A DMA transfer function inversion method and apparatus based on a TDMA calibration platform

Abstract

This invention relates to a method and apparatus for DMA transfer function inversion based on a TDMA calibration platform. The method includes: calibrating the DMA using the TDMA calibration platform to obtain experimental scanning results; obtaining the coarse transfer function of the DMA based on the experimental scanning results; adjusting the parameters of the coarse transfer function to update it, obtaining a set of changes in the transfer function; and performing a weighted average based on the set of changes to determine the fine transfer function of the DMA. Compared to traditional inversion methods, this invention eliminates the assumption that "the shape of the transfer function is triangular," obtaining a transfer function shape with a wider applicability, thereby better reconstructing the transfer function of the DMA measured in the TDMA experiment, and thus improving the inversion accuracy of particle size distribution.

Description

Technical Field

[0001] This invention relates to the field of atmospheric ultrafine particulate matter size spectrum measurement technology, specifically to a DMA transfer function inversion method and apparatus based on a TDMA calibration platform. Background Technology

[0002] In the field of atmospheric ultrafine particulate matter size spectrum measurement technology, the Differential Mobility Analyzer (DMA) is widely used. Its function is to sieve monodisperse particles of a specific size from a group of polydisperse particulate matter samples. The DMA is used in conjunction with a charger and particulate detector (such as a condensation nucleus particle counter, CPC, condensation particle counter, aerosol electrometer, or aerosol electrometer) to form a "charge-sieving-measurement" system, which can be used for particle size spectrum measurement.

[0003] In the inversion process of particle size distribution measurement, the most basic formula is: ,in, Electromigration particle size The height of the particle size spectrum at that location, It is a particle detector in terms of electromigration particle size The measured value of particulate matter concentration at the location, It is the positive single-charge efficiency of the charger for particulate matter (let's assume that DMA uses negative high pressure to screen positive particles). It is the particle size of the electromigration particles The resolution at that point (i.e., in the particle size spectrum) (width of the column) For DMA in electromigration particle size The height of the transfer function. Existing DMA transfer function inversion methods treat the shape of the DMA transfer function as an ideal isosceles triangle, therefore adopting... ,in It is the height of the isosceles triangle. It is half the height and width (i.e., half the length of the base of an isosceles triangle).

[0004] Traditional methods for calibrating the DMA transfer function employ a TDMA calibration platform to meet the requirements of particle size distribution inversion methods. The DMA transfer function is assumed to be a... and A variable isosceles triangle, traversal and The values ​​are integrated separately and compared with the experimental scan results of the TDMA calibration platform. The value that results in the highest correlation between the integration result and the TDMA experimental scan result is selected. and The inversion result, i.e., the calibration result of the DMA transfer function, is obtained. However, traditional methods have some shortcomings. One important premise is that "the DMA transfer function is an ideal isosceles triangle," but the actual DMA transfer function is affected by factors such as manufacturing precision, and its shape is certainly not an ideal isosceles triangle. This ideal assumption does not match reality. Therefore, it is necessary to invent a more widely applicable inversion method to eliminate the assumption that "the transfer function is triangular," obtain a more general transfer function shape, better reconstruct the DMA transfer function measured in TDMA experiments, and thus improve the inversion accuracy of particle size distribution. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a DMA transfer function inversion method and apparatus based on a TDMA calibration platform.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect of the present invention, a DMA transfer function inversion method based on a TDMA calibration platform is disclosed.

[0008] The method includes the following steps:

[0009] The input to this method is the TDMA experimental scan result, and the output is the transfer function of DMA used in the TDMA experiment.

[0010] S1. Use the TDMA calibration platform to calibrate the DMA and obtain the experimental scanning results of the TDMA calibration platform;

[0011] S2. Based on the experimental scanning results of the TDMA calibration platform, obtain the coarse transfer function of the DMA;

[0012] S3. Adjust the parameters of the coarse transfer function of DMA, update the coarse transfer function of DMA, and obtain the set of changes in the transfer function.

[0013] S4. Based on the set of changes in the transfer function, perform a weighted average to determine the fine transfer function of the DMA.

[0014] Furthermore, the method for obtaining the coarse transfer function of the DMA includes:

[0015] Assume the transfer function of the DMA to be calibrated is represented by a histogram. For each column, based on the experimental scanning results of the TDMA calibration platform, the coarse transfer function of DMA is solved by the bisection method.

[0016] Furthermore, adjusting the parameters of the coarse transfer function of the DMA, updating the coarse transfer function of the DMA, and obtaining the set of changes in the transfer function include:

[0017] The assumptions made during the process of obtaining the coarse transfer function The column was changed to , … Repeat step S2 to obtain a total of [number] [items]. A coarse transfer function is used to construct a set of variations of the transfer function.

[0018] Furthermore, determining the fine transfer function of DMA by performing a weighted average based on the set of changes in the transfer function includes:

[0019] The set of changes in the transfer function The coarse transfer functions are weighted and averaged to obtain the fine transfer function of the DMA; the fine transfer function of the DMA is the DMA transfer function obtained by inversion.

[0020] Furthermore, the TDMA calibration platform includes a bipolar charge, a primary DMA, an ultrafine particulate filter, a secondary DMA, and a condensation nucleus particle counter;

[0021] The bipolar charge is connected to a sample gas containing polydisperse particulate matter at its inlet, and its outlet is connected to the inlet of the first-stage DMA. The outlet of the first-stage DMA is connected to the inlet of the ultrafine particulate filter, the outlet of the ultrafine particulate filter is connected to the inlet of the second-stage DMA, and the outlet of the second-stage DMA is connected to the inlet of the condensation nucleus particle counter. The ultrafine particulate filter is in communication with the atmosphere.

[0022] Furthermore, the experimental scanning results of the TDMA calibration platform are used as the input to the inversion method. The following conditions must be met:

[0023] The x-axis is Unitless, the vertical axis is No unit, among which, The electromobility of the scan. For the center mobility, The scanning range is , For scanning electromobility The corresponding particulate number concentration, For centrifugal mobility The corresponding particulate number concentration, The range is The experimental scanning results of the TDMA calibration platform show an intermediate... Highest, lowest on both sides It follows a normal distribution.

[0024] In a second aspect of the invention, a DMA transfer function inversion device based on a TDMA calibration platform is disclosed.

[0025] The device includes: a TMDA experimental result acquisition module, a coarse transfer function acquisition module, a transfer function change set acquisition module, and a fine function acquisition module;

[0026] The TMDA experimental results acquisition module is used to calibrate DMA using the TDMA calibration platform and obtain the experimental scan results of the TDMA calibration platform.

[0027] The coarse transfer function acquisition module is used to acquire the coarse transfer function of DMA based on the experimental scan results of the TDMA calibration platform.

[0028] The module for obtaining the set of changes in the transfer function is used to adjust the parameters of the coarse transfer function of DMA, update the coarse transfer function of DMA, and obtain the set of changes in the transfer function.

[0029] The fine function acquisition module is used to determine the fine transfer function of DMA by performing a weighted average based on the set of changes in the transfer function;

[0030] The coarse transfer function for obtaining the DMA includes:

[0031] Assume the transfer function of the DMA to be calibrated is represented by a histogram. For each column, based on the experimental scanning results of the TDMA calibration platform, the coarse transfer function of DMA is solved by the bisection method;

[0032] The process of adjusting the parameters of the coarse transfer function of the DMA, updating the coarse transfer function of the DMA, and obtaining the set of changes in the transfer function includes:

[0033] The assumptions made during the process of obtaining the coarse transfer function The column was changed to , … One, a total of A coarse transfer function is used to construct a set of variations of the transfer function;

[0034] The step of determining the fine transfer function of DMA by performing a weighted average based on the set of changes in the transfer function includes:

[0035] The set of changes in the transfer function The coarse transfer functions are weighted and averaged to obtain the fine transfer function of the DMA; the fine transfer function of the DMA is the DMA transfer function obtained by inversion.

[0036] Compared with the prior art, the advantages of the present invention are:

[0037] (1) In this invention, the transfer function of DMA calibrated in TDMA experiment is set to a general shape to eliminate the assumption that "the shape of the transfer function is a triangle", and a more general transfer function shape is obtained, so as to better restore the transfer function of DMA measured in TDMA experiment and thus improve the inversion accuracy of particle size spectrum.

[0038] (2) This invention does not employ traversal search when retrieving the coarse transfer function of DMA, but instead uses a binary search method. Let the number of coarse transfer function columns be... The number of changes in the coarse transfer function is The transfer function's ordinate precision is 0.1%. The binary search method reduces the algorithm complexity from... ( Each column has [a certain number of columns]. (Selection options) reduced to (After 10 iterations, the accuracy reaches 0.1%). Traversal search is almost impossible to operate with ordinary computers, while the algorithm described in this invention can be computed by ordinary computers.

[0039] (3) This invention sequentially inverts the coarse and fine transfer functions of DMA, resulting in a smoother inversion result that better reflects the actual situation. From a purely mathematical perspective, the TDMA calibration experiment is a multi-solution problem (multiple transfer functions can be integrated to obtain the TDMA experimental scan result). Therefore, the coarse transfer function of DMA inverted by this invention satisfies the sufficiency of solutions, meaning that this transfer function can be integrated to obtain the TDMA experimental scan result. Multiple changes to the coarse transfer function maximize the search for all possible solutions, and a weighted average is taken to obtain a smoother fine transfer function that better reflects the actual situation, i.e., the final inversion result. Attached Figure Description

[0040] Figure 1 It is a TDMA calibration platform;

[0041] Figure 2 This is a flowchart of the DMA transfer function inversion method based on the TDMA calibration platform in this invention;

[0042] Figure 3 This is a schematic diagram of the integration process in this invention;

[0043] Figure 4 This is a graph showing the scan results of the TDMA experiment;

[0044] Figure 5 This is a graph showing the results obtained using the traditional TDMA inversion method;

[0045] Figure 6This is an integral verification curve of the traditional TDMA inversion results;

[0046] Figure 7 This is a graph showing the result obtained by the inversion method described in this invention;

[0047] Figure 8 This is the integral verification curve of the inversion result of this invention.

[0048] in:

[0049] 101. Gas sample containing particulate matter with polydisperse particle size; 102. Bipolar charge device; 103. Primary DMA; 104. Secondary DMA; 105. Condensation nucleus particle counter; 106. Ultrafine particulate filter connected to the atmosphere. Detailed Implementation

[0050] The present invention will be further described below with reference to the accompanying drawings:

[0051] like Figure 1 The TDMA calibration platform shown includes a bipolar charge 102, a primary DMA 103, an ultrafine particulate filter 106, a secondary DMA 104, and a condensation nucleus particle counter 105. The inlet of the bipolar charge 102 is connected to a sample gas 101 containing polydisperse particulate matter, and its outlet is connected to the inlet of the primary DMA 103. The outlet of the primary DMA 103 is connected to the inlet of the ultrafine particulate filter 106, the outlet of the ultrafine particulate filter 106 is connected to the inlet of the secondary DMA 104, and the outlet of the secondary DMA 104 is connected to the inlet of the condensation nucleus particle counter 105. The ultrafine particulate filter 106 is in communication with the atmosphere.

[0052] The primary DMA 103 and secondary DMA 104 maintain the same mechanical structure, sheath gas flow rate, and sample gas flow rate. The sieving voltage of the primary DMA 103 is fixed, ensuring that the electromobility of the sieved particles is [missing value]. The voltage of the secondary DMA 104 is scanned. Sample gas 101 containing polydisperse particles first enters the bipolar charger 102, where it becomes charged, and then enters the first-stage DMA 103, yielding monodisperse particles with a number concentration of [missing information]. An ultrafine particulate filter 106, connected to the atmosphere, is used to balance the air pressure. The secondary DMA104 scanning voltage is used to further sieve the particles separated by the primary DMA104. Finally, the condensation nucleus particle counter 105 records the secondary DMA104 scanning voltage (the electromobility corresponding to the scanning voltage is...). ) and the number concentration of particulate matter at the 104 outlet ( The relationship between ) is denoted as the scan result. ,in, The scanning range is , The range is .

[0053] like Figure 2 This paper presents a DMA transfer function inversion method based on a TDMA calibration platform. The input to this method is the TDMA experimental scan result, and the output is the transfer function of DMA103 and 104 used in the TDMA experiment. The method includes the following steps:

[0054] S1. Use the TDMA calibration platform to calibrate the DMA and obtain the experimental scanning results of the TDMA calibration platform;

[0055] S2. Based on the experimental scanning results of the TDMA calibration platform, obtain the coarse transfer function of the DMA;

[0056] S3. Adjust the parameters of the coarse transfer function of DMA, update the coarse transfer function of DMA, and obtain the set of changes in the transfer function.

[0057] S4. Based on the set of changes in the transfer function, perform a weighted average to determine the fine transfer function of the DMA.

[0058] Furthermore, the method for obtaining the coarse transfer function of the DMA includes:

[0059] Assume the transfer function of the DMA to be calibrated is represented by a histogram. For each column, based on the experimental scanning results of the TDMA calibration platform, the coarse transfer function of DMA is solved by the bisection method.

[0060] Furthermore, adjusting the parameters of the coarse transfer function of the DMA, updating the coarse transfer function of the DMA, and obtaining the set of changes in the transfer function include:

[0061] The assumptions made during the process of obtaining the coarse transfer function The column was changed to , … Repeat step S2 to obtain a total of [number] [items]. A coarse transfer function is used to construct a set of variations of the transfer function.

[0062] Furthermore, determining the fine transfer function of DMA by performing a weighted average based on the set of changes in the transfer function includes:

[0063] The set of changes in the transfer function The coarse transfer functions are weighted and averaged to obtain the fine transfer function of the DMA; the fine transfer function of the DMA is the DMA transfer function obtained by inversion.

[0064] Furthermore, the TDMA experimental scan results are the input to the inversion method of this invention, such as... Figure 3 (c) shows the TDMA experimental scan results. The following conditions must be met: the x-coordinate is (Unitless), the vertical axis is (No unit), among which, The electromobility of the scan. For the center mobility, The scanning range is , For scanning electromobility The corresponding particulate number concentration, For centrifugal mobility The corresponding particulate number concentration, The range is .

[0065] The TDMA experimental scan results showed an intermediate ( The highest point is on the 1st side, and the lowest points are on both sides. The distribution is similar to a normal distribution.

[0066] Furthermore, the process of obtaining the coarse transfer function is as follows:

[0067] (1) such as Figure 3 As shown in (c), let the minimum x-coordinate that makes the experimental scan result of the TDMA calibration platform non-zero be . The maximum x-coordinate that makes the TDMA experimental scan result non-zero is Let the coarse transfer function to be solved be... .

[0068] like Figure 3 As shown in (b), let... , , ,in, The number of columns, The minimum x-coordinate that makes the y-axis of the coarse transfer function non-zero. To ensure the maximum x-coordinate of the coarse transfer function that is not zero on the y-axis, this formula specifies the maximum x-coordinate of the coarse transfer function. The range of the horizontal coordinates of each column.

[0069] (2) Let = ,in ,like Figure 3 As shown in (a). ,So ,Right now, and The area of ​​the figure enclosed by the axis is 1, and the area of ​​the figure is defined as 1, which corresponds to the normalized scan results of the TDMA experiment.

[0070] (3) According to the input definition, Let the iterative algebra be Let the first The coarse transfer function solution of the algebra is , No. generation Set as , No. The upper limit of the column is set to , No. The lower limit of the column is set to , The initial conditions are: , , , .

[0071] (4) in the The inversion steps within the generation are as follows: take or , So there are a total of This is one of the situations.

[0072] for In each of the following situations, let ,in, “ " is the integration operator, defined as , The domain is The range is .

[0073] set up , The overall standard deviation is defined as , .

[0074] set up ,in, To meet The minimum case, its corresponding , , and They are respectively denoted as , , and .

[0075] make , .

[0076] This step describes the first The inversion process of generations, Pick or This indicates that the value of this column should be in the upper or lower half of the interval. Let's assume the result shows... It should be in the lower half of the zone. Therefore, the upper and lower limits of the next generation of columns should be constructed from the upper and lower limits of the lower half of the zone in order to continue the process. The inversion of the generation.

[0077] (5) Order Repeat the inversion steps in step (4) until... Stop iterating and record the coarse transfer function solution at this point. Record the population standard deviation at this time as That is, in Figure 2 The "coarse transfer function inversion" step in the flowchart shown is obtained and .

[0078] Furthermore, such as Figure 2 As shown, the steps of the coarse transfer function transformation are as follows:

[0079] make Repeated coarse transfer function inversion Next, get , … and , … .

[0080] Furthermore, the fine transfer function inversion step is as follows: Let , This is the final fine transfer function, which is the final solution obtained by the inversion method described in this invention.

[0081] The effects of the method described in this invention are explained below with reference to the scan results. Firstly, TDMA experiments were conducted to obtain... Figure 4 The scan result shown is used to invert the DMA transfer function using the traditional triangle assumption method, resulting in... Figure 5 The transfer function results shown, however, are... Figure 5 The transfer function shown simulates the TDMA scan results, yielding a height that differs from the experimental results, such as... Figure 6 As shown. The DMA transfer function is inverted using the method described in this invention to obtain... Figure 7 The transfer function results shown are as follows: Figure 7 The transfer function shown simulates the TDMA scan results, yielding... Figure 8The results shown almost perfectly match the experimental and verification results. This example illustrates that, in some cases, the traditional triangular transfer function inversion method is not applicable.

[0082] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A DMA transfer function inversion method based on a TDMA calibration platform, characterized in that, The method includes the following steps: S1. Use the TDMA calibration platform to calibrate the DMA and obtain the experimental scanning results of the TDMA calibration platform; S2. Based on the experimental scanning results of the TDMA calibration platform, obtain the coarse transfer function of the DMA; S3. Adjust the parameters of the coarse transfer function of DMA, update the coarse transfer function of DMA, and obtain the set of changes in the transfer function. S4. Based on the set of changes in the transfer function, perform a weighted average to determine the fine transfer function of the DMA; The coarse transfer function for obtaining DMA includes: Assume the transfer function of the DMA to be calibrated is represented by a histogram. For each column, based on the experimental scanning results of the TDMA calibration platform, the coarse transfer function of DMA is solved by the bisection method; The process of adjusting the parameters of the coarse transfer function of the DMA, updating the coarse transfer function of the DMA, and obtaining the set of changes in the transfer function includes: The assumptions made during the process of obtaining the coarse transfer function The column was changed to , … Repeat step S2 to obtain a total of [number] [items]. A coarse transfer function is used to construct a set of variations of the transfer function; The step of determining the fine transfer function of DMA by performing a weighted average based on the set of changes in the transfer function includes: The set of changes in the transfer function The coarse transfer functions are weighted and averaged to obtain the fine transfer function of the DMA; the fine transfer function of the DMA is the DMA transfer function obtained by inversion.

2. The DMA transfer function inversion method based on a TDMA calibration platform according to claim 1, characterized in that, The TDMA calibration platform includes a bipolar charge (102), a primary DMA (103), an ultrafine particulate filter (106), a secondary DMA (104), and a condensation nucleus particle counter (105). The inlet of the bipolar charge (102) is connected to a sample gas (101) containing polydisperse particles, and the outlet is connected to the inlet of the primary DMA (103); the outlet of the primary DMA (103) is connected to the inlet of the ultrafine particulate filter (106), the outlet of the ultrafine particulate filter (106) is connected to the inlet of the secondary DMA (104), and the outlet of the secondary DMA (104) is connected to the inlet of the condensation nucleus particle counter (105). The ultrafine particulate filter (106) is in communication with the atmosphere.

3. The DMA transfer function inversion method based on a TDMA calibration platform according to claim 1, characterized in that, The experimental scanning results of the TDMA calibration platform are used as the input to the inversion method. The following conditions must be met: The x-axis is Unitless, the vertical axis is No unit, among which, The electromobility of the scan. For the center mobility, The scanning range is , For scanning electromobility The corresponding particulate number concentration, For centrifugal mobility The corresponding particulate number concentration, The range is ; The experimental scanning results of the TDMA calibration platform show an intermediate... Highest, lowest on both sides It follows a normal distribution.

4. A DMA transfer function inversion device based on a TDMA calibration platform, characterized in that, The device includes: a TMDA experimental result acquisition module, a coarse transfer function acquisition module, a transfer function change set acquisition module, and a fine function acquisition module; The TMDA experimental results acquisition module is used to calibrate DMA using the TDMA calibration platform and obtain the experimental scan results of the TDMA calibration platform. The coarse transfer function acquisition module is used to acquire the coarse transfer function of DMA based on the experimental scan results of the TDMA calibration platform. The module for obtaining the set of changes in the transfer function is used to adjust the parameters of the coarse transfer function of DMA, update the coarse transfer function of DMA, and obtain the set of changes in the transfer function. The fine function acquisition module is used to determine the fine transfer function of DMA by performing a weighted average based on the set of changes in the transfer function; The coarse transfer function for obtaining DMA includes: Assume the transfer function of the DMA to be calibrated is represented by a histogram. For each column, based on the experimental scanning results of the TDMA calibration platform, the coarse transfer function of DMA is solved by the bisection method; The process of adjusting the parameters of the coarse transfer function of the DMA, updating the coarse transfer function of the DMA, and obtaining the set of changes in the transfer function includes: The assumptions made during the process of obtaining the coarse transfer function The column was changed to , … One, a total of A coarse transfer function is used to construct a set of variations of the transfer function; The step of determining the fine transfer function of DMA by performing a weighted average based on the set of changes in the transfer function includes: The set of changes in the transfer function The coarse transfer functions are weighted and averaged to obtain the fine transfer function of the DMA; the fine transfer function of the DMA is the DMA transfer function obtained by inversion.

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