CN113176320B - Flow velocity compensation method and system of membraneless dissolved oxygen sensor - Google Patents

Flow velocity compensation method and system of membraneless dissolved oxygen sensor Download PDF

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CN113176320B
CN113176320B CN202110308956.8A CN202110308956A CN113176320B CN 113176320 B CN113176320 B CN 113176320B CN 202110308956 A CN202110308956 A CN 202110308956A CN 113176320 B CN113176320 B CN 113176320B
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dissolved oxygen
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oxygen sensor
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flow rate
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向颖聪
黄希
崔莉
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Institute of Computing Technology of CAS
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Abstract

The invention provides a flow velocity compensation method and a flow velocity compensation system of a membraneless dissolved oxygen sensor, which neglect the influence of convection on diffusion distribution, collect the current magnitude in different waiting time in the process of one-time measurement, and respectively calculate the contribution of diffusion current and convection current to the total measurement current according to the change of transient current, thereby realizing the flow velocity compensation.

Description

Flow velocity compensation method and system of membraneless dissolved oxygen sensor
Technical Field
The invention relates to the technical field of instrument verification, in particular to a flow velocity compensation method and a flow velocity compensation system of a membraneless dissolved oxygen sensor for measuring the concentration of dissolved oxygen in flowing seawater.
Background
The concentration of dissolved oxygen in the ocean is one of the key indicators for studying the ecology and biogeochemistry of the ocean. In a liquid environment, oxygen molecules participate in a variety of different biological, chemical, and physiological processes. These processes can be studied and quantified by detecting the concentration of dissolved oxygen, and further, the marine effects of global warming on the geochemistry and circulation of marine organisms, the formation and increase of biological organic matter in seawater, and the estimation of the processes of carbon dioxide absorption by the marine organisms, etc. can be detected.
Currently, there are two main ways to monitor the dissolved oxygen in the ocean. One is an optical dissolved oxygen sensor based on the principle of fluorescence quenching. Its advantages are high precision, not easy drift, and low response speed. A YSI PRO ODO dissolved oxygen sensor is taken as an example. The accuracy is 1% or 0.1mg/L of the indication at a dissolved oxygen concentration of 0-20 mg/L. The maximum time for the sensor reading to stabilize (T-95) was 40 s.
The other is a dissolved oxygen sensor adopting an electrochemical principle, and mainly adopts a Clark electrode based on the electrochemical principle. The electrochemical method is that a fixed voltage is applied to the two ends of the cathode and the anode to generate a potential difference between the two electrodes, and oxidation and reduction reactions occur on the anode and the cathode respectively to consume oxygen. The electrolyte and the liquid to be measured are separated by a ventilated membrane made of polymer materials such as polytetrafluoroethylene and the like. Current I of Clark electrode when the whole electrochemical reaction is diffusion-controlled*Can be given by the following formula (1)。
I*＝kDC* (1)
Wherein D is the diffusion coefficient of the gas-permeable membrane, k is a proportionality constant and can be obtained by experimental calibration, C*Is the dissolved oxygen concentration in the liquid. Therefore, when the factors such as temperature, water flow speed, electrolyte concentration and the like are ensured to be constant, the dissolved oxygen concentration value in the water can be detected by measuring a current signal generated in a loop formed by the electrode and the electrolyte. This method responds very quickly, but requires periodic calibration because of the tendency for long term drift to occur due to the presence of the gas permeable membrane.
The structure of the membraneless dissolved oxygen sensor is shown in figure 1, wherein 1 is a working electrode, 4 is a reference electrode, and 3 is an auxiliary electrode. The micro-hole and ring-disk platinum electrode is obtained by etching and processing with a micro-sodium processing method. Unlike clark electrode, which adopts static measurement method, it consumes dissolved oxygen in micropores by dynamic voltage excitation, and its transient current is proportional to the dissolved oxygen concentration, i.e. I ═ k (t) C*Where K (T) is a complexity coefficient related to temperature, geometry, etc. However, the membraneless sensor must work in water with constant chloride ion concentration, and is sensitive to environmental factors such as water flow speed, temperature and the like. Due to convection, the water flow brings more oxygen to the electrode surface, making the measurement current more systematic, and the larger the water flow, the greater the drift, and therefore drift compensation must be achieved.
Under the prior art, the film-free dissolved oxygen sensor has high response speed and no film structure, but is strongly influenced by water flow, and the larger the water flow is, the larger the drift is. In previous studies, a method has been proposed to achieve flow rate calibration by actually measuring the relative magnitudes of diffusion and convection currents at different flow rates. However, this method requires repeated calibration experiments to calibrate the nonlinear calibration coefficients, which is very complicated. Therefore, there is a need to solve the technical problem of drift of the membrane-less electrochemical dissolved oxygen sensor due to flow rate variation, and to develop a dissolved oxygen measurement method that overcomes the above-mentioned drawbacks.
Disclosure of Invention
The invention aims to provide a dissolved oxygen measuring method for compensating the flow rate influence, which aims to solve the technical problem that a membraneless electrochemical dissolved oxygen sensor drifts due to the flow rate influence. In order to eliminate the factors influencing the measurement accuracy of the dissolved oxygen, the invention provides a compensation measurement method based on multiple measurement fitting.
Aiming at the defects of the prior art, the invention provides a flow velocity compensation method of a membraneless dissolved oxygen sensor, which comprises the following steps:
step 1, applying a dynamic voltage signal to an electrode of a membraneless dissolved oxygen sensor to acquire a current signal, and converting the current signal into a current for an electrochemical reaction of the membraneless dissolved oxygen sensor;
step 2, executing the step 1 at certain time intervals to obtain the current collected by the membraneless sensor at each moment, substituting the current at each moment by the following simultaneous over-determined equation to obtain the diffusion current A (C)*)，
Figure BDA0002988957860000021
Wherein k is1Is a proportionality constant, t is a column vector formed by measuring time, and I (t) is a column vector of a current sequence;
substituting the diffusion current into the following formula to obtain the dissolved oxygen concentration C measured by the membraneless dissolved oxygen sensor*；
Figure BDA0002988957860000022
Wherein α is the proportionality constant of the Clark electrode, A standardReduction of diffusion current for calibration of the membraneless dissolved oxygen sensor, CstandardThe dissolved oxygen concentration of the non-membrane dissolved oxygen sensor was measured, and A was the approximate diffusion current value of the actual measurement.
The flow rate compensation method of the membraneless dissolved oxygen sensor comprises the following steps of 1:
the method comprises the steps of collecting a time sequence of current signals I (t) of the film-free sensor at a certain sampling interval delta t, amplifying the current signals by using a trans-impedance amplifier and carrying out analog-to-digital conversion to obtain a group of digital signals, wherein the matrix representation comprises the following steps:
Figure BDA0002988957860000031
the step 2 comprises the following steps:
fast calculation of A (C) by pseudo-inverse matrix method*) Let us order
Figure BDA0002988957860000032
Then there is TTT(A(C*)，k1)T＝TTI (t) therefore
(A(C*)，k1)T＝(TTT)-1TTI
(TTT)-1TTThe diffusion current A (C) is obtained by matrix multiplication according to the pseudo-inverse of T*) A value of (d);
and the actual measurement is done using the following formula:
Figure BDA0002988957860000033
wherein
Figure BDA0002988957860000034
Is a correction factor.
The flow rate compensation method of the membraneless dissolved oxygen sensor, wherein the step 2 comprises the following steps: the sampling time interval is 20ms, and 10 times of sampling are carried out continuously.
The flow rate compensation method of the membraneless dissolved oxygen sensor is characterized in that voltage signals are applied to a working electrode and a reference electrode of the membraneless dissolved oxygen sensor.
The flow rate compensation method of the membraneless dissolved oxygen sensor comprises the steps that the voltage signal comprises a cleaning voltage, a resting voltage and a measuring voltage.
The invention also provides a flow velocity compensation system of the membraneless dissolved oxygen sensor, which comprises:
the module 1 applies dynamic voltage signals to electrodes of the membraneless dissolved oxygen sensor to acquire current signals, and converts the current signals into current of electrochemical reaction of the membraneless dissolved oxygen sensor;
the module 2 executes the module 1 at certain time intervals to obtain the current collected by the film-free sensor at each moment, and substitutes the current at each moment through the following simultaneous over-determined equation to obtain the diffusion current A (C)*)，
Figure BDA0002988957860000035
Wherein k is1Is a proportionality constant, t is a column vector formed by the measuring time, and I (t) is a column vector of the current sequence;
the diffusion current is substituted into the following formula to obtain the dissolved oxygen concentration C measured by the membrane-free dissolved oxygen sensor*；
Figure BDA0002988957860000041
Wherein α is the proportionality constant of the Clark electrode, AstandardReduction of diffusion current for calibration of the membraneless dissolved oxygen sensor, CstandardThe dissolved oxygen concentration of the non-membrane dissolved oxygen sensor was measured, and A was the approximate diffusion current value of the actual measurement.
The flow rate compensation system of the membraneless dissolved oxygen sensor comprises a module 1 and a control module, wherein the module comprises:
the method comprises the steps of collecting a time sequence of current signals I (t) of the film-free sensor at a certain sampling interval delta t, amplifying the current signals by using a trans-impedance amplifier and carrying out analog-to-digital conversion to obtain a group of digital signals, wherein the matrix representation comprises the following steps:
Figure BDA0002988957860000042
The module 2 comprises:
fast calculation of A (C) by pseudo-inverse matrix method*) Let us order
Figure BDA0002988957860000043
Then there is TTT(A(C*)，k1)T＝TTI (t) therefore
(A(C*)，k1)T＝(TTT)-1TTI
(TTT)-1TTThe diffusion current A (C) is obtained by matrix multiplication according to the pseudo-inverse of T*) A value of (d);
and the actual measurement is accomplished using the following formula:
Figure BDA0002988957860000044
wherein
Figure BDA0002988957860000045
Is a correction factor.
The flow rate compensation system of the membraneless dissolved oxygen sensor comprises a module 2 and a control module, wherein the module comprises: the sampling time interval is 20ms, and 10 times of sampling are carried out continuously.
The flow rate compensation system of the membraneless dissolved oxygen sensor is characterized in that voltage signals are applied to a working electrode and a reference electrode of the membraneless dissolved oxygen sensor.
The flow rate compensation system of the membraneless dissolved oxygen sensor comprises a cleaning voltage, a resting voltage and a measuring voltage.
According to the scheme, the invention has the advantages that:
the current magnitude is collected in different waiting time in the process of one-time measurement, and the influence of flow speed drift is calculated by utilizing the change fitting of transient current, so that the drift caused by the water flow speed is reduced or even eliminated. The method can obviously improve the precision and the stability of measurement, and other mechanical structures such as a water pump and the like do not need to be added.
Drawings
FIG. 1 is a schematic diagram of the operating principle of a membraneless sensor;
FIG. 2 is a flow chart of the dissolved oxygen measurement method of the present invention;
FIG. 3 is an expanded flow chart of step 2 in FIG. 2;
FIG. 4 is an expanded flow chart of step 3 in FIG. 2
FIG. 5 is a schematic diagram of the working principle of the measuring system of the present invention;
FIG. 6 is a schematic diagram of the measurement effect of the present invention;
FIG. 7 is a trapezoidal wave signal diagram of the measurement voltage employed in the present invention.
Detailed Description
The inventors of the present invention have studied a novel filmless dissolved oxygen sensor, and have found that the filmless sensor has a short measurement time and a fast response, and thus it is considered that the peripheral oxygen is hardly consumed. Therefore, we can consider that in the actual measurement process, the transient current of the electrode is only composed of local diffusion current and convection current, and the influence of the convection effect on the diffusion distribution is neglected due to the existence of micropores. In this way, the contributions of the diffusion current and the convection current to the total measurement current can be theoretically calculated respectively, and further drift compensation is realized.
The comparison between diffusion current and convection current is described in equation 6 and equation 7, because the electrode consumes the dissolved oxygen near the electrode during the measurement process, the measured diffusion current is local.
The design method provided by the invention has the key technical points that the influence of convection on diffusion distribution is ignored, the current magnitude is collected in different waiting time in the primary measurement process, and the contribution of diffusion current and convection current to the total measurement current is respectively calculated according to the change of transient current, so that the flow velocity compensation is realized. The basic principle of the key technical point is specifically explained as follows:
The invention aims to solve the technical problem of drift of a membraneless electrochemical dissolved oxygen sensor caused by flow rate influence, and provides a dissolved oxygen measuring method for compensating the flow rate influence, which comprises the following steps:
step 1: a dynamic voltage excitation signal is applied to the working electrode and the reference electrode of the membraneless sensor. Wherein the voltage excitation signal (measurement voltage) here may be a trapezoidal wave signal. A particularly currently used waveform diagram is shown in fig. 7. It should be noted that parameters such as intervals, voltage levels, cleaning voltage periods, etc. in the voltage excitation signal may be modified.
Step 2: the acquired current signal is the current between the working electrode and the reference electrode, and is converted into a current signal of the electrochemical reaction of the film-free sensor, so as to obtain a digital signal;
and step 3: and fitting and calculating according to the digital signal to obtain the actual dissolved oxygen concentration.
The dissolved oxygen measuring method described above, wherein the step 2 includes:
step 21: collecting a current signal of the film-free sensor;
step 22: amplifying the current signal through a trans-impedance amplifier, and correspondingly converting the current signal into an analog voltage signal;
Step 23: and correspondingly converting the analog voltage signal into a digital signal.
The dissolved oxygen measuring method described above, wherein the step 3 includes:
step 31: sampling at certain time intervals in a single measurement by the steps to obtain a current I (t) of the membraneless sensor;
step 32: substituting the simultaneous over-determined equation of the following formula (2) into the current I (t) of the film-free sensor at different moments to calculate the diffusion coefficient A, wherein the contribution of the convection current to the total measurement current is a proportionality constant k in the formula1。
Figure BDA0002988957860000061
Wherein k is1As a proportionality constant for the convection current, t is a measureTime of day;
step 33: substituting the diffusion current coefficient obtained by the previous calculation into the formula (3) to calculate the actual dissolved oxygen concentration C*。
Figure BDA0002988957860000062
Where α is the constant of proportionality of the Clark electrode, and can be obtained by experimental calibration and calculated from the current data of the membraneless sensor in step 32.
In order to make the aforementioned features and effects of the present invention more comprehensible, embodiments accompanied with figures are described in detail below.
The basic idea of the invention is to compensate for the flow rate effects in dissolved oxygen measurements by acquiring transient current data multiple times. Referring to the drawings, FIG. 2 is a flow chart of the method for measuring dissolved oxygen according to the present invention; FIG. 3 is a flow chart of substeps of step 2 of FIG. 2; FIG. 4 is a flow chart of steps of step 3 of FIG. 2. As shown in fig. 2, the dissolved oxygen measurement method of the present invention includes:
Step 1: applying a voltage excitation signal to the membraneless sensor;
step 2: acquiring and converting transient current of the film-free sensor at certain time intervals to obtain a digital signal;
and step 3: and fitting and calculating according to the digital signal to obtain the actually compensated dissolved oxygen concentration.
Further, in the above dissolved oxygen measuring method, the step 2 includes:
step 21: collecting current signals at certain time intervals;
step 22: amplifying the current signal through a trans-impedance amplifier, and converting the current signal into an analog voltage signal;
step 23: and converting the analog voltage signal into a digital signal through an AD converter.
Further, in the above dissolved oxygen measuring method, the step 3 includes:
step 31: obtaining transient current data I (t) of the membraneless sensor by the steps;
step 32: substituting the simultaneous equation of the following formula (4) into the current I (t) of the film-free sensor at different moments to calculate the reduced diffusion current A (C)*)。
Figure BDA0002988957860000071
Wherein C is*Is the dissolved oxygen concentration in the liquid, k1Is a convection current proportionality coefficient, and t is a measurement time;
step 33: the reduced diffusion current A (C) obtained by the previous calculation*) Substituting into formula (5), calculating to obtain actual dissolved oxygen concentration C *。
Figure BDA0002988957860000072
Where α is the constant of proportionality of the Clark electrode, D0The diffusion constant of the gas permeable membrane can be obtained by experimental calibration for calibration, and D is the diffusion constant of the gas permeable membrane for measurement, which is calculated from the current data of the film-free sensor in step 32.
The operation of the dissolved oxygen measuring apparatus according to the present invention will be described in detail with reference to FIG. 5.
For a film-free dissolved oxygen sensor, under dynamic measurement, the current of the film-free dissolved oxygen sensor mainly consists of diffusion current I1And convection current I2And (4) forming. For the diffusion process, the diffusion current I is obtained by solving the simultaneous equation of the first law and the second law of Fick1：
Figure BDA0002988957860000073
Where k (t) is a complex function including temperature, geometry, etc., and needs to be determined by calibration.
However, in practical use, more oxygen is dissolved due to the convectionThe liquid band is carried to the electrode surface to increase the transient current. Neglecting the coupling effect of convection on the diffusion field, we calculate the effect of convection current alone. As shown in fig. 6, let S be the boundary of diffusion, the oxygen concentration of the liquid outside S be C, and the oxygen concentration of the liquid inside S be zero.
Figure BDA0002988957860000074
Is an area element on S, and the direction of the area element is from outside to inside,
Figure BDA0002988957860000079
is that
Figure BDA0002988957860000076
Upper flow rate. In a very short time dt, flows through
Figure BDA0002988957860000077
Has a flow rate of
Figure BDA0002988957860000078
As the electrochemical reaction consumes oxygen in the flow, the current increases:
Figure BDA0002988957860000081
it is worth noting here that
Figure BDA0002988957860000082
From inside to outside, the contribution to the current is 0, not a negative value. Therefore, only the area element is calculated
Figure BDA0002988957860000083
The partial surface integral, so the total current produced by convection is:
Figure BDA0002988957860000084
since the microelectrodes are etched on the surface of the silicon substrate, we reduce the problem to convection currents in rectangular channels. The convection velocity at the electrode surface is zero due to frictional resistance. Then, as the diffusion thickness increases with time, the flow velocity at the diffusion boundary also increases with time, thereby affecting the measurement. The convection current is therefore:
I2＝nFC*2r0δv(δ) (9)
wherein the thickness of diffusion
Figure BDA0002988957860000085
The diffusion boundary is very close to the electrodes and the fluid action can be seen as laminar flow, so
Figure BDA0002988957860000086
We can simply write the convection current as:
I2＝k1t (10)
wherein k is1Is a scaling factor of the convection current and is related to factors such as the diameter, depth and flow velocity of the micropores.
Therefore, the transient current actually measured by the film-less sensor is:
Figure BDA0002988957860000087
wherein A (C)*) The magnitude of the diffusion current after the reduction is proportional to the dissolved oxygen concentration.
The invention aims to provide a dissolved oxygen measuring method for compensating flow velocity influence, which aims to solve the technical problem that a membraneless electrochemical dissolved oxygen sensor drifts due to the flow velocity influence. In order to eliminate the factors influencing the measurement accuracy of the dissolved oxygen, the invention provides a compensation measurement method based on multiple measurement fitting.
The current magnitude can be acquired by different waiting time in one measurement, then the equation set is obtained in a simultaneous mode, and A (C) is obtained by solving through a least square method*) As a result, due to A (C)*) With dissolved oxygen concentration C*Is directly in direct proportion to the total weight of the mixture,it can be used for calibration as the relative current magnitude.
Further, in order to simplify the calculation, the following algorithm is adopted to implement the calculation, and firstly, a time sequence of current signals I (t) of the film-free sensor is collected at a certain sampling interval delta t, and a group of digital signals are obtained through trans-impedance amplifier amplification and analog-to-digital conversion. Expressed in a matrix, then:
Figure BDA0002988957860000088
where i (t) is the column vector of the current sequence and t is the column vector of the time sequence.
We can quickly calculate A (C) by using a pseudo-inverse matrix method*). Order to
Figure BDA0002988957860000089
Then there is TTT(A(C*)，k1)T＝TTI (t) therefore
(A(C*)，k1)T＝(TTT)-1TTI (13)
We call (T)TT)-1TTReferred to as the pseudo-inverse of T. Because the sampling time is fixed and determined, the pseudo-inverse of T can be obtained by calculation, and then A (C) can be obtained by matrix multiplication*) The value of (c).
The actual measurement is modified by the formula (5):
Figure BDA0002988957860000091
where A isstandardReducing the magnitude of the diffusion current, C, for calibrationstandardFor the calibration of the dissolved oxygen concentration, A is the magnitude of the reduced diffusion current for the actual measurement, where
Figure BDA0002988957860000092
Referred to as correction coefficients. In this way we can calibrate for drift and errors due to flow rate And (4) poor.
Preferably, the sampling interval is set to 20ms in this embodiment, with 10 consecutive samples, since any 50Hz ac source that may be present in a laboratory or calibration setting will cause coupled noise.
In view of the above considerations, in the present embodiment, the measurement scheme is given as follows:
1. sample interval with 20ms as a membraneless sensor
2. Applying a voltage excitation signal to the membraneless sensor;
3. collecting and converting a current signal to obtain a digital signal;
4. the final dissolved oxygen concentration was calculated from the membraneless sensor current data in the DSP by substituting equations (13) and (14).
This embodiment achieves flow rate compensation for dissolved oxygen measurement through a series of measures, with higher measurement accuracy than conventional measurement methods.
The following are system examples corresponding to the above method examples, and this embodiment can be implemented in cooperation with the above embodiments. The related technical details mentioned in the above embodiments are still valid in this embodiment, and are not described herein again in order to reduce repetition. Accordingly, the related-art details mentioned in the present embodiment can also be applied to the above-described embodiments.
The invention also provides a flow velocity compensation system of the membraneless dissolved oxygen sensor, which comprises:
The module 1 applies dynamic voltage signals to electrodes of the membraneless dissolved oxygen sensor to acquire current signals, and converts the current signals into current of electrochemical reaction of the membraneless dissolved oxygen sensor;
the module 2 executes the module 1 at certain time intervals to obtain the current collected by the film-free sensor at each moment, and substitutes the current at each moment through the following simultaneous over-determined equation to obtain the diffusion current A (C)*)，
Figure BDA0002988957860000093
Wherein k is1Is a proportionality constant, t is a column vector formed by the measuring time, and I (t) is a column vector of the current sequence;
the diffusion current is substituted into the following formula to obtain the dissolved oxygen concentration C measured by the membrane-free dissolved oxygen sensor*；
Figure BDA0002988957860000101
Wherein α is the proportionality constant of the Clark electrode, AstandardReduction of diffusion current for calibration of the membraneless dissolved oxygen sensor, CstandardThe dissolved oxygen concentration of the non-membrane dissolved oxygen sensor was measured, and A was the approximate diffusion current value of the actual measurement.
The flow rate compensation system of the membraneless dissolved oxygen sensor comprises a module 1 and a control module, wherein the module comprises:
the method comprises the steps of collecting a time sequence of current signals I (t) of the film-free sensor at a certain sampling interval delta t, amplifying the current signals by using a trans-impedance amplifier and carrying out analog-to-digital conversion to obtain a group of digital signals, wherein the matrix representation comprises the following steps:
Figure BDA0002988957860000102
The module 2 comprises:
fast calculation of A (C) by pseudo-inverse matrix method*) Let us order
Figure BDA0002988957860000103
Then there is TTT(A(C*)，k1)T＝TTI (t) therefore
(A(C*)，k1)T＝(TTT)-1TTI
(TTT)-1TTThe diffusion current A (C) is obtained by matrix multiplication according to the pseudo-inverse of T*) A value of (d);
and the actual measurement is accomplished using the following formula:
Figure BDA0002988957860000104
wherein
Figure BDA0002988957860000105
Is a correction factor.
The flow rate compensation system of the membraneless dissolved oxygen sensor comprises a module 2 and a control module, wherein the module comprises: the sampling time interval is 20ms, and 10 times of sampling are carried out continuously.
The flow rate compensation system of the membraneless dissolved oxygen sensor is characterized in that voltage signals are applied to a working electrode and a reference electrode of the membraneless dissolved oxygen sensor.
The flow rate compensation system of the membraneless dissolved oxygen sensor comprises a cleaning voltage, a resting voltage and a measuring voltage.

Claims (10)

1. A flow velocity compensation method of a membraneless dissolved oxygen sensor is characterized by comprising the following steps:
step 1, applying a dynamic voltage signal to an electrode of a membraneless dissolved oxygen sensor to collect a current signal, and converting the current signal into a current for an electrochemical reaction of the membraneless dissolved oxygen sensor;
step 2, executing the step 1 at certain time intervals to obtain the current collected by the membraneless dissolved oxygen sensor at each moment, and substituting the current into the current at each moment through the following simultaneous overdetermined equation to obtain diffusion current A (C) *)，
Figure FDA0002988957850000011
Wherein k is1A constant proportion to the current, t is a column vector formed by the measuring time, and I (t) is a column vector of the current sequence;
the diffusion current is substituted into the following formula to obtain the dissolved oxygen concentration C measured by the membrane-free dissolved oxygen sensor*；
Figure FDA0002988957850000012
Wherein α is the proportionality constant of the Clark electrode, AstandardReduction of diffusion current for calibration of the membraneless dissolved oxygen sensor, CstandardThe dissolved oxygen concentration when the film-less dissolved oxygen sensor was calibrated, and A is an approximate diffusion current value when actually measured.
2. The flow rate compensation method for the membraneless dissolved oxygen sensor according to claim 1, wherein the step 1 comprises:
collecting a time sequence of current signals I (t) of the membrane-free dissolved oxygen sensor at a certain sampling interval delta t, amplifying by a trans-impedance amplifier and carrying out analog-to-digital conversion to obtain a group of digital signals, wherein the matrix representation comprises the following steps:
Figure FDA0002988957850000013
the step 2 comprises the following steps:
fast calculation of A (C) by pseudo-inverse matrix method*) Let us order
Figure FDA0002988957850000014
Then there is TTT(A(C*)，k1)T＝TTI (t) therefore
(A(C*)，k1)T＝(TTT)-1TTI
(TTT)-1TTThe diffusion current A (C) is obtained by matrix multiplication according to the pseudo-inverse of T*) A value of (d);
and the actual measurement is accomplished using the following formula:
Figure FDA0002988957850000015
wherein
Figure FDA0002988957850000016
Is a correction factor.
3. The flow rate compensation method for the membraneless dissolved oxygen sensor according to claim 1, wherein the step 2 comprises: the sampling time interval is 20ms, and 10 times of sampling are carried out continuously.
4. The method for flow rate compensation of a membraneless dissolved oxygen sensor according to claim 1, wherein a voltage signal is applied to the working electrode and the reference electrode of the membraneless dissolved oxygen sensor.
5. The method for flow rate compensation of a membraneless dissolved oxygen sensor according to claim 1, wherein the voltage signal comprises a cleaning voltage, a resting voltage, and a measuring voltage.
6. A flow rate compensation system for a membraneless dissolved oxygen sensor, comprising:
the module 1 is used for applying a dynamic voltage signal to an electrode of the membraneless dissolved oxygen sensor to acquire a current signal and converting the current signal into a current for an electrochemical reaction of the membraneless dissolved oxygen sensor;
a module 2 for executing the module 1 at a certain time interval to obtain the current collected by the membraneless dissolved oxygen sensor at each time, and substituting the current at each time into the simultaneous overdetermined equation of the following formula to obtain the diffusion current A (C)*)，
Figure FDA0002988957850000021
Wherein k is1Is a proportional constant to the convection current, t is a column vector formed by the measuring time, and I (t) is a column vector of the current sequence;
the diffusion current is substituted into the following formula to obtain the dissolved oxygen concentration C measured by the membrane-free dissolved oxygen sensor *；
Figure FDA0002988957850000022
Wherein α is the proportionality constant of the Clark electrode, AstandardReduction of diffusion current for calibration of the membraneless dissolved oxygen sensor, CstandardThe dissolved oxygen concentration of the non-membrane dissolved oxygen sensor was measured, and A was the approximate diffusion current value of the actual measurement.
7. The system for flow rate compensation of a membraneless dissolved oxygen sensor according to claim 6, wherein the module 1 comprises:
collecting a time sequence of current signals I (t) of the membrane-free dissolved oxygen sensor at a certain sampling interval delta t, amplifying by a trans-impedance amplifier and carrying out analog-to-digital conversion to obtain a group of digital signals, wherein the matrix representation comprises the following steps:
Figure FDA0002988957850000023
the module 2 comprises:
fast calculation of A (C) by pseudo-inverse matrix method*) Let us order
Figure FDA0002988957850000024
Then there is TTT(A(C*)，k1)T＝TTI (t) therefore
(A(C*)，k1)T＝(TTT)-1TTI
(TTT)-1TTThe diffusion current A (C) is obtained by matrix multiplication according to the pseudo-inverse of T*) A value of (d);
and the actual measurement is accomplished using the following formula:
Figure FDA0002988957850000031
wherein
Figure FDA0002988957850000032
Is a correction factor.
8. The system for flow rate compensation of a membraneless dissolved oxygen sensor according to claim 6, wherein the module 2 comprises: the sampling time interval is 20ms, and 10 times of sampling are carried out continuously.
9. The flow rate compensation system of claim 6, wherein a voltage signal is applied to the working electrode and the reference electrode of the membrane-less dissolved oxygen sensor.
10. The flow rate compensation system for a membraneless dissolved oxygen sensor according to claim 6, wherein the voltage signal comprises a cleaning voltage, a resting voltage, and a measurement voltage.
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