Finger-stick meters are used to perforate the skin to get a required drop of the patient’s blood. The finger-stick meters are provided with a sharp lancet. The such lancet is designed to be fixed properly in the meter to use it many times later. Many Diabetics could use the same device in different times. Sometimes the ordinary disinfectants do not work to get rid of germs and bacteria that are on the lancet. While we were working on developing our device, we have also considered the expenses for such a development.
The fault detection and identification system applied in this work is based on the wavelet decomposition theory. This technique was chosen because it is capable of revealing aspects of data that other signal analysis techniques miss, aspects like trends, breakdown points, discontinuities in higher-order derivatives, and self-similarity. Apart from that, it helps estimating the magnitude of the deviation which is one of the most useful characteristics that were followed in this work. These properties are really useful in a closed-loop environment like the one presented in this work.
Taking into account that, where the systems are under control, like in this case, several times, the faults are masked by the control. In fact, for the sensor fault considered here (measurement offset), it looks like a perturbation effect in the blood glucose level. It has a transitory of short duration, usually of high frequency that seems to disappear due to the regulation capacity of the control structure. Indeed, as the measurement (erroneous) remains in the desired operating point, the real process variable changes towards another undesirable point, related to the failure magnitude. This effect is not directly observable from the process measurements, and it is necessary to rely on any tool that has the ability to quickly detect and estimate this abnormal event. One of the only tools available, capable of analyzing the transient response with good temporal and frequency resolution, is the well-known wavelet transform. The decomposition at different levels of the process measurements allows us to identify anomalies at different frequency ranges and to estimate their magnitudes at the right moment. This is the main reason for proposing the fault detection using wavelet decomposition.
3.1. Wavelet Analysis
Wavelet analysis  represents a logical step in signal processing tools; it is a windowing technique of variable dimension. Hence, using greater time intervals, the information at low frequencies becomes more precise, and with smaller regions, the focus is posed in the information at high frequencies. The resulting mapping is of the scale-time form, being the frequency related to the scale.
In the wavelet transform, the base functions are little signals called wavelets. Therefore, the signal being analyzed𝑠 ( ) is decomposed utilizing scaled versions and temporarily displaced of a unique functionΨ ( ) called mother wavelet. This set of signals,1 𝜓 ( 𝑎 , 𝑏 , 𝑡 ) =√𝑎𝜓 𝑡 − 𝑏𝑎 , ( 2 )forms an orthogonal basis (not redundant) of functions, where 𝑎 and 𝑏 are the scale and displacement parameters, respectively. Having 𝑠 ( 𝑡 ) as the signal to be analyzed, the DWT is defined by the internal product, 𝐶 ( 𝑎 , 𝑏 ) = 𝑠 ( 𝑡 ) 𝜓 ( 𝑎 , 𝑏 , 𝑡 ) 𝑑𝑡 , ( 3 )where 𝑎 = 2𝑗 and 𝑏 = 𝑘 2𝑗 with 𝑗 , 𝑘∈𝑍, are the discrete values of scaling and displacement also known as dyadic values. Index𝑗 is known as level and 1 / 𝑎 or 2− 𝑗 as resolution. From an intuitive point of view, the wavelet decomposition consists of calculating a similarity index 𝐶 ( , 𝑏 ) between the signal and the wavelet localized in 𝑏 and scaled by 𝑎.
Similar to other signal-processing tools, there exists an inverse wavelet transform. That is to say, a synthesis methodology by which the original signal is reconstructed is utilizing the wavelet coefficients of the decomposition. This inverse transform could be expressed as𝑠 ( 𝑡 ) = Σ𝑗∈𝑍Σ𝑘∈𝑍𝐶 ( 𝑗 , 𝑘 ) 𝜓 ( 𝑗 , 𝑘 , 𝑡 ) = Σ𝑗∈𝑍𝐷𝑗( 𝑡 ) , ( 4 )where 𝐷𝑗(𝑡 ) = Σ𝑘∈𝑍𝐶 ( 𝑗 , 𝑘 ) 𝜓 ( 𝑗 , 𝑘 , 𝑡 ) is the detail of the original signal at level 𝑗. Taking as a reference a given level, say𝐽, it could be expressed asΣ𝑗∈𝑍𝐷𝑗= 𝐷1+ 𝐷2+ ⋯ + 𝐷𝐽+ 𝐷𝐽 + 1+ ⋯ + 𝐷𝑁= 𝐷𝐽+ 𝐴𝐽, ( 5 )where 𝐴𝑗= Σ𝑗 > 𝐽𝐷𝑗 is called approximation at level 𝐽 and groups all the details at levels higher than 𝐽which represent an approximation of the signal at lower resolution. The details of higher resolution (𝑗 ≤ 𝐽) are grouped into𝐷𝑗= Σ𝑗 ≤ 𝐽𝐷𝑗 and are called the details of the signal at level 𝐽. Therefore, a relation between the levels of the approximations and details could be obtained in the following form:= 𝐴𝐽 + 1+ 𝐷𝐽 + 1,
The price tag on the finger-stick meter is not the key. A supervision Clinical study was perform to estimate the performance of the “Glucowatch” in youth age group within 10-19 years. The point of this study is to show how the “Glucowatch’s” results are more accurate than the finger-stick clinically and the arithmetic investigation is depending on the information that comes from the comparison between the two devices. Moreover, the results will be taken in a certain time and depending on some clinical criteria. “The accuracy of the Glucowatch was based on the estimated bias (defined as the difference from the y=x line to the Deming linear regression line) at five medical decision levels of glucose (50, 80, 100, 150 and 200 mg/dL)”.
We adopted the FDI based on wavelets decomposition because of the successful application presented in . According to the faulty behavior of the noninvasive sensor explained in Section 2.2, it is clear that if an FDI is available and able to detect the quick changes in the measured signal, it will be useful for having accurate measurements provided by the noninvasive sensor. Another important reason is the fact that only if the correct glycaemia value is available, the insulin dosage will be properly administrated. For the application considered here, the Daubechies wavelet family of the second order was used, and the decomposition scale was selected to be equal to one. In Section 6 (Figure 11), it will be presented the wavelet detail decomposition of the noninvasive sensor signal when failure no. 1 occurs. There it can be easily seen how the wavelet detail at level 1 can detect the moment when the sensor gives the wrong measurement. Negative deviations (peaks) correspond to positive shift in the sensor signal and vice versa. In addition, the height of the peak is closely related with the magnitude of the shift measurement. For more details about the implementation of DWT to a faulty biosensor, the reader should see .
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