from the sampled signal.

[0085] In some embodiments, the sampled signal may be filtered in a different domain to the frequency domain. For example in some embodiments, the sampled signal may be filtered using a discrete wavelet transform (DWT). As such, in step 103 the controller 30 may be configured to determine a discrete wavelet transform (DWT) of the sampled signal. The DWT of the sampled signal aims to identify the presence of a predetermined wavelet within the sampled signal. The predetermined wavelet may be selected to correspond to the acoustic event of interest (i.e. the presence of bubbles). The controller 30 may then apply a threshold to the DWT of the sampled signal. The threshold filters out relatively low intensity signals in the DWT of the sampled signal, leaving behind signals which are indicative of the presence of the predetermined wavelet (i.e. bubbles). The controller 30 then determines the inverse DWT of the thresholded DWT of the sampled signal. Thus, the DWT thresholded signal is returned to the time domain, at which point the signal has been filtered to remove background noise which is not associated with the predetermined wavelet.

[0086] The predetermined wavelet may be selected based on a priori knowledge of the nature of the acoustic events associated with bubbles. In some embodiments, the predetermined wavelet may be calibrated by analysing a (calibration) sampled signal for the stirred tank in which bubbles were known to be present. The analysis may aim to identify a wavelet which maximises the DWT of the (calibration) sampled signal. Further discussion of DWT- based embodiments are provided below.

[0087] In step 104, the controller 30 extracts an envelope of the sampled signal. According to this disclosure, the envelope of the sampled signal is a smooth curve which outlines the extremes of the signal. In some embodiments, where the envelope of the sampled signal comprises an upper envelope (i.e. having a generally positive value) and a lower envelope (having a generally negative value), either the upper envelope or the lower envelope may be used for further analysis.

[0088] Fig. 8 shows an example in which the controller 30 extracts an upper envelope of the sampled signal by determining the Hilbert transform of the sampled signal. By taking the Hilbert transform of the sampled signal over the predetermined time period, the controller can manipulate the sampled signal in order to more efficiently and accurately detect acoustic events associate with the presence of bubbles.

[0089] In some embodiments, the controller may additionally or alternatively utilise a Savitzky Golay filter in order to extract a signal which is representative of the envelope of the sampled signal. Other signal processing methods for extracting an envelope of a sampled signal may also be utilised by the skilled person. In step 104, the controller 30 detects, based on the envelope of the sampled signal, acoustic events above a predetermined threshold value which are indicative of the presence of bubbles in the tank. Fig. 9 shows a graph of the envelope of Fig. 8 with a predetermined threshold value of 5 V applied. In the embodiment of Fig. 9, peaks of the envelope having an amplitude above the predetermined threshold value are identified as being events which are indicative of bubbles being present in the liquid. It will be appreciated that the predetermined threshold value used to identify acoustic events will depend on the nature of the stirred tank 1 and the measurement system 10. Thus, in some embodiments, the predetermined threshold value may be determined empirically by performing a calibration measurement using the stirred tank 1 under conditions (e.g. rotation speed of impeller 5) at which bubbles are known to occur.

[0090] In some embodiments, the controller 30 may be configured to detect each event above the predetermined threshold value and count the number of events which occur during the predetermined time period. The number of detected events for each measurement may be output by the controller 30 for further analysis.

[0091] In some embodiments, the controller 30 may further analyse the thresholded signal to normalise the detected events. For example, the controller 30 may determine a time period associated with the detected acoustic events occurring. The time period may be the total time period that the envelope of the sampled signal is above the predetermined threshold value. The controller 30 may then calculate a ratio of the time period to the predetermined time period in order to provide an indication of the amount of bubbles present in the stirred tank. As such, the ratio is an indication of the normalized thresholded events, normalised against the predetermined time period. Thus, the measurement system 10 may be capable of comparing signals obtained using different duration predetermined time periods.

[0092] Fig. 10 shows a graph of the normalised thresholded events detected for a range of different rotation speeds. As shown in Fig. 10, for rotation speeds of less than 460 rpm the normalised thresholded events detected are negligible. At a rotation speed of 460 rpm, the stirred tank 1 was operated at the limit of air entrainment, and so a non-zero value for the normalised thresholded events was detected (but no greater than about 0.05). For rotation speeds above 460 rpm, the normalised thresholded events detected increases to about 0.3 to about 0.5. It will be appreciated that between the values of about 460 rpm and 500 rpm, the amount of bubbles detected increases. As such, the degree to which air is entrained in the liquid 7 may be controlled by controlling the rotational speed of the impeller 5 over this range. The measurement system 10 according to this disclosure allows the control profile for the speed-air entrainment relationship to be determined empirically for subsequent use in a control scheme.

[0093] Thus, in accordance with method 100, it will be appreciated that the measurement system 10 may be used to monitor a stirred tank and detect when bubbles (i.e. when air is being entrained) are present in a stirred liquid of the stirred tank 1.

[0094] As discussed above, in some embodiments the controller 30 may filter the sampled signal by applying a DWT filter. One advantage of using a DWT filter, relative to frequency domain-based filters, is that information from the time domain is preserved in the transformed signal. As such, the time series data may be decomposed into a set of wavelets which have an approximate period and location in time, which allows information from both the time domain and the frequency domain to be taken into account when detecting the presence of bubbles.

[0095] In some embodiments, the DWT filter applied by the controller 30 may utilise a Debauchies wavelet. In other embodiments, other families of wavelets may be used by the DWT filter. In some embodiments, the wavelet utilised may selected from the wavelets provided as part of the ‘pywavelets’ package available in Python. In one embodiment, the wavelet ‘db30’ from the ‘pywavelets’ package may be used.

[0096] Fig. 12 shows a schematic diagram of a DWT filter according to an embodiment of the disclosure. In effect, the DWT filter is a recursive function in which the signal is broken down into approximation coefficients using a scaling function and details coefficients using a wavelet function at each level of the filter. The approximation coefficients capture low frequency information, while the details coefficients capture high-frequency information. When determining the details coefficients and the approximation coefficients, the coefficients may be down-sampled (not shown in Fig. 12). As shown in Fig. 12, the details coefficients form the coefficients of the DWT transform for each level. The approximation coefficients (e.g. from level 1) can be down-sampled and further decomposed into details and approximation coefficients (e.g. level 2 coefficients). In the diagram of Fig. 12, a cascading three level filter is shown, but in other embodiments one more levels may be used.

[0097] By way of example, Fig. 13 shows a graph of the ‘db30’ wavelet function which may be used to generate the details coefficients of a signal. The wavelet function has the effect of high pass filtering the signal. Fig.14 shows a graph of the ‘db30’ scaling function which may be used to generate the approximation coefficients of a signal. It will be appreciated that the scaling function has the effect of low pass filtering the signal.

[0098] As will be appreciated by the skilled person, the DWT is not a single vector space of frequencies, but a two-dimensional space of time and decomposition level. To illustrate this, Fig. 15 shows a graph of the power spectra of the ‘db30’ wavelet function by level for a sampling frequency of 100 kHz, and Fig. 16 shows a graph of the power spectra of the ‘db30’ scaling function by level at a sampling frequency of 100 kHz.

[0099] It will be appreciated that the DWT can be inverted to reconstruct the time domain signal. When reconstructing the signal, typically the highest level of the scaling function is used (i.e. the lowest filter).

[0100] By way of example, Fig. 17 shows two 10 ms snippets of signal sampled at 100 kHz. One signal is representative of a time when bubbles are present, and the other is representative of data where bubbles are largely not present. The signals have been transformed using the DWT using the ‘db30’ wavelet function and ‘db30’ scaling function. As shown in Fig.

[0101] 17, coefficients for the five wavelet levels are shown along with the level 5 scaling coefficients. The amplitude of the coefficients is largest in wavelet levels 3 and 4, which is consistent with the bandwidth of the level 3 and 4 wavelets and the expected bandwidth of the signal (c.f. the bandwidth of the signal shown in Fig. 6).

[0102] In some embodiments, the DWT transformed signal may be smoothed to remove noise from the time series data. Smoothing of the signal may be achieved by setting relatively small components of the DWT transformed signal to zero prior to reconstructing the time series data. Accordingly, in some embodiments, a threshold may be applied to the DWT of the sampled signal. Signal levels (i.e. details coefficients and approximation coefficients) falling below the threshold value may be set to zero. Where the DWT transform comprises a plurality of levels, the threshold may be applied to each of the levels of the DWT. In some embodiments, the threshold value may be a predetermined value selected by a user based on a calibration measurement or other setting specified by a user.

[0103] By way of example, Fig. 18 shows the thresholded coefficients for the five wavelet levels of and the level 5 scaling coefficients of Fig. 17, where the predetermined threshold value is 150 mV.

[0104] Following the thresholding of the DWT transformed signal, the time series data can be reconstructed using an inverse DWT. Fig. 19a shows an example of reconstructed time series data using the level 5 scaling coefficients of Fig. 17 (i.e. with no thresholding applied). Fig. 19b shows an example of reconstructed time series data using the thresholded level 5 scaling coefficients of Fig. 18. As shown in Figs. 20a and 20b, a Hilbert transform may then be applied to the reconstructed time series data to extract the envelope of the signals. Fig. 20a is the envelope of Fig. 19a, and Fig. 20b is the envelope of Fig.

[0105] 19b. It will be appreciated that the application of the thresholding as part of the DWT is to broadly suppress the signal when no bubbles are present and to leave the signal when bubbles are present broadly unchanged. Accordingly, as shown in Figs. 19 and 20, a detection threshold of 87.1 mV may be used to distinguish between signals where bubbles are present, and signal where bubbles are not present. The use of the DWT with thresholding may allow for improved accuracy in the determination of the state of the stirred tank.

[0106] To further illustrate this, Fig. 21a shows a graph of a power spectra of some reconstructed time series data where thresholding is not utilised as part of the DWT. Fig. 21 b shows a graph of the power spectra where thresholding is applied to the DWT signal prior to reconstruction.

[0107] Figs. 22a and 22b show graphs of the normalised thresholded events detected based on the reconstructed time series data used to generate the power spectra of Figs. 21a and 21b. In Fig. 22a, bubbles were present when the normalised thresholded events were about > 0.95, and the normalised thresholded events when bubbles were not present was about <0.7. In Fig. 22b, bubbles were present when the normalised thresholded events were about > 0.95 (similar to Fig. 22a), and the normalised thresholded events when bubbles were not present was about <0.12. So, as will be appreciated from Figs. 22a and 22b, the use of thresholding as part of the DWT improves the distinction between periods where bubbles are present and where bubbles are not present by suppressing the signal when bubbles are not present. That is to say, the impact of machinery noise on the detection of bubbles has been suppressed or eliminated by application of thresholding to the DWT transformed signal.

[0108] In some embodiments, the controller 30 may be further configured to control the rotational speed of the impeller 5. As such, the controller 30 may be configured to vary the rotation speed of the impeller 5 based on the detection of acoustic events above a predetermined threshold value which is indicative of the presence of bubbles in the stirred tank 1. For example, the controller 30 may be configured to control the rotational speed of the stirred tank 1 to stir the liquid 7 at a rotational speed as close as possible to the onset of air entrainment, but without air entrainment occurring. It will be appreciated that higher rotation speeds may allow for a manufacturing process to be completed in a more time efficient manner. However, due to minor variations in manufacturing conditions, the rotational speed at which air entrainment occurs may vary slightly. Thus, the measurement system 10 may allow a stirred tank to be operated closer to the limit of air entrainment due to the feedback from the acoustic sensor 20.

[0109] In some embodiments, the controller 30 may be configured to provide a desired amount of bubbles / air entrainment in a stirred liquid 7. For example, in the embodiment of Fig. 10, the rotational speed of the impeller 5 may be controller between about 460 rpm and 500 rpm in order to control the rate at which air is entrained in the liquid 7. Thus, measurement system 10 may also provide a feedback system for the control of manufacturing processes where it is desirable to entrain air in a stirred liquid 7 in a controlled manner.

[0110] In some manufacturing processes, bubbles may be formed in a stirred tank 1 due to a reaction occurring. The measurement system 10 may be used to monitor the presence of bubbles throughout the reaction. As such, the measurement system 10 may provide a way to non-invasively monitor the reaction progress. For example, Fig. 11 shows an example of a reaction between copper carbonate and a zeolite slurry in a stirred tank. As shown in Fig. 11, the normalized thresholded events detected increases during an initial time period from 0 to about 20 minutes shown in Fig. 11 as the reaction is started. The normalised thresholded events then decreases from about 20 minutes to 40 minutes as the reaction completes. Thus, it will be appreciated that the measurement system 10 may be incorporated into a wider control system or monitoring system of a manufacturing process. For example, the controller 30 may be configured to monitor a reaction process and to control the rotational speed of the impeller 5 in order to control the progress of the reaction. For example, the rotational speed of the impeller 5 may be increased to speed up the progress of the reaction and decreased (or even stopped) to slow down the progress of the reaction.

[0111] In some embodiments, the controller 30 may be further configured to output the sampled signal to a cloud-based storage medium 40. Thus, the sampled signal may be accessed at a later time for further analysis. In some embodiments, the sampled signal may be output in a Hierarchical Data Format version 5 (HDF5) format to the cloud-based storage medium 40. In some embodiments, the data output to the cloud may comprise sampled signals from a plurality of acoustic sensors of the measurement system. Other intermediate data signals determined by the controller may also be output to the cloud. By outputting the data in an HDF5 format, the data may be compressed during file transfer.

[0112] The cloud-based storage medium 40 may be any suitable storage medium which is accessible via an internet connection. For example, the controller 30 may transfer data to the cloud-based storage medium via a wired internet connection or via one or more wireless networks. In some embodiments, the controller 30 may be configured to operate as an Internet of Things (loT) device which communicates with the cloud-based storage medium via a wireless network.

[0113] In particular, in the embodiment of Fig. 1 the cloud-based storage medium 40 may be configured to store the sampled signal from the acoustic sensor 40. Utilising cloud-based storage may be advantageous given that the acoustic sensor 20 may generate data files comprising data samples at a rate of e.g. 100 kHz for up to about 30s per measurement. For example, data files of a measurement may have a size of at least 10 Mbytes, or at least 30 Mbytes. Such data files may exceed the capacity of a local storage medium of the controller 30 relatively quickly, so it may be advantageous to transfer the data to a cloudbased storage medium 40. Furthermore, uploading the data to a cloud-based storage medium 40 may allow the data uploaded to comply with FAIR principles (findability, accessibility, interoperability, and reusability).

[0114] As discussed above, the controller 30 detects acoustic events based on a predetermined threshold value. In some embodiments, the predetermined threshold value may be set by e.g. a user based performing calibration measurements using the measurement system. In other embodiments, the controller 30 may utilise a machine learning process to determine a suitable predetermined threshold value.

[0115] Similar, to the embodiments discussed above, the controller 30 may obtain a signal indicative of the acoustic waves in the tank and sample the signal over a predetermined time period to generate a sampled signal.

[0116] While in some embodiments, the machine learning process may detect events in the time domain of the sampled signal, in some embodiments the machine learning process may detect and classify events using a transformed signal. For example, in some embodiments, prior to extracting the envelope of the sampled signal the controller 30 may be configured to transform the sampled signal using a discrete wavelet transform, wherein the envelope is extracted from the transformed signal. The controller may then be configured to detect acoustic events which are indicative of the presence of bubbles in the tank based on the envelope of the sampled signal using a trained machine learning model. A schematic block diagram outlining a method such a machine-learning based process is shown in Fig. 23.

[0117] As shown in Fig. 23, a sampled signal of a predetermined duration (e.g. 5 s) may be obtained by the controller 30 in accordance with the methods described above. A DWT of the sampled signal may be obtained similar to the method described above. The controller may be configured to transform the sampled signal using a discrete wavelet transform having a plurality of levels to generate a transformed signal comprising details coefficients and approximation coefficients for each of the plurality of levels. For example, the signal may be sampled at a frequency of 100 kHz, following which a level 5 DWT is performed on the sampled signal to obtain a transformed signal. As such, 5 levels of details coefficients and 5 levels of approximation coefficients may be obtained for the 5 s duration of the sampled signal.

[0118] As shown in Fig. 23, an envelope may be extracted from the transformed sampled signal. The envelope may be extracted using the Hilbert transform on the transformed sampled signal. In some embodiments, an envelope is extracted from the details coefficients of one or more levels of the transformed signal and / or the approximations coefficients of one or more levels of the transformed signal. As such, not all of the levels of the DWT may be processed for analysis by the machine learning algorithm. That is to say, some levels of the DWT may include information which is more relevant than other levels for the detection of bubbles and / or classification of other events. Fig. 24 shows graphs of the envelope of the transformed sampled signal for a snippet of the 5 s signal. The details coefficients for the 5 levels of the transformed signal along with the approximation coefficients for level 5 of the transformed signal are shown in Fig. 24.

[0119] The envelope of the transformed signal may then be windowed in order to generate a plurality of events for classification by the machine learning process. As shown in Fig. 25, the controller may generate a plurality of events over the duration of the sampled signal. Each event has an associated amplitude and a time. As shown in Fig. 24, each event is calculated based on the mean amplitude of the transformed signal over a predetermined event time period. In some embodiments, the amplitude of each of details and / or approximation coefficients may be normalised prior to determining the plurality of events. As shown in Fig. 25, the plurality of events (i.e. the amplitude of the transformed signal) for each level of the DWT may each have an event number which corresponds to a point in time of the 5 s duration sampled signal. In the example of Figs. 24 and 25, each event has a duration of 20 ms, and so 250 events cover the 5 s duration of the sampled signal.

[0120] The controller 30 is configured to detect acoustic events which are indicative of the presence of bubbles by classifying the plurality of events using a trained machine learning model. In some embodiments, the trained machine learning model may be used to classify the events into events which are indicative of bubbles and events which are indicative of no bubbles (similar to the embodiments described above).

[0121] In some embodiments, the machine learning model may be configured to classify the events into more than two categories. For example, the machine learning model may also be configured to detect when the sensor is not correctly attached to the stirred tank. The machine learning model may also be configured to detect when machinery noise is present in the sampled signal. As such, in some embodiments, the machine learning model may be configured to classify the events into the following categories:

[0122] Table 1

[0123] In order to classify the events into the above categories, the machine learning model may be trained with sampled signal data which is indicative of each of the above categories. For example, a multinomial regression model may be used to train the machine learning model. As such, the trained machine learning model may be a trained multinomial regression model which estimates the probability of an event being in a given category. The probability of the Ithcategory may be calculated based on: is a linear combination of the features and the weights given by ui=Pio + Pilxl + Pi2x2 + - Pipxp

[0124] In the above, {%1,x2, } may be the chosen features of the model and { n , Pi2 Pip } are weights of the trained machine learning model.

[0125] The machine learning model may be trained using a set of training data. Any suitable training method may be used. For example, the training method may be method which aims to arrive at a set of weights , pi2, ... , PiP} which minimizes the cross-entropy loss function: is the true value of the jthobservation in jthcategory and is the corresponding predicted value. The values of y^ can either be 0 or 1 depending on whether the observation is in the category or not. Training of the model may be performed using, for example, the ‘scikit-learn’ package available in Python.

[0126] By way of example, Fig. 26 shows a confusion matrix for the trained machine learning model which has been validated using some test data. In tests, the trained machine learning model correctly classified 99.4 % of the test data.

Claims

CLAIMS:

1. A measurement system for detecting bubbles in a tank comprising: an acoustic sensor configured to detect acoustic waves in the tank; a controller configured to receive a signal indicative of the acoustic waves from the acoustic sensor, wherein the controller is configured to: sample the signal received from the acoustic sensor over a predetermined time period to generate a sampled signal; extract an envelope of the sampled signal; detect, based on the envelope of the sampled signal, acoustic events above a predetermined threshold value which are indicative of the presence of bubbles in the tank.

2. A measurement system according to claim 1 , wherein the signal is sampled at a frequency of at least 40 kHz, preferably at least 50 kHz, more preferably at least 100 kHz.

3. A measurement system according to claim 1 or claim 2, wherein in order to extract the envelope of the sampled signal, the controller is configured to: determine a Hilbert transform of the sampled signal.

4. A measurement system according to claim 3, wherein prior to determining the Hilbert transform, the controller is configured to filter the sampled signal.

5. A measurement system according to claim 4, wherein the controller is configured to filter the sampled signal using a low pass filter.

6. A measurement system according to claim 5, wherein the controller is configured to low pass filter the sampled signal with a low pass filter having a cut-off frequency of no greater than 20 kHz.

7. A measurement system according to claim 4, wherein the controller is configured to filter the sampled signal by: determining a discrete wavelet transform (DWT) of the sampled signal,applying a threshold to the DWT of the sampled signal, and determining the inverse DWT of the thresholded DWT of the sampled signal.

8. A measurement system according to any of claims 1 to 7, wherein the controller is further configured to: determine a time period associated with the detected acoustic events occurring; and calculate a ratio of the time period to the predetermined time period in order to provide an indication of the amount of bubbles present in the tank.

9. A measurement system according to any of claims 1 to 8, wherein the predetermined time period is at least 0.2 s.10 A measurement system according to any of claims 1 to 9, wherein the controller is further configured to output the sampled signal to a cloud-based storage medium.

11. A measurement system according to any of claims 1 to 10, wherein the acoustic sensor is configured to detect acoustic waves associated with air entrainment in a stirred tank and / or acoustic waves associated with bubbles generated as a reaction product within the tank.

12. A measurement system according to any of claims 1 to 11 , wherein the measurement system is configured to be used with a stirred tank, the measurement system further comprising a sensor configured to sense a rotational speed of a stirrer of the stirred tank, wherein the controller is configured to receive data indicative of the rotational speed of the stirred tank over the predetermined time period.

13. A measurement system according to claim 12, wherein the controller is further configured to control the rotational speed of the stirrer based on the detection of acoustic events above a predetermined threshold value which are indicative of the presence of bubbles in the stirred tank.

14. The measurement system of any of claims 1 to 13 when provided as part of a tank, optionally a stirred tank, wherein optionally the stirred tank is an unbaffled stirred tank or a baffled stirred tank.

15. The measurement system of any of claims 1 to 14, wherein prior to extracting the envelope, the controller is configured to transform the sampled signal using a discrete wavelet transform (DWT).

16. The measurement system of any of claims 1 to 15, wherein prior to extracting the envelope of the sampled signal, the controller is further configured to transform the sampled signal using a discrete wavelet transform, wherein the envelope is extracted from the transformed signal; and the controller is configured to detect acoustic events which are indicative of the presence of bubbles in the tank based on the envelope of the sampled signal using a trained machine learning model.

17. The measurement system of claim 16, wherein the controller is configured: to determine a plurality of events from the transformed signal, wherein each event is determined based on an average amplitude of the envelope over an event time period, wherein the controller is configured to detect acoustic events which are indicative of the presence of bubbles by classifying the plurality of events using the trained machine learning model.

18. The measurement system of claim 17, wherein the controller is configured to classify the plurality of events into a plurality categories comprising two or more categories selected from the group comprising: Machinery Noise with Bubbles, Machinery Noise with No Bubbles, Detached Sensor, Anomalous Sensor Reading, Background Machinery Noise, No Machinery Noise with Bubbles, No Machinery Noise with No Bubbles.

19. The measurement system of any of claims 16 to 18, wherein the controller is configured to transform the sampled signal using a discrete wavelet transform having a plurality of levels to generate a transformed signal comprising details coefficients and approximation coefficients for each of the plurality of levels.

20. The measurement system of claim 19, wherein an envelope is extracted from the details coefficients of one or more levels of the transformed signal and / or the approximations coefficients of one or more levels of the transformed signal.

21. A method of detecting bubbles in a tank, optionally a stirred tank, comprising: detecting acoustic waves in the tank using an acoustic sensor to generate a signal indicative of the acoustic waves: sampling the signal over a predetermined time period to generate a sampled signal; extracting an envelope of the sampled signal; and detecting, based on the envelope of the sampled signal, acoustic events above a predetermined threshold value which are indicative of the presence of bubbles in the tank.

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