Mobile convolution-based microwave density detection edge effect compensation method and system

Abstract

The application provides a microwave density detection edge effect compensation method and system based on mobile convolution, and relates to the technical field of nondestructive testing. A scanning model is established by scanning a standard rod; a simulation model of the axial theoretical density distribution of a column body (such as a cigarette) to be detected is constructed according to the design parameters of the column body; virtual units with background density are virtually extended at both ends of the column body to be detected represented by the simulation model, so that a detection virtual model is formed; forward convolution operation is performed based on the scanning model and the detection virtual model, so that a predicted density distribution containing edge effect interference is obtained; the microwave actually measured display density of the column body to be detected is acquired, regularization deconvolution operation is performed by using the scanning model, so that the column body inversion density distribution compensated for the edge effect is reconstructed; the inversion weight of the column body is calculated based on the inversion density distribution, and is compared with the theoretical weight of the column body to be detected, so that the final column body real density distribution is obtained, and the accuracy and reliability of the detection data are improved.

Description

Technical Field

[0001] This invention relates to the field of nondestructive testing technology, and in particular to a method and system for edge effect compensation in microwave density detection based on moving convolution. Background Technology

[0002] Column density distribution is a key indicator in many industries, and microwave density detection has become the mainstream method for column density detection due to its core advantages of being non-contact, non-destructive, and highly accurate. Its core principle is to invert the density distribution by measuring the propagation characteristics of microwaves in a medium. Specifically, it uses a moving window to scan multiple length units and then performs a weighted average to obtain the "displayed density," which is essentially a convolutional smoothing of the actual density.

[0003] This detection method is widely used in industries such as tobacco. Taking cigarette testing as an example, the tobacco filling density of a cigarette (cylindrical) directly affects key qualities such as smoking experience and combustion performance, and is a core parameter for product digitalization research and development. However, the density distribution of cigarettes has multi-segment heterogeneous characteristics, covering multiple regions such as the compaction segment at the ignition end, the transition segment, and the filling segment. It also has special structures such as the gold ring line of the tipping paper and the flavor capsule of the filter tip, which are naturally suitable for triggering the "edge effect" of microwave detection.

[0004] Existing technologies lack systematic mathematical compensation methods. The tobacco industry can only correct the deviation by deleting data from both ends, which still cannot solve the problem of false fluctuations in "displayed density" and deviations from the true density. As a result, the data is difficult to play a guiding role in product design and process control. Other industries face the same bottleneck in similar tests. There is an urgent need for a universal and highly accurate edge effect compensation method to improve the authenticity and usability of measurement results. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a microwave density detection edge effect compensation method and system based on moving convolution. By establishing a rigorous mathematical model, the method systematically compensates for measurement distortions caused by the scanning window at the end face, density transition area, and material conversion area of ​​a column (including cylinders, square prisms, triangular prisms, etc.), thereby obtaining detection results that truly reflect the axial density distribution of the column.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a microwave density detection edge effect compensation method based on moving convolution, comprising: The spatial response characteristics of the detection equipment are obtained by scanning a standard bar with microwave, and a scanning model is established. Based on the design parameters of the column to be tested, a simulation model of the theoretical axial density distribution of the column is constructed; Virtual units with background density are virtually extended from both ends of the column to be detected as represented by the simulation model to form a detection virtual model; A forward convolution operation is performed based on the scanning model and the detection virtual model to obtain a predicted density distribution that includes edge effect interference; The cylinder to be tested is placed into the testing device, the microwave measured density is obtained, and the regularized deconvolution operation is performed using the scanning model to reconstruct the cylinder inversion density distribution that compensates for edge effects. The inverted weight of the column is calculated based on the inverted density distribution, and compared and calibrated with the theoretical weight of the column to be tested to obtain the final true density distribution of the column.

[0007] Secondly, the present invention provides a microwave density detection edge effect compensation system based on moving convolution, comprising: The scanning model construction module is configured to acquire the spatial response characteristics of the detection device by scanning a standard bar with microwave and then establish a scanning model. The simulation model building module is configured to build a simulation model of the theoretical axial density distribution of the column based on the design parameters of the column to be tested. The virtual extension module is configured to virtually extend virtual units with background density at both ends of the column to be detected represented by the simulation model, thereby forming a detection virtual model. The forward convolution module is configured to perform forward convolution operations based on the scanning model and the detection virtual model to obtain a predicted density distribution that includes edge effect interference. The inversion and reconstruction module is configured to place the column to be detected into the detection device, obtain the microwave measured display density, and perform regularized deconvolution operation using the scanning model to reconstruct the column inversion density distribution that compensates for edge effects. The calibration module is configured to calculate the inversion weight of the column based on the inversion density distribution, compare and calibrate it with the theoretical weight of the column to be tested, and obtain the final true density distribution of the column.

[0008] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the microwave density detection edge effect compensation method based on moving convolution described in the first aspect.

[0009] Fourthly, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the microwave density detection edge effect compensation method based on moving convolution described in the first aspect.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention effectively compensates for the edge effect of microwave density detection through the whole process design of standard bar scanning modeling, virtual unit extension, forward and reverse convolution operation and weight calibration; it not only accurately corrects the false density fluctuations at both ends of the cylinder (such as cigarettes) and eliminates background interference (such as cigarette tipping paper loops, filter beads, etc.), but also realizes high-precision reconstruction of the axial true density distribution, and the inversion results are highly consistent with the theoretical weight; the authenticity and reliability of the detection data are significantly improved, and it can provide accurate data support for the digital R&D, process optimization and quality assessment of cigarette products.

[0011] (2) By introducing virtual detection point technology and a strict convolution / deconvolution mathematical model, this invention fundamentally solves the edge effect problem caused by the scanning window covering multiple density regions, so that the reconstructed density curve is highly consistent with the real density distribution.

[0012] (3) The method provided by the present invention is a general technical framework. Its core model is independent of specific prisms (such as cylinders, square prisms, triangular prisms, etc.) and can be widely applied to the density detection of prisms of different industries and specifications.

[0013] (4) The present invention can predict the test results and optimize the process parameters in the product design stage through "forward convolution"; it can also correct the measured data and restore the true density distribution through "backward convolution", making it flexible in application scenarios.

[0014] (5) When applied to the cigarette industry, the present invention can accurately obtain the true density axial distribution of cigarettes (cylinders), providing extremely accurate data support for the digital design of cigarette products, intelligent quality control and lean process improvement, and can effectively promote the stability of cigarette sensory quality.

[0015] (6) Through the implementation of a dedicated system, equipment and program, the present invention can be conveniently integrated into the existing detection process, thereby improving the level of automation and the consistency of results.

[0016] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0017] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute a limitation thereof.

[0018] Figure 1 This is a schematic diagram of cigarette density distribution provided in an embodiment of the present invention; Figure 2The main flowchart of a microwave density detection edge effect compensation method based on moving convolution provided for an embodiment of the cigarette (cylinder) of the present invention; Figure 3 This is a schematic diagram of the density characteristic segment of a cigarette (cylinder) provided in an embodiment of the present invention; Figure 4 This is a graph showing the relationship between the density detection value and the theoretical prediction value provided in an embodiment of the present invention. Figure 5 This is a graph showing the relationship between microwave density detection correction value and true density provided in an embodiment of the present invention. Figure 6 The R-curve and inverted m′ curve of the nondestructive testing of the metal calibration bar provided in the embodiments of the present invention. Detailed Implementation

[0019] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] The tobacco filling density in a cigarette (cylinder) reflects the spatial proportion of tobacco and indirectly characterizes the porosity of the cigarette (cylinder). Therefore, it is a key indicator affecting the smoking experience, ventilation characteristics, combustion performance, smoke generation and sensory quality of cigarettes. It is a basic parameter for modeling the ventilation characteristics of cigarettes and characterizing the combustion effect, and it is an essential research content of the tobacco industry's major scientific and technological project of "digital R&D design and application of cigarette products".

[0021] like Figure 1 As shown, the density distribution of cigarettes is determined by the specifications of the cigarette leveling disc and the length of the filter tip during the production process. It is generally divided into six sections: the compacted section at the ignition end (section A, high density), the transition section (zone I, arithmetic transition), the filling section (section B, filling density), the transition section (zone II, arithmetic transition), the compacted section at the receiving end (section C, high density), and the filter rod section. Among them, the first five sections are the cigarette stick (cylindrical) sections filled with tobacco, and the filter rod section is the filter tip section filled with tobacco bundle.

[0022] Therefore, microwave density detection of cigarette sticks (cylindrical) covers the three major "edge effects" of microwave density detection. The obtained cigarette density curve shows a false downward trend at the lit end of the cigarette stick (cylindrical) and a false upward trend at the cigarette tipping end. In addition, the gold ring line of the tipping paper and the filter capsule of some cigarettes also have a significant impact on the "displayed density" of the cigarette. Therefore, the "displayed density" cannot accurately reflect the true axial density distribution of the cigarette, which seriously affects the application effectiveness of this data.

[0023] Although the tobacco industry has corrected the imbalance by deleting data from both ends, the data distortion still makes it difficult for the data to play its due guiding role in product design, process control and quality assessment, and the model data in related studies have obvious irrationality.

[0024] In existing microwave detection technologies across other industries, there is also a lack of systematic mathematical methods to compensate for the systematic errors introduced by the "edge effect" in the physical scanning process. Therefore, this invention proposes a microwave density detection edge effect compensation method, system, medium, and device based on moving convolution to compensate for edge effects in microwave density detection and improve the authenticity, reliability, and usability of measurement results.

[0025] Example 1 like Figure 2 As shown, this embodiment discloses a microwave density detection edge effect compensation method based on moving convolution, including the following steps: S1: Obtain the spatial response characteristics of the detection equipment by scanning a standard bar with microwave and establish a scanning model; S2: Based on the design parameters of the column to be tested, construct a simulation model of the theoretical axial density distribution of the column; S3: Virtual units with background density are virtually extended at both ends of the column to be detected as represented by the simulation model to form a detection virtual model; S4: Perform forward convolution operation based on the scanning model and the detection virtual model to obtain the predicted density distribution including edge effect interference; S5: Place the column to be detected into the detection device, obtain the microwave measured density, and use the scanning model to perform regularized deconvolution operation to reconstruct the column inversion density distribution that has been compensated for edge effects. S6: Calculate the inversion weight of the column based on the inversion density distribution, compare and calibrate it with the theoretical weight of the column to be tested, and obtain the final true density distribution of the column.

[0026] Next, combined Figure 2 This embodiment provides a detailed description of a microwave density detection edge effect compensation method based on moving convolution.

[0027] S1: Microwave Scanning Model Construction This step serves as system calibration, aiming to accurately characterize the scanning characteristics of a specific microwave density detector and obtain key parameters of the convolution kernel.

[0028] (1) Selecting a standard bar Select a radius ( r A known, homogeneous standard bar with uniform density along the axial direction (such as a uniform filter bar or other homogeneous material bar).

[0029] (2) Scanning measurement The standard bar was placed in a microwave density detector for axial scanning measurement, and its density measurement curve was recorded and plotted.

[0030] (3) Determine the half-length of the scan P Analyze the density measurement curves at both ends of the standard bar, and take the axial projection length of the curve from the background value (e.g., 0) to the stable value as the half-length of the scan. P 1 (left end) and P 2 (Right end). Total width of the scanning window. W = P 1+ P 2.

[0031] For a general-purpose standard microwave density meter P 1= P 2, its half-length is defined as P Window width W =2 P .

[0032] (4) Calculate the scanning window volume V According to the scanning geometry ( Figure 1 ), scan window size V This is the volume of the overlapping portion between the scan window and the cylinder. Taking a cylinder as an example, the scan volume of the window is:

[0033] (5) Calculate the convolution weights oh x .

[0034] According to the scanning geometry ( Figure 1 Divide the scanning window into 2 P A length unit is defined, and an axial coordinate system is established, with the origin at the left end set to 0. The coordinates of the right boundary of each length unit are then taken sequentially. x =1, 2, ..., P , P +1, ..., 2 P Calculate the relative position of the left window. x cumulative volume V ( x ).

[0035] Taking a cylinder as an example, a typical calculation formula is as follows: ; in, , where is the geometric parameter.

[0036] Clearly, the volume per unit length of the left half-window scan... v x : ; Because the window is symmetrical, the volume per unit length of the right half-window scan is: ; Normalized convolution weights oh x The calculation formula is as follows:

[0037] This weight vector oh x This is the kernel for subsequent convolution operations.

[0038] For example, select a radius r A filter rod with a diameter of 2.7 mm and uniform density was used as a homogeneous standard rod and placed in an MW3220 microwave density analyzer for axial scanning measurement. The density measurement curve was recorded and plotted. The axial projection length of the curve from the left and right endpoints to the stable value was taken as the half-length of the scan, thus obtaining... P =5 mm, then the convolution window width W =2 P =10 mm. Based on the output results of the microwave detector, the unit length in this embodiment is 1 mm.

[0039] The calculated window scan volume is ; According to the scan geometry (e.g.) Figure 1 As shown), the scanning window is divided into 10 segments, and an axial coordinate system is established. The origin at the left end is set to 0, and the coordinates of the right boundary of each segment are taken sequentially. x =1, 2, ……, 10.

[0040] Calculate the relative position of the left window x cumulative volume V ( x Volume of the left window unit length scan segment v x And the volume of the right half-window unit length scan segment. This gives the volume of the window unit length scan segment. v x The value is: Table 1. Volume of scan segment per unit length of window ( ); 1 2 3 4 5 6 7 8 9 10 <![CDATA[ v x ]]> 1.330 5.821 11.450 17.081 21.572 21.572 17.081 11.450 5.821 1.330 Determine the scan volume per unit length of the window v Normalized weights oh x , , x =1, 2, ..., 10; This weight vector This is the kernel for subsequent convolution operations.

[0041] ≈[0.012, 0.051, 0.1, 0.149, 0.188, 0.188, 0.149, 0.1, 0.051, 0.012]; In this embodiment, a microwave scanning model was constructed to accurately characterize the scanning characteristics of a specific microwave density detector, providing key parameter support for system calibration. By selecting a homogeneous standard bar with a known radius for axial scanning measurement, the half-length of the scan and the window volume can be accurately determined, thereby establishing the correspondence between length units and cumulative volumes and calculating reliable convolution weights. This not only effectively avoids the errors caused by relying on empirical parameters in traditional calibration but also provides a unified quantitative benchmark for subsequent density detection, improving detection accuracy and system stability.

[0042] S2: Construction of Column Simulation Model This step serves as theoretical modeling, discretizing the column based on its design or manufacturing parameters. L One length unit.

[0043] (1) Establish a cylindrical coordinate system Establish an axial coordinate system with the origin at 0. The coordinates of the right boundary of each length unit are as follows: i =1, 2, 3, ... L The axial "theoretical density" per unit length is determined based on the design and manufacturing parameters of the column. m i The theoretical distribution.

[0044] (2) Determine the density distribution characteristics For a column with a segmented axial density distribution (a complete set of several consecutive unit lengths with a fixed density), a segmented model is constructed, and a segmented density line graph is plotted, with the names of each density segment indicated.

[0045] Take length L =67 mm, radius r A smoke column of 2.7 mm is discretized into 67 unit lengths. An axial coordinate system is established with the origin at 0. The coordinates of the right boundary of each segment are as follows: i =1, 2, 3, ..., 67. Its processing parameters are determined by the specifications of the leveling plate (center distance between grooves, groove spacing, groove width, groove depth, groove length), and are divided into five density characteristic segments: A, I, B, II, and C. Figure 3 As shown. Length of the cigarette (cylindrical). L The center distance of the leveling grooves on the leveling plate is given. Section B is the spacing between the leveling grooves. Section I is the groove width of the deep leveling groove. Section II is the groove width of the shallow leveling groove. Section A is half the length of the deep leveling groove minus the length of Section I. Section C is half the length of the shallow leveling groove minus the length of Section II.

[0046] The length of leveling trough A in this embodiment is...L 槽A =32 mm, C-groove length L 槽C =32 mm, depth and shallow groove width are both W 槽 =3 mm, therefore the length of segment A is 13 mm ( i =1, 2, ..., 13), with density being a constant. M A Section B is 35 mm long. i =17, 18, ..., 51), density is a constant. M B Segment C is 13 mm long. i =55, 56, ..., 67), density is constant. M C Zone I is a transition zone, 3mm in length. i =14, 15, 16), density from M A Towards M B Gradual transition; Zone II is a transition zone 3 mm long ( i =52, 53, 54), density from M B Towards M C Arithmetic progression.

[0047] S3: Detection of Virtual Model Construction (Boundary Processing) To address the edge effect, virtual units must be introduced at both ends of the simulation model.

[0048] (1) Add to both ends of the cylinder simulation model respectively P Each virtual unit is used to construct a new virtual model.

[0049] (2) If the original sequence number remains unchanged, the virtual model index will be as follows: i = 1- P ,2- P ,3- P , ..., 0, 1, ..., L , L +1, ... L + P Set the density of the virtual cells to the background density value. For example, set the background density value of cigarettes to 0.

[0050] In the cigarette (cylindrical) simulation model M i Five virtual units are added to each end to construct a new virtual model, i.e., a simulation model.i =-4, -3, -2, -1, 0, 1, ……, 67, 68, 69, 70, 71, 72, “-4, -3, -2, -1,0” and “68, 69, 70, 71, 72”, the virtual cell density background value is 0.

[0051] The shared model described above forms the basis for both forward prediction and reverse reconstruction.

[0052] S4: Density Convolution Model Construction (Forward Prediction) This model is used to deduce "predicted density" from "theoretical density" and is a mathematical tool for product design and process control.

[0053] (1) Establish a detection value index Microwave density measurement begins at the left end face of the cylinder, with one measurement point taken per unit length, continuing until the right end face. Therefore, the measured value... R j The total number is L +1. Among them, j For the detection point number, j =0, 1, 2, ... L .

[0054] (2) Forward convolution Column j The "predicted density" of a point is the density convolution value of the scan window, and the unit length index of this window is given by the following formula.

[0055] Therefore, "predicted density" R j Calculated using the following formula:

[0056] in, This includes the density of both physical and virtual units.

[0057] According to product requirements, the cigarette stick (cylindrical) of S2 is designed to weigh 374 mg, and a leveling trough of equal specifications is used. M A = M C The cigarettes are produced using a leveling coil rolling process, and it is assumed that the compaction ratio of the cigarettes (cylindrical) is 1.5. M A =1.5 M B ). Calculations show that the theoretical densities of a cigarette (cylindrical) are respectively... M A =300 mg / cm 3 ,M B =200 mg / cm 3 , M C =300 mg / cm 3 The densities in Zone I are 275, 250, and 225 mg / cm³, respectively. 3 The densities in zone II are 225, 250, and 275 mg / cm³, respectively. 3 .

[0058] Microwave density detection starts from the left end face of the cigarette (cylinder) (reference position 0 mm), and a value is measured every 1 mm, for a total of 68 values, numbered sequentially as follows: j =0, 1, ……, 67.

[0059] The "predicted density" is calculated using the following formula for forward convolution:

[0060] Specific examples of convolution methods are as follows: (1) When the detection point j When =0, the smoke section is covered. i Given the intervals -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, the effective density range is: i =1, 2, 3, 4, 5. Its predicted density is as follows: R 0= oh 6×300+ oh 7×300+ oh 8×300+ oh 9×300+ oh 10 ×300=150.00.

[0061] (2) When the detection point j =14, covering smoke section i Ranges 10, 11, 12, 13, 14, 15, 16, 17, 18, and 19 are all effective density ranges. Their predicted densities are as follows: R 14 = oh 1×300+ oh 2×300+ oh 3×300+ oh 4×300+ oh 5×275+ oh 6×250+ oh 7×225+ oh 8×200+ oh 9×200+ oh 10 ×200=258.44.

[0062] As the convolution window moves across the cigarette (cylinder), the covered section of cigarette moves accordingly, and so on, to complete the construction of the density convolution model.

[0063] Table 2. Calculation results of forward convolution of predicted density at each detection point of the cigarette (cylinder); 0 150.00 17 213.70 34 200.00 51 225.91 1 206.52 18 205.91 35 200.00 52 241.56 2 251.27 19 201.85 36 200.00 53 258.44 3 281.27 20 200.29 37 200.00 54 274.09 4 296.52 21 200.00 38 200.00 55 286.30 5 300.00 22 200.00 39 200.00 56 294.09 6 300.00 23 200.00 40 200.00 57 298.15 7 300.00 24 200.00 41 200.00 58 299.71 8 300.00 25 200.00 42 200.00 59 300.00 9 299.71 26 200.00 43 200.00 60 300.00 10 298.15 27 200.00 44 200.00 61 300.00 11 294.09 28 200.00 45 200.00 62 300.00 12 286.30 29 200.00 46 200.00 63 296.52 13 274.09 30 200.00 47 200.29 64 281.27 14 258.44 31 200.00 48 201.85 65 251.27 15 241.56 32 200.00 49 205.91 66 206.52 16 225.91 33 200.00 50 213.70 67 150.00 Roll cigarettes according to the above leveling plate parameters, adjusting until the weight of each cigarette (cylindrical) is 374 mg. Measure the density of 20 cigarettes using a MW3220 microwave densitometer, and take the average value as the displayed density. R j ′ The results are as follows: Table 3. Density measurement results at various testing points of the cigarette (cylindrical); 0 146.71 17 221.29 34 209.77 51 232.41 1 202.37 18 214.65 35 210.35 52 244.14 2 247.54 19 211.51 36 209.83 53 259.59 3 275.11 20 210.61 37 209.59 54 271.88 4 291.07 21 209.64 38 210.13 55 282.86 5 293.90 22 209.77 39 210.07 56 288.65 6 293.84 23 209.92 40 209.37 57 292.64 7 293.76 24 210.00 41 209.43 58 293.02 8 294.25 25 209.27 42 209.53 59 292.85 9 293.87 26 209.10 43 210.51 60 294.17 10 292.58 27 209.38 44 210.58 61 294.02 11 287.96 28 210.06 45 210.16 62 293.28 12 282.91 29 209.98 46 210.15 63 290.65 13 272.69 30 209.33 47 209.68 64 275.37 14 259.22 31 211.04 48 211.85 65 245.43 15 244.47 32 209.46 49 214.55 66 202.11 16 232.13 33 210.25 50 220.81 67 147.43 Comparison shows density R′ Compared to predicted density R The distribution patterns differ, mainly manifested in the lower "display density" at the two ends of the 14 measurement points and the higher "display density" in the middle section, such as... Figure 4 As shown, it is demonstrated that under the condition of the leveling plate groove depth, the actual compaction ratio of the cigarette (cylinder) is different from that expected, and further deconvolution analysis is required.

[0064] S5: Density-based deconvolution model construction (reverse reconstruction) This model is used to reconstruct the true density from measured values ​​and is key to accurate detection.

[0065] (1) Obtain the measured density vector R′ The actual cylinder was placed in a microwave density meter for measurement, resulting in the displayed density vector R′ (with dimensions of ( L +1)×1).

[0066] (2) Construct the convolution relation matrix A Due to the existence of virtual smoke segments, a ( L +1)×( L +2 P A sparse matrix A of dimension 1, which is composed of unit scan segment weights. oh Decide.

[0067] Matrix elements are defined as follows:

[0068] in, The relative position of the convolution kernel x。 therefore, .

[0069] (3) Establish a mathematical model of deconvolution The convolution process can be expressed as a system of linear equations: A × m′ = R′. Where m′ is the (L+2P)×1-dimensional density vector to be determined (the virtual segment has elements corresponding to 0).

[0070] (4) Regularization solution Due to matrix A T A is usually ill-conditioned, and Tikhonov regularization is used to solve it: m ′=( A T A + λI ) 1 A T R ′ (5) Apply boundary constraints During or after the solution process, the inversion density can be... m Apply physical constraints.

[0071] For example: non-negative density. Lower limit of density for each characteristic segment, limit of density fluctuation for each characteristic segment, etc.

[0072] (6) Verification and optimization (iteration): Inversion density m Substituting into the forward convolution model S4, we obtain the validation density. R ′′, compared with the original display density R Compare the residuals. If the residuals do not meet the requirements, adjust λ and repeat this step until the reconstruction effect is satisfactory.

[0073] Specifically, based on the display density obtained from S4, its vector is determined. R′ The dimension is 68×1.

[0074] Due to the existence of virtual units, a 68×77 dimensional sparse matrix A can be constructed, which is composed of unit scan segment weights. oh Decide.

[0075] Matrix elements are defined as follows:

[0076] in, That is, the relative position of the scanning window. x The following example illustrates this: (1) When j When = 0, the element in the first row of matrix A is: A(0, -4) = oh（-4-0+5） = oh 1 = 0.012, i =-4; Similarly A(0, -3) = oh 2 = 0.051, i =-3; A(0, -2) = oh 3 = 0.1 i =-2; A(0, -1) = oh 4 = 0.149 i =-1; A(0,0)= oh 5 = 0.188 i =0; A(0,1)= oh 6 = 0.188 i =1; A(0,2)= oh 7 = 0.149 i =2; A(0,3)= oh 8 = 0.1 i =3; A(0,4)= oh 9 = 0.051 i =4; A(0,5)= oh 10 =0.012, i =5;

[0077] Right now, j The microwave scanning window at point =0 is the 4th to 5th mm, and the remaining elements of matrix A are A(14, i All values ​​are 0. Since -4 to 0 mm is a virtual segment, the effective window is 1 to 5 mm.

[0078] (2) When j When =14, the element in the 15th row of matrix A is: A(14, 10) = ω （10-14+5） =ω1=0.012, i =10; A(14, 11) = ω² = 0.051, i =11; A(14, 12) = ω3 = 0.1, i =12; A(14, 13) = ω4 = 0.149, i =13; A(14, 14) = ω5 = 0.188, i =14; A(14, 15) = ω6 = 0.188, i =15; A(14, 16) = ω7 = 0.149, i =16; A(14, 17) = ω8 = 0.1, i =17; A(14, 18) = ω9 = 0.051, i =18; A(14, 19) = ω 10 =0.012, i =19.

[0079] Right now, j The microwave scanning window with point =14 is from the 10th to the 19th mm. The remaining elements of matrix A are A(14, i All are 0. And so on. Since matrix A has a large number of elements, they will not be listed one by one.

[0080] The convolution process can be expressed as a system of linear equations: A × m′ = R′ .in, m′ This is the 77×1 dimensional "inversion density" vector to be determined. The background value of the element corresponding to the virtual segment is 0, therefore... m′ Only a 67×1 density vector is required.

[0081] With testing points j Taking 14 as an example, its convolution equation is:

[0082] Following the above method, all 68 measured values ​​( R j ′ Solve the equations one by one to form a system of equations. m i A system of linear equations with unknowns.

[0083] Due to the matrix A T A Typically, deconvolution is overdetermined and ill-conditioned. To ensure the uniqueness and stability of the deconvolution results, Tikhonov regularization is used to obtain a cigarette (cylinder) density deconvolution model.

[0084] Where I refers to the 67×67 identity matrix. l This is the regularization parameter.

[0085] when l When = 0, the formula for the inverse convolution model degenerates to: , which is the standard least squares solution of the normal equation.

[0086] For cigarettes with a length of 50-140 mm and a diameter of 5.0-8.0 mm, l The value range is 0.005~0.05, and in this embodiment, it is taken as... l =0.01.

[0087] make: ,but The right-hand side of the equation is: ; The deconvolution equation is reduced to: M×m′=b; Solve the system of linear equations, where the boundary constraints are: Lower limit of cigarette (cylindrical) density M A = M C >260 mg / cm 3 , M B >190 mg / cm 3 ; Density within each feature segment A, B, and C m i The range of all values ​​is less than 20 mg / cm. 3 .

[0088] After automatic calculation by the system, the following inversion density is output. m i ′ : Table 4. Calculation results of inversion density for each element of the cigarette (cylinder); -4 0 16 231.44 36 209.65 56 293.63 -3 0 17 209.64 37 210.17 57 294.38 -2 0 18 210.22 38 210.41 58 293.80 -1 0 19 210.32 39 209.87 59 294.73 0 0 20 210.05 40 209.93 60 295.15 1 294.29 21 209.63 41 210.63 61 293.83 2 294.02 22 210.36 42 210.57 62 293.98 3 292.70 23 210.23 43 210.47 63 294.72 4 294.53 24 210.08 44 209.49 64 293.94 5 293.51 25 210.00 45 209.42 65 294.27 6 294.10 26 210.73 46 209.84 66 294.81 7 294.16 27 210.90 47 209.85 67 294.27 8 294.24 28 210.62 48 210.56 68 0 9 293.75 29 209.94 49 209.71 69 0 10 293.89 30 210.02 50 210.41 70 0 11 293.87 31 210.67 51 210.70 71 0 12 295.07 32 208.96 52 230.36 72 0 13 293.58 33 210.54 53 252.77 14 272.55 34 209.75 54 272.50 15 251.87 35 210.23 55 294.35 The inversion results show that the inversion density m i The distribution is obviously different from the theoretical density. m i The distribution varies considerably. Analysis shows... m′ A ≈ m′ C ≈294 mg / cm 3 , m B ′ ≈210 mg / cm 3 Obviously m′ and R′ Relationship such as Figure 5 As shown, and M ′A =1.4 M′ B Therefore, the actual compaction ratio of cigarettes (cylindrical) produced using this leveling trough specification is 1.4, not the pre-designed compaction ratio of 1.5. Thus, designers can achieve the designed compaction ratio by selecting different leveling trough depths and other specification parameters based on the above analysis, or by directly using the actual compaction ratio to correct the theoretical density distribution, thereby achieving their overall design expectations.

[0089] Finally, the inversion density m Substituting into the forward convolution model S4, we obtain the validation density. R" and will R" With display density R The residuals should meet the design requirements; if they do not, the regularization parameters should be optimized and adjusted. l, Iterate until the residual meets the design requirements.

[0090] S6: Inversion Density Calibration Based on the determined inversion density, the inversion weight of the cylinder is calculated and compared with the theoretical weight of the cylinder to obtain the microwave density measurement response coefficient k of the measurement medium. The inversion density is then corrected to the calibration density using k, which is the true density of the cigarette (cylinder).

[0091] To determine the conformity of the displayed density, let: 3 in, The actual weight of the cigarette is 374 mg.

[0092] The results show that the inverted density is 1.3% higher than the theoretical density. Therefore, it is necessary to... m i Corrected to calibration density m i "， Right now 。

[0093] The calibration density in this embodiment is as follows: Table 5. Calibration density results of cigarettes (cylindrical); -4 0 16 228.47 36 206.96 56 289.86 -3 0 17 206.95 37 207.47 57 290.60 -2 0 18 207.52 38 207.71 58 290.03 -1 0 19 207.62 39 207.18 59 290.95 0 0 20 207.35 40 207.24 60 291.36 1 290.51 21 206.94 41 207.93 61 290.06 2 290.25 22 207.66 42 207.87 62 290.21 3 288.94 23 207.53 43 207.77 63 290.94 4 290.75 24 207.38 44 206.80 64 290.17 5 289.74 25 207.31 45 206.73 65 290.49 6 290.33 26 208.03 46 207.15 66 291.03 7 290.38 27 208.19 47 207.16 67 290.49 8 290.46 28 207.92 48 207.86 68 0 9 289.98 29 207.25 49 207.02 69 0 10 290.12 30 207.32 50 207.71 70 0 11 290.10 31 207.97 51 208.00 71 0 12 291.28 32 206.28 52 227.40 72 0 13 289.81 33 207.84 53 249.53 14 269.05 34 207.06 54 269.00 15 248.64 35 207.53 55 290.57 The calibration density is the true density of the medium. The k-value is a parameter related to the characteristics of the measured medium, reflecting the detection response amplitude of different media in microwave measurements, and is called the medium response coefficient.

[0094] The response coefficients of different media vary significantly, leading to differences in their displayed density during microwave detection, which are then transmitted as differences in inversion density during convolution. In product design, process control, and quality evaluation, the inversion density should be corrected to a calibration density based on the different media's response coefficients to ensure the reliability of the technical results.

[0095] As one implementation method, the application of the solution provided in this embodiment in other non-smoke general fields (metal rod flaw detection) is described.

[0096] A factory produces 50 mm long metal calibration rods. Before leaving the factory, they need to undergo microwave density non-destructive testing to prevent internal voids. The displayed density R′ of one of the calibration rods is shown in the table below: Table 6. Display density of calibration rods; 0 450 9 853 18 900 27 900 36 900 46 890 1 620 10 857 19 900 28 900 37 900 47 844 2 754 11 868 20 900 29 900 38 900 48 754 3 844 12 880 21 900 30 900 39 900 49 620 4 888 13 892 22 900 31 900 40 900 50 450 5 893 14 898 23 900 32 900 41 900 6 882 15 900 24 900 33 900 42 900 7 869 16 900 25 900 34 900 43 900 8 858 17 900 26 900 35 900 44 900 Following the parameters and steps in S1-S5, deconvolve the sample to obtain the inversion density m′ as follows: Table 7. Inversion density of calibration rods; 1 900 11 900 21 900 31 900 41 900 2 900 12 900 22 900 32 900 42 900 3 900 13 900 23 900 33 900 43 900 4 900 14 900 24 900 34 900 44 900 5 900 15 900 25 900 35 900 45 900 6 900 16 900 26 900 36 900 46 900 7 900 17 900 27 900 37 900 47 900 8 900 18 900 28 900 38 900 48 900 9 790 19 900 29 900 39 900 49 900 10 758 20 900 30 900 40 900 50 900 Clearly, the rod contains holes in the 9th and 10th millimeter sections, as shown in the inversion curve. Figure 6 .

[0097] To determine the size, the hole is considered equivalent to a frustum-shaped cone with a right base and left top, where the mid-section cross-sectional area is approximately [a fraction of the cross-sectional area of ​​the metal rod]. The median diameter of the equivalent frustum of the hole is approximately 7.3% of the diameter of the metal rod, which constitutes a serious defect in the hole.

[0098] This invention fundamentally solves the edge effect problem caused by the scanning window covering multiple density regions by introducing virtual detection point technology and a rigorous convolution / deconvolution mathematical model, ensuring that the reconstructed density curve closely matches the true density distribution. Secondly, it provides a universal technical framework whose core model construction is independent of the specific cylindrical shape (such as cylinders, square prisms, triangular prisms, etc.), making it widely applicable to density detection of cylinders of different industries and specifications. Simultaneously, it can predict detection results and optimize process parameters during the product design stage through "forward convolution," and correct measured data through "reverse convolution" to restore the true density distribution, offering flexible application scenarios. Furthermore, when applied to the cigarette industry, it can accurately obtain the true axial density distribution of cigarettes (cylinders), providing highly accurate data support for digital product design, intelligent quality control, and lean process improvement, effectively promoting the stability of cigarette sensory quality. Fifthly, through the implementation of dedicated systems, equipment, and programs, this method can be conveniently integrated into existing detection processes, improving automation levels and result consistency.

[0099] This specific embodiment fills the gap in the existing technology for the lack of systematic mathematical means to compensate for edge effects. It addresses the core pain point of the deviation between the "displayed density" and the actual density in microwave detection by proposing an innovative solution that combines virtual unit extension and regularized deconvolution, breaking through the limitations of traditional data deletion correction. It is not only applicable to the density detection of multi-segment heterogeneous structures in cigarettes, but can also be transferred to column detection scenarios in other industries, providing universal technical support for similar edge effect problems.

[0100] Example 2 This embodiment provides a microwave density detection edge effect compensation system based on moving convolution, including: The scanning model construction module is configured to acquire the spatial response characteristics of the detection device by scanning a standard bar with microwave and then establish a scanning model. The simulation model building module is configured to build a simulation model of the theoretical axial density distribution of the column based on the design parameters of the column to be tested. The virtual extension module is configured to virtually extend virtual units with background density at both ends of the column to be detected represented by the simulation model, thereby forming a detection virtual model. The forward convolution module is configured to perform forward convolution operations based on the scanning model and the detection virtual model to obtain a predicted density distribution that includes edge effect interference. The inversion and reconstruction module is configured to place the column to be detected into the detection device, obtain the microwave measured display density, and perform regularized deconvolution operation using the scanning model to reconstruct the column inversion density distribution that compensates for edge effects. The calibration module is configured to calculate the inversion weight of the column based on the inversion density distribution, compare and calibrate it with the theoretical weight of the column to be tested, and obtain the final true density distribution of the column.

[0101] Example 3 This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the microwave density detection edge effect compensation method based on moving convolution as described in Embodiment 1 above.

[0102] Example 4 This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the microwave density detection edge effect compensation method based on moving convolution as described in Embodiment 1 above.

[0103] The steps or modules involved in Embodiments 2 to 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0104] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A microwave density detection edge effect compensation method based on moving convolution, characterized in that, include: The spatial response characteristics of the detection equipment are obtained by scanning a standard bar with microwave, and a scanning model is established. Based on the design parameters of the column to be tested, a simulation model of the theoretical axial density distribution of the column is constructed; Virtual units with background density are virtually extended from both ends of the column to be detected as represented by the simulation model to form a detection virtual model; A forward convolution operation is performed based on the scanning model and the detection virtual model to obtain a predicted density distribution that includes edge effect interference; The cylinder to be tested is placed into the testing device, the microwave measured density is obtained, and the regularized deconvolution operation is performed using the scanning model to reconstruct the cylinder inversion density distribution that compensates for edge effects. The inverted weight of the column is calculated based on the inverted density distribution, and compared and calibrated with the theoretical weight of the column to be tested to obtain the final true density distribution of the column.

2. The microwave density detection edge effect compensation method based on moving convolution as described in claim 1, characterized in that, The step of obtaining the spatial response characteristics of the detection device and establishing a scanning model by scanning a standard bar with microwaves specifically includes: Analyze the characteristics of the measurement curve at the end of the standard rod to determine the effective half-length of the system; Based on the scan half-length, the convolution window parameters and their weight distribution for characterizing the spatial response characteristics of the device are determined, and a scan model is established.

3. The microwave density detection edge effect compensation method based on moving convolution as described in claim 1, characterized in that, The step of constructing a simulation model of the theoretical axial density distribution of the column based on its design parameters specifically includes: Based on the physical structural parameters and theoretical filling specifications of the column, its axial coordinate system is established; Under the coordinate system, the theoretical density values ​​at each position along the axial direction are assigned or calculated to form a simulation model of the cylinder.

4. The microwave density detection edge effect compensation method based on moving convolution as described in claim 1, characterized in that, The process involves virtually extending virtual units with background density at both ends of the column to be detected, as represented by the simulation model, to form a detection virtual model. Specifically, this includes: The simulation model is extended axially at both ends, and the length of the extended virtual unit is equal to the effective half-length of the scan model. The density value of the extended portion is set to be consistent with the density value of the detection environment background in order to construct a complete detection virtual model.

5. The microwave density detection edge effect compensation method based on moving convolution as described in claim 1, characterized in that, The step of performing a forward convolution operation based on the scanning model and the detection virtual model to obtain a predicted density distribution including edge effect interference specifically includes: The convolution weights represented by the scanning model are moved and convolved along the axis of the detection virtual model. By simulating the microwave detection process through computation, a predicted density distribution curve that includes the inherent ambiguity effect of the device is generated.

6. The microwave density detection edge effect compensation method based on moving convolution as described in claim 1, characterized in that, The process of placing the cylinder to be detected into the detection device, obtaining the microwave measured density, and performing regularized deconvolution operations using the scanning model to reconstruct the cylinder inversion density distribution compensated for edge effects specifically includes: The scanning model is then converted into a system matrix. The system matrix and the measured density vector are inverted using a regularization algorithm to suppress the instability of the solution; The inverted density distribution of the cylinder with compensated edge effects is obtained by solving the problem.

7. The microwave density detection edge effect compensation method based on moving convolution as described in claim 1, characterized in that, The process of calculating the inversion weight of the column based on the inversion density distribution, comparing and calibrating it with the theoretical weight of the column to be tested, and obtaining the final true density distribution of the column specifically includes: The inverted density distribution is integrated along the axis to obtain the calculated inversion weight of the cylinder. The ratio of the inverted weight to the known theoretical weight of the cylinder is calculated and used as the system response calibration coefficient. The inverted density distribution is scaled overall using the calibration coefficients to obtain the calibrated final density distribution.

8. A microwave density detection edge effect compensation system based on moving convolution, characterized in that, include: The scanning model construction module is configured to acquire the spatial response characteristics of the detection device by scanning a standard bar with microwave and then establish a scanning model. The simulation model building module is configured to build a simulation model of the theoretical axial density distribution of the column based on the design parameters of the column to be tested. The virtual extension module is configured to virtually extend virtual units with background density at both ends of the column to be detected represented by the simulation model, thereby forming a detection virtual model. The forward convolution module is configured to perform forward convolution operations based on the scanning model and the detection virtual model to obtain a predicted density distribution that includes edge effect interference. The inversion and reconstruction module is configured to place the column to be detected into the detection device, obtain the microwave measured display density, and perform regularized deconvolution operation using the scanning model to reconstruct the column inversion density distribution that compensates for edge effects. The calibration module is configured to calculate the inversion weight of the column based on the inversion density distribution, compare and calibrate it with the theoretical weight of the column to be tested, and obtain the final true density distribution of the column.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the microwave density detection edge effect compensation method based on moving convolution as described in any one of claims 1-7.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the microwave density detection edge effect compensation method based on moving convolution as described in any one of claims 1-7.

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