CN109580549B - Method and device for calculating and calibrating material content - Google Patents

Method and device for calculating and calibrating material content Download PDF

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CN109580549B
CN109580549B CN201811354820.5A CN201811354820A CN109580549B CN 109580549 B CN109580549 B CN 109580549B CN 201811354820 A CN201811354820 A CN 201811354820A CN 109580549 B CN109580549 B CN 109580549B
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黎伟禧
虞坤桥
甘泉
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Edan Instruments Inc
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Abstract

The invention is suitable for the technical field of biochemical detection, provides a method and a device for calculating and calibrating the content of a substance, by detecting signal values corresponding to a plurality of time values in a preset time period and fitting a regression equation according to the corresponding relation between the time values and the signal values, stably reflecting the change trend of the signal value, inputting the time value in a preset time period as an independent variable into the regression equation, taking a dependent variable calculated by the regression equation as a signal theoretical value corresponding to the time value, calculating the difference value of the signal theoretical values corresponding to the two preset time values according to a regression equation to be used as a signal difference value, finally determining the content of the target substance according to the corresponding relation between the preset signal difference value and the content, the method and the device can eliminate the calculation error of the change quantity of the signal value caused by the inaccurate selection of the preset time value, thereby improving the accuracy degree of calculating the content of the target substance.

Description

Method and device for calculating and calibrating material content
Technical Field
The invention belongs to the technical field of biochemical detection, and particularly relates to a method and a device for calculating and calibrating substance content.
Background
Currently, when detecting the content of a specific protein, an immunoturbidimetry method is often adopted, taking an antigen as an example, and the specific principle is as follows: when the specific antigen to be detected is combined with the specific antibody, the reaction liquid is turbid, and when the content of the antibody is fixed, the turbidity variation of the reaction liquid is positively correlated with the content of the antigen. The antigen content in the sample can be calculated by detecting the turbidity variation of the reaction solution and comparing with a series of standard products. Wherein, the measurement of the reaction liquid turbidity can adopt a scattering turbidity method or a transmission turbidity method, namely, when the reaction is started, light with a specific frequency is emitted from one side of the reaction cup, the scattering light intensity or absorbance is measured from the other side, the scattering light intensity or absorbance is generally called as a signal value in the field, and the larger the reaction liquid turbidity is, the larger the signal value is, and vice versa. Therefore, the signal value variation represents the turbidity variation, and the antigen content in the sample can be calculated according to the relationship between the signal value variation and the antigen content.
However, there are two methods for calculating the amount of change in the signal value, namely a two-point method and an end-point method. The two-point method is also called a fixed time method, and comprises the step of measuring the amount of change in signal value [ v1, v2] of a reaction solution [ v2-v1 ] in a certain period of time after antigen-antibody binding [ t1, t2 ]. Although the calculation of the two-point method is very simple, the selection time of the two points is very critical, if the selection time is too early, the result is easily interfered by instability at the initial stage of the reaction of the base solution, and if the selection time is too late, the result is easily influenced by the slow speed at the final stage of the reaction, so that the result becomes inaccurate. The end-point method, which is a method in which a signal value after complete binding of an antigen and an antibody is measured as a signal value change amount, is one less than the two-point method, but it is also necessary to select a very precise sampling timing. Can be imagined. If the calculated signal value variation is deviated, the inaccuracy of the finally calculated antigen content in the sample is directly caused.
Disclosure of Invention
In view of this, embodiments of the present invention provide a method and an apparatus for calculating and calibrating a substance content, so as to solve the problem of low accuracy in calibrating or calculating the substance content in the prior art.
A first aspect of an embodiment of the present invention provides a method for calculating a substance content, including: detecting signal values corresponding to a plurality of moment values and representing a reaction process in the reaction process of a reaction solution with unknown content of a target substance; fitting a regression equation according to the corresponding relation between the time value and the signal value; respectively inputting two time values as independent variables into the regression equation, taking a dependent variable calculated by the regression equation as a signal theoretical value corresponding to the time value, and calculating a difference value of the signal theoretical values corresponding to the two time values as a target signal difference value; and determining the content corresponding to the target signal difference according to the corresponding relation between the signal difference and the content, and taking the content as the content of the target substance.
A second aspect of an embodiment of the present invention provides a calibration method, including: respectively carrying out reaction tests on a plurality of standard substances with known target substance contents, and determining standard signal values representing the reaction process of the standard substances corresponding to a plurality of time values; respectively fitting a standard regression equation corresponding to each standard product according to the corresponding relation between the time value and the standard signal value for each standard product; respectively inputting the two time values as independent variables into a standard regression equation corresponding to each standard product, taking a dependent variable calculated by the standard regression equation as a standard signal value corresponding to the time value, and calculating a difference value of the standard signal values corresponding to the two time values as a signal difference value of each standard product; and establishing a corresponding relation between the signal difference value and the content according to the content of the target substance in each standard substance and the signal difference value of the standard substance.
A third aspect of an embodiment of the present invention provides a substance content calculation apparatus, including: the detection module is used for detecting signal values corresponding to a plurality of moment values and representing a reaction process in the reaction process of the reaction liquid with unknown content of the target substance; the fitting module is used for fitting a regression equation according to the corresponding relation between the time value and the signal value; the calculation module is used for respectively inputting the two time values as independent variables into the regression equation, taking the dependent variable calculated by the regression equation as a signal theoretical value corresponding to the time value, and calculating the difference value of the signal theoretical values corresponding to the two time values as a target signal difference value; and the determining module is used for determining the content corresponding to the target signal difference value according to the corresponding relation between the signal difference value and the content, and taking the content as the content of the target substance.
A fourth aspect of the embodiments of the present invention provides a calibration apparatus, including:
the measuring module is used for respectively carrying out reaction tests on a plurality of standard substances with known target substance contents and measuring standard signal values representing the reaction process of the standard substances corresponding to a plurality of time values; the standard fitting module is used for respectively fitting a standard regression equation corresponding to each standard product according to the corresponding relation between the time value and the standard signal value; the difference value calculation module is used for inputting the two time values as independent variables into a standard regression equation corresponding to each standard product, taking a dependent variable calculated by the standard regression equation as a standard signal value corresponding to the time value, and calculating the difference value of the standard signal values corresponding to the two time values as a signal difference value of each standard product; and the calibration module is used for establishing the corresponding relation between the signal difference value and the content according to the content of the target substance in each standard product and the signal difference value of the standard product.
A fifth aspect of an embodiment of the present invention provides a substance content calculation apparatus, including: memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the steps of the method provided by the first aspect of an embodiment of the present invention are implemented when the computer program is executed by the processor.
A sixth aspect of embodiments of the present invention provides a computer-readable storage medium, which stores a computer program, characterized in that the computer program, when executed by a processor, implements the steps of the method provided by the first aspect of embodiments of the present invention.
Compared with the prior art, the embodiment of the invention has the following beneficial effects: detecting signal values representing a reaction process corresponding to a plurality of time values in the reaction process of a reaction solution containing a target substance; fitting a regression equation according to the corresponding relation between the time value and the signal value; inputting the time value as an independent variable into the regression equation, taking a dependent variable calculated by the regression equation as a signal theoretical value corresponding to the time value, and calculating a difference value of the signal theoretical values corresponding to two preset time values as a signal difference value; and determining the content of the target substance according to the corresponding relation between the preset signal difference value and the content so as to eliminate the calculation error of the change quantity of the signal value caused by the inaccuracy of the preset time value and further improve the accuracy of calculating the content of the target substance.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise.
FIG. 1 is a flow chart of a method for calculating a substance content according to an embodiment of the present invention;
FIG. 2 is a flowchart illustrating an implementation of the method S102 for calculating the content of the substance according to an embodiment of the present invention;
FIG. 3 is a flowchart illustrating another embodiment of a method S102 for calculating a substance content according to an embodiment of the present invention;
FIG. 4 is a diagram of a fitting effect provided by a third embodiment of the present invention;
FIG. 5 is a diagram of another effect of the fitting provided by the third embodiment of the present invention;
fig. 6 is a flowchart of an implementation of the scaling method according to the fourth embodiment of the present invention;
FIG. 7 is a block diagram of a device for calculating the content of a substance according to a fifth embodiment of the present invention;
fig. 8 is a block diagram of a scaling apparatus according to a sixth embodiment of the present invention;
FIG. 9 is a schematic diagram of a device for calculating the amount of a substance provided by an embodiment of the present invention.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular system structures, techniques, etc. in order to provide a thorough understanding of the embodiments of the invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.
In order to explain the technical means of the present invention, the following description will be given by way of specific examples.
Example one
Fig. 1 shows an implementation flow of the method for calculating the substance content according to the first embodiment of the present invention, which is detailed as follows:
in S101, in a reaction process of a reaction solution in which the content of a target substance is unknown, signal values representing the reaction process corresponding to a plurality of time values are detected.
Alternatively, in the embodiment of the present invention, a reaction solution containing a target substance but having an unknown content is poured into a reaction cup, light of a specific frequency is emitted from one side of the reaction cup during a reaction of the reaction solution, and scattered light intensity or absorbance is measured from the other side. It is understood that since the intensity of the scattered light or the absorbance is a signal detected in the test apparatus, the intensity of the scattered light or the absorbance can be collectively referred to as a signal value, and the signal value also includes other types of data, not limited to the intensity of the scattered light or the absorbance.
Illustratively, in the present embodiment, taking a target substance as an antibody as an example, a reaction solution containing an unknown amount of the antibody is poured into a reaction cup, and a plurality of signal values are continuously measured during the reaction of the reaction solution. The duration of the preset time period is positioned for n seconds, and m signal values are continuously measured at equal intervals in the preset time period, wherein m is a natural number greater than or equal to 2.
Alternatively, for convenience of calculation, the time value of a certain time in the embodiment of the present invention may be a time difference between the time and an initial time of the preset time period, for example, if the preset time period is 10 points 00 minutes 00 seconds to 10 points 00 minutes 10 seconds, the time value of 10 points 00 minutes 00 seconds may be 1 point 00 minutes 01 seconds, and the time value of 10 points 00 minutes 10 seconds may be 10.
It can be understood that, because the signal values corresponding to the time values are collected within the preset time period, the change trend of the signal values can be reflected better in the subsequent process.
In S102, a regression equation is fitted according to the correspondence between the time value and the signal value.
In the embodiment of the invention, the corresponding relation between the time value and the signal value is fitted by adopting a regression analysis method. It can be understood that, assuming that the time value is used as the abscissa in the coordinate system and the signal value is used as the ordinate in the coordinate system, the corresponding relationship between each time value and the signal value is represented as a coordinate point in the coordinate system, and a curve or a straight line can be fitted according to the coordinate points by the regression analysis method, i.e. a regression equation can be fitted.
Optionally, the fitting a regression equation according to the corresponding relationship between the time value and the signal value includes: and fitting the corresponding relation between the time value and the signal value by a least square method to generate a linear regression equation.
Specifically, let the linear regression equation be f (x)i)=axi+ b, wherein xiRepresents the ith time value in the preset time period, a represents the slope parameter, b represents the intercept parameter, f (x)i) And (3) representing a signal theoretical value corresponding to the ith time value, and defining an objective function as follows according to a least square method:
Figure GDA0003097619650000061
finally, find out
Figure GDA0003097619650000062
Wherein xiIndicates the ith time value, yiRepresenting the ith signal value. It will be appreciated that the regression equation can reflect the general regularity and trend of the change in signal value very well since the criterion for establishing the regression equation is to minimize the sum of squared distances of the equation from each measurement point.
It is to be understood that other ways of fitting a linear equation or a non-linear equation may be used in embodiments of the present invention.
In S103, the two time values are respectively used as independent variables and input into the regression equation, the dependent variable calculated by the regression equation is used as a signal theoretical value corresponding to the time value, and a difference value between the signal theoretical values corresponding to the two time values is calculated as a target signal difference value.
It can be understood that, after the time value is input into the regression equation as an independent variable, a value on the regression line corresponding to the time value, that is, a theoretical value of the signal may be calculated, and the theoretical value of the signal may have a certain difference from a theoretical value of the signal corresponding to a real time value. However, since the actual signal values measured at different times may have a certain error due to environmental factors or contingencies of the reaction of the compounds, it is necessary to correct the actually measured signal values to a certain extent, for example, the reaction of the bottom liquid of the test sample is unstable in the initial stage of the reaction of the test sample containing the antibody, and the reaction rate of the test sample is slow in the final stage of the reaction of the test sample containing the antibody. The signal theoretical value is calculated by a regression equation reflecting the overall variation trend of the signal value, so that the contingency can be eliminated to a great extent, and the error is reduced.
Preferably, in the embodiment of the present invention, one time value may be selected as the time value when the signal value is detected for the first time in the preset time period, and another time value may be selected as the time value when the signal value is detected for the last time in the preset time period. It can be understood that the signal theoretical value corresponding to the time value when the signal value is detected for the first time after the correction by the regression equation is not interfered by the instability of the detection sample at the initial reaction stage of the base solution, and the signal theoretical value corresponding to the time value when the signal value is detected for the last time after the correction by the regression equation is not affected by the reduction of the rate at the final reaction stage, so that the calculated target signal difference value is ensured to be small in interference degree.
In the embodiment of the present invention, the selection of the two preset time values is not limited to the above selection manner.
It will be appreciated that the target signal difference value may reflect the amount of change in the signal value between two predetermined time values, and that the signal difference value thus calculated may better characterize the change in the test sample since the signal theoretical value corrected according to the regression equation eliminates occasional errors in each measurement of the signal value.
In S104, determining a content corresponding to the target signal difference according to the correspondence between the signal difference and the content, and using the content as the content of the target substance.
Since there is a certain correlation between the content of the target substance in the detection sample and the variation of the signal value, the embodiment of the present invention uses the signal difference value from which the influence of the incidental factors is eliminated as the variation of the signal value, and since the correspondence between the signal difference value and the content is established in advance according to a plurality of standards whose contents of the target substance are known before calculating the content of the substance in the detection sample, the content corresponding to the target signal difference value calculated by the embodiment of the present invention can be determined according to the correspondence between the signal difference value and the content in the calculation process of the content of the reaction solution whose content of the target substance is unknown, and the content can be used as the content of the target substance.
It should be noted that the calibration process according to the plurality of standards in the embodiment of the present invention is performed before the reaction process of the reaction solution with unknown content of the target substance, and the specific calibration method will be described in detail in the following embodiment.
In the embodiment of the invention, a regression equation is fitted by detecting signal values corresponding to a plurality of time values in a preset time period and according to the corresponding relation between the time values and the signal values to stably reflect the change trend of the signal values, the time values in the preset time period are used as independent variables to be input into the regression equation, a dependent variable calculated by the regression equation is used as a signal theoretical value corresponding to the time value, the difference value of the signal theoretical values corresponding to two preset time values is calculated according to the regression equation and is used as a target signal difference value, and finally the content of a target substance is determined according to the corresponding relation between the preset signal difference value and the content, so that the calculation error of the change quantity of the signal values caused by the inaccuracy of the selection of the preset time values is eliminated, and the accuracy of calculating the content of the target substance is further improved.
Example two
In the above embodiment S102, it is mentioned that the regression equation is fitted according to the corresponding relationship between the time value and the signal value, but considering that, in the detection process of the actual signal value, a large error may occur in the signal value detected at some time due to a detection problem of the device or an influence of an environmental factor, and the error may cause a change trend of the signal value that the fitted regression equation does not reflect well, in the embodiment of the present invention, it is necessary to delete a part of data corresponding to the time value with a large error and fit the regression equation by using the signal values corresponding to the remaining time values. Fig. 2 shows a specific implementation flow of S102 provided in the first embodiment of the present invention, which is detailed as follows:
in S201, a first equation is generated by fitting the correspondence between the time value and the signal value.
In the embodiment of the invention, a first equation is fitted based on the corresponding relation between all time values and signal values in a preset time period.
Optionally, the corresponding relationship between the time value and the signal value is fitted by a least square method to generate the first equation.
Specifically, let the linear regression equation be f (x) i)=axi+ b, wherein xiRepresents the ith time value in the preset time period, a represents the slope parameter, b represents the intercept parameter, f (x)i) And representing a signal theoretical value corresponding to the ith time value, and defining an objective function according to a least square method as follows:
Figure GDA0003097619650000081
finally to find out
Figure GDA0003097619650000082
Wherein xiIndicates the ith time value, yiRepresenting the ith signal value.
In S202, an abnormal time value is determined by the first equation.
Optionally, the time value in the preset time period is used as an independent variable to be input into the first equation, and the dependent variable calculated by the first equation is used as a signal evaluation value (f (x) corresponding to the time valuei) ); calculating the signal evaluation value (f (x)) corresponding to the time value in the preset time periodi) With said signal value (y)i) Is taken as the difference value (| f (x) corresponding to the time valuei)-yiI)); if the difference value corresponding to the time value is larger than a preset difference threshold value, the time value is compared with a preset difference threshold valueThe time value is determined as an abnormal time value.
In S203, the regression equation is fitted according to the correspondence between the time values other than the abnormal time value and the signal value.
Exemplarily, assuming that 10 signal values are acquired at 10 times in total in a preset time period, wherein the 2 nd and 7 th time values are determined as abnormal time values according to the above identification process, the time values other than the 2 nd and 7 th time values in the preset time period are taken as normal time values, and the corresponding relationship between the normal time values and the signal values is fitted by a least square method to generate a regression equation.
According to the embodiment of the invention, the abnormal signal value elimination operation is added, so that the establishment of the regression equation is not influenced by the abnormal signal value, and the signal theoretical value corrected by the regression equation can be closer to the law of reaction.
EXAMPLE III
An embodiment of the present invention provides another implementation method for S102 in the first embodiment, and fig. 3 shows another specific implementation flow of S102 provided in the first embodiment of the present invention, which is detailed as follows:
in S301, the signal values are normalized to generate signal mapping values.
In the embodiment of the invention, considering that the range of the signal value may be different in each detection process, the signal value detected each time needs to be normalized, so that the subsequently calculated signal difference has more consistency, and the comparison with the corresponding relation between the preset signal difference and the content is convenient.
Optionally, by the formula:
Figure GDA0003097619650000091
mapping the detected signal values to [0,1 ]]Wherein Y'iFor the signal mapping value, y, corresponding to the ith time valueiIs the signal value corresponding to the ith time value.
In S302, a preset regression model is obtained, and an objective function corresponding to the regression model is established.
Optionally, the expression of the preset regression model is: f (x)i)=wTφ(xi) + b, wherein φ (x)i) The regression equation is of the form chosen for the user, for example: phi (x)i)=xi、φ(xi)=log(xi) Or other user-selected form of equation, xiRepresenting the ith time value in a preset time period, wherein w is a parameter vector of the regression model, b is an error coefficient, and f (x)i) And the signal theoretical value is corresponding to the ith time value.
Optionally, the objective function corresponding to the regression model that may be obtained includes:
Figure GDA0003097619650000101
wherein, Y'iA signal mapping value corresponding to the ith time value,
Figure GDA0003097619650000102
the term, referred to as the structural risk term, is used to characterize the regression model solution, p is a first predetermined constant,
Figure GDA0003097619650000103
the term is called an empirical risk term and is used for describing the fit degree of the regression model and the data, and C is a second preset constant. As can be appreciated, the first and second electrodes,
Figure GDA0003097619650000104
and
Figure GDA0003097619650000105
are mutually restrictive, one item is large while the other is necessarily small. In addition, l (z) is a predetermined loss function, and ∈ is loss sensitivity, which determines the tolerance of the regression equation to signal values with large deviations.
From the point of view of minimizing the risk of experience,
Figure GDA0003097619650000106
which may be referred to as a regularization term, the closer p is to 0, the more sparse the solution w, i.e., the number of non-zero componentsThe number is as small as possible, and the larger p is, the more balanced the solution w is, i.e. the number of non-zero components is as dense as possible. In general p will not take a negative number. Preferably, in the embodiment of the present invention, p is 2, so that the solution of the objective function is relatively balanced, and meanwhile, the calculation solution is relatively simple. And the loss sensitivity epsilon determines the tolerance degree of the regression equation to the point with larger deviation, if the signal value is smaller than epsilon or larger than-epsilon than the value of the corresponding moment of the regression equation, the point is considered as a normal point, and if not, the point is an abnormal point. The larger the difference between the two is, the larger the degree of harm of the abnormal point is considered to be, and the point can be automatically eliminated in the fitting process.
The embodiment of the invention takes the change loss function as the preset loss function. Compared with the common secondary loss function L (z) ═ z2The loss function is in [ - ε, ε due to change]The intra-interval loss is zero, so that the regression equation is selective to the signal value points. It will be appreciated that each time instant value corresponds to a point in the coordinate system, and that in solving the regression equation, only points closer to the initially fitted regression equation are picked by the loss function to further fit the regression equation.
In S303, the parameters in the objective function are solved, and the parameters of the regression model are calculated based on the parameters in the objective function to fit the regression equation.
Optionally, in order to facilitate solving the regression equation, the embodiment of the present invention solves the dual-form equation of the objective function by constructing the dual-form equation of the objective function to obtain the parameter in the objective function.
Specifically, a Larsian operator method is adopted to perform mathematical derivation on the basis of the original objective function so as to construct an equation of a dual form of the objective function corresponding to the regression model. Specifically, the equation of the dual form of the objective function is:
Figure GDA0003097619650000111
Wherein,
Figure GDA0003097619650000112
and aiAs an objective functionTwo parameters, Y'iAnd mapping the signal corresponding to the ith time value.
It will be appreciated that by solving the dual form of the equation shown above, two parameters in the objective function can be derived, namely
Figure GDA0003097619650000113
And ai. And then according to the formula:
Figure GDA0003097619650000114
calculating two parameters b and w in the regression equation, and fitting the regression equation: f (x)i)=wTφ(xi) + b, wherein, xiRepresenting the ith time value in a preset time period, wherein w is a parameter vector of the regression model, b is an error coefficient, and f (x)i) Is a signal theoretical value corresponding to the ith moment value, and epsilon is a preset loss sensitivity, Y'iAnd mapping the signal corresponding to the ith time value.
In the embodiment of the present invention, since the original objective function is constructed according to the regression equation obtained as required, the regression equation f (x) is finally obtainedi) The method has the characteristics required by users, namely, the method has the property of fitting normal data points and reducing the influence of abnormal points. In other words, even if there are abnormal points in the signal values measured a plurality of times, the trend of the data fitted by this method is less disturbed by the abnormal points, so that the initial and final signal values corrected by this trend are guaranteed to be less disturbed, and the amount of change in the disturbed signal values is calculated. The effect graphs of the fitting are shown in fig. 4 and 5.
It can be understood that, because the embodiment of the present invention adds the structural risk control when solving the regression equation, so that the solution of the fitted equation has controllability, and at the same time, by using an insensitive loss function to replace the square loss used in the least square regression, the obtained regression equation has the sensitivity of reducing the points with larger deviation, and the normal points in a plurality of data points can be identified, so as to fit according to the trend of the normal points, so that the embodiment of the present invention combines the abnormal signal value elimination and the regression establishment modes, and even if a plurality of abnormal signal values with larger deviation exist, the embodiment of the present invention can establish the regression equation according to the general trend of the normal data, thereby ensuring that the signal values at the initial stage and the final stage of the reaction are accurately corrected, so as to calculate the correct signal difference.
Example four
Embodiments of the present invention relate to a method for calibration based on a standard. It should be noted that the calibration method may be implemented before the flow of the method for calculating the substance content in the first embodiment, and may be further integrated with the method for calculating the substance content as a whole, or may be implemented independently of the method for calculating the substance content. Fig. 6 shows an implementation flow of the scaling method provided by the fourth embodiment of the present invention, which is detailed as follows:
S601, respectively carrying out reaction tests on a plurality of standard substances with known content of the target substance, and determining standard signal values corresponding to a plurality of time values and representing the reaction process of the standard substances.
Alternatively, in the embodiment of the present invention, a plurality of standards containing a target substance and having known contents are poured into different reaction cups, respectively, and during the reaction of the standards, light of a specific frequency is emitted from one side of the reaction cup and the scattered light intensity or absorbance is measured from the other side. It is understood that since the scattered light intensity or absorbance is a signal detected in the test apparatus, the scattered light intensity or absorbance can be collectively referred to as a standard signal value, and the standard signal value also includes other types of data, not limited to the scattered light intensity or absorbance.
Illustratively, in the present embodiment, taking a target substance as an antibody as an example, a reaction solution containing an unknown amount of the antibody is poured into a reaction cup, and a plurality of standard signal values are continuously measured during the reaction of the reaction solution. Positioning the duration of the preset time period for n seconds, and continuously measuring m standard signal values at equal intervals in the preset time period, wherein m is a natural number greater than or equal to 2, and understandably, the larger the number of m is, the more the corresponding relationship between the collected time value and the standard signal value is.
Alternatively, for convenience of calculation, the time value of a certain time in the embodiment of the present invention may be a time difference between the time and an initial time of the preset time period, for example, if the preset time period is 10 points 00 minutes 00 seconds to 10 points 00 minutes 10 seconds, the time value of 10 points 00 minutes 00 seconds may be 1 point 00 minutes 01 seconds, and the time value of 10 points 00 minutes 10 seconds may be 10.
It can be understood that, because the signal values corresponding to the time values are collected within the preset time period, the change trend of the standard signal value can be reflected better in the subsequent process.
And S602, respectively fitting a standard regression equation corresponding to each standard product according to the corresponding relation between the time value and the standard signal value.
Optionally, the linear standard regression equation is generated by fitting the correspondence between the time value and the standard signal value by a least square method.
Optionally, the first equation is generated by fitting a least square method to a corresponding relationship between the time value and the signal value. Specifically, let the linear regression equation be f (x)i)=axi+ b, wherein xiRepresents the ith time value in the preset time period, a represents the slope parameter, b represents the intercept parameter, f (x) i) And representing a signal theoretical value corresponding to the ith time value, and defining an objective function according to a least square method as follows:
Figure GDA0003097619650000131
finally to find out
Figure GDA0003097619650000132
Wherein x isiIndicates the ith time value, yiRepresenting the ith signal value.
Further, an abnormal time value is determined by the first equation.
Optionally, the time value in the preset time period is used as an independent variable and input into the first equation, and the factor calculated by the first equation is usedThe variable is used as a signal evaluation value (f (x)) corresponding to the time valuei) ); calculating the signal evaluation value (f (x)) corresponding to the time value in the preset time periodi) With said signal value (y)i) Is taken as the difference value (| f (x) corresponding to the time valuei)-yiI)); and if the difference value corresponding to the time value is greater than a preset difference threshold value, determining the time value as an abnormal time value.
Further, the standard regression equation is fitted according to the corresponding relation between the time values except the abnormal time value and the standard signal value.
Exemplarily, assuming that 10 signal values are acquired at 10 moments in total in a preset time period, wherein the 2 nd and 7 th moment values are determined as abnormal moment values according to the above identification process, the moment values other than the 2 nd and 7 th moment values in the preset time period are taken as normal moment values, and the corresponding relationship between the normal moment values and the standard signal values is fitted by a least square method to generate a standard regression equation.
Optionally, the standard signal value is normalized to generate a signal mapping value.
In the embodiment of the present invention, it is considered that the ranges of the standard signal values may be different in each detection process, so that the standard signal values detected each time need to be normalized, so that the subsequently calculated standard signal difference values have more consistency.
Further, by the formula:
Figure GDA0003097619650000141
mapping the detected standard signal values to [0,1 ]]Wherein Y'iFor the signal mapping value, y, corresponding to the ith time valueiIs the signal value corresponding to the ith time value.
Further, a preset regression model is obtained, and a target function corresponding to the regression model is established.
Assuming that the expression of the preset regression model is:
Figure GDA0003097619650000142
wherein,
Figure GDA0003097619650000143
the regression equation is of the form chosen for the user, for example:
Figure GDA0003097619650000144
or other user-selected form of equation, xiRepresenting the ith time value in a preset time period, wherein w is a parameter vector of the regression model, b is an error coefficient, and f (x)i) And the signal theoretical value is corresponding to the ith time value.
Optionally, the objective function corresponding to the regression model that may be obtained includes:
Figure GDA0003097619650000145
wherein, Y'iA signal mapping value corresponding to the ith time value,
Figure GDA0003097619650000146
The term, referred to as the structural risk term, is used to describe the behavior of the regression model solution, p is a first predetermined constant,
Figure GDA0003097619650000147
the term is called an empirical risk term and is used for describing the fit degree of the regression model and the data, and C is a second preset constant. As can be appreciated, the first and second electrodes,
Figure GDA0003097619650000148
and
Figure GDA0003097619650000149
are mutually restrictive, one item is large while the other is necessarily small. In addition, l (z) is a predetermined loss function, and ∈ is loss sensitivity, which determines the tolerance of the regression equation for signal values with large deviations.
From the point of view of minimizing the risk of experience,
Figure GDA00030976196500001410
the more p is close to 0, the more sparse the solution w is, i.e. the number of non-zero components is as small as possible, and the larger p is, the more balanced the solution w is, i.e. the number of non-zero components is as dense as possible. In general p will not take a negative number. Preferably, in the embodiment of the present invention, p is 2, so that the solution of the objective function is relatively balanced, and meanwhile, the calculation solution is relatively simple. And the loss sensitivity epsilon determines the tolerance degree of the regression equation to the point with larger deviation, if the value of the standard signal is smaller than epsilon or larger than-epsilon than the value of the corresponding moment of the regression equation, the standard signal is considered as a normal point, and if not, the standard signal is considered as an abnormal point. The larger the difference between the two is, the larger the degree of harm of the abnormal point is considered to be, and the point can be automatically eliminated in the fitting process.
The embodiment of the invention takes the change loss function as the preset loss function. Compared with the common secondary loss function L (z) ═ z2The loss function is in [ - ε, ε due to change]The intra-interval loss is zero, making the standard regression equation selective for signal value points. It will be appreciated that the correspondence between each time-of-day value and the standard signal value is a point in the coordinate system, and in solving the regression equation, only points closer to the initially fitted regression equation are selected by the loss function to further fit the regression equation.
Further, parameters in the objective function are solved, and parameters of the regression model are calculated based on the parameters in the objective function to fit the standard regression equation.
Optionally, in order to facilitate solving the regression equation, the embodiment of the present invention solves the dual-form equation of the objective function by constructing the dual-form equation of the objective function to obtain the parameter in the objective function.
Specifically, a Larsian operator method is adopted to perform mathematical derivation on the basis of the original objective function so as to construct an equation of a dual form of the objective function corresponding to the regression model. Specifically, the equation of the dual form of the objective function is:
Figure GDA0003097619650000151
Wherein,
Figure GDA0003097619650000152
and aiIs two parameters of the objective function, Y'iAnd mapping the signal corresponding to the ith time value.
It will be appreciated that by solving the dual form of the equation shown above, two parameters in the objective function can be derived, namely
Figure GDA0003097619650000153
And ai. And then according to the formula:
Figure GDA0003097619650000154
calculating two parameters b and w in the regression equation, and fitting the regression equation:
Figure GDA0003097619650000155
wherein x isiRepresenting the ith time value in a preset time period, wherein w is a parameter vector of the regression model, b is an error coefficient, and f (x)i) Is a signal theoretical value corresponding to the ith moment value, and epsilon is a preset loss sensitivity Y'iAnd mapping the signal corresponding to the ith time value.
And S603, inputting the two time values as independent variables into a standard regression equation corresponding to each standard product, taking a dependent variable calculated by the standard regression equation as a standard signal value corresponding to the time value, and calculating a difference value of the standard signal values corresponding to the two time values as a signal difference value of each standard product.
It can be understood that, after the time value is input into the regression equation corresponding to each standard product as an independent variable, a value on the regression line corresponding to the time value, that is, a theoretical value of the signal, may be calculated, and the theoretical value of the signal may have a certain difference from the real standard signal value corresponding to the time value. However, since the actual standard signal values measured at different times may have errors due to environmental factors or contingencies in the reaction of the compounds, it is necessary to correct the actually measured signal values to some extent, for example, in the initial stage of the reaction of the antibody-containing standard, the reaction of the base solution of the standard is unstable, and in the final stage of the reaction of the antibody-containing standard, the reaction rate of the standard is slow. The signal theoretical value is calculated by a standard regression equation reflecting the overall variation trend of the signal value, so that the contingency can be eliminated to a great extent, and the error is reduced.
S604, establishing a corresponding relation between the signal difference value and the content according to the content of the target substance in each standard product and the signal difference value of the standard product.
It can be understood that, since the content of the target substance in the standard substance is known, and the signal difference corresponding to each standard substance is calculated through S601-S603, the correspondence between the signal difference and the content can be established.
Optionally, a calibration curve may be fitted according to the corresponding relationship between the signal difference and the content, an abscissa of the calibration curve represents the signal difference, and an ordinate represents the content of the target substance, and when the content of the substance is subsequently calculated, the calibration curve may be directly used to determine the content corresponding to the target signal difference as the content of the target substance under the condition that the target signal difference is known.
It can be understood that the corresponding relation between the signal difference value and the content determined by the embodiment of the invention eliminates the problem of inaccurate calibration caused by the measurement error of the standard product in the test process.
EXAMPLE five
Fig. 7 shows a block diagram of a calculating apparatus for calculating a substance content according to an embodiment of the present invention, which corresponds to the calculating method for a substance content described in the above embodiment, and only shows a part related to the embodiment of the present invention for convenience of explanation.
Referring to fig. 7, the apparatus includes:
the detection module 701 is used for detecting signal values corresponding to a plurality of time values and representing a reaction process in the reaction process of a reaction solution with unknown content of a target substance;
a fitting module 702, configured to fit a regression equation according to a correspondence between the time value and the signal value;
a calculating module 703, configured to input the two time values as independent variables into the regression equation, use a dependent variable calculated by the regression equation as a signal theoretical value corresponding to the time value, and calculate a difference between the signal theoretical values corresponding to the two time values as a target signal difference;
a determining module 704, configured to determine, according to the correspondence between the signal difference and the content, a content corresponding to the target signal difference, and use the content as the content of the target substance.
Optionally, the fitting module 702 comprises:
the first fitting submodule is used for fitting the corresponding relation between the time value and the signal value to generate a first equation;
the abnormity determining submodule is used for determining an abnormity time value through the first equation;
and the second fitting submodule is used for fitting the regression equation according to the corresponding relation between the time values except the abnormal time value and the signal value. Optionally, the anomaly determination sub-module is specifically configured to: inputting the time value as an independent variable into the first equation, and taking a dependent variable calculated by the first equation as a signal evaluation value corresponding to the time value; calculating a difference value between the signal evaluation value corresponding to the time value and the signal value, and taking the difference value as a difference value corresponding to the time value; and if the difference value corresponding to the time value is greater than a preset difference threshold value, determining the time value as an abnormal time value. .
Optionally, the fitting module 702 further comprises:
and the linear fitting submodule is used for fitting the corresponding relation between the time value and the signal value by a least square method to generate a linear regression equation.
Optionally, the fitting module 702 further comprises:
the normalization submodule is used for performing normalization processing on the signal value to generate a signal mapping value; the selection submodule is used for acquiring a preset regression model and establishing a target function corresponding to the regression model; and the solving submodule is used for solving the parameters in the objective function and calculating the parameters of the regression model based on the parameters in the objective function so as to fit the regression equation.
Optionally, the apparatus further comprises:
the measuring module is used for respectively carrying out reaction tests on a plurality of standard substances with known target substance contents and measuring standard signal values representing the reaction process of the standard substances corresponding to a plurality of time values;
the standard fitting module is used for respectively fitting a standard regression equation corresponding to each standard product according to the corresponding relation between the time value and the standard signal value;
the difference value calculation module is used for inputting the two time values as independent variables into a standard regression equation corresponding to each standard product, taking a dependent variable calculated by the standard regression equation as a standard signal value corresponding to the time value, and calculating the difference value of the standard signal values corresponding to the two time values as a signal difference value of each standard product;
And the calibration module is used for establishing the corresponding relation between the signal difference value and the content according to the content of the target substance in each standard product and the signal difference value of the standard product.
It can be understood that, in the embodiment of the present invention, a regression equation is fitted by detecting signal values corresponding to a plurality of time values within a preset time period and according to a corresponding relationship between the time values and the signal values to stably reflect a change trend of the signal values, the time values within the preset time period are input to the regression equation as independent variables, a dependent variable calculated by the regression equation is used as a signal theoretical value corresponding to the time value, a difference between the signal theoretical values corresponding to two preset time values is calculated according to the regression equation and is used as a signal difference, and finally, the content of the target substance is determined according to a corresponding relationship between the preset signal difference and the content to eliminate a calculation error of a change amount of the signal value caused by inaccurate selection of the preset time values, so as to improve an accuracy degree of calculating the content of the target substance.
EXAMPLE six
Fig. 8 shows a block diagram of a calibration apparatus provided in an embodiment of the present invention, which corresponds to the method for calculating the substance content described in the above embodiment, and only shows the relevant parts in the embodiment of the present invention for convenience of description.
The determining module 801 is configured to perform reaction tests on a plurality of standard substances with known target substance contents, and determine standard signal values representing a reaction process of the standard substances corresponding to a plurality of time values;
a standard fitting module 802, configured to respectively fit a standard regression equation corresponding to each standard product according to a correspondence between the time value and the standard signal value;
a difference value calculating module 803, configured to input the two time values as independent variables into a standard regression equation corresponding to each standard product, use a dependent variable calculated by the standard regression equation as a standard signal value corresponding to the time value, and calculate a difference value between the standard signal values corresponding to the two time values as a signal difference value of each standard product.
And the calibration module 804 is configured to establish a correspondence between the signal difference and the content according to a correspondence between the content of the target substance in each standard substance and the signal difference of the standard substance.
FIG. 9 is a schematic diagram of a device for calculating the amount of a substance according to an embodiment of the present invention. As shown in fig. 9, the substance content calculation device of this embodiment includes: a processor 90, a memory 91 and a computer program 92, such as a substance content calculation program, stored in said memory 91 and executable on said processor 90. The processor 90, when executing the computer program 92, implements the steps in the above-described embodiment of the method for calculating the content of each substance, such as the steps S101 to S104 shown in fig. 6. Alternatively, the processor 90, when executing the computer program 92, implements the functions of the modules/units in the above-mentioned device embodiments, such as the functions of the modules 701 to 704 shown in fig. 7.
Illustratively, the computer program 92 may be partitioned into one or more modules/units, which are stored in the memory 91 and executed by the processor 90 to implement the present invention. The one or more modules/units may be a series of computer program instruction segments capable of performing specific functions for describing the execution of the computer program 92 in the substance content calculating means 9. For example, the computer program 92 may be divided into a recognition module and a search module (module in a virtual device), and the specific functions of each module are as follows:
the recognition module is used for recognizing the gesture of a user and/or the expression of the user and determining a user instruction according to the gesture and/or the expression;
and the searching module is used for searching the bullet screen content corresponding to the user instruction in a preset bullet screen library.
The calculating device 9 of the substance content may be a desktop computer, a notebook, a palm computer, a cloud server, or other calculating devices. The computing device/means of the substance content may include, but is not limited to, a processor 90, a memory 91. Those skilled in the art will appreciate that fig. 9 is merely an example of a substance content calculating means 9 and does not constitute a limitation of the substance content calculating means 9 and may comprise more or less components than those shown, or some components may be combined, or different components, for example the substance content calculating means may further comprise input and output devices, network access devices, buses, etc.
The Processor 90 may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic, discrete hardware components, etc. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory 91 may be an internal storage unit of the calculating means of the substance content, such as a hard disk or a memory of the calculating means 9 of the substance content. The memory 91 may also be an external storage device of the substance content calculating means/device 9, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card) or the like provided on the substance content calculating means/device 9. Further, the memory 91 may also comprise both an internal memory unit and an external memory device of the substance content calculation means/arrangement 9. The memory 91 is used for storing the computer program and other programs and data required by the calculating means/means of the substance content. The memory 91 may also be used to temporarily store data that has been output or is to be output. It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-mentioned division of the functional units and modules is illustrated, and in practical applications, the above-mentioned function distribution may be performed by different functional units and modules according to needs, that is, the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-mentioned functions. Each functional unit and module in the embodiments may be integrated in one processing unit, or each unit may exist alone physically, or two or more units are integrated in one unit, and the integrated unit may be implemented in a form of hardware, or in a form of software functional unit. In addition, specific names of the functional units and modules are only for convenience of distinguishing from each other, and are not used for limiting the protection scope of the present application. The specific working processes of the units and modules in the system may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In the above embodiments, the description of each embodiment has its own emphasis, and reference may be made to the related description of other embodiments for parts that are not described or recited in any embodiment.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the technical solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
In the embodiments provided in the present invention, it should be understood that the disclosed apparatus/device and method may be implemented in other ways. For example, the above-described apparatus/device embodiments are merely illustrative, and for example, the division of the modules or units is only one logical division, and there may be other divisions when actually implemented, for example, a plurality of units or components may be combined or may be integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one position, or may be distributed on multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit may be implemented in the form of hardware, or may also be implemented in the form of a software functional unit.
The integrated module/unit, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, all or part of the flow of the method according to the embodiments of the present invention may also be implemented by a computer program, which may be stored in a computer-readable storage medium, and when the computer program is executed by a processor, the steps of the method embodiments may be implemented. . Wherein the computer program comprises computer program code, which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, usb disk, removable hard disk, magnetic disk, optical disk, computer Memory, Read-Only Memory (ROM), Random Access Memory (RAM), electrical carrier wave signals, telecommunications signals, software distribution medium, and the like. It should be noted that the computer readable medium may contain content that is subject to appropriate increase or decrease as required by legislation and patent practice in jurisdictions, for example, in some jurisdictions, computer readable media does not include electrical carrier signals and telecommunications signals as is required by legislation and patent practice.
The above-mentioned embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not substantially depart from the spirit and scope of the embodiments of the present invention, and are intended to be included within the scope of the present invention.

Claims (7)

1. A method of calculating a substance content, comprising:
respectively carrying out reaction tests on a plurality of standard substances with known target substance contents, and determining standard signal values representing the reaction process of the standard substances corresponding to a plurality of time values;
respectively fitting a standard regression equation corresponding to each standard product according to the corresponding relation between the time value and the standard signal value;
inputting the two time values as independent variables into a standard regression equation corresponding to each standard product, taking a dependent variable calculated by the standard regression equation as a standard signal value corresponding to the time value, and calculating a difference value of the standard signal values corresponding to the two time values as a signal difference value of each standard product;
Establishing a corresponding relation between the signal difference value and the content according to the content of the target substance in each standard product and the signal difference value of the standard product;
continuously detecting signal values corresponding to a plurality of moment values at equal intervals within a preset time period in the reaction process of a reaction solution with unknown content of a target substance, wherein the signal values represent the reaction process;
fitting the corresponding relation between the time value and the signal value by a least square method to generate a first equation;
determining an abnormal time value through the first equation;
fitting a regression equation according to the corresponding relation between the time values except the abnormal time value and the signal value;
inputting two preset time values as independent variables into the regression equation, taking a dependent variable calculated by the regression equation as a signal theoretical value corresponding to the time value, and calculating a difference value of the signal theoretical values corresponding to the two preset time values as a target signal difference value; the two preset time values are the same as the two time values of the standard regression equation corresponding to each standard product input as independent variables;
determining the content corresponding to the target signal difference value according to the corresponding relation between the signal difference value and the content, and taking the content as the content of the target substance;
And in the two time values as the independent variables, one time value is the time value when the signal value is detected for the first time in the preset time period, and the other time value is the time value when the signal value is detected for the last time in the preset time period.
2. The method of calculating a substance content according to claim 1, wherein determining an abnormal time value by the first equation comprises:
inputting the time value as an independent variable into the first equation, and taking a dependent variable calculated by the first equation as a signal evaluation value corresponding to the time value;
calculating a difference value between the signal evaluation value corresponding to the time value and the signal value, and taking the difference value as a difference value corresponding to the time value;
and if the difference value corresponding to the time value is greater than a preset difference threshold value, determining the time value as an abnormal time value.
3. The method of calculating a substance content according to claim 1, wherein fitting a regression equation according to the correspondence between the time value and the signal value further comprises:
normalizing the signal value to generate a signal mapping value;
acquiring a preset regression model, and establishing a target function corresponding to the regression model;
And solving parameters in the objective function, and calculating parameters of the regression model based on the parameters in the objective function so as to fit the regression equation.
4. The method of claim 3, wherein solving for the parameters in the objective function comprises:
and constructing an equation in a dual form of the objective function, and solving the equation in the dual form of the objective function to obtain parameters in the objective function.
5. A device for calculating a substance content, comprising:
the measuring module is used for respectively carrying out reaction tests on a plurality of standard substances with known target substance contents and measuring standard signal values representing the reaction process of the standard substances corresponding to a plurality of time values;
the standard fitting module is used for respectively fitting a standard regression equation corresponding to each standard product according to the corresponding relation between the time value and the standard signal value;
the difference value calculation module is used for inputting the two time values as independent variables into a standard regression equation corresponding to each standard product, taking a dependent variable calculated by the standard regression equation as a standard signal value corresponding to the time value, and calculating a difference value of the standard signal values corresponding to the two time values as a signal difference value of each standard product;
The calibration module is used for establishing a corresponding relation between the signal difference value and the content according to the content of the target substance in each standard product and the signal difference value of the standard product;
the detection module is used for continuously detecting signal values corresponding to a plurality of moment values at equal intervals within a preset time period in the reaction process of the reaction liquid with unknown content of the target substance, wherein the signal values represent the reaction process;
the fitting module is used for fitting the corresponding relation between the time value and the signal value through a least square method to generate a first equation, determining an abnormal time value through the first equation, and fitting a regression equation according to the corresponding relation between the time values except the abnormal time value and the signal value;
the calculation module is used for respectively inputting two preset time values as independent variables into the regression equation, taking a dependent variable calculated by the regression equation as a signal theoretical value corresponding to the time value, and calculating a difference value of the signal theoretical values corresponding to the two preset time values as a target signal difference value; the two preset time values are the same as the two time values of the standard regression equation corresponding to each standard product input as independent variables;
The determining module is used for determining the content corresponding to the target signal difference value according to the corresponding relation between the signal difference value and the content, and taking the content as the content of the target substance;
and in the two time values as the independent variables, one time value is the time value when the signal value is detected for the first time in the preset time period, and the other time value is the time value when the signal value is detected for the last time in the preset time period.
6. A device for calculating a substance content, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of the method according to any one of claims 1 to 4 when executing the computer program.
7. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of a method according to any one of claims 1 to 4.
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