GB2522099A

GB2522099A - Determining a resonant frequency of a sensing element

Info

Publication number: GB2522099A
Application number: GB1418975.7A
Authority: GB
Inventors: Andrew Smith
Original assignee: Hydronix Ltd
Current assignee: Hydronix Ltd
Priority date: 2014-10-24
Filing date: 2014-10-24
Publication date: 2015-07-15
Anticipated expiration: 2034-10-24
Also published as: GB201418975D0; GB2522099B

Abstract

A resonant frequency of a sensing element, such as a cavity resonator in a moisture sensor, is determined by performing a frequency scan to obtain scan samples around a resonant peak of the sensing element, and determining the resonant frequency based on a zero-crossing point of a derivative of the scan samples. An approximation to the derivative function can be obtained by calculating the differences between adjacent pairs of samples from the fine frequency scan. The scan samples may be obtained by performing a coarse frequency scan to determine an approximate position of the resonant peak, and performing a fine frequency scan to obtain fine scan samples around the approximate peak position. The coarse scan can be performed by recording amplitude measurements related to the impedance of a resonant sensing element. In some embodiments, an adaptive coarse scan algorithm is also used to reduce the time taken to complete the coarse frequency scan.

Description

Determining a Resonant Frequency of a Sensing Element

Technical Field

The present invention relates to determining a resonant frequency of a sensing element.

Background of the Invention

Moisture sensors have been developed which can measure the moisture content of various types of material in real time during industrial processes, including inorganic io materials such as concrete, aggregate and asphalt, and organic materials such as animal feed, grain, nuts, oils and biomass products. The sensors use a contact measurement technique in which the resonant frequency of a sensing element such as a cavity resonator is periodically determined. The resonant frequency is dependent upon the moisture content of material in proximity to the sensing element, as shown in Fig. 1, i which illustrates typical frequency-amplitude curves obtained for materials of vaiying moisture contents.

Tn Fig. 1, the solid line 101 iflustrates the resonant peak when a relatively dry material is in proximity to the sensing element, the dot-dash line 103 illustrates the resonant peak for a relatively wet material, and the dashed line 102 illustrates the resonant peak for a materia' of intermediate moisture content. As shown in Fig. 1, as the moisture content reduces the resonant frequency increases, the peak becomes sharper, and the amplitude at the peak decreases.

Conventional moisture sensors are typically designed to be capable of achieving a measurement rate of 25 moisture readings per second, which allows a window of 40 milliseconds (ms) for each measurement to be captured. As the peak detection algorithm which analyses frequency samples to locate the resonant peak is relatively slow, conventional moisture sensors have to use a voltage-controlled oscillator (VCO) to perform the frequency scan at a sufficiently high rate to keep the total measurement time within the 40 ms window. AVCO has a short response time and can quickly switch from one frequency to another. However, a drawback of using a VCO for frequency measurements is that the exact output frequency cannot be known precisely.

The invention is made in this context.

Summary of the Invention

According to the present invention, there is provided a method of determining a resonant frequency of a sensing element, the method comprising: performing a frequency scan to obtain scan samples around a resonant peak of the sensing element; and determining the resonant frequency based on a zero-crossing point of a derivative of the scan samples.

Determining the resonant frequency based on the zero-crossing point of the derivative of the scan samples can comprise: obtaining approximate derivative values for the scan Jo samp'es by taking a difference in amplitude between a pair of adjacent scan samples as an approximate derivative value; fitting a curve to the approximate derivative values; and determining the resonant frequency as being the zero-crossing point of the fitted curve. The approximate derivative values maybe obtained for a predetermined number of the scan samples around the scan sample having the lowest amplitude, for examp'e 12 scan samp'es.

The method can further comprise filtering the scan samples before determining the resonant frequency based on the zero-crossing point of the derivative of the filtered scan samples. In some embodiments, the scan samples are filtered using a moving average filter.

The method may further comprise determining an amplitude va'ue associated with the determined resonant frequency by using an interpolation algorithm. The interpolation a'gorithm may be a Catmull-Rom spline interpolation algorithm.

The frequency scan may be performed using a frequency synthesizer.

Performing the frequency scan to obtain the scan samp'es can comprise: performing a coarsc frcqucncy scan to obtain coarsc scan samplcs; dctcrmining an approximatc position ofthe resonant peak based on the coarse scan samples; and performing a fine frequency scan to obtain fine scan samples around the approximate peak position, wherein the resonant frequency is determined based on the zero-crossing point of the derivative of the fine scan samples.

The method may further comprise setting a starting frequency for the coarse frequency scan based on a previously-determined value of the resonant frequency.

Performing the coarse frequency scan can comprise: scanning in a first frequency direction from a starting frequency; in response to an increase in amplitude being detected while scanning in the first frequency direction, scanning in the opposite frequency direction from the starting frequency; and in response to an increase in amplitude being detected while scanning in the opposite frequency direction, stopping the coarse frequency scan.

Detecting an increase in amplitude while scanning in the first frequency direction or jo the opposite frequency direction can comprise: comparing a current amplitude value to a minimum ampUtude value obtained so far during the coarse frequency scan; and detecting an increase in amplitude if the difference between the current amplitude value and the minimum amplitude value exceeds a threshold.

The method can further comprise setting a step size of the fine frequency scan according to the sharpness of a peak in the coarse frequency scan, by setting a larger step size for a broader peak and a smaller step size for a sharper peak.

Setting the step size of the fine frequency scan can comprise selecting one of a plurality of predetermined step sizes based on the lowest amplitude value recorded during the coarse frequency scan, wherein each of the predetermined step sizes can be associated with a different range of amplitude values, and said one of the predetermined step sizes is selected by selecting the predetermined step size for which the lowest amplitude value lies in the associated range of amplitude values.

According to the present invention, there is also provided a computer-readable storage medium storing computer program instructions which, when executed, perform any of the methods described herein.

According to the present invention, there is also provided apparatus for determining a resonant frequency of a sensing element, the apparatus comprising: means for receiving signal samples; and processing means for processing the received signal samp'es, wherein the processing means is configured to perform a frequency scan to obtain scan samples around a resonant peak of the sensing element, and determine the resonant frequency based on a zero-crossing point of a derivative of the scan samples.

The apparatus may further comprise a frequency synthesiser configured to generate signals at variable frequencies for performing the frequency scan, and/or may further comprise the sensing element, wherein the means for receiving the signal samples comprises a sensor interface configured to receive the signal samples from the sensing element.

Brief Description of the Drawings

Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which: o Figure 1 illustrates signals obtained from a sensing element in a moisture sensor for different levels of moisture content; Figure 2 is a flowchart showing a method of determining a resonant frequency of a sensing element, according to an embodiment of the present invention; Figure 3 is a flowchart showing a coarse frequency scan algorithm, according to an embodiment of the present invention; Figure 4 illustrates coarse scan samples obtained when starting at a frequency below the resonant frequency, according to an embodiment of the present invention; Figure 5 illustrates coarse scan samples obtained when starting at a frequency above the resonant frequency, according to an embodiment of the present invention; Figure 6 is a flowchart showing a method of determining the resonant frequency based on derivatives of the fine scan samples, according to an embodiment of the present invention; Figure 7 illustrates approximate derivative values obtained from fine scan samples, according to an embodiment of the present invention; Figure 8 is a flowchart showing a method of determining a resonant frequency of a sensing element, according to an embodiment of the present invention; Figures 9A and 9B illustrate peak amplitude values obtained using Catmull-Rom spline interpolation, according to an embodiment of the present invention; and Figurc 10 schematically illustrates a moisturc sensor, according to an embodiment of the present invention.

Detailed Description

Referring now to Fig. 2, a method of determining a resonant frequency of a sensing element is illustrated, according to an embodiment of the present invention. First, in step S2o1 a coarse frequency scan is performed to obtain coarse scan samples. The coarse scan can be performed by recording amplitude measurements related to the impedance of a resonant sensing element included in the moisture sensor, for different input signal frequencies. The amplitude and frequency values are stored as the coarse scan samples. In the present embodiment, measurements are taken at regular frequency intervals, and the difference in frequency between adjacent samples can be referred to as the coarse scan step size. In the present embodiment the coarse scan step size is 3.3 megahertz (MHz), but in other embodiments any step size may be chosen.

In some embodiments, the coarse frequency scan may be performed over a fixed frequency range, encompassing a predetermined range of frequency values. The o frequency range can be determined during calibration of the moisture sensor, by determining the position of the resonant peak under air (o% moisture) and water (ioo% moisture) conditions. The fixed frequency range can be selected to include all possible positions of the resonant peak between these two extremes. However, in the present embodiment an efficient coarse scan algorithm is provided which reduces the time taken to perform the coarse frequency scan, by stopping the coarse frequency scan once a peak has been detected. The coarse scan algorithm maybe referred to as an intelligent' algorithm, since it is capable of adapting the frequency range of the coarse scan according to the current position of the resonant peak.

After recording the coarse scan samples, in step S2o2 an approximate peak position is determined based on the coarse scan samples. tn the present embodiment, the frequency of the lowest-amplitude measurement among the coarse scan samples is taken as being the approximate peak position. However, in other embodiments a curve-filling algorithm could be used to estimate an interpolated position of the resonant peak between the coarse scan samp'e points.

Then, in step S2o3 a fine frequency scan is performed to obtain fine scan samples around the approximate peak position. Like the coarse frequency scan, in the present cmbodimcnt thc finc frcqucncy scan is pcrformcd by rccording amplitudc measurements at regular frequency intervals, smaller than the coarse scan step size. In the present embodiment the fine frequency scan is performed within the frequency range defined by the two coarse scan samp'es either side of the lowest-ampUtude coarse scan sample. However, in other embodiments a different frequency range maybe chosen for the fine frequency scan.

Next, after obtaining the fine scan samples, in step S2o4 the resonant freqnency is determined based on a zero-crossing point of a derivative of the fine scan samples. The zero-crossing point corresponds to the point at which the derivative function equals zero, that is, the point in the frequency-amplitude curve at which the gradient is zero.

Since the gradient will be zero at the resonant peak, the zero-crossing point in the derivative function will be equal to the frequency of the resonant peak. Investigations by the inventors have shown that this approach enables the frequency of the resonant peak to be accurately identified more quickly than by using other methods, such as fitting a polynomial function to the fine scan samples.

Tt is typically required for a moisture sensor to be capable of achieving a measurement rate of 25 moisture readings per second, which allows a window of 40 milliseconds (ms) for each measurement to be captured. In this time, the coarse and fine frequency scans must be performed, and the position of the resonant peak must be determined.

Tn a conventional moisture sensor, the peak detection algorithm consumes a significant portion of the 40 ms window, meaning that a voltage-controlled oscillator (VCO) has to be used in order to perform the frequency sweeps for the coarse and fine frequency scans at a sufficiently high rate to keep the total measurement time within the 40 ms window. A VCO has a short response time and can quickly switch from one frequency to another. However, a drawback of using a VCO for frequency measurements is that the exact output frequency cannot be known precisely.

In comparison to conventional designs, embodiments of the present invention can increase the time available for performing the coarse and fine frequency scans within the target measurement time of 40 ms, since the derivative-based technique allows the resonant peak to be quickly identified from fewer fine scan samples. This in turn can allow the use of a slower, more accurate frequency synthesizer when performing the coarse and fine frequency scans. In the present embodiment a Phase-Locked Loop (PLL) is used to gcneratc test signals at known frcqucncics during the coarsc frcqucncy scan and fine frequency scan, although in other embodiments a different type of frequency synthesizer maybe used.

Referring now to Figs. 3 to 5, the intelligent coarse scan a'gorithm of the present embodiment will now be described in more detail. Figure 3 is a flowchart illustrating steps performed when executing the coarse scan algorithm, and Figs. 4 and j illustrate coarse scan samples obtained when the starting point of the coarse frequency scan as below and above the resonant peak, respectively.

First, in step S3o1 the starting frequency for the coarse frequency scan (ñ) is set based on a previously-determined value of the resonant frequency. In the present embodiment, the value of the resonant frequency determined during the previous moisture reading is used as the starting point for the current coarse frequency scan, on the assumption that the moisture content and therefore the position of the resonant peak will not have changed significantly in the < 40 ms since the previous reading was o taken. However, in other embodiments a different approach maybe used. For examp'e, changes in the resonant frequency may be recorded over time, aflowing a trend in the variation of moisture content over time to be determined. An expected value of the resonant frequency at the current point in time could then be estimated based on the previous position of the resonant peak and the observed rate of change in the resonant frequency over time. Alternatively, the same default starting frequency may always be used for the coarse frequency scan.

The coarse scan algorithm then proceeds to scan in a first frequency direction, which in the present embodiment corresponds to an increase in frequency, until an increase in amplitude is detected. The algorithm then returns to the starting frequency and scans in the opposite direction until another increase in amplitude is detected. As shown in Figs. 4 and 5, this ensures that at least one coarse scan sample is captured on either side of the resonant peak, regardless of whether the starting frequency happens to be above or below the resonant frequency. This procedure will now be described in more detail with reference to Fig. 3.

Next, in step S3o2 the amplitude is measured at the starting frequency and an amplitude value is recorded as the first coarse scan sample. Then, in step S3o3 the PLL is controllcd to increase the frcqucncy of thc test signal outputted by the PLL by an amount equal to the coarse scan step size, Af, and another ampfitude value is recorded.

Tn step S304, the algorithm checks whether the current amplitude value is higher or lower than the minimum value that has been measured so far. To allow for small increases in ampfltude which may occur due to noise while moving towards the resonant peak, the increase may be compared to a threshold value. tf an increase is detected in step S3o4 but is less than the threshold, then it is assumed to be the result of noise and the algorithm returns to step 8303 to continue scanning in the first frequency direction. Similarly, if the amplitude has decreased, then the scan is still proceeding towards the resonant peak and the algorithm returns to step 8303 to record another coarse scan samp'e.

The process is repeated until an amplitude increase which is greater than the threshold is detected in step 8304, at which point the coarse frequency scan algorithm sets a new scan frequency at one step below the starting frequency in step 8305, and records a new amplitude value in step 8306. In step S3o7, it is checked whether the amplitude measured in step 5306 is higher or lower than the minimum value that has been o measured so far. Tf the new amplitude value is lower, then the a'gorithm proceeds to step 8308 and records a new coarse scan sample at a lower frequency, and repeats until an amplitude increase which is greater than the threshold is detected in step 8307. The coarse frequency scan operation then ends in step 5309.

By using a coarse frequency scan algorithm such as the one described above with reference to Figs. 3 to 5, it can be ensured that coarse scan samples are recorded on either side of the resonant peak, without spending additional time unnecessarily recording samples at frequencies far away from the resonant peak.

Referring now to Figs. 6 and 7, a method of determining the resonant frequency based on derivatives of the fine scan samples will now be described, according to an embodiment of the present invention. First, in step 8601 the fine scan samples are obtained during a fine frequency scan, as described above. Then, in step 8602 a predetermined number of fine scan samples are selected around the lowest-amplitude sample among the fine scan samples. By selecting only a limited number of the fine scan samples to be used when computing the zero-crossing point of the derivative function, the processing time can be kept to a minimum. In the present embodiment, twelve fine scan samples are selected, since investigations by the inventors have shown that this numbcr of samplcs rcprcscnts thc bcst compromisc bctwccn mcasurcmcnt accuracy and processing time. However, in other embodiments a different predetermined number of fine scan samples maybe selected, or alternatively a variable number of fine scan samples or all fine scan samples maybe used.

Then, in step 8603, the difference in amplitude between each pair of selected samples is calculated as an approximate derivative value. Here, by a pair' of fine scan samples, it is meant that the fine scan samples are adjacent in frequency, that is, are separated by one fine scan step Af. Next, in step S6o4 a cnrve is fitted to the approximate derivative values, in the present embodiment, as shown in Fig. 7, a line 701 is fitted to obtain an equation of the form y = mx + c for the approximate derivative function. However, in other embodiments of the invention any type of curve may be fitted, for example a polynomial function maybe fitted to the derivative values. Then, in step S6o5 the zero-crossing point is determined by selling y = 0 to determine the frequency (x) at which the derivative function crosses the x-axis, which is taken as being the resonant frequency.

jo Tn other embodiments of the invention, instead of obtaining approximate derivative vahies as described above, a curve maybe fitted to the fine scan samples. The curve function could then be differentiated and solved for y = 0 in order to find the crossing point. However, approximate derivate values are used in the present embodiment as this approach requires less processing time than for performing curve-fitting and differentiation.

Referring now to Fig. 8 a method of determining a resonant frequency of a moisture sensor is illustrated according to an embodiment of the present invention. Certain steps in the method of Fig. 8 are similar to steps performed in the method of Fig. 2, and a detailed description will not be repeated here. The method of Fig. 8 differs from the above-described methods in that a step size of the fine frequency scan is set according to the sharpness of a peak from the coarse frequency scan, by setting a larger step size for a broader peak and a smaller step size for a sharper peak, and also in that the fine scan samples are filtered and an amplitude value at the resonant peak is determined.

First, in step S8oi a coarse frequency scan is performed as described above, to obtain coarse scan samples. Then, in step S8o2 a measure of the peak sharpness is obtained from the coarse scan samples. In the present embodiment, the lowest amplitude value among thc coarsc scan sampics is takcn as bcing rcprcscntativc of thc peak sharpncss, since as shown in Fig. 1, broader resonant peaks typicafly have a higher ampfitude at the peak. This approach is used because the intelligent coarse scan algorithm may only capture a small number of samp'es on one side of the peak, as shown in Figs. 4 and 5.

However, in other embodiments different approaches maybe used. For example, if the coarse frequency scan is always performed over a fixed, broad, frequency range, the full peak may be contained within the coarse scan samples, and another measure of peak sharpness maybe used, for example the full-width half-maximum (FWHM). -10-

Next, in step 8803 one of a plurality of predetermined step sizes is selected based on the lowest amplitude value recorded during the coarse frequency scan, which as described above, can be taken as being an indicator of the peak sharpness. For example, each of the predetermined step sizes can be associated with a different range of amplitude values, and said one of the predetermined step sizes can be selected by selecting the predetermined step size for which the lowest amplitude value lies in the associated range of amplitude values. In the present embodiment, one PLL step of 166.6 kilohertz (kHz) is taken as the default fine scan step size, and arger step sizes are jo selected for broader peaks by increasing the fine scan step size to two PLL steps (333.3 kHz), three PLL steps (500 kHz), and so on. By setting the fine scan step size according to the peak sharpness, it can be ensured that a large amplitude difference will exist between adjacent samples even when a relatively flat peak exists (e.g. curve 103 in Fig. i).

After setting an appropriate fine scan step size, the fine frequency scan is performed in step 8804. Next, in step S8o the fine scan samples are filtered using a moving average filter, before determining the resonant frequency in step S8o6. In the present embodiment the moving average filter is configured to cakulate the average amplitude within a window spanning samples, but in other embodiments of the invention a different size window may be used for the moving average filter.

Finally, after determining the frequency of the resonant peak in step 8806, then in step 8807 an amplitude value associated with the resonant frequency is determined using an interpolation algorithm. In the present embodiment a Catmuil-Rom spline interpolation algorithm is used, as the inventors have found that this class of interpolation algorithm most close'y matches the shape of the frequency response curve from a sensing element. However, in other embodiments an alternative type of interpolation algorithm could bc uscd, for example cubic intcrpolation.

The Catmull-Rom interpolation algorithm of the present embodiment operates as follows. First, the position of the resonant frequency peak is expressed in terms of a proportion of the fine scan step size, for examp'e 0.407869 x AJ. In the present embodiment, for faster processing speed this is then converted to an integer value (j4, which in this example would be 4. Then, the interpolated amplitude Y is calculated using the following set of equations: -11 -a0 =-y0 +-3y1 -3y, +y.

a1 = 2y0 -5y1 + 4y2 -y3 (L, = -a0713 a1712 a,ce 1= + -I--+a 2000 200 20 where m and Y2 are the amplitude values of the fine scan samples on either side of the resonant frequency, andy0 and y3 are the amplitude values of the next closest fine scan samples to the resonant frequency.

As described above, embodiments of the present invention can enable the frequency and amplitude of a resonant peak to be quickly and accurately measured. Figures 9A and 9B illustrate peak amplitude values obtained from real-world data using the above-described Catmull-Rom spline interpolation. In Figs. 9A and 9B, real data points are plotted as solid diamonds and the interpolated peak position 902, 904 is plotted as a solid square. in each of Figs. 9A and 9B, a best-fit curve 901, 903 is also illustrated as an indication of the actual frequency-response curve, it can be seen from Figs. 9A and 9B that the above-described method provides a more accurate measure of the frequency and amplitude of the resonant peak than simply taking the frequency and amplitude of the lowest recorded samp'e.

A worked example will now be described with reference to Fig. 9B, in which the following values are plotted:

Table 1

Frequency Ampfitude 4798 439 4799 422 4800 402 4801 400 4802 402 4803 395 4804 402 -12 -4805 418 4806 439 The samples at frequencies 4801, 4802,4803 and 4804 are taken as Yo, i, y2, and tj respectively. The coefficients are then calculated as follows:

Table 2 p 5 p2 25

p3 125 a0 23 a1 -32 a2 -5 a3 402 V 398.1875 Referring now to Fig. 10, an apparatus for determining a resonant frequency of a moisture sensor is illustrated, according to an embodiment of the present invention. As io shown in Fig. 10, the apparatus 1000 comprises means for receiving signal samples, in the form of a sensor interface 1001 configured to receive the signal samples from the sensing element 1010. The apparatus further comprises a processing module 1002 for processing the received signa' samples, and a frequency synthesizer 1003 configured to generate signah at variable frequencies for performing the coarse frequency scan and i fine frequency scan. Tn the present embodiment, the frequency synthesizer 1003 is a PLL. The frequency synthesizer 1003 can be controlled by the processing module 1002 to output a test signal at a particular frequency to the sensing element 1010 via the sensor interface 1001.

ao The processing means can be configured to perform any of the above-described methods. In particular, the processing means is configured to perform a coarse frequency scan to obtain coarse scan samples, determine an approximate peak position based on the coarse scan samples, perform a fine frequency scan to obtain fine scan samples around the approximate peak position, and determine the resonant frequency based on a zero-crossing point of a derivative of the fine scan samples. Depending on -13 -the embodiment, the processing means can be implemented as software instructions included in one or more computer programs executed by one or more processors, as dedicated hardware such as an application specific integrated circuit (ASTC), or as a combination of hardware and software elements.

In the embodiment shown in Fig. 10, the signal processing apparatus 1000 and the sensing element 1010 are physically separate devices. The sensor interface 1001 may be configured to communicate with the sensing element 1010 via any suitable wired or wireless connection. In other embodiments, the signal processing apparatus and jo sensing element maybe included in the same physical device, which maybe referred to as a moisture sensor' if the sensing element is configured to detect changes in moisture content of a composite material.

Embodiments of the invention have been described in which a coarse frequency scan is performed in order to determine the approximate location of the resonant peak, before performing a fine frequency scan to obtain more data samples in the vicinity of the resonant peak. However, in other embodiments a single frequency scan maybe performed instead of separate coarse and fine frequency scans. For example, a singk scan could be performed using an intermediate step size to the coarse scan step size and fine scan step size described above.

Also, although embodiments of the present invention have been described in the context of a moisture sensor for measuring the moisture content of a composite material, in other embodiments a different property may be measured. For example, the principles disclosed herein may a'so be applied when determining the resonant frequency of a sensing element used to measure the sugar content, in degrees Brix, of an aqueous solution.

Whilst ccrtain cmbodimcnts of thc invcntion havc bccn dcscribcd hcrcin with rcfcrcncc to the drawings, it will be understood that many variations and modifications will be possible without departing from the scope of the invention as defined in the accompanying claims.