A multi-channel detection method for the thickness of the invert of a tunnel based on the impact echo method

Abstract

The present invention discloses a multi-channel detection method for the thickness of the invert of a tunnel based on the impact echo method. First, all the reflected waves of the acceleration sensor used as a reference and the acceleration sensor used for calibration are calibrated. These reflected waves are regarded as a set, and any subset is taken from it for updating. Under the calibration effect of the Pythagorean theorem, a matching reflected wave can be found. If no matching result can be found, it indicates the interference of voids or other defects, and the measuring line needs to be replaced. The present invention uses a geometric method for reference calibration to obtain accurate thickness indicators.

Description

Technical Field

[0001] The present invention relates to the field of thickness measurement, and particularly relates to a multi-channel method for detecting the thickness of the invert arch of a tunnel based on the impact echo method. Background Art

[0002] The invert arch is a reverse arch structure arranged at the bottom of the tunnel to improve the stress conditions of the upper support structure. It is one of the main components of the tunnel structure. On the one hand, it effectively transfers the formation pressure above the tunnel through the tunnel side wall structure or the load on the road surface to the ground, and also effectively resists the reaction force transmitted from the lower formation of the tunnel. The invert arch and the secondary lining form the whole tunnel, increasing the structural stability. However, in the actual construction process, there is often a phenomenon of insufficient invert arch thickness. For the phenomenon of insufficient invert arch thickness, the industry mainly uses electromagnetic wave radar, impact echo method, and core drilling method for thickness testing.

[0003] Due to the high excitation frequency and short wavelength of the electromagnetic wave radar method, even when using a low-frequency radar, the detection depth is relatively shallow, and the invert arch thickness cannot be accurately detected.

[0004] The impact echo method has a relatively low frequency and has the function of detecting thick concrete. However, the bottom of the invert arch is an arc structure with many interference signals. The existing technology cannot accurately collect the signals at the bottom of the invert arch, resulting in large test errors. Summary of the Invention

[0005] The purpose of the present invention is to provide a multi-channel method for detecting the thickness of the invert arch of a tunnel based on the impact echo method, and use a geometric method for reference calibration to obtain accurate thickness indicators.

[0006] A multi-channel method for detecting the thickness of the invert arch of a tunnel based on the impact echo method includes the following steps:

[0007] S1. Mark a measuring line on the front surface of the tunnel invert arch body. The measuring line is a line segment perpendicular to the center line of the tunnel direction and located on the front surface; the center line of the tunnel direction is a line segment perpendicular to the tunnel cross-section;

[0008] S2. Arrange 1 excitation point, 1 acceleration sensor for reference, and at least 2 acceleration sensors for calibration. The acceleration sensor for reference is located at the intersection of the center line of the tunnel direction and the measuring line. The acceleration sensors for calibration are arranged at intervals along the measuring line. The excitation point, the acceleration sensor for reference, and the acceleration sensors for calibration are all on the same measuring line;

[0009] S3. Use an excitation hammer to strike the excitation point, and the waveform recording instrument simultaneously records the P-wave waveform data corresponding to the acceleration sensor for reference and the acceleration sensors for calibration;

[0010] S4. Parse the propagation time of the P-wave reflected by the arch bottom interface inside the tunnel invert body for each acceleration sensor from each P-wave waveform, and record them as: T df 0, T df 1, T df 2... T df N;

[0011] T df 0 is the propagation time of the P-wave corresponding to the acceleration sensor used as a reference, reflected by the arch bottom interface (13) inside the tunnel invert body, T df 1, T df 2... T df N is the propagation time of the P-wave corresponding to the acceleration sensor used for calibration, reflected by the arch bottom interface inside the tunnel invert body;

[0012] The P-wave waveform data is a time history curve. The X-axis of the P-wave waveform data is the time value, and the Y-axis is the acceleration amplitude value;

[0013] Specifically, S4 is as follows:

[0014] S41. Calibrate 1 incident wave and 1 reflected wave from the time history curve corresponding to each P-wave waveform data;

[0015] S42. Extract the time values T RS , T FS corresponding to the starting point RS of 1 incident wave and the starting point FS of 1 reflected wave of each P-wave waveform data, and calculate the time value difference △T corresponding to each P-wave waveform data, and record them as: △T0, △T1, △T2... △TN, △T = |T RS - T FS |, △T is the total propagation duration of the P-wave in the tunnel invert body; among them, the starting point RS of the incident wave of all P-wave waveform data is the starting point RS of the P-wave waveform data of the acceleration sensor used as a reference;

[0016] S43. Calculate the propagation time of the P-wave reflected by the arch bottom interface inside the tunnel invert body for each acceleration sensor according to △T respectively, and the corresponding calculation formula is:

[0017] T df 0 = △T0 / 2,

[0018] T df 1 = △T1 - T df 0, T df 2 = △T2 - T df 0... T df N = △TN - T df 0;

[0019] S5. According to the standard P-wave velocity V and T of the tunnel invert body df 0, T df 1, T df 2... T df N, calculate the propagation distances of the P-waves corresponding to each acceleration sensor reflected by the arch bottom interface inside the tunnel invert body, and denote them as: D0, D1, D2... DN respectively;

[0020] D0 is the propagation distance of the P-wave corresponding to the acceleration sensor used as the reference reflected by the arch bottom interface inside the tunnel invert body, and D1, D2... DN are the propagation distances of the P-waves corresponding to the acceleration sensors used for calibration reflected by the arch bottom interface inside the tunnel invert body;

[0021] S6. Calculate the corresponding calibration thicknesses R1, R2... RN according to D1, D2... DN using the Pythagorean theorem,

[0022] R1 = 、R2 = 、...、RN = , where L1, L2,..., LN are the physical distances on the measuring line from the corresponding acceleration sensors used for calibration to the acceleration sensor used as the reference respectively;

[0023] S7. Take D0 as the reference thickness to be calibrated and denote it as R, and comprehensively determine the measured thickness of the tunnel invert body under the center line in the tunnel direction based on R, R1, R2... RN;

[0024] The comprehensive determination process is as follows:

[0025] First, remove the gross error values from R1, R2... RN and then calculate the average value;

[0026] If R is close to the average value, take R or the average result of R and the average value as the final measured thickness;

[0027] If R is not close to the average value, update the reflected wave in S41 and repeat S42, S43, S5, S6, S7.

[0028] Preferably, L1, L2,..., LN increase in increments of 0.2 m to 0.5 m.

[0029] Preferably, the exciting hammer is determined according to the designed thickness of the tunnel invert body. The exciting hammer is a small round stainless steel hammer with an annealing hardness not greater than 235 HB, and the diameter specifications of the small hammer include 28 mm, 48 mm, and 60 mm.

[0030] The dynamic range of the acceleration sensor is 1 - 70 kHz.

[0031] Preferably, the process of removing the gross error values from R1, R2... RN is as follows:

[0032] If the absolute value of the difference between a certain value in R1, R2... RN and other values is greater than the first threshold, then this value is removed as a gross error value;

[0033] If the absolute value of the difference between R and the average value is less than the second threshold, it is determined that R is close to the average value;

[0034] If the absolute value of the difference between R and the average value is greater than the second threshold, it is determined that R is not close to the average value.

[0035] The beneficial effects of the present invention are as follows:

[0036] 1. The bottom surface of the inverted arch is arc-shaped, and multiple signals are likely to appear in the arch bottom reflection. Using multi-channel simultaneous signal acquisition is beneficial for the elimination of interference signals, and thus more accurate signals at the bottom of the inverted arch can be picked up;

[0037] 2. The elastic wave has a lower frequency than the electromagnetic wave radar. Media such as steel bars, muddy inclusions, and water have less influence on it, and the detection depth is relatively deep, which provides the possibility for accurately detecting the thickness of the tunnel inverted arch. Description of the Drawings

[0038] Figure 1 It is a side view of the detection layout of the present invention.

[0039] Figure 2 It is a three-dimensional view of the detection layout of the present invention.

[0040] The reference numerals in the figures are respectively represented as: 1, tunnel inverted arch body; 11, tunnel direction center line; 12, measuring line; 13, arch bottom interface; 2, excitation hammer; 3, acceleration sensor; 4, waveform recording instrument. Specific Embodiments

[0041] The following combines the embodiments and the drawings to further elaborate on the present invention in detail, but the implementation manners of the present invention are not limited thereto.

[0042] Embodiment 1

[0043] As Figure 1 - Figure 2 shown.

[0044] A method for multi-channel detecting the thickness of a tunnel inverted arch based on the impact echo method includes the following steps:

[0045] S1. Mark the measuring line 12 on the front surface of the tunnel inverted arch body 1. The measuring line is a line segment perpendicular to the tunnel direction center line and located on the front surface; the tunnel direction center line is a line segment perpendicular to the tunnel cross-section;

[0046] S2. Arrange 1 excitation point, 1 acceleration sensor 3 for reference, and at least 2 acceleration sensors 3 for calibration. The acceleration sensor 3 for reference is located at the intersection of the center line of the tunnel direction and the measuring line. The acceleration sensors 3 for calibration are arranged at intervals along the measuring line. The excitation point, the acceleration sensor 3 for reference, and the acceleration sensors 3 for calibration are all on the same measuring line 12;

[0047] S3. Use the excitation hammer 2 to strike the excitation point, and the waveform recording instrument 4 simultaneously records the P-wave waveform data corresponding to the acceleration sensor 3 for reference and the acceleration sensors 3 for calibration;

[0048] S4. Analyze from each P-wave waveform the propagation time of the P-wave sensed by each acceleration sensor when reflected by the arch bottom interface 13 inside the tunnel invert body 1, and record them respectively as: T df 0, T df 1, T df 2... T df N;

[0049] T df 0 is the propagation time of the P-wave sensed by the acceleration sensor 3 for reference when reflected by the arch bottom interface 13 inside the tunnel invert body 1, and T df 1, T df 2... T df N is the propagation time of the P-wave sensed by the acceleration sensor 3 for calibration when reflected by the arch bottom interface 13 inside the tunnel invert body 1;

[0050] The P-wave waveform data is a time history curve. The X-axis of the P-wave waveform data is the time value, and the Y-axis is the acceleration amplitude value;

[0051] S4 is specifically as follows:

[0052] S41. Calibrate 1 incident wave and 1 reflected wave from the time history curve corresponding to each P-wave waveform data;

[0053] S42. Extract the moment values T RS 、T FS corresponding to 1 incident wave starting point RS and 1 reflected wave starting point FS of each P-wave waveform data, calculate the time value difference △T corresponding to each P-wave waveform data, and record them respectively as: △T0, △T1, △T2... △TN, △T = |T RS - T FS |, and △T is the total propagation duration of the P-wave in the tunnel invert body 1; among them, the incident wave starting point RS of all P-wave waveform data is the incident wave starting point RS of the P-wave waveform data of the acceleration sensor 3 for reference;

[0054] S43. Calculate the propagation time of the P-wave sensed by each acceleration sensor and reflected by the arch bottom interface 13 inside the tunnel invert body 1 according to △T respectively. The corresponding calculation formula is:

[0055] T df 0 = △T0 / 2,

[0056] T df 1 = △T1 - T df 0、T df 2 = △T2 - T df 0……T df N = △TN - T df 0;

[0057] S5. According to the standard P-wave velocity V of the tunnel invert body 1 and T df 0、T df 1、T df 2……T df N, calculate the propagation distances of the P-waves sensed by each acceleration sensor and reflected by the arch bottom interface 13 inside the tunnel invert body 1 respectively, and record them as: D0, D1, D2……DN;

[0058] D0 is the propagation distance of the P-wave sensed by the acceleration sensor 3 used as a reference and reflected by the arch bottom interface 13 inside the tunnel invert body 1, and D1, D2……DN are the propagation distances of the P-waves sensed by the acceleration sensor 3 used for calibration and reflected by the arch bottom interface 13 inside the tunnel invert body 1;

[0059] S6. Calculate the corresponding calibrated thicknesses R1, R2……RN according to D1, D2……DN using the Pythagorean theorem,

[0060] R1 = 、R2 = 、……、RN = , where L1, L2,……, LN are the physical distances of the corresponding acceleration sensors for calibration to the acceleration sensor for reference on the measuring line;

[0061] S7. Take D0 as the reference thickness to be calibrated and record it as R, and comprehensively determine the measured thickness of the tunnel invert body 1 under the center line in the tunnel direction based on R, R1, R2……RN;

[0062] The comprehensive determination process is:

[0063] First, remove the gross error values in R1, R2……RN and then calculate the average value;

[0064] If R is close to the average value, take R or the average result of R and the average value as the final measured thickness;

[0065] If R is not close to the average value, update one of the reflected waves in S41, and repeat S42, S43, S5, S6, and S7.

[0066] The design principle of the present invention is:

[0067] First of all, in the application scenario of invert thickness measurement, the use of impact echo measurement technology has not been seen yet. First of all, the meaning of invert thickness in the present invention refers to the dimension from the center point of the positive surface of the tunnel invert body 1 vertically downward to the outer boundary of the tunnel invert body. Generally, impact echo is indeed a common technology for measuring thickness, and it is commonly used in the measurement of structures with equal thickness, such as the measurement of the thickness of a cube and the measurement of the length of a cylinder. In these scenarios, generally, a relatively obvious incident wave and a relatively obvious reflected wave will be generated. Therefore, only the time points of one incident wave and one reflected wave need to be recorded, and they are regarded as two equal-length travel distances. Therefore, by dividing the time by 2, the one-way travel time can be obtained. After obtaining the calibration wave velocity of the measurement object, the thickness can be calculated through the wave velocity and the one-way travel time. Therefore, the impact echo method is generally more commonly applied to the case where the bottom surface is parallel to the surface.

[0068] However, since the tunnel invert body 1 is an arc-shaped structure, generally, this arc structure is not a standard circular arc, but generally an elliptical arc segment or other situations. Therefore, if only one impact echo sensor is arranged in the theoretical direction of thickness measurement, when the shock wave reaches the arc-shaped boundary, many reflected waves will be reflected upward, and the differences between these reflected waves are small, and it is impossible to calibrate the reflected wave required for thickness measurement from these reflected waves.

[0069] To solve this problem, in order to improve the measurement accuracy, the present invention is proposed. The design concept of the present invention is: arrange an acceleration sensor 3 for reference and at least two acceleration sensors 3 for calibration on the above-defined measuring line 12. Among them, the acceleration sensor 3 for reference is arranged in the theoretical direction of thickness measurement, and the acceleration sensors 3 for calibration will be farther and farther away from the excitation point. During measurement, only tap once. In the P-wave waveform data sensed by the acceleration sensor 3 for reference, there is one relatively obvious incident wave and multiple approximate reflected waves. Among them, the reflected wave in the vertical direction may be the first reflected wave or the second reflected wave... Therefore, without the assistance of the acceleration sensor 3 for calibration, it is impossible to calibrate the reflected wave required for thickness calculation.

[0070] For steps S4 - S7 of the present invention, it represents a process of cyclic inspection. Specifically, for the P - wave waveform data corresponding to the acceleration sensor 3 for reference, if there are multiple calibrated reflected waves, in S41, the first reflected wave is taken for substitution and calculation. Similarly, for the P - wave waveform data corresponding to the acceleration sensor 3 for calibration, if there are multiple calibrated reflected waves, in S41, the first reflected wave is taken for substitution and calculation. Therefore, through the Pythagorean theorem, the present invention can calibrate one R and R1…RN. If R is close to the average value, then either R or the average result of R and the average value is taken as the final measured thickness; otherwise, a new reflected wave is taken. Taking a new reflected wave can be an update of the reflected wave of a single acceleration sensor or multiple acceleration sensors (multiple acceleration sensors include multiple acceleration sensors for calibration 3 or "the acceleration sensor 3 for reference and one acceleration sensor 3 for calibration" or "the acceleration sensor 3 for reference and the reflected - wave update of multiple acceleration sensors for calibration", and so on. If still no final measured thickness can be obtained after such analogies, then the measuring line is replaced and S2 - S7 are repeated.

[0071] This embodiment schematically shows the above - mentioned process with the simplest data volume as follows:

[0072] Assume: There are 2 reflected waves calibrated by the acceleration sensor 3 for reference, namely reflected wave B01 and reflected wave B02, and their corresponding times are set as T01 and T02, and the time of the incident wave is Tx.

[0073] Assume: There are 2 acceleration sensors 3 for calibration. Each of the 2 acceleration sensors 3 for calibration has 2 reflected waves, namely reflected wave B11, reflected wave B12, reflected wave B21, reflected wave B22, and their corresponding times are set as T11, T12, T21, T22, and the time of the incident wave is Tx.

[0074] For the first calculation:

[0075] Take T01, T11, T21.

[0076] Then, T df 0 = (T01 - Tx) / 2.

[0077] T df 1 = (T11 – Tx) - (T01 - Tx) / 2, T df 2 = (T21 – Tx) - (T01 - Tx) / 2.

[0078] Substitute T df 0, T df 1, T dfSubstituting 2 into S5, S6, and S7 can obtain R, R1, and R2. Only after comprehensive determination, if the thickness cannot be determined, then perform an update calculation.

[0079] Update calculation ("update T01 to T02" or "update T11, T21 to T12, T22" or "update T11 to T12" or "update T21 to T22" or "update T01 to T02 and update T11, T21 to T12, T22"... etc.) (The update scheme can be the reflection wave update of any one acceleration sensor, or the reflection wave update of any two acceleration sensors, or the reflection wave update of any three acceleration sensors):

[0080] Substitute T df 0, T df 1, T df Substituting 0, 1, 2 into S5, S6, and S7 can obtain R, R1, and R2. Only after comprehensive determination, if the thickness cannot be determined, then perform the next update calculation.

[0081] Generally speaking, the updated reflected wave described in the present invention can be understood as follows: First, calibrate all the reflected waves of the acceleration sensor for reference and the acceleration sensor for calibration, regard these reflected waves as a set, and arbitrarily take subsets from them for update. Under the calibration of the Pythagorean theorem, it is possible to find matching reflected waves. If no matching result can be found, it means that there is interference from voids or other defects, and then the measuring line needs to be replaced.

[0082] It should be further noted that: S4, S5, S6, and S7 in this application are all for the measurement of a set of data. When the effective measured thickness cannot be obtained, the parameters need to be updated and recalculated. The core technical contribution of the present invention lies in the combination of echo measurement, calibration, and geometric solution of the Pythagorean theorem, so that the echo method can be used for the measurement of arc-shaped structures.

[0083] It should be further noted that: The measuring line of this application is the basis for facilitating the calibration of the Pythagorean theorem.

[0084] Specifically, L1, L2,..., LN increase in increments of 0.2 m to 0.5 m.

[0085] Specifically, the excitation hammer is determined according to the designed thickness of the tunnel invert body 1. The excitation hammer is a small round stainless steel hammer with an annealing hardness not greater than 235 HB, and the diameter specifications of the small hammer include three types: 28 mm, 48 mm, and 60 mm.

[0086] Specifically, the dynamic range of the acceleration sensor is 1 - 70 kHz.

[0087] Specifically, the process of removing the gross error values from R1, R2... RN is as follows:

[0088] If the absolute value of the difference between a certain value among R1, R2... RN and other values is greater than the first threshold value, then this value is removed as a gross error value;

[0089] If the absolute value of the difference between R and the average value is less than the second threshold value, then it is determined that R is close to the average value;

[0090] If the absolute value of the difference between R and the average value is greater than the second threshold value, then it is determined that R is not close to the average value.

[0091] It can be understood that the above embodiments are merely exemplary embodiments adopted to illustrate the principle of the present invention, however, the present invention is not limited thereto. For those of ordinary skill in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also regarded as the protection scope of the present invention.

Claims

1. A multi-channel detection method for the thickness of the invert of a tunnel based on the impact echo method, characterized in that It includes the following steps: S1. Mark a measuring line (12) on the front surface of the tunnel invert body (1). The measuring line is a line segment perpendicular to the center line of the tunnel direction and located on the front surface. The center line of the tunnel direction is a line segment perpendicular to the tunnel cross-section. S2. Arrange 1 excitation point, 1 acceleration sensor (3) for reference, and at least 2 acceleration sensors (3) for calibration. The acceleration sensor (3) for reference is located at the intersection of the center line of the tunnel direction and the measuring line. The acceleration sensors (3) for calibration are arranged at intervals along the measuring line. The excitation point, the acceleration sensor (3) for reference, and the acceleration sensors (3) for calibration are all on the same measuring line (12). S3. Use an impact hammer (2) to strike the excitation point, and a waveform recording instrument (4) simultaneously records the P-wave waveform data corresponding to the acceleration sensor (3) for reference and the acceleration sensors (3) for calibration. S4. Analyze the propagation time of the P-wave sensed by each acceleration sensor and reflected by the arch bottom interface (13) inside the tunnel invert body (1) according to each P-wave waveform, and record them respectively as: T df 0, T df 1, T df 2... T df N; T df T is the propagation time of the P-wave corresponding to the acceleration sensor (3) for the reference 0 reflected by the arch bottom interface (13) inside the tunnel invert body (1). df 1. T df 2... T df N is the propagation time of the P-wave corresponding to the acceleration sensor (3) for calibration reflected by the arch bottom interface (13) inside the tunnel invert body (1); The P-wave waveform data is a time history curve. The X-axis of the P-wave waveform data is the time value, and the Y-axis is the acceleration amplitude value. S4 is specifically: S41. Calibrate 1 incident wave and 1 reflected wave from the time history curve corresponding to each P-wave waveform data. S42. Extract the time values T corresponding to one incident wave starting point RS and one reflected wave starting point FS of each P-wave waveform data RS and T FS , calculate the time value difference △T corresponding to each P-wave waveform data, denoted as: △T0, △T1, △T2…△TN respectively, △T = |T RS - T FS |, and △T is the total propagation duration of the P-wave in the invert body (1) of the tunnel; among them, the incident wave starting point RS of all P-wave waveform data is the incident wave starting point RS of the P-wave waveform data of the reference acceleration sensor (3). S43. Calculate the propagation time of the P-wave corresponding to each acceleration sensor and reflected by the arch bottom interface (13) inside the tunnel invert body (1) according to △T. The corresponding calculation formula is: T df 0 = △T0 / 2, T df 1 = △T1 - T df 0, T df 2 = △T2 - T df 0……T df N = △TN - T df 0; S5. According to the standard P-wave velocity V and T of the tunnel invert body (1) df 0, T df 1, T df 2... T df N, calculate the propagation distances of the P-waves respectively sensed by each acceleration sensor reflected by the arch bottom interface (13) inside the tunnel invert body (1), and denote them as: D0, D1, D2... DN; D0 is the propagation distance of the P-wave corresponding to the acceleration sensor (3) for reference and reflected by the arch bottom interface (13) inside the tunnel invert body (1). D1, D2... DN are the propagation distances of the P-waves corresponding to the acceleration sensors (3) for calibration and reflected by the arch bottom interface (13) inside the tunnel invert body (1). S6. Calculate the corresponding calibrated thicknesses R1, R2... RN according to D1, D2... DN using the Pythagorean theorem. R1 = , R2 = , ……, RN = , where L1, L2, ……, LN are the physical distances on the survey line from the corresponding acceleration sensors for calibration to the acceleration sensor for reference respectively; S7. Take D0 as the reference thickness to be calibrated and denote it as R. Based on R, R1, R2... RN, comprehensively determine the measured thickness of the tunnel invert body (1) under the center line of the tunnel direction. The comprehensive determination process is: First, remove the gross error values from R1, R2... RN and then calculate the average value. If R is close to the average value, take R or the average result of R and the average value as the final measured thickness. If R is not close to the average value, update the reflected wave in S41 and repeat S42, S43, S5, S6, S7.

2. The method for multi-channel detecting the thickness of the tunnel invert based on the impact echo method according to claim 1, wherein L1, L2,..., LN increase in increments of 0.2m to 0.5m.

3. The method for multi-channel detecting the thickness of the tunnel invert based on the impact echo method according to claim 1, wherein The impact hammer is determined according to the designed thickness of the tunnel invert body (1). The impact hammer is a small round stainless steel hammer with an annealing hardness not greater than 235HB. The diameter specifications of the small hammer include 28mm, 48mm, and 60mm.

4. A method for multi-channel detecting the thickness of the invert of a tunnel based on the impact echo method according to claim 1, characterized in that The dynamic range of the acceleration sensor is 1 - 70kHz.

5. According to the method for multi-channel detecting the thickness of a tunnel invert based on the impact echo method described in claim 1, it is characterized in that The process of removing the gross error values from R1, R2... RN is: If the absolute value of the difference between a certain value in R1, R2... RN and other values is greater than the first threshold, then take this value as the gross error value and remove it. If the absolute value of the difference between R and the average value is less than the second threshold, it is determined that R is close to the average value; If the absolute value of the difference between R and the average value is greater than the second threshold, it is determined that R is not close to the average value.

Images