CN114444635B - Method and system for predicting grain water content and temperature based on RFID (radio frequency identification) tag - Google Patents
Method and system for predicting grain water content and temperature based on RFID (radio frequency identification) tag Download PDFInfo
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Abstract
The application discloses a method and a system for predicting grain water content and temperature based on RFID labels, which relate to the technical field of non-contact measurement, and specifically comprise the following steps: acquiring data: obtaining perception data; calculating the tag impedance: processing the perceived data by using a multi-classification SVM method and a Fresnel reflection coefficient to obtain tag impedance; predicting the water content and temperature of the grain: according to the correlation between the impedance of the tag and the temperature and humidity of the grain, predicting the water content of the grain by using a linear regression method or a machine learning method; according to the application, the tag impedance is corrected by the multi-classification SVM method and the Fresnel reflection coefficient, so that the measured tag impedance can obtain stable measured values under different rotation angles and different distances, and the accuracy of the prediction results of the temperature and the humidity of grains is ensured.
Description
Technical Field
The application relates to the technical field of non-contact measurement, in particular to a method and a system for predicting grain water content and temperature based on RFID (radio frequency identification) tags.
Background
Grain storage is an effective way to meet future grain demands, prevent warfare, famine, or other emergencies. Therefore, food reserves are of great importance. In particular, grain storage safety becomes more and more important, and key factors (i.e., temperature and humidity) thereof have a great influence on grain storage safety. However, how to accurately and effectively measure and monitor these two factors is a challenging research problem between consumers and producers and at different stages of the grain circulation chain.
Existing wheat moisture measurement techniques can be divided into a drying method, a capacitance method, a resistance method, a microwave method and a neutron meter method. The temperature and humidity of the wheat stacks are generally measured by adopting a multi-line serial sensor method, and once the measuring nodes are damaged, the measuring nodes are not easy to replace. Thus, conventional sensor-based measurement methods have failed to meet the current social development needs. Currently, wireless awareness is attracting a great deal of attention in internet of things (IOT) applications. In particular, several wireless technologies are used for non-contact sensing applications, including tracking, health monitoring, and positioning. In previous studies, wi-Fi signals were used for non-contact wheat moisture and mold detection. However, wi-Fi signals are susceptible to environmental changes (e.g., walking by humans), which greatly reduces the robustness of the wheat moisture and mold detection system.
Recently, RFID tags have been used in temperature measurement schemes. For example, a standard-compliant discharge cycle measurement scheme is proposed using a volatile memory of the tag, and a mapping model between discharge cycle and temperature is built to improve robustness. However, the accuracy of the system depends on the length of the tag circuit discharge duration, while its identification accuracy is affected by distance. Furthermore, the discharge duration is not linear with temperature. A passive RFID temperature sensor using a bi-metallic coil as a temperature sensing unit has therefore been proposed. In addition, a system has been constructed that uses a pair of tags to counteract other environmental effects. However, this method calculates the tag impedance using a number of hypothetical parameters, ignoring the effect of frequency on impedance. Furthermore, the temperature obtained by using the phase difference is susceptible to the surrounding environment.
Although most of the RFID-based sensing techniques described above utilize antenna gain or phase difference as a feature to sense location, material characteristics, health monitoring, and temperature. However, most of them are still affected by the distance and angle of the RFID system; it is therefore a great need for those skilled in the art to develop a measurement method that is independent of the distance and angle of the RFID system.
Disclosure of Invention
In view of the above, the present application provides a method and system for predicting the moisture content and temperature of food based on RFID tags, which overcomes the above-mentioned drawbacks.
In order to achieve the above object, the present application provides the following technical solutions:
the method for predicting the grain water content and the temperature based on the RFID tag comprises the following specific steps:
acquiring data: obtaining perception data;
calculating the tag impedance: processing the perceived data by using a multi-classification SVM method and a Fresnel reflection coefficient to obtain tag impedance;
predicting the water content and temperature of the grain: and predicting the water content of the grain by using a linear regression method or a machine learning method according to the correlation between the impedance of the tag and the temperature and the humidity of the grain.
Optionally, the sensing data includes an S parameter and a resonant frequency.
Optionally, the step of correcting the tag impedance by using the multi-classification SVM method includes:
simultaneously constructing a training data set and a test data set;
selecting kernel functions and parameters of the multi-classification support vector machine;
training the SVM model through samples in the training data set;
the trained SVM model is used for impedance classification with random angles.
Optionally, the kernel function is a gaussian radial basis function.
Optionally, based on fresnel reflection coefficients, the expression of the S parameter is:
wherein, Γ 12 For the Fresnel reflection coefficient of the first medium and the second medium surface, i.e. the Fresnel reflection coefficient of the label, Z c Representing the impedance of the tag chip, Z d Representing the input impedance of the tag;representing Z d Is a conjugate of (c).
Wherein, the expression of the reflection coefficient S11 of the first port is:
wherein d represents the thickness of the second medium; gamma represents a propagation constant; e (E) 1r And E is 1i Respectively representing the reflected wave and the incident wave at the junction of the first medium and the second medium, τ 1 、τ 2 Respectively representing transmission coefficients of electromagnetic waves in a first medium and a second medium; Γ -shaped structure 1 、Γ 2 、Γ 3 The Fresnel reflection coefficients of the first medium, the second medium and the third medium are respectively represented;
let τ=τ 1 τ 2 ，C＝e -2γd Then the formula (3) is simplified as:
optionally, the step of correcting the tag impedance by using the fresnel reflection coefficient specifically includes:
step 21, when Γ 1 Fresnel reflection coefficient for air interface; τ 1 The transmission coefficient from the air interface to the grain interface; Γ -shaped structure 2 Fresnel reflection coefficient is used for grain interface; τ 2 Is the grain boundaryA transmission coefficient of the face-to-air interface; epsilon air Is the dielectric constant of air; epsilon wheat The dielectric constant of the grain is obtained according to the Fresnel reflection coefficient and the theory of a magnetic wave transmission line:
according to formulas (5), (6) and (7), we get:
step 22, after the metal plate is placed in the target box, i.e. Γ 3 -1; s after placing the metal plate is obtained by the formula (3) and the formula (4) 11 Can be expressed as:
step 23, removing the metal plate; according to definition, Γ is available 1 ＝-Γ 3 According to formula (3), there is no metal plate S 11 Can be expressed as:
step 24, according to expressions (8), (9) and (10), a ternary equation set is obtained:
step 25, solving the formula (11) to obtain a reflection coefficient Γ 1 Substituting formula (2) obtains a tag impedance value independent of distance.
A system for identifying moisture content and temperature of food based on RFID tags, comprising: the system comprises a data sensing module, a data preprocessing module, a multi-classification support vector machine module and a temperature and humidity prediction module; wherein,,
the data sensing module is used for reading the S parameter of the measurement target and the impedance of the tag;
the data preprocessing module is used for obtaining a tag impedance value irrelevant to the distance;
the multi-classification support vector machine module is used for obtaining the impedance of the tag antenna at an irrelevant angle;
and the temperature and humidity prediction module predicts the temperature and humidity of the grain by linear regression and machine learning respectively.
Optionally, the sensing module includes an RFID tag, the RFID tag is an RFID tag with a circuit chip removed, and the RFID tag is connected with the multi-classification support vector machine module.
Compared with the prior art, the method and the system for predicting the grain water content and the temperature based on the RFID tag are disclosed, and the tag impedance is corrected through a multi-classification SVM method and a Fresnel reflection coefficient, so that the measured tag impedance can obtain stable measured values under different rotation angles and different distances, and the accuracy of a grain temperature and humidity prediction result is ensured.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present application, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a block diagram of a prediction system according to the present application;
FIG. 2 is a schematic diagram showing the variation of the impedance of the tag according to the present application at different distances and different angles;
FIG. 3 is a graph showing the relationship between the moisture content of the wheat and the tag impedance (real part) according to the present application;
FIG. 4 is a graph showing the relationship between the temperature of the wheat and the impedance of the label (real part);
FIG. 5 is a graph showing a temperature-fitted wheat graph of different moisture contents according to the present application;
FIG. 6 is a schematic flow chart of the method of the present application.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
The embodiment of the application discloses a method and a system for predicting grain water content and temperature based on an RFID tag, wherein, wheat is taken as an example, VNA (vector network analyzer) equipment and an RFID antenna are used for acquiring a reflection signal of the tag; in the preprocessing module, a distance irrelevant algorithm and a multi-angle method based on Fresnel reflection coefficients are designed, so that the tag impedance irrelevant to the distance and the angle is obtained. For the temperature and humidity estimation module, linear regression and machine learning are used to predict the temperature and humidity of the wheat, respectively.
Example 1
The utility model provides a grain water content and temperature's prediction system based on RFID label, as shown in fig. 1, includes data perception module, data preprocessing module, multi-classification support vector machine module, temperature and humidity prediction module, wherein:
the data sensing module is used for reading the S parameter and other information of the measurement target;
the data preprocessing module is used for obtaining a tag impedance value irrelevant to the distance;
the multi-classification support vector machine module is used for obtaining the impedance of the tag antenna at an irrelevant angle;
the temperature and humidity prediction module predicts the temperature and humidity of the wheat using linear regression and machine learning, respectively.
The steps of the method for predicting the moisture content and the temperature of the grain based on the RFID tag are shown in fig. 6, and specifically comprise the following steps:
step 1, acquiring data
Placing a target with wheat in a sensing area, and emitting electromagnetic waves to the surrounding by an RFID antenna in the sensing area; if the tag gets enough energy, it will reflect the signal back to the antenna, and the system can then read the S parameter and other information through the VNA device; wherein the other information includes the resonant frequency of the tag when in operation; setting the frequency scanning range of the VNA to 860MHz to 960MHz, and sending the perceived data to a PC for preprocessing.
The S parameter is collectively referred to as the Scatter parameter. The S parameter describes the frequency domain characteristics of the transmission channel, and when the serial link SI analysis is performed, it is an important link to obtain the accurate S parameter of the channel, through which almost all the characteristics of the transmission channel can be seen.
Step 2, calculating the impedance of the tag
Step 21, in order to make the system face practical application and realize any effective accurate identification of moisture and temperature of wheat, the embodiment provides a distance irrelevant impedance algorithm based on Fresnel reflection coefficients and electromagnetic wave transmission line theory.
Fresnel reflection coefficient: the S-parameter of the system can be described as, according to the definition of the Fresnel reflection coefficient
Wherein, Γ 12 Representing the Fresnel reflection coefficients of the surfaces of media 1 and 2, i.e. the Fresnel reflection coefficients of the labels, Z c Representing the impedance of the tag chip, Z d Representing the input impedance of a tag。
The reflection coefficient S11 of port 1 is defined by:
wherein d represents the thickness of the wheat (medium 2), in meters, gamma represents the propagation constant, typically complex, E 1r And E is 1i Respectively representing the reflected wave and the incident wave at the junction of the medium 1 and the medium 2, τ 1 、τ 2 Representing the transmission coefficients of electromagnetic waves in medium 1 and medium 2, respectively; Γ -shaped structure 1 、Γ 2 、Γ 3 Respectively representing the fresnel reflection coefficient of the medium.
Let τ=τ 1 τ 2 ，C＝e -2γd The method comprises the steps of carrying out a first treatment on the surface of the Then formula (3) reduces to:
wherein, Γ 1 Representing the fresnel reflection coefficient at the interface, may be used to obtain the input impedance of the tag. As can be derived from equation (4), the reflection coefficient Γ of the tag is independent of the antenna-to-tag distance, and is only related to the thickness of the wheat sample. In this example, the thickness of the cartridge (i.e., 18 cm) is known.
Therefore, the specific steps of the impedance algorithm of the irrelevant distance in this embodiment are:
step 211, assuming Fresnel reflection coefficient and transmission coefficient of electromagnetic waves incident on the air interface air → wheat and wheat → air Γ respectively 1 、τ 1 And Γ 2 、τ 2 . If epsilon air And epsilon wheat Representing the dielectric constants of air and wheat, and obtaining according to the theory of electromagnetic wave transmission lines in the medium
Also for the transmission coefficient τ 2 Can obtain
For equations (5), (6) and (7), the following relationship can be obtained by the following equation:
Γ 1 2 ＝τ 1 τ 2 +1 (8)；
according to Γ 1 And Γ 2 Definition of Γ 1 Representing the reflection coefficient from air to wheat, Γ 2 Representing the reflection coefficient from wheat to air, therefore Γ 1 ＝-Γ 2 。
Step 212, placing a metal plate behind the target box; when electromagnetic wave is incident on metal plate, total reflection occurs, i.e. Γ 3 = -1. From the formulas (3) and (4), S after the metal plate is placed 11 Can be expressed as:
step 213, removing the metal plate. According to definition Γ 1 ＝-Γ 3 According to formula (2), there is no metal plate S 11 Can be expressed as:
step 214, obtaining the following ternary equation set according to the expressions (8), (9) and (10)
Wherein S parameter S' 11 And S' 11 Can be obtained from VNA, and the reflection coefficient Γ can be obtained by solving the formula (11) 1 The tag impedance value independent of distance is then obtained by equation (2).
Wherein, also include the verification to label sensibility:
first, the circuit chip of the RFID tag is removed, and two ports of the tag antenna are connected to the VNA device, and S parameters of the VNA device are observed to obtain the impedance of the tag antenna.
In general, input impedance refers to the equivalent impedance of the input of a circuit. The current I can be observed by adding a voltage source to the input port. The derivation of the tag antenna input impedance is based on the S parameter, which is defined as follows:
wherein S is 11 And S is 21 Representing the reflection coefficient of port 1 and the transmission coefficient from port 1 to port 2, respectively, S 11 And S is 21 Can be read from a vector network analyzer, Z 0 Is the characteristic impedance of the transmission line, in this embodiment 50 (ohms). Tag antenna impedance Z d0 Can be obtained from equation (1).
And verifying the sensitivity degree of the tag antenna to the temperature and humidity of the wheat through the relevance of the impedance of the tag antenna and the temperature and humidity of the wheat.
Step 22, tag impedance for extraneous angles
For wheat moisture and temperature sensing systems, it is not practical to require that the target to be measured be always in the same position or at the same angle. In order to make the system more practical, according to a multi-angle method, the influence caused by placing the object to be measured at different angles is reduced.
The solution is achieved in two steps:
1) Circularly polarized antenna: the antenna polarization may describe the spatial direction in which the antenna radiates electromagnetic wave vectors. It regards the spatial direction of the electric field vector as the polarization direction of the electromagnetic wave radiated by the antenna. Another characteristic of an antenna is the angle of direction, which determines the direction in which electromagnetic waves scatter. Thus, antenna polarization with a large directional angle can well reduce the directional sensitivity of the tag. The circularly polarized antenna deployed by the system has a 65-degree direction, so that the influence caused by multiple angles is reduced.
2) Multi-class support vector machine: the idea of the tag sensing temperature and humidity is to map the tag impedance to the wheat moisture and temperature. Therefore, it is critical to obtain a stable tag impedance value. However, in reality the accuracy of the impedance value is affected by the placement angle of the tag. Thus, by a multi-classification SVM method, stable impedance is obtained as follows:
step 221, measuring tag impedance values from-90 DEG to +90 DEG (recording impedance values once every 5 DEG) to construct a data set, and normalizing the data to be in the range of [0,1 ];
step 222, building training and testing data sets, building at the same time, and randomly extracting; taking the impedance value corresponding to the tag at 0 DEG as a training target;
step 223, selecting kernel functions and parameters of the multi-class support vector machine. In the present embodiment, a gaussian Radial Basis Function (RBF) is used as a kernel function;
step 224, training the SVM model using the wheat samples in the training dataset, wherein the libvm toolbox is used for implementing multi-angle impedance classification;
the training models in step 225, step 224 may be used for classification of new impedances with random angles.
Step 3, temperature and humidity prediction is carried out
Measuring the change condition of the impedance value of the electronic tag of the sample in the temperature change process of the wheat and fitting by using a linear regression mode to obtain a fitting curve; the relation between the real part and the imaginary part of the impedance of the tag and the temperature and humidity can be obtained according to the fitting curve; the temperature and humidity of the wheat are predicted according to the method.
Example 2
The apparatus employed in this embodiment: one sample box (31.5 cm x 18cm in size), one passive RFID tag (Alien 9640 of Higgs 3 chip), one RFID reading antenna (Laird 2S 9028 PCR), one vector network analyzer (tex TTR506A, power 10 dB), one tablet computer and one metal plate (copper, 1 mm). The label is attached to a wheat sample box, and the sample box is located in the sensing area. The reading antenna is connected to a VNA device that can send and receive electromagnetic waves. The measurement signal may be displayed on a tablet computer. In addition, a total reflection experiment was performed using the metal plate.
Measurements of the different samples were performed in a chamber at a temperature of 20 ℃. The tagged wheat box was rotated from-90 ° to +90°, then tag impedance values were recorded every 5 ° and the sweep frequency range was set to 860MHz to 960MHz. Verification of the "distance independent" algorithm was performed over a range of 100cm, each time 2cm of movement, and the value of the tag impedance was recorded, with a distance in the range of 3cm to 100cm.
From the above values, fig. 2 can be obtained, in fig. 2 it can be seen that the tag impedance remains unchanged over different distances and remains around 86 ohms. Only when the distance exceeds 80cm will it fluctuate. This means that when the distance is more than 80cm, the system becomes unstable. Fig. 2 also shows the variation of the tag impedance at different rotation angles. It can be seen that as the rotation angle increases, there are more crossover points for the impedance values for different moisture contents. Nevertheless, the system is still capable of achieving 98.6% accuracy over a distance of 80cm, with rotation angles in the range-30 ° to +30°.
When the measured samples were wheat with moisture contents of 7.7%, 9.5%, 10.6%, 14.0%, 16.0%, 17.2%, respectively, the room temperature was 20 ℃. The test gave a resonant frequency of 942.5MHz. The tag impedance versus moisture content curve is shown in fig. 3. It can be seen that the tag impedance (real part) increases with increasing moisture content.
Freezing wheat with water content of 14.0% in refrigerator to-10deg.C, taking out, placing in sensing region, and observing tag impedance change at room temperature along with temperature rise, as shown in figure 4, wherein R has good linear relationship with tag impedance 2 ＝0.9968。
Table 1 shows the recognition accuracy of six kinds of wheat moisture content rotated by different angles based on the multi-classification support vector machine method, and it can be seen that the rotation angleWhen the angle is 0 DEG, the recognition accuracy reaches 100 percent. Table 2 shows R of the best fit curve 2 And a relative error rate, wherein M represents different moisture content, R 2 Indicating the proximity between the fitted curve and the test data. Fig. 5 shows 6 wheat with different moisture contents, the temperature of which is matched with the impedance of the label, and it is not difficult to find that the slopes of the temperature-impedance curves with different moisture contents are similar, and the temperature increases with the increase of the impedance.
Table 1: accuracy of identifying moisture content of wheat by system under different angles
Table 2: at different moisture contents, the temperature and impedance of the wheat are fitted with a curve R 2 Error rate
From fig. 5 and table 2, it can be concluded that the tag impedance can well represent the change in temperature (i.e., the temperature and impedance (real part) can be well fitted by a linear function), so that the temperature and humidity of the grain can be predicted by using linear regression and machine learning, respectively, and the accuracy of the prediction result is ensured.
In the embodiment, firstly, the temperature and humidity sensing system is designed, and comprises a data basic data sensing, a distance irrelevant label impedance algorithm and a multi-classification SVM algorithm, so that the influence of sensing distance and sensing angle on a measurement result is respectively solved. Measurement results show that the system can obtain higher humidity and temperature sensing precision under different rotation angles and different distances.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (4)
1. The method for predicting the moisture content and the temperature of the grain based on the RFID tag is characterized by comprising the following specific steps:
acquiring data: obtaining perception data;
calculating the tag impedance: processing the perceived data by using a multi-classification SVM method and a Fresnel reflection coefficient to obtain tag impedance;
predicting the water content and temperature of the grain: according to the correlation between the impedance of the tag and the temperature and humidity of the grain, predicting the water content of the grain by using a linear regression method or a machine learning method;
wherein the sensing data comprises an S parameter and a resonant frequency;
based on the Fresnel reflection coefficient, the expression of the S parameter is:
wherein, Γ 12 For the Fresnel reflection coefficient of the first medium and the second medium surface, i.e. the Fresnel reflection coefficient of the label, Z c Representing the impedance of the tag chip, Z d Representing the input impedance of the tag;representing Z d Conjugation of (2);
wherein, the expression of the reflection coefficient S11 of the first port is:
wherein d represents the thickness of the second medium; gamma represents a propagation constant; e (E) 1r And E is 1i Respectively representing the reflected wave and the incident wave at the junction of the first medium and the second medium, τ 1 、τ 2 Respectively representing transmission coefficients of electromagnetic waves in a first medium and a second medium; Γ -shaped structure 1 、Γ 2 、Γ 3 The Fresnel reflection coefficients of the first medium, the second medium and the third medium are respectively represented;
let τ=τ 1 τ 2 ，C＝e -2γd The method comprises the steps of carrying out a first treatment on the surface of the Then formula (3) reduces to:
the step of correcting the tag impedance by using the fresnel reflection coefficient specifically includes:
step 21, when Γ 1 Fresnel reflection coefficient for air interface; τ 1 The transmission coefficient from the air interface to the grain interface; Γ -shaped structure 2 Fresnel reflection coefficient is used for grain interface; τ 2 The transmission coefficient from the grain interface to the air interface; epsilon air Is the dielectric constant of air; epsilon wheat The dielectric constant of the grain is obtained according to the Fresnel reflection coefficient and the theory of a magnetic wave transmission line:
according to formulas (5), (6) and (7), we get:
step 22, after the metal plate is placed in the target box, i.e. Γ 3 -1; s after placing the metal plate is obtained by the formula (3) and the formula (4) 11 Expressed as:
step 23, removing the metal plate; according to definition Γ 1 ＝-Γ 3 According to formula (3), there is no metal plate S 11 Expressed as:
step 24, according to expressions (8), (9) and (10), a ternary equation set is obtained:
step 25, solving the formula (11) to obtain a reflection coefficient Γ 1 Substituting the value into formula (2) to obtain a tag impedance value irrelevant to the distance;
the obtained tag impedance is the tag impedance of an irrelevant angle, and comprises two steps of: circularly polarized antenna and correcting the impedance of the tag based on a multi-classification support vector machine;
the method for correcting the tag impedance by using the multi-classification SVM method comprises the following steps:
simultaneously constructing a training data set and a test data set;
selecting kernel functions and parameters of the multi-classification support vector machine;
training the SVM model through samples in the training data set;
the trained SVM model is used for impedance classification with random angles.
2. The method for predicting grain moisture content and temperature based on an RFID tag of claim 1, wherein the kernel function is a gaussian radial basis function.
3. An RFID tag-based grain moisture content and temperature prediction system employing the method of claim 1, comprising: the system comprises a data sensing module, a data preprocessing module, a multi-classification support vector machine module and a temperature and humidity prediction module; wherein,,
the data sensing module is used for reading the S parameter of the measurement target;
the data preprocessing module is used for obtaining a tag impedance value irrelevant to the distance;
the multi-classification support vector machine module is used for obtaining the impedance of the tag antenna at an irrelevant angle;
and the temperature and humidity prediction module predicts the temperature and humidity of the grain by linear regression and machine learning respectively.
4. A system for predicting moisture content and temperature of a food item based on an RFID tag as claimed in claim 3, wherein the sensing module comprises an RFID antenna and a vector network analyzer, the RFID antenna and the vector network analyzer being configured to obtain the reflected signal of the RFID tag.
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