Active acoustic method for predicting properties of process fluids comprising solid particles or gas/liquid volumes based on their size distribution and concentration
09772311 · 2017-09-26
Assignee
Inventors
- Thomas Liljenberg (Västerås, SE)
- Stevan Backa (Karlstad, SE)
- Lennart Thegel (Västerås, SE)
- Mats Åbom (Järfälla, SE)
Cpc classification
International classification
Abstract
In the present invention a controllable acoustic source (14) in connection with the process fluid (10) emits a signal (18) into the fluid (10), consisting of a suspension of particles (12), being volumes of gas, liquid or solid phase. The controllable acoustic signal (18) is allowed to interact, with the particles (12), and the acoustic (pressure) signals (22) resulting from such an interaction is measured preferably via a sensor (24). A spectrum is measured. The spectrum is used to predict properties, content and/or size of the particles (12) and/or used to control a process in which the process fluid (10) participates. The prediction is performed in the view of the control of the acoustic source (14). The used acoustic signal has preferably a frequency below 20 kHz.
Claims
1. A method for predicting properties of a process fluid flowing in a pipe, the process fluid being a suspension of solid particles or an emulsion of gas or liquid volumes, wherein the properties are based on particles or volumes size distribution and concentration the method comprising: emitting a controllable acoustic signal from an acoustic emitter attached to the outer side of the pipe into said process fluid for interaction with the volumes or the particles, said acoustic emitter connected to a controller to control the acoustic signal by frequency, amplitude, phase or timing with the acoustic signal comprising audible frequencies below 20 kHz and wavelengths larger than the sizes of the particles or volumes; tuning the controllable acoustic signal with the controller to enhance acoustic response of the particles or volumes in the process fluid; measuring acoustic spectrum resulted from modified acoustic signals emitted from the emitter and acoustic signals emitted from the particles or volumes with at least one acoustic sensor, wherein the measurement is made for corresponding amplitudes, phase, time or spatial dependencies of resulting acoustic signals, and wherein the at least one acoustic sensor is attached to the outer side of the pipe apart from the acoustic emitter; processing the resulting acoustic spectrum to correlate the measured acoustic spectrum to properties, content or distribution of the particles or volumes within the process fluid with a processor connected to the at least one sensor and the controller, wherein the processor utilizes a predetermined model, wherein the predetermined model is developed by correlating acoustic measurements for a known process liquid with corresponding properties of the known process fluid obtained by non-acoustic methods using a multivariate statistical analysis.
2. The method according to claim 1, wherein said step of correlating comprises: applying a partial least squares analysis to a sequence of non-acoustic measurements and a sequence of acoustic spectra.
3. The method according to claim 2, wherein said step of correlating further comprises: removing non-relevant frequencies of said acoustic spectra with low correlation with said non-acoustic measurements.
4. The method according to claim 1, wherein said step of correlating comprises: performing principal component analysis separately on said acoustic spectrum and on said non-acoustic measurements.
5. The method according to claim 1, wherein said acoustic emitter is smaller than the wavelength of the emitted acoustic signal.
6. The method according to claim 1, wherein said at least one acoustic sensor are two acoustic sensors, separated in a direction along a flow path of the process fluid by a distance smaller than the wavelength of the emitted acoustic signal, and wherein the method further comprises measuring the propagation speed of the acoustic signals within the flowing process fluid or its flow rate.
7. The method according to claim 1, wherein said at least one acoustic sensor are two acoustic sensors separated substantially perpendicularly to a flow path of the flowing process fluid.
8. An analyzing apparatus for performing the method of claim 1, said analyzing apparatus comprising: an acoustic emitter capable of emitting audible frequencies below 20 kHz, attached to the outer side of the pipe with the flowing process fluid; at least one acoustic sensor attached at the same side of the pipe and at a distance from the acoustic emitter along the pipe; a processor, and a controller connected to said acoustic emitter, said at least one acoustic sensor, and said processor, wherein said controller is arranged and configured to: control said acoustic emitter to emit a controllable acoustic signal from the acoustic emitter into the process fluid for interaction with the volumes or the particles in the process fluid, wherein the controller controls the acoustic signal by frequency, amplitude, phase and/or timing with the acoustic signal comprising audible frequencies below 20 kHz and wavelengths larger than the sizes of the particles or volumes; tune the controllable acoustic signal to enhance acoustic response of the particles or volumes in the process fluid; control the at least one acoustic sensor for measuring acoustic spectrum resulted from modified acoustic signals emitted from the acoustic emitter and acoustic signals emitted from the particles or volumes, wherein the acoustic sensor measures corresponding amplitudes, phase, time or spatial dependencies of resulting acoustic signals; control the processor connected to the at least one acoustic sensor and the controller to process the resulting acoustic spectrum to correlate the measured acoustic spectrum to the properties of the flowing process fluid based on size distribution and concentrations of the particles or volumes within the process fluid, wherein the processor utilizes a predetermined model, wherein the predetermined model is developed by correlating acoustic measurements for a known process liquid with corresponding properties of the known process fluid obtained by non-acoustic methods using a multivariate statistical analysis.
9. The apparatus according to claim 8, wherein said acoustic emitter is smaller than the wavelength of the emitted acoustic signal.
10. The apparatus according to claim 8, wherein said at least one acoustic sensor are two acoustic sensors, separated in a direction along a flow path of the process fluid by a distance smaller than the wavelength of the emitted acoustic signal.
11. The apparatus according to claim 8, wherein said at least one acoustic sensor are two acoustic sensors separated substantially perpendicularly to a flow path of the process fluid.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) The invention, together with further objects and advantages thereof, may best be understood by making reference to the following description taken together with the accompanying drawings, in which:
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DETAILED DESCRIPTION
(13)
(14) This influence will, for waves with a wavelength much larger than the size of the particles and distance between them, mainly manifest itself as a changed fluid compressibility. This will lead to a change in the phase speed and to absorption of the acoustic signals 18 which will be frequency dependent. In particular, large changes can be expected in frequency ranges where the suspended particles 12 exhibit resonant vibration behavior. The resonance frequencies depend, e.g., on density, dimensions, stiffness, bonding within the particle and bonding between particles and many other properties. This frequency range is for almost all practical applications located in the audible subultrasonic region, i.e. below 20 kHz. Since the influence of even small particle concentrations, e.g. air bubbles in water, on fluid compressibility can be very large, a method based on long waved acoustic signals is potentially very sensitive for detecting fluid mix variations. Of course this high sensitivity also implies that special measures might be needed to control any unwanted influence on the fluid properties. This can be achieved by applying special signal processing techniques, as discussed further below.
(15) Furthermore, by using frequencies well below the ultrasonic range coherent signals can be provided making measurements of both amplitude and phase response possible. This is described further in detail below.
(16) The particles 12 will thus influence the acoustic transmission properties (phase speed) of the process fluid and absorb vibration energy and thereby change the originally emitted acoustic signals. The vibrating particles 12 will also themselves emit energy in the form of acoustic signals 20. These signals will typically be in the same frequency range as the particle vibrations, i.e. in the frequency range below the ultrasonic range. The modified emitted acoustic signals 18 from the emitter 14 and the acoustic signals emitted from the particles 20 will together form a resulting acoustic signal 22.
(17) An acoustic signal sensor 24 is arranged at the system for measuring acoustic signals in the process fluid 10. At least one component of the acoustic spectrum of the acoustic signals is measured. These acoustic signals are the resulting signals 22 from the interaction between the emitted acoustic signals 18 and the particles 12. Since the interaction between acoustic signals and the particles 12 is indicative of the nature of the particles 12, the measured acoustic signals comprise information related to the particles 12 suspended in the process fluid 10. The analyzing device further comprises a processor 28, which is connected to the sensor 24 by a sensor connection 26. The processor 28 is an evaluation unit arranged for correlating the measured acoustic signals to properties, content or distribution of the particles 12 within the process fluid 10. The emitter control unit 16 is preferably controllable by the processor 28 through an emitter connection 30 in order to tune or control the emitted acoustic signals dependent or coordinated with the measurement operation.
(18) In a typical case, the processor 28 operates according to a certain model of the involved system. The model is preferably based on theories about the physical interaction between the particles and the acoustic waves. The model or parameters in the model are calibrated by using a set of acoustic signal measurements and corresponding laboratory measurements of the particle properties of interest. The model is then possible to use for predicting the particle properties from acoustic spectra of unknown samples. Specific examples of how a model may be derived are given below.
(19) A corresponding method for system identification is illustrated in the flow diagram of
(20)
(21) A process control unit 40 controls the operation parameters of the subprocess and is connected by a control connection 42 to the processor 28 of the analyzing device 13. By supplying the processor 28 with information about how the parameter settings of the subprocess influence the properties of the process fluid particles, the processor 28 will be able to provide the process control unit 40 with appropriate control information, based on the actual properties of the particles. This information can e.g. be used by an operator to control the subprocess to give particles with certain predetermined properties accordingly. Alternatively, the processor 28 provides values of the predicted particle properties to the process control unit 40 as input parameters. A feed-forward control is thus accomplished.
(22)
(23) A process control unit 40 controls the operation parameters of the subprocess and is connected by a control connection 42 to the processor 28 of the analyzing device 13. By supplying the processor 28 with information how the parameter settings of the subprocess influence the properties of the process fluid particles, the processor 28 will be able to provide the process control unit 40 with appropriate control information, based on the properties of the particles resulting from the subprocess. Alternatively, the processor 28 provides values of the predicted particle properties to the process control unit 40 as input parameters. A feed-back control is thus accomplished.
(24) Obviously, these two different modes of system control can be combined in any configuration.
(25) A corresponding method for system control is illustrated in the flow diagram of
(26) The controllability of the acoustic source is very important. By selecting amplitude, frequency, phase and/or timing of the acoustic signals, different properties of the particles can be addressed. By controlling the frequency, the acoustic signals may e.g. be tuned to certain resonance frequencies connected to the particles, addressing specific properties. By modulating the amplitude of the signal source, noise reduction may be performed, or time dependent interactions may be emphasized or suppressed. By controlling the phase, dynamic measurements are facilitated. By controlling the timing of the acoustic signals, processes having time dependencies may be investigated. Such investigations are not possible to perform using only passive sources of acoustic signals. A few examples of simplified situations will illustrate the possibilities of controlling the signal source.
(27) In
(28) Assuming a process fluid having solid particles of slights differing dimensions. Knowing that a certain resonance vibration is related to a certain dimension of the particle can be used to investigate the size distribution of the particles in the fluid.
(29) In this manner, the frequency can be used for revealing different aspects related to the particles. The frequency may thus comprise e.g. a single constant frequency, a single frequency varying with time, a number of single constant frequencies, a number of single frequencies varying with time, or different types of limited frequency bands, such as white or pink noise.
(30) The timing of the emitted acoustic signals may also be used, e.g. by using pulsed acoustic signals emitted during limited time intervals.
(31) More sophisticated background reduction methods would be available by amplitude modulating the emitted acoustic signal. In
(32) From the above examples, it is obvious that the sensors should be able to measure different properties of the resulting acoustic signals. In a corresponding manner as for the emitted signals, the sensors measure e.g. amplitude, frequency, phase and/or timing of the acoustic signals resulting from the interaction with the particles in the process fluid. It is preferred if the sensors may measure at least three of the above mentioned characteristics, since a robust multivariate analysis then can be performed. The use of more variable dimensions is illustrated by a simplified example.
(33) Assume an emitted acoustic signal according to
(34) The above examples are only given as oversimplified examples to increase the understanding of the possibilities of a system with controllable active acoustic sources. In real cases the situations are far more complicated and multivariate statistical analysis or neural networks are for instance used to evaluate the measured acoustic spectra.
(35) The recorded acoustic spectra are preferably Fourier transformed to obtain intensity variations as a function of frequency. The acoustic spectra are then preferably analyzed using different kinds of multivariate data analysis. The basics of such analysis may e.g. be found in “Multivariate Calibration” by H. Martens and T. Naes, John Wiley & Sons, Chicester, 1989, pp. 116-163. Commercially available tools for multivariate analysis are e.g. “Simca-P 8.0” from Umetrics or PLS-Toolbox 2.0 from Eigenvector Research, Inc. for use with MATLAB™. PLS (Partial Least Square) methods of first or second order are particularly useful. Neural network solutions, such as Neural Network Toolbox for MATLAB™, are also suitable to use for analysis purposes.
(36) To improve the model predicting ability, a pre-treatment of spectral data is sometimes beneficial. Such a pre-treatment can include orthogonal signal correction or wavelength compression of data. Furthermore, both the real and imaginary part of the acoustic signal can be used in multivariate calculations.
(37) The relative geometrical positioning and/or the number of emitters and/or sensors can also be used to increase the reliability of the measured signals and thereby the properties of the particles. In
(38) The positioning of sensors can be used also in other ways. In
(39) The acoustic signal emitter can be of different types. One obvious choice for gases is to use loudspeakers. In particular at frequencies of a few hundred Hz up to a few kHz a loudspeaker can generate high power signals without any severe problems. For hot gases or dirty environments, the loudspeaker is preferably provided with cooling facilities and protection devices, respectively. For liquid process fluids, at low and intermediate frequencies, more specially constructed sound sources have to be used. One possibility is e.g. to use an electrodynamic shaker driving a membrane or a light-weight piston.
(40) Sensors, detecting acoustic signals, are readily available in the prior art. Since the quantity of primary interest here is fluctuating pressure, the best alternative is probably to use pressure sensors or transducers. For applications in gases at normal temperatures (<70° C.) standard condenser or electric microphones are preferably used. Some well-known manufacturers are Bruel & Kjaer, Larson & Davies, GRAS. and Rion. These microphone types are sensitive and accurate, but for applications in hot or dirty environments they must be cooled and protected. Also very high levels (>140 dB) can be a problem. An alternative for hot and difficult environments is piezoelectric pressure transducers. These are much more expensive than condenser microphones but can be used up to temperatures of several hundred degrees Celsius. Drawbacks are that the pressure sensitivity is much lower than for condenser microphones and that this transducer type can pick up vibrations. An advantage is that many piezoelectric transducers can be used both in liquids and gases. However, special types for liquids also exist and are normally called hydrophones. A leading manufacturer of piezoelectric transducers is Kiestler.
(41) If measuring the pressure, the sensor has to be in direct contact with the fluid. However, this has some obvious disadvantages since it is necessary to make a hole in a pipe or wall for mounting purposes. An alternative choice of sensors is vibration sensors, which can be mounted on a wall and measure the vibrations induced by the acoustic signals. Here, no direct contact with the fluid is required, why the mounting can be made more flexible and protected. However, a wall mounted vibration transducer will also pick up vibrations caused by other means, e.g. by machines comprised in the system. To some extent these wall vibrations will also radiate sound waves into surrounding fluid, which could be picked up by a pressure transducer, but normally, at least in gas filled systems, this effect represents a much smaller disturbance.
(42) In cases where both amplitude and phase measurements are of interest, further dimensional limitations are put on the sensors and frequencies. In order to be able to detect the phase of an acoustic signal, the sensor has to have a size that is small compared with the wave length of the acoustic signals. This puts in practice an upper limit of the frequency that can be used. If, as an example, the phase is going to be measured by a sensor of around 1 cm in size, the wavelength of the acoustic signal should be in the order of at least 15 cm. The speed of sound in e.g. water is in the order of 1500 m/s, which means that a maximum frequency of 10 kHz can be used. Smaller sensor sizes allows higher frequencies.
(43) As mentioned above, the particles can be of any phase; gas, liquid or solid, and of e.g. gel or sol type. However, the interaction of the acoustic signals with the particles becomes typically particularly intense if the phase of the particle matter differs from the phase of the fluid itself. The main explanation for this is the large variation in compressibility that normally exists between different phases. Thus are solid particles in liquid or gas, liquid particles in gas and gas particles in liquids good measurements targets.
(44) Regarding vibration transducers, the standard choice for all frequencies used in the present invention is so called accelerometers, which typically are piezoelectric sensors that gives an output proportional to acceleration. Regarding manufacturers the ones already listed for condenser microphones also apply in this case.
(45) The analysis device and method according to the present invention can be applied in many various fields. A couple of examples will be described briefly below.
(46) In the pulp and paper industry, the acoustic sensor could be installed in all positions where a flow or transportation of pulp is performed. A position of particular interest is in the vicinity of the refiner. The refiner is the most important sub-process step in mechanical pulping and there exist very clear economic benefits for implementation of a more advanced control of the refiner based on new information.
(47) After refining, the ground pulp fibers suspended in the water mixture exits the refiner at high pressure via an exit pipe 120. The high pressure is reduced, which causes some of the (by the refining process) heated water to evaporate into steam. The steam 124 is separated from the fiber mixture in a cyclone 122 before the fibers are introduced into the following pulping process steps.
(48) An emitter 14 with a control unit 16 is arranged at the exit pipe 120. A sensor 24 is also arranged at the exit pipe a distance from the emitter 14. The emitter 14 and sensor 24 are connected to an evaluation unit 28 comprising a processor. The emitter 14 is controlled to emit acoustic signals into the pulp mixture within the edit pipe 120. The sensor 24 records the resulting acoustic signals and the processor 28 evaluates the results.
(49) Paper strength issues are a vast area with many different laboratory measurement methods and evaluation possibilities. Nevertheless, it is probably the most common and important quality parameter demanded by the customers. Basically, the final paper strength is influenced by three parameters; the single fiber intrinsic strength, the area of fiber-to-fiber bond per length unit of the fiber and the strength of each fiber bond. Longer fibers will provide opportunities for more fiber-to-fiber bonds and therefore the fiber network will be stronger and consequently also the paper. If the fibers are excited, the vibrate with different frequencies depending on their length. The point of self-oscillation will be at a lower frequency for long fibers compared to short ones.
(50) Furthermore, the above property of the refined pulp mixture depends on certain input parameters of the refining process. The first parameter is the type and quality of the wood chips. Such information can be entered into the control system e.g. by an operator. Other parameters which determines the effect of the refining is the water content, the rate in which the chips are entered into the refiner, the disc velocity and the force between the refiner discs 110, 112. The relations between these parameters and the properties of the pulp are normally rather well known, or may be obtained empirically. Based on such relations, the analyzing device 13 may find appropriate changes in the settings of the disc speed, disc force, water content or chip feeding speed by signal connections 126 in order to improve the properties of the resulting fibers. The analyzing device thus constitutes a feed-back system, operating on the final process fluid from the refiner sub-process.
(51) Another example of a process system for which the present invention is suited is pharmaceutical manufacturing. In certain process lines, liquid particles of active substances are produced in a dilute form and are further processed in a refiner, in order to increase the active substance content.
(52) The actual concentration of active substance in the original fluid may vary considerably due to production processes that are difficult to control in a totally consistent manner. The operation of the refiner 202 thus has to be adjusted to the differing raw material, i.e. to the actual active substance concentration of the incoming fluid.
(53) An emitter 14 with a control unit 16 is arranged at the introduction pipe 200. A sensor 24 is also arranged at the introduction pipe a distance from the emitter 14. The emitter 14 and sensor 24 are connected to an evaluation unit 28 comprising a processor. The emitter 14 is controlled to emit acoustic signals into the fluid within the exit pipe 120. The sensor 24 records the resulting acoustic signals and the processor 28 evaluates the results.
(54) The active substance exists as small droplets emulgated in the fluid. The substance droplets have different acoustic properties as compared with the remaining part of the fluid. The changing properties makes the droplets in the emulsion to scattering objects for acoustic signals. The scattering properties are determined basically by the droplet size and droplet density. An acoustic signal emitted into the fluid will interact with the substance droplets and result in a resulting acoustic signal, which can be detected. The actual features of the detected signal depends on the droplet size and droplet density, i.e. on the active substance concentration. The processor 28 may therefore evaluate the active substance concentration of the introduced raw fluid. By knowing the relations between the operating conditions of the refiner and the substance concentration ratio, the operation of the refiner can be controlled continuously by the acoustic monitoring, by control connections 210 to the control unit 206, in order to produce a well-controlled active substance concentration in the outgoing process fluid.
(55) The pre-calibrated model referred to above, to be used for predicting properties of a fluid, can for example be established according to the following general procedure:
(56) 1) Measuring system properties
(57) 2) Creating a linear model from measurements
(58) 3) Validating the linear model
(59) In step 1), referring to
(60) Next, the frequency spectrum of the signal output from the sensor 24 is acquired, for example using FFT on the vector of voltage values. The result of the FFT is a vector of values (such as voltage values) representing the amplitude of the vibration in the tank wall, ordered in terms of vibration frequency. This vector is referred to as the frequency spectrum of the signal. To facilitate handling of the very large number of values, the values in the frequency spectrum are summarized for frequency intervals, so-called frequency bins. Conveniently, a frequency bin may correspond to a frequency interval of about 10 Hz.
(61) The received signal may also comprise noise originating from the environment of the measuring apparatus, which may be referred to as passive noise.
(62) The received signal is, following FFT as described above, taken to represent the active acoustic spectrum frequencies (AASF).
(63) When establishing the model, the received acoustic spectra are correlated with reference measurements. Hence, for each emitted signal, a corresponding reference measurement is performed for determining a desired property of the fluid, such as specific surface area of particles in the fluid or fluid viscosity. The reference measurement is typically performed by a conventional measurement method, which is typically a non-acoustic method. Which conventional measurement method is suitably used will, as is well known to one of ordinary skill in the art, depend on the property of the fluid that should be determined. Conventional methods may, for example, include optical refractometer measurements, radioactive measurements, or fluid samples taken from the pipe and analyzed by titration, optical methods or standardized tests, such as the test SCAN-N-22:96 (according to the Scandinavian pulp, paper and board testing committee—http://www.pfi.no/Documents/Scan_test_methods/N/N_22-96.pdf, which is expressly incorporated by reference herein) for determining dry matter content and fiber content in black liquor.
(64) In step 2) (Creating a linear model from measurements), the partial least squares (PLS) method is applied on the AASF together with the corresponding data from reference measurements to reduce the dimensionality of the regressors, thereby making further regression possible. When applying the PLS-method, non-relevant frequencies of the AASF can be sorted out due to low correlation with reference data. Noise cancellation and the discarding of non-relevant information is an intrinsic feature of the PLS dimension reduction method and is commonly used in the field of chemometrics.
(65) Depending on the application, Principal Component Analysis (PCA) may be performed separately on the acoustic spectra and on the reference measurements in order to identify any deviations in the results. The use of PCA for this purpose is, for example, described in detail in the above referenced book “Multivariate Calibration” by H. Martens and T. Naes, John Wiley & Sons, Chicester, 1989. Deviating samples (reference measurements and corresponding acoustic spectra) identified using PCA may be removed before applying the above-mentioned PLS-method.
(66) After the PLS method has been applied, linear regression analysis (RA) is applied to determine the parameters β.sub.0 and β of the linear equation:
Y=β.sub.0+βX, Equation 1
which defines the statistical model. β.sub.0 and β are vectors defining the approximate linear relationship between the amplitudes of the AASF X and reference measurement data Y. The combination of PLS and RA is commonly referred to as Partial Least Squares Regression (PLSR).
(67) In step 3) (Validating the linear model), once β.sub.0 and β values have been established in the calibration phase, the model is validated against reference measurement data (Y) of the particular fluid property of interest measured by a different method, such as a relevant one of the above-mentioned conventional non-acoustic methods. The reference measurements are taken at the same point in time as the AASF-spectra from the acoustic measurement and the well-known procedure of cross-validation is used to determine the validity of the model.
(68) The acoustic spectrum amplitude (X) is multiplied element-wise with the derived property parameters (β) and summed up. Finally the intercept constant β.sub.0 is added which results in the prediction Ŷ. Mathematically this can be expressed as:
(69)
where #f(bins) represents the active acoustic frequency spectrum discretized in bins as described further above. The prediction result Ŷ is compared with reference measurement data Y.sub.ref to give a measure of the performance of the model.
(70) An illustrative example of the above-described procedure of establishing a pre-calibrated model is shown in
(71)
(72) To validate the model, the model data is compared with further samples from the process as illustrated in
(73) Next, it is evaluated if the deviation between the reference validation fluid property values obtained using the conventional non-acoustic method and the fluid property values estimated based on acoustic measurements using the model is sufficiently small for the particular property of the fluid and the particular process.
(74) To further validate the model, acoustic spectra (each being provided as a vector of amplitude values) received at regular intervals were then input to the model, and the output of the model is a predicted value of the fluid property as a function of time. The diagram in
(75) As a further example of the above discussed method, determination of the specific surface area of particles in a colloidal silicon sol will be described where a model is derived using the general steps outlined above. The specific surface area of the particles is given by the relation:
(76)
(77) where A.sub.d is the specific surface area, d.sub.s is the particle diameter of a particle with a specific surface area corresponding to the average surface area of the particles, and ρ is the density.
(78) As a first step before any determination of the specific surface area of the particles can be carried out based on acquired acoustic spectra, the model is established as described above. In this particular example, a series of (physical) samples of the silicon sol are taken. For each sample taken, an acoustic spectrum is acquired, preferably at the same time as the sample is taken. The specific surface area of the particles in the samples taken is determined using conventional analysis, such as through so-called Sears titration. This is a well-known empirical method for determining the surface area of colloidal silicon through titration of the silicon sol with NaOH.
(79) A model is then established as generally described above by correlating the specific surface area values of the samples determined using Sears titration with the corresponding acoustic spectra. This procedure may also be referred to as “calibration”. As was generally described above, the calibration correlation is carried out in two steps. First, Principal Component Analysis (PCA) is performed separately on the acoustic spectra and on the lab results obtained using Sears titration.
(80) After having removed the deviating samples that were identified using PCA, the PLS-method is used to identify a relation between the acoustic spectra and the corresponding lab results. The result is an empirical statistical model that can be used to determine the specific surface area of the particles in the silicon sol based on an acquired acoustic spectrum.
(81) As a further illustration of the applied model,
(82) To improve the signal-to-noise ratio of the received signal, it may be undesirable noise may be removed from the received acoustic signal. In particular, frequencies in the received signal below 5 kHz are sometimes discarded since the lower end of the frequency range is known to have a lower signal-to-noise ratio. In other words, at least a portion of passive noise originating from application specific features can be separated from the received signal by removing frequencies below 5 kHz from the received signal. A suitable cut-off frequency for noise reduction is preferably determined for each specific application and installation.
(83) In practice, noise reduction may be achieved by first determining where in the acoustic spectrum the background signal is strong. Based on this determination (or previous knowledge about the particular system), a portion of the acoustic spectrum can be disregarded when the empirical statistical model is established and when predictions are carried out.
(84)
(85)
(86) By comparing the passive spectrum 920 in
(87) The method according to the present invention may be implemented as software, hardware, or a combination thereof. A computer program product implementing the method or a part thereof comprises a software or a computer program run on a general purpose or specially adapted computer, processor or microprocessor. The software includes computer program code elements or software code portions that make the computer perform the method using at least one of the steps previously described in
(88) It will be understood by those skilled in the art that various modifications and changes may be made to the present invention without departure from the scope thereof, which is defined by the appended claims.
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