CN104296846A - Granary and stored grain weight detection system based on optimum bottom pressure intensity measurement point - Google Patents

Abstract

The invention relates to a granary and its storage grain weight detection system based on the optimal bottom pressure measurement point. According to the characteristics of the pressure distribution on the bottom surface of the granary and the change characteristics of the pressure measurement value, a granary storage grain quantity based on the optimal bottom pressure measurement point is proposed. Detection method, the core technology includes the consistency measurement model of the bottom pressure measurement point, the position detection method of the optimal bottom pressure measurement point, the granary weight detection model based on the optimal bottom pressure measurement point, system calibration and modeling methods and other technologies. The proposed method has high detection accuracy, requires few pressure sensors, only 2 to 3, and has strong versatility, which is suitable for the storage quantity detection of various granary structure types. The proposed detection method has great application value and provides a new technical means for ensuring the national food quantity security.

Description

Grain silo and its storage grain weight detection system based on the optimal bottom pressure measurement point

technical field

The invention relates to a granary and its stored grain weight detection system based on the optimum bottom surface pressure measurement point.

Background technique

Food security includes quantity security and quality security. The research and application of online grain quantity detection technology and system is an important guarantee technology for national grain quantity security. Carrying out research and application in this area is related to national food security, which is of great significance and will generate huge social and economic benefits.

Due to the important position of grain in national security, the online detection of grain pile quantity is required to be accurate, fast and reliable. At the same time, due to the huge amount of grain and the low price, it is required that the online detection equipment for the amount of grain piles is low in cost, simple and convenient. Therefore, the high precision of the detection and the low cost of the detection system are the key issues that must be solved in the development of the online detection system for the number of granaries.

The patent "Method for detecting the quantity of stored grain in grain depot based on pressure sensor" (patent authorization number: ZL201010240167.7), and the patent "Method for detecting the quantity of stored grain in shallow and round warehouses" (patent authorization number: ZL201210148522) both involve the amount of stored grain, namely Stored grain weight detection. Specifically, ZL201010240167.7 involves the calculation model and specific system calibration method of the grain storage quantity based on the average output value of the pressure sensor on the bottom surface and side of the granary. ZL201210148522 involves the compensation of the influence of side friction based on the square of the mean value of the output of the bottom pressure sensor, the weight prediction model of grain piles based on the mean value of the output of the bottom pressure sensor, the modeling of the prediction model based on the error ratio of grain weight, and new methods such as fast system calibration.

The above two methods have their own characteristics and advantages. However, in order to detect, the detection system itself requires a large number of sensors, and the cost of the detection system is relatively high. Granary construction and maintenance costs have also increased accordingly.

Contents of the invention

The purpose of the present invention is to provide a granary and its storage grain weight detection system based on the optimal bottom pressure measurement point, so as to solve the problems of large number of sensors and high cost required by the existing detection system.

To achieve the above object, the solution of the present invention includes:

A storage grain weight detection system based on the optimum bottom pressure measurement point, comprising at least two bottom surface pressure sensors, which are arranged at the optimum bottom surface pressure measurement point of the granary, and the optimum bottom surface pressure measurement point is a measurement point with high detection consistency.

The best bottom pressure measurement point is mainly located in the area with a certain distance from the side and the grain inlet.

The measurement point selection rule with high consistency is as follows: there are n _W kinds of stored grain weights W _i , i=1,...,n _w , and each stored grain weight is measured n _M times; for any given granary The bottom surface pressure measurement point s, the measured value of the measurement point s during the kth measurement of the grain weight W _i in the grain storage is Q _B (s,W _i ,k), k=1,...,n _M , defined

$<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 100</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}}{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

is the consistency measure of the bottom surface pressure measurement point s; for any measurement point s, the smaller the CM(s), the higher the measurement consistency, and vice versa.

A granary, provided with a storage grain weight detection system, the storage grain weight detection system includes at least two bottom surface pressure sensors, which are arranged at the optimal bottom surface pressure measurement point of the granary, and the optimal bottom surface pressure measurement point is a measurement point with high detection consistency .

The best bottom pressure measurement point is mainly located in the area with a certain distance from the side and the grain inlet.

The measurement point selection rule with high consistency is as follows: there are n _W kinds of stored grain weights W _i , i=1,...,n _w , and each stored grain weight is measured n _M times; for any given granary The bottom surface pressure measurement point s, the measured value of the measurement point s during the kth measurement of the grain weight W _i in the grain storage is Q _B (s,W _i ,k), k=1,...,n _M , defined

$<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 100</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}}{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

is the consistency measure of the bottom surface pressure measurement point s; for any measurement point s, the smaller the CM(s), the higher the measurement consistency, and vice versa.

The grain weight detection system for grain storage of the present invention requires few measurement points, only 2 to 3, and has high measurement accuracy, but has high requirements on the performance of the sensor, especially the repeatability error and the consistency of the performance of the sensor.

Furthermore, the present invention provides a highly consistent measurement point distribution law and experimental selection steps to guide practical operations.

Description of drawings

Figure 1 Arrangement of pressure sensors in flat warehouses;

Fig. 2 Arrangement of pressure sensors in shallow round silos;

Fig. 3 Sensor layout and grain feeding area for optimal measurement point detection;

Figure 4 The CM(s) value of the second row of measurement points in the flat warehouse;

Figure 5 CM(s) value of the second round of measuring points in the shallow round silo;

Figure 6 is a schematic diagram of the implementation steps of the detection method.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings.

The invention provides a granary and its stored grain weight detection system:

The detection system includes at least two bottom surface pressure sensors, which are arranged at the optimal bottom surface pressure measurement point of the granary, and the optimal bottom surface pressure measurement point is a measurement point with high detection consistency.

For a given granary and grain storage weight, how to select a limited number of bottom pressure measurement points so that the average value of the measured value has a high consistency in each grain intake is a sufficient and necessary condition to ensure the accuracy of weight detection, high consistency Then the detection accuracy must be high, and vice versa. According to the pressure distribution characteristics of the bottom surface of the granary, due to the inhomogeneity of grain composition and volume mass distribution in the grain heap, the consistency of the contact degree between the grain heap and the force surface of each pressure sensor, and the randomness of the side pressure, the pressure measurement of the granary bottom surface There are different degrees of randomness in the measurement values of the points, but the degree is obviously different. There are a large number of measurement points with small randomness, which shows that the measurement values of these measurement points have strong robustness.

For consistency, according to the above description, there can be many specific evaluation rules.

For example, for a given granary and stored grain type, it is assumed that there are n _W kinds of stored grain weights W _i , i=1,...,n _w , and each stored grain weight is measured n _M times. For any given pressure measurement point s on the bottom surface of the granary, the measured value of the measurement point s during the kth measurement of the grain weight W _i in the granary is Q _B (s,W _i ,k), k=1,... ,n _M , define

$<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 100</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; W</span>}}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}}{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

is the consistency measure of the bottom pressure measurement point s. It can be seen from formula (1) that CM(s) represents the average percentage discrete error of the measured value of the measuring point s. Obviously, for any measurement point s, the smaller the CM(s), the higher the measurement consistency, and vice versa. For a given granary, storage type and grain feeding method, if CM(s)<Th, Th is a given threshold parameter, and 0<Th, then the measurement point s is the best bottom pressure measurement point.

As another example, variance is used to evaluate consistency.

In the following, the selection principle of the optimal bottom pressure measurement point is introduced through the experimental data, and the consistency is evaluated by formula (1).

For the flat warehouse and shallow round warehouse shown in Figure 1 and Figure 2, the pressure sensors of the flat warehouse are arranged in 6 rows, as shown by the dots in the figure, 15 in each row, 90 in total, and the measurement point number of the first row is 1 #～15#, the measurement points in the second row are numbered 16#～30#, and the other rows are numbered by analogy. Shallow round silo pressure sensors are arranged in 3 circles, 20 in the first circle (number 1#～20#), 20 in the second circle (number 21#～40#), 15 in the third circle (number 41#～55# ), a total of 55.

The bungalow is 9m long, 4.2m wide, and has an area of 37.8m2, C _B /A _B ≈0.35. The diameter of the shallow round silo is 6m, the area is 28.26m2, and C _B /A _B ≈0.67. Both granaries are small granaries, and C _B /A _B is relatively large. A _B is the area of the bottom surface of the grain pile, and C _B is the perimeter of the bottom surface. The type of experimental grain is wheat, and a total of 4 experiments were carried out in the bungalow warehouse. In each experiment, the grain was divided into 6 times, and the grain was fed for about 1 meter each time and spread flat. A total of 3 experiments were carried out in the shallow round warehouse. The experimental conditions were the same as those of the first three times in the flat warehouse. In each experiment, the grain was divided into 8 times, and the grain was fed for about 1 meter each time and spread flat. According to the 4 experimental data of the bungalow warehouse, Th=8 is taken, and the set of stored grain weight is {35,60,90,120,150,168}, and the measured estimated value of each detection point is obtained by interpolation, and the bottom pressure measurement of the flat warehouse obtained is The consistency metrics of the points are shown in Table 1.

According to the three experimental data of the shallow round silo, Th=10, and the set of stored grain weights is {30, 50, 70, 90, 110, 130, 150, 170}, the calculation results of the consistency measure of the pressure measurement points on the bottom surface of the shallow round silo are shown in the table As shown in 2, the blackened ones are the measurement points with small CM(s), and the values of 1E32 indicate that the sensor is faulty. The measurement points circled in Fig. 1 and Fig. 2 are schematic diagrams of the position of the measurement points with a small CM(s) on the bottom surface, and the grain outlet in the figure is also the grain inlet. As can be seen:

(1) The pressure measurement values of each measurement point in different experiments have significant inconsistency and randomness, but the degree of inconsistency is obviously different, and there are a large number of measurement points with little inconsistency and randomness. For example, flat warehouses 17#, 22#, 24#, 52# and 67#, etc., shallow round warehouses 26#, 29#, 30#, 31#, 34#, 51# and 52#, etc.

(2) For flat warehouses, the measurement points with small CM(s) are mainly located in the second row, and for shallow round warehouses, the measurement points with small CM(s) are mainly located in the second circle. Therefore, the measurement points with small CM(s) are mainly located in the area with a certain distance from the side and the grain inlet. A certain distance from the side can reduce the influence of side friction, and a certain distance from the grain inlet can reduce the impact of grain intake. The measurement points with small CM(s) are mainly related to the side friction force and the feeding method. For the large granaries that are commonly used, the grain feeding method is generally unchanged, and there are measurement points with small MD(s) in stable positions.

The technical difficulty of granary weight detection lies in the randomness of the bottom and side pressure measurement values. The measured values of the bottom pressure measurement points all have different degrees of randomness. How to overcome this randomness has always been an urgent problem to be solved in the field of granary weight detection technology. The best bottom pressure measurement point is the measurement point with small randomness of the measurement value, which shows that the measurement value of these measurement points has strong robustness, and is affected by the inhomogeneity of grain composition and volume mass distribution in the grain heap, the relationship between the grain heap and each The consistency of the contact degree of the force surface of the pressure sensor and the randomness of the side pressure are less affected. The detection of the weight of the granary through the pressure detection of these points can provide a new way for the detection of the number of granaries.

Table 1 Calculation results of the consistency measure of the pressure measurement points on the bottom of the flat warehouse

Table 2 Calculation results of the consistency measure of the pressure measurement points on the bottom of the shallow round silo

The law of the best bottom pressure measurement point in different granaries is given above. According to this law, the best measurement point can be selected artificially, or the specific best measurement point can be obtained by experimental methods.

The specific experimental method is as follows:

The optimal position of the bottom pressure measurement point is related to the specific structure of the granary, the way of feeding grain, and also related to the consistency of the repeated measurement error of the pressure sensor used. Therefore, for a granary with a given granary structure and size, if the repeated measurement error consistency of the pressure sensor is high, the optimal bottom pressure measurement point position is only related to the grain feeding method. If the grain feeding methods are similar, and the structure and size of the granary are similar, the optimal bottom pressure measurement point positions are basically the same. If the repeated measurement error consistency of the pressure sensor is poor, it means that the sensor is not interchangeable, and the best measurement point position detection must be carried out for each granary.

Since the CM(s) is small, the measurement points are mainly located in the area with a certain distance from the side and the grain inlet. Therefore, according to this principle, the sensor layout and the position of the grain storage pile proposed in this paper are shown in Figure 3, where ab and bc are the candidate areas for the assumed sensor positions, and the actual detection should be based on the normal grain intake Reasonable selection based on the requirements of the method and testing requirements; the coloring area is the grain intake area to reduce the actual grain intake in the experiment and reduce the cost of the experiment.

Figure 4 shows the relationship between the consistency measure CM(s) of the 15 measuring points in the second row of the flat warehouse and the grain intake height, and Figure 5 shows the relationship between the consistency measure CM(s) and the feeding height of the 20 measuring points in the second row of the shallow round warehouse. Grain height relationship. It can be seen from the figure that the order of each point according to the value of CM(s) is related to the height of grain intake. When the feeding height is less than 3 meters, the order of each point changes greatly with the feeding height, and when the feeding height is greater than 4 meters, the order is basically fixed. Therefore, the best measurement point position detection experimental steps proposed in this paper are as follows:

(1) Initially select the location of the detection point and arrange the sensors. According to the principle of having a certain distance from the side and the grain inlet, and taking into account the requirements of the usual grain feeding method, it is convenient to feed in and out and avoid damage to the sensor, and the location of the detection point should be reasonably selected and the sensor should be arranged. In Figure 3, the distance d between the sensor and the side (d refers to the distance from the nearest side for the one-story warehouse) is 2-3m, and the distance between the sensors is about 1m (not less than 1m).

(2) The height of each grain intake is fixed, preferably about 0.9 meters, and the top is flattened to ensure that the width of the top surface of the grain pile above the sensor is not less than 1 meter, and the sensor values are collected.

(3) Repeat 3 to 4 times, calculate the CM(s) value of each point according to the formula (1), sort by the value, and the smaller CM(s) is the best bottom pressure measurement point.

After the detection value of the best measurement point is detected, it is brought into the stored grain weight detection model based on the bottom surface pressure for calculation to obtain the stored grain weight. It can be implemented according to the implementation mode shown in Figure 6, and the specific steps are implemented as follows:

(1) System configuration

Select a specific pressure sensor, and configure the corresponding data acquisition, data transmission and other systems.

(2) Position detection of the best bottom pressure measurement point

According to the principle of having a certain distance from the side and the grain inlet, and taking into account the requirements of the usual grain feeding method, it is convenient to feed in and out and avoid sensor damage, reasonably select the detection point and arrange the sensor. As shown in Figure 3, the sensor and grain feeding area for optimal measurement point detection are arranged. In the figure, the distance d between the sensor and the side is taken as 2-3m, and the distance between each sensor is taken as about 1m. Every time 0.9 meters of grain is fed, the top is flattened to ensure that the width of the top surface of the grain pile above the sensor is not less than 1 meter, and the values of each sensor are collected. Repeat 3 to 4 times, calculate the CM(s) value of each point according to the formula (1), sort by the value, and the smaller CM(s) is the best bottom pressure measurement point.

(3) Bottom surface pressure sensor installation

According to the detected optimal bottom pressure measurement points, select 2 to 5 optimal bottom pressure measurement points with small CM(s), and arrange the sensors.

(4) System calibration and modeling

Arrange the sensors according to the position of the best bottom pressure measurement point, and use sandbags to establish a calibrated grain intake area. The distance between the sandbags and the sensors is about 3 to 4 meters, and the height of the sandbag wall is 1.5 to 2 meters. Grain is fed step by step, and each batch of grain is flattened after 0.5 meters. Record the weight of the grain and the value of each pressure sensor, and calculate the weight of the entire granary at the corresponding height according to the ratio of the area of the calibrated grain area to the total area of the granary. In this way, 3 to 4 sets of experimental data can be obtained. Then load the grain in the normal way. After the completion, record the total weight of the grain and the value of the pressure sensor on the bottom of the granary, so that 4 to 5 sets of data can be obtained. Using the obtained 4-5 sets of data, the detection model is constructed from formula (2) to formula (5).

For multiple calibration experiments, use the data of each calibration experiment to establish the model shown in formula (2), and use the mean values of a ₀ , a ₁ , and a ₂ model coefficients to establish a detection model.

(5) Real warehouse weight inspection.

If the system has been calibrated, detect the output of the pressure sensor on the bottom surface and use the model shown in formula (2) to detect the quantity of grain stored in the grain storage.

Specifically, the granary weight detection model based on the optimal bottom pressure measurement point is shown in formula (2).

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; BOP</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; BOP</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

in, is the weight estimation of the granary based on the best bottom pressure measurement point; AB is the bottom area of the granary; is the average pressure measurement value of all the best bottom pressure measurement points, is the pressure measurement value of the i-th best bottom pressure measurement point, n _OP is the number of the best bottom pressure measurement points; a ₀ , a ₁ , a ₂ are model coefficients.

For the granary grain pile weight detection model shown in formula (2), it is assumed that n weight and pressure experiment sample points have been obtained Among them, W _i is the weight of food intake, is the mean value of the measured values of the corresponding optimal bottom surface pressure measurement points, then it can be deduced that the calculation formula of each coefficient in formula (2) is

a ₀ =(b ₀ (c ₂ c ₄ -c ₃₃ )+b ₁ (c ₂₃ -c ₁₄ )+b ₂ (c ₁₃ -c ₂₂ ))/Δ(3)

a ₁ =(b ₀ (c ₂₃ -c ₁₄ )+b ₁ (c ₀ c ₄ -c ₂₂ )+b ₂ (c ₁₂ -c ₀₃ ))/Δ(4)

a ₂ =(b ₀ (c ₁₃ -c22)+b ₁ (c ₁₂ -c ₀₃ )+b ₂ (c ₀₂ -c ₁₁ ))/Δ(5) where Δ=(c ₀₂ -c ₁₁ )c ₄ +2.c ₁₂ c ₃ -c ₂₂ c ₂ -c ₀ ^* c ₃₃ ; c ₁₁ =c ₁ c ₁ ; c ₂₂ =c ₂ c ₂ ; c ₃₃ =c ₃ c ₃ ; c ₃₃ =c ₃ c ₃ ; c ₃₃ = c ₃ c ₃ ; c ₀₂ = c ₀ c ₂ ; c ₀₃ = c ₀ c ₃ ; c ₁₂ = c ₁ c ₂ ; c ₁₃ = c ₁ c ₃ ; c ₁₄ = c ₁ c ₄ ; c ₂₃ = c ₂ c ₃ ;

${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; BOP</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; BOP</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; BOP</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ;</span>$

${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; BOP</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; BOP</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; .</span>}$

System calibration and detection model modeling are carried out in the following steps:

(1) Establish a calibrated grain intake area. Arrange the sensor according to the position of the selected optimal bottom pressure measurement point, and use sandbags to establish the calibration grain feeding area. The distance between the sandbag and the sensor is about 3 to 4 meters, so as to reduce the instability of the sandbag wall to the calibration grain feeding area. Influenced by the pressure distribution, the height of the sandbag wall is 1.5-2 meters, and the pressure sensors are evenly arranged.

(2) Calibration data acquisition. For the calibrated grain-feeding area, feed grain gradually, spread out after 0.5 meters of each batch of grain, record the weight of the grain and the value of each pressure sensor, and calculate the entire granary of the corresponding height according to the ratio of the area of the calibrated grain-feeding area to the total area of the granary Feed weight. In this way, 3 to 4 sets of experimental data can be obtained. Then load the grain in the normal way. After the completion, record the total weight of the grain and the value of the pressure sensor on the bottom of the granary, so that 4 to 5 sets of data can be obtained.

(3) Detection model modeling.

Since the grain heap weight detection model shown in formula (2) is relatively simple, less data is required for modeling, so the ideal detection effect can be obtained by directly using the obtained 4-5 sets of data.

For multiple calibration experiments, use the data of each calibration experiment to establish the model shown in formula (2), and use the mean values of a0, a ₁ and a ₂ model coefficients to establish the detection model.

Experimental data are given below to prove the practical effect of the present invention.

According to the average pressure measurement data of the 3 small CM(s) measurement points (17#, 22# and 24#) in the second row of the flat warehouse, using the data of two experiments (experiment 2 and experiment 3) to model, The prediction model established by formula (2) is shown in formula (6), and the calculation results of grain weight in each experiment are shown in Table 3 to Table 6.

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0.05945</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.08099</span>}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; BOP</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.0002528</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; BOP</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

According to the average pressure measurement data of two small CM(s) measurement points (21#, 29#) in the second circle of the shallow round silo, using the data of two experiments (experiment 2 and experiment 3) to model, the formula (2) The established prediction model is shown in formula (7), and the calculation results of the weight of stored grain in each experiment are shown in Table 7 to Table 9.

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; 16002</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.06602</span>}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; BOP</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.000592725</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; BOP</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

Table 3 Calculation result of stored grain weight in flat warehouse experiment 1 4 Calculation result of stored grain weight in flat warehouse experiment 2

Table 5 Calculation results of stored grain weight in flat warehouse experiment 1 Table 6 Calculation results of stored grain weight in flat warehouse experiment 2

Table 7 Calculation results of stored grain weight in shallow round silo experiment 1 Table 8 Calculation results of stored grain weight in shallow round silo experiment 2

Table 9 Calculation results of stored grain weight in shallow round silo experiment 3

It can be seen from the calculation results of the grain weight of the grain storage based on the average value of the measurement point of the best bottom surface pressure measurement point that the detection results of other detection points are relatively ideal except for the small weight of the stored grain. Therefore, this method of grain weight monitoring in grain storage requires few measuring points, only 2 to 3, and has high measurement accuracy, but has high requirements on the performance of the sensor, especially the repeatability error and the consistency of sensor performance.

For the flat warehouse shown in Figure 1, the detection results of the detection model constructed using the previous method and all 90 measurement point data are shown in Table 10 to Table 13. For the shallow round silo shown in Figure 2, the detection results of the detection model constructed using the previous method and all 55 measurement point data are shown in Table 14 to Table 16.

Table 10 Calculation result of stored grain weight in flat warehouse experiment 1 Table 11 Calculation result of stored grain weight in flat warehouse experiment 2

Table 12 Calculation result of stored grain weight in experiment 3 of flat warehouse Table 13 Calculation result of stored grain weight in experiment 4 of flat warehouse

Table 14 Calculation results of stored grain weight in shallow round silo experiment 1 Table 15 Calculation results of stored grain weight in shallow round silo experiment 2

Table 16 Calculation results of stored grain weight in shallow round silo experiment 3

It can be seen from the calculation results of the stored grain weight using the previous method that although there are many measurement points, when the stored grain weight is large, the prediction results of some points still exceed 3%. This shows that the method proposed in this patent has higher measurement accuracy and requires fewer bottom surface pressure sensors.

Select the best measurement point for measurement, instead of arranging more and denser sensors like the existing technology, so that the detection results can more comprehensively reflect more and more comprehensive environmental parameters. As everyone knows, although the continuous increase of sensors seems to be The amount of data is very rich, but due to the particularity of the granary, the process of grain feeding and grain storage has different effects on the measurement results at different locations. The rich data not only cannot improve the detection accuracy, but may be mixed with more random information to dilute the existing data. Valuable measurement data degrades measurement accuracy. Therefore, the present invention does the opposite, and the detection scheme not only greatly reduces the number of sensors, but also improves measurement accuracy.

A specific embodiment has been given above, but the present invention is not limited to the described embodiment. The basic idea of the present invention lies in the above-mentioned solution. For those of ordinary skill in the art, according to the teaching of the present invention, it does not need to spend creative labor to design various deformation models, formulas and parameters. Changes, modifications, substitutions and variations to the implementations without departing from the principle and spirit of the present invention still fall within the protection scope of the present invention.

Claims (6)

1. A stored grain weight detection system based on an optimal bottom pressure measurement point is characterized by comprising at least two bottom pressure sensors and the optimal bottom pressure measurement point arranged on a granary, wherein the optimal bottom pressure measurement point is a measurement point with high detection consistency.

2. The stored grain weight detection system based on the optimal floor pressure measurement point of claim 1, wherein the optimal floor pressure measurement point is mainly located in an area having a distance from the side surface and the grain inlet.

3. The stored grain weight detection system based on the optimal bottom pressure measurement point as claimed in claim 1, wherein the measurement point selection rule with high consistency is as follows: is provided with n_WWeight W of seed grain_i，i＝1,...,n_wMeasuring the weight of each stored grain by n_MSecondly; for any given pressure measurement point s on the bottom surface of the granary, the weight W of the stored grain in the granary_iThe measured value of the measurement point s at the k-th measurement of (1) is Q_B(s,W_i,k)，k＝1,...,n_MDefinition of

<math> <mrow> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>100</mn> <msub> <mi>n</mi> <mi>W</mi> </msub> </mfrac> <munder> <mi>&Sigma;</mi> <mi>i</mi> </munder> <mrow> <mo>(</mo> <mfrac> <munder> <mrow> <mi>max</mi> <mrow> <mo>(</mo> <msub> <mi>Q</mi> <mi>B</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <munder> <mi>min</mi> <mi>k</mi> </munder> <mrow> <mo>(</mo> <msub> <mi>Q</mi> <mi>B</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mi>k</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> <mi>k</mi> </munder> <mfrac> <mn>1</mn> <mrow> <msub> <mi>n</mi> <mi>k</mi> </msub> <munder> <mi>&Sigma;</mi> <mi>k</mi> </munder> <msub> <mi>Q</mi> <mi>B</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>

A consistency measure for the bottom pressure measurement point s; for any measurement point s, the smaller the CM(s), the higher the measurement consistency, and vice versa.

4. A granary is provided with a stored grain weight detection system and is characterized in that the stored grain weight detection system comprises at least two bottom surface pressure sensors and is arranged at an optimal bottom surface pressure measurement point of the granary, and the optimal bottom surface pressure measurement point is a measurement point with high detection consistency.

5. The grain bin according to claim 4, wherein the optimal floor pressure measurement point is located primarily in a region spaced from the side and the grain inlet.

6. The grain bin according to claim 5, wherein the measurement point selection rule with high consistency is as follows: is provided with n_WWeight W of seed grain_i，i＝1,...,n_wMeasuring the weight of each stored grain by n_MSecondly; for any given feedFixed pressure measuring point s on the bottom surface of the granary and weight W of stored grains in the granary_iThe measured value of the measurement point s at the k-th measurement of (1) is Q_B(s,W_i,k)，k＝1,...,n_MDefinition of

<math> <mrow> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>100</mn> <msub> <mi>n</mi> <mi>W</mi> </msub> </mfrac> <munder> <mi>&Sigma;</mi> <mi>i</mi> </munder> <mrow> <mo>(</mo> <mfrac> <munder> <mrow> <mi>max</mi> <mrow> <mo>(</mo> <msub> <mi>Q</mi> <mi>B</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <munder> <mi>min</mi> <mi>k</mi> </munder> <mrow> <mo>(</mo> <msub> <mi>Q</mi> <mi>B</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mi>k</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> <mi>k</mi> </munder> <mfrac> <mn>1</mn> <mrow> <msub> <mi>n</mi> <mi>k</mi> </msub> <munder> <mi>&Sigma;</mi> <mi>k</mi> </munder> <msub> <mi>Q</mi> <mi>B</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>

A consistency measure for the bottom pressure measurement point s; for any measurement point s, the smaller the CM(s), the higher the measurement consistency, and vice versa.