A testing method for the transverse slope of pavement paving under random vibration of a paver

Abstract

The present invention relates to a test method for the pavement paving cross slope under the random vibration of a paver. A fixed bracket for an angle sensor with shock absorption is installed on the paver, and the angle data signal is converted into data, then calculated and filtered, and finally the pavement cross slope is displayed as a percentage; the fixed bracket of the angle sensor adopts a multi-layer rubber tube air cushion shock absorption process, and the relationship is established by calculating the precision of the collected original data and the results of the rubber tube hardness and the number of rubber tube layers, and the optimal hardness and number of layers of the shock absorption rubber tube are obtained based on the minimum precision standard for the connection between the fixed bracket of the angle sensor and the sensor; a multi-step weighted filtering algorithm is adopted, which is carried out in turn: select the weight trial calculation array, convert the weight percentage, sort the original test values from large to small × the weight percentage, and determine the interval where the representative value is located by data clustering to calculate the representative value, and finally realize the acquisition and filtering of the cross slope data under the random amplitude vibration state of the paver to ensure the stability and accuracy of the cross slope data display.

Description

Technical Field

[0001] The present invention relates to the technical field of road engineering, and particularly relates to a method for testing the cross slope of a road surface during paving by a paver under random vibration. Background Art

[0002] When designing an asphalt pavement, in order to ensure that rainwater can be discharged along the cross slope of the road surface in a timely manner, the cross slope of the road surface is designed to be 2% in the straight section. At the turning of the road, the superelevation height is increased on the basis of the original cross slope. When it rains, the surface water of the road surface can be completely discharged within 5 minutes. However, during the road construction process, the importance of the cross slope is poorly emphasized, and it is easy to have a situation where the cross slope of the straight section is 0, which seriously affects the road surface drainage effect. Insufficient cross slope of the road surface is likely to form surface runoff on the road surface, and then reduce the contact area between the tires of high-speed vehicles and the ground, making it easy to occur water skidding or hydroplaning, resulting in a decrease in the friction coefficient between the tires and the road surface and a poor adhesion of the wheels, ultimately causing safety accidents. Therefore, in the face of the construction requirements of rapid and efficient drainage for high-speed and first-class highway projects, porous asphalt pavements with rapid drainage, high anti-skid performance and low noise are often adopted, and a good drainage cross slope is the main focus of attention in drainage for each construction project. Summary of the Invention

[0003] In view of the above problems, the present invention provides a method for testing the cross slope of a road surface during paving by a paver under random vibration. In view of the irregular jitter during the paving process of the paver, an effective multi-step weighted filtering method is adopted to make the test of the cross slope of the road surface during the jitter state of the paver as stable as the static test.

[0004] A method for testing the cross slope of a road surface during paving by a paver under random vibration, which installs a shock-absorbing angle sensor fixing bracket on the paver, uses an angle sensor with a static angle test accuracy of 0 to 0.001° to collect angle data, converts the angle data signal into data, then performs calculation and filtering, and finally displays the cross slope of the road surface as a percentage;

[0005] The fixing bracket of the angle sensor adopts a multi-layer rubber tube air cushion shock-absorbing process. By calculating the relationship between the precision of the collected original data and the hardness and number of layers of the rubber tube, the optimal hardness and number of layers of the shock-absorbing rubber tube are obtained based on the minimum precision, and are used for the connection between the angle sensor fixing bracket and the sensor;

[0006] The road paver generates vibrations of 40 Hz during the paving process, and the vibration amplitude is 0 - 6 mm. A multi-step weighted filtering algorithm is adopted, and the following steps are carried out in sequence: select a weight trial calculation array, convert the weight percentage, sort the original test values from largest to smallest × the weight percentage, and determine the interval where the representative value is located through data clustering to calculate the representative value. Finally, the cross slope data collection and filtering under the random amplitude vibration state of the paver are realized to ensure the stability and accuracy of the cross slope data display.

[0007] Furthermore, the selection weight trial calculation array:

[0008] The value range of the weight follows a normal distribution. The weight value is the Y value corresponding to the uniform distribution of the X value in the normal distribution graph. In the normal distribution interval with a confidence level of 95%, when the thin and tall state curve in the normal distribution graph gradually changes to the short and fat state, n uniformly distributed X values will generate n normal distribution Y values; when the normal distribution μ = 0 and σ takes different values, different weight trial calculation arrays will be generated.

[0009] The converted weight percentage:

[0010] When the weight trial calculation arrays generated when the normal distribution μ = 0 and σ takes different values are in the form of each column, they are converted into the ratio of each value to the sum of the entire column, and the data of m columns are converted in turn.

[0011]

[0012] γ i - Weight percentage array, expressed in three decimal places;

[0013] A i - Weight value generated by using the normal distribution function;

[0014] n - represents the number of weight values generated by using the normal distribution function when μ = 0 and σ takes a value;

[0015] m - represents the number of weight trial calculation arrays generated when μ = 0 and σ takes different values;

[0016] The tested original value is sorted from large to small × weight percentage:

[0017] After each test of the angle sensor, select n consecutive numerical values as a set of test data, and the test interval is 1 s; calculate the tested original value sorted from large to small × weight percentage through Equation 2, and use β m to represent.

[0018]

[0019] Y i - Weight percentage, expressed in three decimal places;

[0020] a i - Sensor tested original value;

[0021] β m - Calculation result of the tested original value and each group of weight coefficients;

[0022] m - represents the number of weight trial calculation arrays generated when μ = 0 and σ takes different values;

[0023] The data clustering determines the interval where the representative value is located and calculates the representative value:

[0024] For β m Cluster the values in it from the minimum value to the maximum value at an interval of t = 0.005, select the interval with the most data and the second most data in each interval, calculate according to Equation 3 and Equation 4, and use these two intervals as the criteria to take the arithmetic mean of the values in β m array that fall into the two intervals, and this arithmetic mean value is used as the representative value F for filtering this group of data D Calculate according to Equation 5

[0025] P max1 = firstmax(S k ) Equation 3

[0026] P max2 = secondmax(S k ) Equation 4

[0027] F D = f(P max1 , P max2 ) Equation 5

[0028] k - After sorting β m from largest to smallest as an array, and dividing this array at a certain interval, the number of arrays k can be obtained;

[0029] S k - The number of values of β m falling into each divided interval;

[0030] P max1 - Represents the interval corresponding to the maximum value in S k ;

[0031] P max2 - Represents the interval corresponding to the second largest value in S k ;

[0032] F D - Represents the arithmetic mean of the values in the β m array that fall into the P max1 , P max2 intervals.

[0033] The present invention consists of a test sensor with a static angle test accuracy reaching 0 to 0.0001°. Under the condition of random vibration of the paver, a multi-step weighted filtering algorithm is adopted. Through the weight array generated by the normal distribution curve, the interval where the optimal representative value is located is calculated under the condition of the best comprehensive accuracy, and the arithmetic mean of the weighted values falling within the interval is taken as the representative value for different test times. The absolute error of the dynamic test result meets within ±0.025% of the set value, which can fully meet the stable measurement of the paving cross slope of the random vibration paver. The device updates the cross slope value once per second, so that the construction personnel can adjust the paving cross slope of the paver immediately according to the measured cross slope value, ensuring the relative accuracy of the cross slope during the paving process. Description of the Drawings

[0034] Figure 1 It is a top view of the data acquisition structure of the cross slope section monitor;

[0035] Figure 2 It is a side view of the data acquisition structure of the cross slope section monitor;

[0036] Figure 3 It is a weight normal distribution curve graph of the data in Table 2;

[0037] Figure 4 It is a distribution graph of the original data, representative value, and average value of the first test;

[0038] Figure 5 It is a distribution graph of the original data, representative value, and average value of the second test;

[0039] Figure 6 It is a distribution graph of the original data, representative value, and average value of the third test;

[0040] Figure 7 It is a distribution graph of the original data, representative value, and average value of the fourth test;

[0041] Figure 8 It is a distribution graph of the original data, representative value, and average value of the fifth test;

[0042] Figure 9 It is a working schematic diagram of the cross slope full-section monitor during the pavement paving process;

[0043] Figure 10 Distribution graph of the measured value, average value, and representative value of Data 1;

[0044] Figure 11 Distribution graph of the measured value, average value, and representative value of Data 2;

[0045] Figure 12 Distribution graph of the measured value, average value, and representative value of Data 3.

[0046] In the figure:

[0047] Angle sensor 1, sensor carrier plate 2, sensor carrier plate fixing screw holes (3, 4), sensor lead wire 5, screw rod 6, shock-absorbing rubber tube 7, load-bearing vertical plate 8, sensor fixing clamping plates (9, 10, 11), fixing screw 12, LED display screen 13, paver fixing plate 14, paver top 15, paver body 16, paver arm 17, paved mixture 18, soil subgrade 19. Specific implementation method

[0048] The following further elaborates in detail on a method for testing the cross slope of a pavement during random vibration of a paver according to the present invention in combination with the accompanying drawings and specific embodiments:

[0049] Embodiment:

[0050] The data acquisition structure of the cross slope full-section monitor is shown in Figure 1 , Figure 2 , which mainly includes an angle sensor 1, a sensor carrier plate 2, sensor carrier plate fixing screw holes (3, 4), a sensor lead wire 5, a screw rod 6, a shock-absorbing rubber tube 7, a load-bearing vertical plate 8, sensor fixing clamping plates (9, 10, 11), a fixing screw 12, an LED display screen 13, a built-in filter circuit board, powered by a 24V battery of the paver, and a paver fixing plate 14.

[0051] The cross slope full-section monitor is driven by a 24V vehicle-mounted DC power supply to collect the test values of the high-precision angle sensor at a frequency of 5 - 50 times per second, and then through a multi-step weighted filtering method, stable and smooth angle numbers are calculated, converted into slope numbers, and finally displayed in real time on the LED display screen.

[0052] The assembly of this structure includes the upper part and the clamping part of the sensor carrier plate. The upper part of the sensor carrier plate is the part above the load-bearing vertical plate 8, and the clamping part is the part including the load-bearing vertical plate 8 and below.

[0053] An angle sensor 1 is installed on the sensor carrier plate 2, holes are drilled according to the hole positions of the angle sensor, and the hole diameter is 2mm larger than the aperture of the angle sensor. For example, Figure 1 in the middle hole, a screw rod 6 with a diameter of 2.5mm passes through the hole. Stack 1 - 5 layers of the shock-absorbing rubber tube 7 up and down, and connect and fasten the angle sensor 1, the screw rod 6, and the shock-absorbing rubber tube 7. After connection, see Figure 2 . Since the diameter of the screw rod 6 is much smaller than the inner diameter of the fixing hole on the sensor carrier plate 2, during the operation of the instrument, the shock force of the paver is completely transmitted to the angle sensor 1 by the shock-absorbing rubber tube 7, and the shock-absorbing rubber tube 7 will play a strong shock-absorbing effect. After installation, by adjusting the tightness of the 4 screw rods 6, calibrate the display value of the cross slope meter to be consistent with the actual test value.

[0054] The clamping part adopts a bearing plate vertical plate 8, sensor fixing clamping plates (9, 10, 11), and fixing screws 12. First, loosen the fixing screws 12, fix the sensor fixing clamping plates on the paver fixing plate 14, and ensure that the sensor fixing clamping plates are rigidly connected to the paver.

[0055] The LED display screen 13 is driven by the 24V vehicle-mounted direct current of the paver, and an internal drive and operation circuit board is provided. Connect the signal line of the LED display screen 13 to the angle sensor 1 to achieve real-time angle instant acquisition, filtering, operation, and slope percentage display.

[0056] To ensure a certain degree of compaction in the initial state during road paving, the paver will generate vibrations of about 40Hz. The amplitude of the paver's vibrating mechanism is defaulted to 0 - 6mm, that is, about 40 times of vibrations with a random amplitude of 0 - 6mm will be generated per second. This vibration significantly reduces the accuracy of the angle sensor's acquisition.

[0057] Finally, fix the LED display screen on the top of the paver 15, and install the angle sensor on the paver arm 17, then the test can start.

[0058] In a vibrating working environment, the angle sensor has strong instability in data acquisition. The test results will generate random errors, systematic errors, and accidental errors, but generally will fluctuate around the true value. In order to quickly find test data that can represent the true value, the original test results need to be filtered and specially operated, and the obtained results can be used for actual use. The present invention adopts a multi-step weighted filtering algorithm. First, trial calculations are carried out with different weights to analyze the reliability of each single value in each group of test data for representing the true value. The data clustering method is used to obtain the interval where the true value most likely falls generated by the clustering of each single value under different weighted filtering algorithms. Finally, the arithmetic mean of the weighted test data falling into this interval is calculated based on this interval, and this average value is used as the representative value of the true value of this test.

[0059] The multi-step weighted filtering algorithm intelligently converges the single values with a large contribution rate to the calculation of the representative value, has the ability to automatically analyze data and intelligently discard data, and finally realizes the intelligent filtering of data. This algorithm greatly improves the accuracy of the filtering result. Compared with the direct arithmetic average method, the accuracy of the filtering result has obvious superiority.

[0060] The designed value of the cross slope of the road surface is 2% ± 0.3%. It can be seen that the requirement for the absolute error of the cross slope measurement is not greater than 0.1%. The cross slope results calculated at different angles are shown in Table 1. From Table 1, it can be seen that when the actual slope is assumed to be 2.0%, if the slope value is stably displayed as 2.0%, the fluctuation range of the collected data angle is 1.12° - 1.17°. That is, relative to the median angle, when the angle error does not exceed ±0.025°, the slope test can stably display 2.0%. Therefore, when the test accuracy after sensor filtering in a vibration environment is less than or equal to 0.025°, the instrument can stably collect the slope. Therefore, the high-precision angle sensor of this instrument uses an angle sensor test with a static angle test accuracy of 0 - 0.001°. However, when used dynamically, data filtering is still required before use. The cross slope value calculation formula is shown in Equation 1.

[0061] δ = tanα × 100 Equation 1

[0062] α - cross slope angle, unit is °,

[0063] δ - cross slope value, unit is %.

[0064] Table 1 Cross Slope Accuracy Calculation Table

[0065]

[0066]

[0067] The filtering chip uses the multi-step weighted filtering method for filtering. First, n values are quickly collected within 1 s, and the collected data is sorted from large to small. The sorted data is processed using the weight algorithm in Table 2 (the trial weight percentages in Table 2 are derived from Tables 6 - 8) to achieve the first-step weighted trial calculation of the data. And so on, the trial calculations of all the trial weight percentages in Tables 6 - 8 are completed. Subsequently, the sum of the middle m weighted values is obtained, and 35 trial values can be obtained. The 35 trial values are clustered at a certain interval, and the intervals with the most and the second most occurrences in the clustering interval are selected. Then, the arithmetic mean of the weighted data of the original test data falling into the above intervals is calculated. Finally, this arithmetic mean is used as the representative value of the collected data this time. In Table 2, it is assumed that m = 11, and K + 0 to k + 10 are the m values in this algorithm.

[0068] The specific process is: select the weight trial calculation array → convert the weight percentage → sort the original test values from large to small × weight percentage → data clustering to determine the interval where the representative value is located, and calculate the representative value.

[0069] Table 2 Weight Calculation Table

[0070]

[0071]

[0072] Note: The weight value is a set of weights, not fixed.

[0073] (1) Select the weight trial calculation array

[0074] The value range of the weights in Table 2 follows a normal distribution. For example, Figure 3 , the weight value is the Y value corresponding to the uniform distribution of the X values in the normal distribution graph. In the normal distribution interval with a confidence level of 95%, when the "skinny and tall" state curve in the normal distribution graph gradually changes to the "short and fat" state, n uniformly distributed X values will generate n normal distribution Y values.

[0075] For the weight selection of this algorithm, the normal distribution formula is used as the generator of weight values. When gradually changing from the "skinny and tall" state to the "short and fat" state of the normal distribution graph, μ = 0, σ = 0.1, 0.2, 0.3..., and the generated data are shown in Tables 3, 4, and 5. In the selected normal distribution Y values this time, the values are retained to 3 significant figures. Centered on the Y value, using the method of equal spacing of X1, X2... values, 11 Y values are generated and listed in each column of Tables 3, 4, and 5. In Table 3, when σ = 0.1, 11 values with 3 significant figures cannot be generated, so the array with σ = 0.1 is discarded. In addition, the interval of σ in this method is 0.1, 1, 5, which is set by the researchers, and the selection of this value is determined by the researchers themselves.

[0076] Table 3 Weight trial calculation array 1

[0077]

[0078]

[0079] Table 4 Weight trial calculation array 2

[0080]

[0081] Table 5 Weight trial calculation array 3

[0082]

[0083]

[0084] (2) Convert the weight percentage

[0085] Convert the weight trial calculation arrays in Tables 3 - 5 into the ratio of each value to the sum of the entire column in the form of each column. At this time, n = 11, and the 35 columns of data are converted in sequence. The results are shown in Tables 6 - 8. The calculation of the weight percentage is shown in Equation 2.

[0086]

[0087] Y i- Weight percentage, expressed in three decimal places (not as a percentage); A i - Weight values generated using the normal distribution function;

[0088] n - represents the number of weight values generated using the normal distribution function when μ = 0 and σ takes a value.

[0089] Table 6 Weight percentage array 1

[0090]

[0091] Table 7 Weight percentage array 2

[0092]

[0093] Table 8 Weight percentage array 3

[0094]

[0095]

[0096] (3) Test the original values sorted from largest to smallest × weight percentage

[0097] Table 9 shows the original test values of the angle of the sensor in the vibration state. Since the amount of original test values of the cross slope of the sensor is huge, only 5 groups of original test values are listed here. Each time a test is conducted, 11 consecutive numerical values are selected as a group of test data, and the test interval is 1 s. At this time, n = 11 and m = 35. The calculation formula is shown in Equation 3. Through the calculation of Equation 3, β1, β2, β3 up to β can be calculated for each group of test values. 35 .

[0098]

[0099] Y i - Weight percentage, expressed in three decimal places (not as a percentage);

[0100] a i - Original test value of the sensor;

[0101] β m - Calculation result of each group of original test values and each group of weight coefficients.

[0102] m - represents the number of weight trial calculation arrays generated when μ = 0 and σ takes different values.

[0103] Table 9 Original test values of the cross slope sensor / °

[0104]

[0105] First, sort the original test values in each row from largest to smallest, and then multiply by the weight percentage. The results of each original test value × weight percentage are shown in Tables 10 - 12.

[0106] Data results of sorted original test values × weight percentage in Table 10

[0107]

[0108] Sorted original test values × weight percentage data table 2 in Table 11

[0109]

[0110] Sorted original test values × weight percentage data table 3 in Table 12

[0111]

[0112] (4) Determine the interval where the representative value is located by data clustering and calculate the representative value

[0113] Perform data clustering on the test results in Tables 10 - 12 (not calculated together for 5 times) at intervals of 0.005 from the minimum value to the maximum value, select the interval with the most data and the second most data in each interval, and the calculation is shown in Equations 4 and 5. Based on these two intervals, for the β m Take the arithmetic mean of the values in the β array that fall into the two intervals, and this arithmetic mean is used as the representative value for filtering the data in this group, denoted by F D as shown in Equation 6. Table 13 shows the representative value results calculated for 5 test cases. All the above calculations are automatically completed by the computer.

[0114] P max1 = firstmax(S k ) Equation 4

[0115] P max2 = secondmax(S k ) Equation 5

[0116] F D = f(P max1 , P max2 ) Equation 6

[0117] k - After sorting β m from largest to smallest as an array, divide the array at a certain interval (0.005 interval in the present invention), and the number of arrays k can be obtained;

[0118] S k - The number of values in the β array that fall into each divided interval; m The number of values in the β array that fall into each divided interval;

[0119] P max1 - Indicates Sk The interval corresponding to the maximum value;

[0120] P max2 - represents S k The interval corresponding to the second - largest value;

[0121] F D - represents β m The arithmetic mean of the data in the array that falls within P max1 、P max2 interval data.

[0122] Table 13 Results of representative value calculation for data clustering

[0123]

[0124]

[0125] Table 14 Accuracy table of representative value calculation for data clustering

[0126]

[0127] During implementation, the on - site mechanical layout, mixture, and subgrade are as shown in Figure 9 , where the top of the paver is 15, the body of the paver is 16, the paving arm is 17, the paved mixture is 18, and the soil subgrade is 19.

[0128] Pre - input the calculation weights of this paver into the program. During the test, first measure the cross - slope of the asphalt pavement just after paving, and then by adjusting the fastening screws of the cross - slope meter angle sensor, make the cross - slope value displayed on the LED display correspond to the measured value, then the accurate calculation of the representative value can be achieved. The absolute error of the slope does not exceed 0.1%.

[0129] Table 15 Weight calculation table of this paver

[0130]

[0131] Table 16 Test results of paving cross - slope

[0132]

[0133] Adopt the cross - slope full - section monitor for the pavement paving process developed by the present invention, install it on the top of the paver, and at the same time install a high - precision angle sensor on the paving arm. The power supply is powered by the 24 - volt DC power supply on the paver vehicle.

[0134] The test sensor with a static angle test accuracy of 0 to 0.0001° is used. Under the condition of random vibration of the paver, the multi-step weighted filtering algorithm is adopted. Through the weight array generated by the normal distribution curve, under the condition of the optimal comprehensive accuracy, the interval where the optimal representative value is located is calculated, and the arithmetic mean of the weighted values falling within the interval is taken as the representative value for different test times (calculated by the program itself), as shown in Table 14. It can be seen from Table 14 that the absolute error of the dynamic test result meets within ±0.025% of the set value, which can fully meet the stable measurement of the paving cross slope of the random vibration paver. The device updates the cross slope value once per second, so that the construction personnel can adjust the paving cross slope of the paver immediately according to the measured cross slope value to ensure the relative accuracy of the cross slope during the paving process.

[0135] The above embodiments have been described in detail with reference to the examples of the present invention. However, the present invention is not limited to the above examples. Various changes that can be made without departing from the spirit of the present invention within the knowledge scope of those of ordinary skill in the art should also be regarded as the protection scope of the present invention.

Claims

1. A method for testing the cross slope of road paving under random vibration of a paver, characterized in that: An angle sensor fixing bracket with shock absorption is installed on the paver, and an angle sensor with a static angle test accuracy of 0 to 0.001° is used to collect angle data. The angle data signal is converted into data, and then calculated and filtered, and finally the cross slope of the road surface is displayed as a percentage; The angle sensor's fixed bracket adopts a multi-layer hose air cushion shock absorption process. By calculating the relationship between the precision of the collected original data and the hose hardness and the number of hose layers, the optimal hardness and number of layers of the shock-absorbing hose are obtained based on the minimum precision, which is used to connect the angle sensor fixed bracket with the sensor. During the paving process, the paver generates 40Hz vibration with a vibration amplitude of 0-6mm. A multi-step weighted filtering algorithm is used to perform the following steps: select the weight trial calculation array, convert the weight percentage, sort the original test values from large to small × weight percentage, and use data clustering to determine the representative value interval to calculate the representative value. Finally, the cross slope data collection and filtering are realized under the random amplitude vibration state of the paver to ensure the stability and accuracy of the cross slope data display.

2. The method for testing the cross slope of road paving under random vibration of a paver according to claim 1, characterized in that: The selection weight trial array: The weight value is required to obey the normal distribution. The weight value is the Y value corresponding to the uniform distribution of the X value in the normal distribution graph. In the normal distribution interval with a confidence level of 95%, when the thin and tall state curve in the normal distribution graph gradually changes to the short and fat state, n uniformly distributed X values will produce n normally distributed Y values; when the normal distribution μ=0, σ takes different values, different weight trial calculation arrays will be generated; The conversion weight percentage: When the normal distribution μ=0 and σ takes different values, the weight trial array generated is converted into the ratio of each value to the sum of the entire column in the form of each column, and the m columns of data are converted in turn. Formula 1 - An array of weight percentages, represented with three decimal places; - Weight values generated using the normal distribution function; ; ; The original test values are sorted from largest to smallest × weight percentage: After each test of the angle sensor, select n consecutive values as a set of test data, with a test interval of 1 s; calculate the original test values sorted from large to small × weight percentage through Equation 2, and use to represent. Formula 2 - Weight percentage, expressed to three decimal places; - Original test value of the sensor; ; － ; The data clustering determines the interval where the representative value is located and calculates the representative value: For the values in are subjected to data clustering at intervals of t = 0.005 from the minimum value to the maximum value, and the interval with the most data and the second most data falling into each interval are selected. Calculated according to Equation 3 and Equation 4, and taking these two intervals as the criteria, for the numerical values in the array falling into the two intervals are averaged arithmetically, and the obtained arithmetic mean value is used as the representative value for filtering the data in this group Calculated according to Equation 5 ) Formula 3 ) Formula 4 Formula 5 k - pair After sorting from large to small and taking it as an array, splitting the array at certain intervals gives the number k of arrays; - The number of values of the data falling into each segmentation interval; Indicates the interval corresponding to the maximum value in; represent the interval corresponding to the second largest value therein; － 。

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