The possibility of using statistical non-digital data processing in homeostatic biotechnical systems with biofeedback is considered. It is shown that the non-digital representation of the primary data of the connection between the input action and the output response of the organism is more consistent with the model of the physiological system. The impossibility of using arithmetic transformations when processing non-digital data for sliding windows with a small number of samples has shown the advantages of using the Kemeny median. Comparative analysis of data processing with abnormal emissions by sliding linear and nonlinear filters operating in real time mode of biological object functioning is carried out. The advantage of using nonlinear filtering when working with time sequences containing anomalous sample values has been substantiated. For biotechnical regulatory systems for medical purposes with biofeedback, an option for making decisions on the criterion of signs is presented, which increases the stability of the system.
Methods of non-digital statistics [
The original feature space of a biological
object is probable due to the low level of output
signals, the application of heterogeneous signals,
noise and external influences [
In addition, sign signals, such as the resistance
of the skin, obtained in different parts of the body,
have a significant variance [
A fundamentally different principle of
information processing in biological and technical
objects is a significant problem of data processing
in homeostatic biotechnical systems [
processing the information approach to original feature
The qualitative nature of the samples in contrast to the quantitative representation has its own characteristics. Thus, the values of the samples cannot be made, because the obtained values lose their meaning. If we assume that the sequence of samples are elements x1 , x2 ,, xn of a nonlinear set X , then under these restrictions it becomes clear that the determination of the average value of the sample requires other approaches compared to those adopted. Even when analyzing the samples of a series, the arithmetic mean value is acceptable only for the case of a sufficiently uniform value of the members of the series. If there is an anomalous value in the sample, the value of the arithmetic mean does not always adequately characterize the average, because the influence of this component is much more significant than others.
In non-digital statistics, the measure of
difference is an indicator d : X 2 [0, ] , the
essence of which is to capture the fact that the
more d (x, y) , the more different x and y [
En (d ) Arg min d (xi , x), x X , (1) 1in where the mean En (d ) represents the set x X for which the function f n (x)
d (xi , x) ,
n 1in
reaches the minimum value on the set X and is
the median or mean for a sample of rankings by
Kemeny. In [
It also follows from the peculiarities of qualitative representation that the increase in the sample size may not lead to an increase in the reliability of the assessment, as it is impossible to talk about the stationary and centeredness of the analyzed process, along with the negative consequences of such a statement samples. This fact is critical for real-time systems, as it introduces a delay of at least half the sampling time. The small sample size leads to a significant variation of the indicators relative to the average, because, for example, for control systems, the indicator of stability is important.
If we consider the stability as the absence of control effects on the tolerances, the reaction of a biological object of the type "cold-warm", or "comfortable-uncomfortable" is more stable than the perception of the values of ambient temperature. The feeling of warmth is perceived by each person individually, the physiological reaction of the organism is primary, and the quantitative description of conditions is secondary.
The scales of qualitative features are the ordinal scale and the scale of names [2a], the first of which corresponds to the problem to be solved. Comparison of the two samples Y and Z can be done by their average values: f (Y1 ,Y2 ,,Yn ) f (Z1 , Z 2 ,, Z n ) . (3)
If the transformation in the ordinal scale , such Yi as Z i normalization, is allowed, then (Yi ) and (Z i ) change to and.
To form the average of the data set, you can use the sign of the distance from a given point to the points of the neighborhood, and the degree of proximity are smaller distances. Since it is not possible to use the summation operation for qualitative values, we use the difference indicator. For problems with a limited sample, it is necessary to determine the empirical average, which under certain conditions provides convergence with the theoretical average.
For a space of arbitrary form X with elements
x1 , x2 ,, xn of a real-valued function f (x, y)
with value in X , the values of the difference
function differ f (x, y) the more, the more x and
_
y differ. The average value x relative to the
degree of difference f (x, y) is the solution of the
optimization problem [
The theoretical average does not differ from the classical average for the law of large numbers when n , in accordance with Hinchin's theorem, tends to a mathematical expectation: 1 n
f ( xi , y) Mf ( x, y) . (5) n i1 When f (x, y) x y and with an odd number of samples n 2k 1, the value of the _ mean is equal to x xk 1 , i.e. we obtain a sample median. With an even number of sample members, we obtain the half-sum of the sample values xk and xk 1 . To exclude arithmetic operations, you can limit the odd number of samples.
To determine the average of Kemeny, it is
necessary to rank the data. The filter delay for
real-time systems is determined by half of the
sample, so it cannot be large. With a limited
sample, the ranking operation consists in
arranging the data in a non-killing order, ie
increasing with the possibility of the existence of
elements with the same values. Algorithms for
implementing this function are known and consist
in a sequential comparison of the current element
of the sample with the elements constructed in
ascending order. Next, the median is determined,
which is the average of Kemeny [
The qualitative nature of the samples leads to nonparametric models of process description. The parametric probability-statistical model is represented by a vector of fixed dimension, which does not depend on the sample size. In nonparametric models, the notion of distribution density is unacceptable, so it can be replaced by the probability of -hitting the -region. The formation of the -area in the simplest case can be the setting of the noise level and the signal being processed, the required sensitivity or other criteria. In the initial stage it is possible to provide a variant of asymptotic approach to the purpose of regulation, and then to specify depending on existing restrictions. This solution will allow us to talk about the ability of the proposed approach.
For the task of controlling the intensity of human infrared radiation on its physiological characteristics, it is important that the stability of the determination of the physiological response is higher than the numerical values of the devices, because it is primary. It is obvious that the use in addition to the resistance of the skin, other signs of human response to infrared radiation allows you to maintain the nature of these signals. Thus, heart rate and respiration only indirectly reflect the fact of increased heat extraction by the peripheral vascular and respiratory systems.
In a biological object, the response to each reaction is accompanied by the formation of an elementary goal, the implementation of an active act, checking its achievement, adjusting the elementary goal, and so on. These actions take place within the framework of a higher level goal, such as maintaining the temperature conditions of the body's functioning. Naturally, this is a very simplified model, but it can serve as a basis for reconciling mathematical and functional models.
Sampling x1 , x2 ,, xn of the initial probable
size X of a biological object due to the above
reasons cannot have a known distribution
function. As the sample size increases F (x) ,
according to the central limit theorem, the
distribution function tends to the normal
distribution law. For a non-parametric model, the
most appropriate solution to the decision-making
problem are two criteria: the criterion of signs and
the criterion of sign ranks [
(6)
If the value m0 corresponds to the response of the sensor in the active part of the process, the presented connection reflects the decision in the vicinity of the active therapeutic zone. The decision "-1" indicates that the radiation intensity must be increased, "+1" – the radiation intensity must be reduced, "" x j m0 – to remain unchanged. This approach is known as the principle of follow-up balancing. The main advantage of the following balance is the high stability of the conversion at a low signal-to-noise ratio, the disadvantage is the low speed of entering the mode. If the latter disadvantage is not fundamental, for example, due to the preheating of the emitters before the procedure, the decisionmaking on the control of infrared emitters may be limited to the criterion of signs in this case. Thus, the qualitative representation of the initial features of the biological object, which is in the feedback circuit of the biotechnical system, allows to form requests for control of the intensity of infrared radiation by the physiological response of the organism. According to the initial physiological information, both reactions to external thermal influence, and to internal adaptation of an organism to own purposes and the executed processes, change of external influence taking into account ambiguity of transformation is carried out. The implementation of the presented variant of non-digital data processing for controlling the intensity of heating of the patient in the infrared peloidotherapy chamber is made on the basis of ARDUINO technology. Limitations of radiation intensity of infrared emitters were chosen on condition of discomfort of stay indoors. This condition is met by the value of the resistance of the leather above 400 Koh. From the point of view of carrying out procedure the range is not of interest as dry epithelium signals absence of the remains of heat in an organism. The value of skin resistance is less than 100 ohms with significant sweating close to pain and can serve as the upper limit of the heating intensity range.
Modern methods of filtering anomalous
emissions are based on the calculation of a sample
variance followed by data substitution, in which
the deviation exceeds the threshold for
noisetolerant estimation of mathematical expectation,
or on rejection of emissions using statistical
hypothesis testing, which provides a sufficient
number of members in biotechnical systems [
We compare the processing of the time series of a nonstationary process, which is the characteristic information of a biological object (heart rate read with a period of 20 seconds), the sliding linear window in determining the sampling center as the arithmetic mean and the median of Kemeny. From the given fragment of time sequence of samples it follows that process cannot be carried to a stationary series (Figure 1). The obtained data are influenced by obstacles, cyclic processes, trendy long-term processes that take place in the body during its functioning, so in the short term the time series is non-stationary. It is impossible to increase the size of the sample window due to the increase of the delay time on the analyzed effect.
We process this fragment with a 5-element sliding window (Figure 2).
We make it with the replacement of the arithmetic mean value and the average Kemen average ranking of the sample values in the window and the selection of the median.
Analysis of curves 2 and 3 shows that there is
no significant difference between them, except for
sections 17–19 and 35–37, which requires a
separate study and comparison of the reactions of
linear and nonlinear filters. Methods of research
of filters are worked out in detail in the literature
on filtering of signals and time series therefore
their detailed analysis to result in the given work
can be considered inexpedient. One of the main
problems of data processing, which is
characterized by the ambiguity of the values due
to the reaction of the biological object to the
impact, is the rejection of abnormal values, or
emissions. The most commonly used method of
filtering anomalous emissions is to calculate
sample variances with subsequent replacement of
data in which the deviation of the mean exceeds a
certain specified value of the calculated variance.
The general approach to emission rejection is to
use noise-tolerant assessment and test statistical
hypotheses. The presented simulation
experiments showed that the proposed filtering of
anomalous measurements effectively works up to
18% of single emissions, and at 20% no longer
works [
The reading of primary information by contact means from mobile patients is associated with problems with the conductivity of contact connections of the epidermis with electrodes, which leads to uncontrolled changes in the recorded data, ie the appearance of artifacts in the time series. When a person moves in a peloidotherapy chamber, the skin is bent in the places of reading the primary data, ie the appearance of various contact resistances is the basis of the physiotherapeutic method.
To assess the degree of influence of anomalous emissions on the possibility of using the results of primary features on the control capabilities in the experimentally obtained nonstationary series, we make anomalous emissions and process them with a linear and nonlinear filter (Figure 3–7).
Analysis of figure 3 shows that when processing a time series with single anomalous emissions by a linear filter, the effect of the anomalous component is significant because it is included in the arithmetic mean and shifts the filtered value towards the emission. When processing the time sequence by a nonlinear filter, the anomalous emissions have almost no effect on the results, because a single emission can only affect the displacement of the selected element on the neighboring ranked from the median.
In figure 4 presents the results of time series
processing of paired anomalous emissions by
linear and nonlinear filters. The results of linear
filtration show that anomalous emissions
significantly affect the results, shifting the filtered
curve towards anomalous emissions more than for
single emissions. This is obvious, because the
arithmetic mean value significantly depends on
the anomalous emissions that are emitted at the
level of other informative members of the series.
When treated with a nonlinear 5-point filter, the
effect of paired anomalous emissions is
insignificant and is associated only with the
homogeneity of the three remaining informative
members of the series. Accordingly, in contrast to
[
In figure 7 presents the resulting processing of the time series, which contains anomalous emissions of different signs and durations.
In figure 5 presents the results of processing for three consecutive abnormal emissions of one sign relative to the signal. As the results of processing by a nonlinear window show, the filter does not cope with the task, because the median is anomalous value. That is, a filter with an odd number of elements (2n + 1) is operational provided that the number of consecutive anomalous emissions does not exceed n.
In figure 8 presents the results of processing the experimentally obtained time series of values of the resistance of the skin under the influence of infrared radiation when moving the patient inside the chamber.
In figure 6 presents a variant of anomalous emissions consecutive on the sign, alternating. As shown by the results of treatment with a nonlinear filter, there is a mutual compensation of anomalous emissions, and the above condition for the number of anomalous emissions n can be exceeded.
The analysis of the primary data shows that, according to the criterion of stability of control, they are not suitable for direct use in a feedback system. Linear filter treatment showed that the effect of anomalous emissions is significant and significantly depends on the amplitude of the anomalous emissions. Non-linear filter treatments provide clear treatment for anomalous emissions, resulting in sustainable results that can be used for biological feedback systems.
It also follows from the above analysis that the proposed method of data processing allowed to process information that contains the uncertainty of the reaction of the biological object to the input effect.
A feature of nonlinear filtering compared to
linear is the high dynamics of the process, because
the median is not affected by neighboring ranked
samples.
biotechnical systems with biological feedback as
a system for maintaining the intensity of infrared
radiation for an individual patient according to the
characteristic physiological response of the
patient. The vague presentation of the
characteristic information of the biological object
and its processing by the technical component of
the biotechnical system indicates a deeper overlap
of functional and cybernetic models, ie the
potential emergence of the emergence effect, for
example in the form of new treatments [
The implementation of a fuzzy decisionmaking algorithm based on the resistance of the leather cover allows you to change the number of pulses of infrared emitters from 1 the central "zero" zone to the maximum, for example 8 , in the upper and lower boundary zones. This allows you to quickly get out of uncomfortable areas and ensure the stability of the therapeutic area.
Fuzzy processing of information in non-digital form is important. Consider the function of belonging A (x) to a fuzzy set A of elements x from a set X , in relation to the decision problem in the following interpretation. Define the membership function A (x) as the degree x of proximity A to the prototype or similarity of affiliation A x, A (x). Then A represents a set of alternatives, and the A (x) degree of preference and suitability of the choice as the value of the variable b . In this interpretation, the membership function plays the role of the ordering relation associated with the predicate A relation x A x ' , which shows that x it corresponds more to another value x ' of the same parameter in the current situation A . Continuing these considerations, we can show that inequality Q (x, x' ) Q (x, x'' ) describes a situation in which this expression means closer x ' to x than x' x x'' . Alternatives can be represented as fuzzy sets on a non-numerical scale, then a fuzzy set B {(b, B(b)} in the form where (b, B(b)) the set of fuzzy objects.
In static mode, it was possible to divide the core into components, which require a more detailed analysis of this area to improve the quality of decision-making. Thus, the use of fuzzy conversion of the original data allowed the use of 1. The expediency of qualitative representation of the initial features is substantiated and the flow of the original features is processed by the methods of non – numerical statistics with the determination of the average in the sliding window as the medians of Kemeny.
2. A comparison of the results of processing non-stationary feature data with anomalous emissions typical of biological objects, linear and nonlinear filters showed that linear filters are inoperable. The use of nonlinear filters allowed to process time series with the number of anomalous emissions up to 40% of the number of samples in the window compared to 18% for existing anomalous emission filters.
3. It is shown that the levels of resistance signs in the central and peripheral zones differ more than 2 times, and the proposed methods of nondigital representation of information in conjunction with fuzzy logic provide information processing almost invariant to the scatter of the level of signs.