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

Abstract

The present invention relates to a DMA transfer function inversion method and apparatus based on a TDMA calibration platform. The method comprises: using a TDMA calibration platform to calibrate a DMA, so as to acquire an experiment scanning result of the TDMA calibration platform; on the basis of the experiment scanning result of the TDMA calibration platform, acquiring a coarse transfer function of the DMA; adjusting parameters of the coarse transfer function of the DMA, and updating the coarse transfer function of the DMA, so as to acquire a set of transfer function changes; and on the basis of the set of transfer function changes, performing weighted averaging, and determining a fine transfer function of the DMA. Compared with conventional inversion algorithms, the present invention eliminates the hypothesis of "the shape of a transfer function being a triangle", and obtains a transfer function shape having a wider application range, such that a transfer function of a DMA that is measured by means of a TDMA experiment can be better restored, thereby improving the inversion accuracy of particle size spectrums.

Description

A DMA transfer function inversion method and device based on TDMA calibration platform Technical Field

[0001] The present invention relates to the technical field of atmospheric ultrafine particle size spectrum measurement, and in particular to a DMA transfer function inversion method and device based on a TDMA calibration platform. Background Art

[0002] In the field of atmospheric ultrafine particle size spectrometry, differential mobility analyzers (DMAs) are widely used to separate monodisperse particles of a specific size from a polydisperse sample. DMAs are combined with a charger and particle detector (such as a condensation particle counter (CPC) or an aerosol electrometer (AE)) to form a "charging-sieving-measurement" system for particle size spectrometry.

[0003] In the inversion process of particle size spectrum measurement, the most basic formula is Among them, dN(d p ) is the electromigration particle size d p The particle size spectrum height at 测量 (d p ) is the particle size d of the particle detector at the electromigration p The measured value of the particle concentration at p(1,d p ) is the positive single charging efficiency of the charger for particles (assuming that DMA uses negative high voltage to screen positive particles), w′(d p ) is the particle size d of the particle during electromigration p The resolution at (i.e. the particle size spectrum d p The width of the column), S(d p ) is the particle size d of DMA in electromigration p The existing DMA transfer function inversion algorithm regards the shape of the DMA transfer function as an ideal isosceles triangle, so S(d p )=h(d p )·w(d p ), where h(d p ) is the height of the isosceles triangle, w(d p ) is the width at half height (half the length of the base of the isosceles triangle).

[0004] When calibrating the DMA transfer function, the traditional method uses a TDMA calibration platform to meet the requirements of the particle size spectrum inversion algorithm. The TDMA calibration platform is an experimental platform for calibrating and optimizing TDMA (time division multiple access) technology, and is widely used in communication systems, atmospheric particulate matter measurement and other fields. The DMA transfer function is assumed to be an isosceles triangle with variable h and w. The values ​​of h and w are traversed and integrated respectively, and compared with the experimental scan results of the TDMA calibration platform. The h and w that make the integration result and the TDMA experimental scan result most correlated are taken as the inversion result, that is, the calibration result of the DMA transfer function. However, the traditional method has some defects. It has an important premise assumption, namely, "the shape of the DMA transfer function is an ideal isosceles triangle", but the actual transfer function of the DMA is affected by factors such as processing accuracy, and its shape is definitely not an ideal isosceles triangle. This ideal assumption does not conform to the actual situation.

[0005] Therefore, it is necessary to invent an inversion algorithm with a wider range of applications to eliminate the assumption that "the shape of the transfer function is a triangle", obtain a more general transfer function shape, better restore the transfer function of the DMA measured by the TDMA experiment, and thus improve the inversion accuracy of the particle size spectrum. Summary of the Invention

[0006] In order to address the deficiencies in the prior art, the present invention aims to provide a DMA transfer function inversion method and device based on a TDMA calibration platform.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] In a first aspect of the present invention, a DMA transfer function inversion method based on a TDMA calibration platform is disclosed.

[0009] The method comprises the following steps:

[0010] The input of this method is the TDMA experiment scan result, and the output is the transfer function using DMA in the TDMA experiment.

[0011] S1. Use the TDMA calibration platform to calibrate the DMA and obtain the experimental scanning results of the TDMA calibration platform.

[0012] S2. Obtaining a coarse transfer function of the DMA according to the experimental scanning results of the TDMA calibration platform.

[0013] S3. Adjust the parameters of the coarse transfer function of the DMA, update the coarse transfer function of the DMA, and obtain a set of changes in the transfer function.

[0014] S4. Perform weighted averaging based on the set of changes in the transfer function to determine a fine transfer function of the DMA.

[0015] Furthermore, obtaining the coarse transfer function of the DMA includes:

[0016] The transfer function of the DMA to be calibrated is assumed to be P bars of a histogram. According to the experimental scanning results of the TDMA calibration platform, the rough transfer function of the DMA is solved by the bisection method.

[0017] Furthermore, the adjusting the parameters of the DMA coarse transfer function, updating the DMA coarse transfer function, and obtaining a set of changes in the coarse transfer function include:

[0018] The P columns assumed in the process of obtaining the rough transfer function are changed to P+1, P+2, ..., P+R, and step S2 is repeated to obtain a total of R+1 rough transfer functions. The R+1 rough transfer functions are used to construct a variation set of the rough transfer function.

[0019] Furthermore, performing weighted averaging on R+1 coarse transfer functions in the coarse transfer function variation set according to the coarse transfer function variation set to determine the DMA fine transfer function includes:

[0020] The R+1 coarse transfer functions in the variation set of the coarse transfer function are weighted 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.

[0021] Furthermore, the TDMA calibration platform includes a bipolar charger, a primary DMA, an ultrafine particle filter, a secondary DMA and a condensation nucleus particle counter.

[0022] The inlet of the bipolar charger is connected to the particulate sample gas containing polydisperse particle sizes, and the outlet of the bipolar charger is connected to the inlet of the first-level DMA; the outlet of the first-level 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-level DMA, and the outlet of the second-level DMA is connected to the inlet of the condensation nucleus particle counter; the ultrafine particulate filter is connected to the atmosphere.

[0023] Furthermore, the experimental scanning result of the TDMA calibration platform is the input of the inversion algorithm, and the experimental scanning result of the TDMA calibration platform N / N * =f scan (Z p / Z p * ) need to meet the following requirements:

[0024] The horizontal axis is Z p / Z p * , no unit, the vertical coordinate is N / N *, unitless, where Z p is the scanned electrical mobility, Z p * is the center mobility, Z p / Z p * The scanning range is (0,2], N is the scanning mobility Z p The corresponding particle number concentration, N * is the central mobility Z p * The corresponding particle number concentration, N / N * The range is [0,1); the experimental scanning results of the TDMA calibration platform show the middle (Z p / Z p * =1) is the highest, and the lowest on both sides (N / N * =0).

[0025] In a second aspect of the present invention, a DMA transfer function inversion device based on a TDMA calibration platform is disclosed.

[0026] The device comprises: a TMDA experiment result acquisition module, a coarse transfer function acquisition module, a transfer function change set acquisition module and a fine function acquisition module.

[0027] The TMDA experimental result acquisition module is used to calibrate the DMA using the TDMA calibration platform and obtain the experimental scanning results of the TDMA calibration platform.

[0028] The coarse transfer function acquisition module is used to acquire the coarse transfer function of DMA according to the experimental scanning result of the TDMA calibration platform.

[0029] The transfer function variation set acquisition module is used to adjust the parameters of the DMA coarse transfer function, update the DMA coarse transfer function, and acquire the variation set of the coarse transfer function.

[0030] The fine function acquisition module is configured to perform weighted averaging on R+1 coarse transfer functions in the coarse transfer function variation set according to the coarse transfer function variation set to determine the fine transfer function of the DMA. Industrial Applicability

[0031] (1) The present invention sets the transfer function of the DMA calibration in the TDMA experiment to a general shape to eliminate the assumption that "the shape of the transfer function is a triangle", obtain a more general transfer function shape, better restore the transfer function of the DMA measured by the TDMA experiment, and thus improve the inversion accuracy of the particle size spectrum.

[0032] (2) The present invention does not use traversal search when inverting the coarse transfer function of DMA, but adopts binary search. Assuming the number of coarse transfer function columns is P, the number of coarse transfer function changes is R, and the vertical coordinate accuracy of the transfer function is 0.1%, compared with traversal search, the binary search method reduces the algorithm complexity from 10 3P (P columns, each with 1 / 0.1% = 1000 choices) is reduced to R×10×2 P+R (The accuracy reaches 0.1% after 10 generations of iteration), and the traversal search is almost impossible to operate with an ordinary computer, while the algorithm described in the present invention can be operated by an ordinary computer.

[0033] (3) The present invention sequentially inverts the coarse transfer function and fine transfer function of the DMA, and can obtain smoother inversion results that better reflect the actual situation. From a mathematical perspective, the TDMA calibration experiment is a multi-solution problem (multiple transfer functions can be integrated to obtain the TDMA experimental scanning results). Therefore, the coarse transfer function of the DMA inverted by the present invention can meet the sufficiency of the solution, that is, this transfer function can be integrated to obtain the TDMA experimental scanning results. The changes in the coarse transfer function multiple times can maximize the search for all possible solutions, and the weighted average can be used to obtain a smoother fine transfer function that better reflects the actual situation, that is, the final inversion result, thereby improving the inversion accuracy of the atmospheric ultrafine particle size spectrum. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a schematic diagram of the TDMA calibration platform;

[0035] FIG2 is a flow chart of a method for inverting a DMA transfer function based on a TDMA calibration platform according to the present invention;

[0036] FIG3 is a schematic diagram of the integration process of the present invention;

[0037] FIG4 is a graph showing the scanning results of a TDMA experiment;

[0038] FIG5 is a graph showing the results obtained by the conventional TDMA inversion method;

[0039] FIG6 is an integral verification curve diagram of the traditional TDMA inversion result;

[0040] FIG7 is a graph showing the results obtained by the inversion algorithm of the present invention;

[0041] FIG8 is a graph showing an integral verification curve of the inversion result obtained by the present invention.

[0042] Among them: 101. Sample gas containing particulate matter with polydisperse particle sizes, 102. Bipolar charger, 103. Primary DMA, 104. Secondary DMA, 105. Condensation nucleus particle counter, 106. Ultrafine particulate matter filter connected to the atmosphere. DETAILED DESCRIPTION

[0043] The present invention will be further described below with reference to the accompanying drawings:

[0044] The TDMA calibration platform shown in Figure 1 includes a bipolar charger 102, a primary DMA 103, an ultrafine particle filter 106, a secondary DMA 104 and a condensation nucleus particle counter 105; the inlet of the bipolar charger 102 is connected to the particle sample gas 101 containing polydispersed particle sizes, and the outlet of the bipolar charger 102 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 particle filter 106, the outlet of the ultrafine particle 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 particle filter 106 is connected to the atmosphere.

[0045] The mechanical structure, sheath gas flow rate, and sample gas flow rate of the first-stage DMA 103 and the second-stage DMA 104 are kept consistent, and the screening voltage of the first-stage DMA 103 is fixed so that the electric mobility of the screened particles is Z p * , scan the voltage of the secondary DMA 104. The sample gas 101 containing particles with polydispersed particle size first enters the bipolar charger 102 for charging, and then enters the primary DMA 103. The primary DMA 103 obtains monodispersed particles with a number concentration of N * The ultrafine particle filter 106 connected to the atmosphere is used to balance the air pressure. The secondary DMA 104 scans the voltage and continues to screen the particles screened by the primary DMA 104. Finally, the condensation nucleus particle counter 105 records the secondary DMA 104 scanning voltage (the electrical mobility corresponding to the scanning voltage is Z p ) and the particle number concentration (N) at the outlet of the secondary DMA 104, recorded as the scan result N / N * =f scan (Z p / Z p * ), where Z p / Z p * The scanning range is (0,2], N / N * The range is [0,1).

[0046] As shown in FIG2 , a DMA transfer function inversion method based on a TDMA calibration platform is described. The input of the method is the TDMA experimental scan result, and the output is the transfer function of DMA 103 and 104 used in the TDMA experiment. The method includes the following steps:

[0047] S1. Use the TDMA calibration platform to calibrate the DMA and obtain the experimental scanning results of the TDMA calibration platform.

[0048] S2. Obtaining a coarse transfer function of the DMA according to the experimental scanning results of the TDMA calibration platform.

[0049] S3. Adjust the parameters of the DMA coarse transfer function, update the DMA coarse transfer function according to the adjusted parameters of the DMA coarse transfer function, and obtain a change set of the coarse transfer function.

[0050] S4. According to the variation set of the coarse transfer function, perform weighted averaging on each coarse transfer function in the variation set of the coarse transfer function to determine a fine transfer function of the DMA.

[0051] Furthermore, in step S2, obtaining the coarse transfer function of the DMA includes:

[0052] The transfer function of the DMA to be calibrated is assumed to be P bars of a histogram. According to the experimental scanning results of the TDMA calibration platform, the rough transfer function of the DMA is solved by the bisection method.

[0053] Furthermore, in step S3, adjusting the parameters of the DMA coarse transfer function, updating the DMA coarse transfer function, and obtaining a set of changes in the coarse transfer function include:

[0054] The P columns assumed in the process of obtaining the rough transfer function are changed to P+1, P+2, ..., P+R, and step S2 is repeated to obtain a total of R+1 rough transfer functions, and a change set of transfer functions is constructed.

[0055] Furthermore, in step S4, performing weighted averaging on each coarse transfer function in the coarse transfer function variation set according to the coarse transfer function variation set to determine the fine transfer function of the DMA includes:

[0056] The R+1 coarse transfer functions in the variation set of the coarse transfer function are weighted 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.

[0057] Furthermore, the TDMA experimental scanning result is the input of the inversion algorithm of this invention, as shown in FIG3(c), the TDMA experimental scanning result N / N * =f scan (Z p / Z p * ) needs to satisfy: the horizontal coordinate is Z p / Z p * (unitless), the vertical axis is N / N* (unitless), where Z p is the scanned electrical mobility, Z p * is the center mobility, Z p / Z p * The scanning range is (0,2], N is the scanning mobility Z p The corresponding particle number concentration, N * is the central mobility Z p * The corresponding particle number concentration, N / N * The range is [0,1).

[0058] The TDMA experimental scan results show that the middle (Z p / Z p * =1) is the highest, and the lowest on both sides (N / N * =0).

[0059] Furthermore, the process of obtaining the rough transfer function is as follows:

[0060] (1) As shown in Figure 3(c), let the minimum horizontal coordinate that makes the experimental scanning result of the TDMA calibration platform not equal to 0 be ω u , so that the maximum horizontal coordinate of the TDMA experimental scanning result is not 0 is ω v , let the rough transfer function to be solved be f(Z p / Z p * ).

[0061] As shown in Figure 3(b), let f(Z p / Z p * )=Q k ,

[0062] k=0,1,2,…,(P-1), where P is the number of columns, The minimum horizontal coordinate that makes the vertical axis of the rough transfer function non-zero is: In order to make the maximum abscissa of the coarse transfer function ordinate non-zero, this formula specifies the abscissa range of the kth column of the coarse transfer function.

[0063] (2) Let f s (Z p / Z p * )=f(Z p / Z p * )×η, where η=1 / S t, as shown in Figure 3(a), So That is, f s (Z p / Z p * ) and the x-axis is 1. Specifying a graphic area of ​​1 corresponds to the normalized scanning result of the TDMA experiment.

[0064] (3) According to the input definition, Q k ∈[0,1), let the iterative number be i, and let the rough transfer function solution of the i-th generation be N / N * =f i (Z p / Z p * ), Q of the i-th generation k Set to Q ik , the upper limit of the column of the i-th generation is set to UP ik , the lower limit of the column of the i-th generation is set to LW ik ,k=0,1,2,…,(P-1). The initial conditions are: i=1,UP ik =1,LW ik =0, k=0,1,2,…,(P-1).

[0065] (4) The inversion steps in the i-th generation are as follows: ik =LW ik +(UP ik -LW ik ) / 4 or Q ik =LW ik +(UP ik -LW ik )×3 / 4, k=0,1,2,…,(P-1), then there are 2 P situation.

[0066] For 2 P In each case, let ANS ic =f s *f, where c = 1, 2, ..., 2 P , “*” is the integral operator symbol, defined as ANS ic The domain of is (0,2] and the range is [0,1].

[0067] Set SD k =k×2 / P+1 / P, k=0,1,2,…,(P-1), the population standard deviation is defined as

[0068] set up Among them, c *In order to satisfy the minimum σ, the corresponding f i , Q ik UP ik and LW ik Denoted as f i * , Q ik * UP ik * and LW ik * .

[0069] Order UP (i+1)k =Q ik * +(UP ik -LW ik ) / 4, LW (i+1)k =Q ik * -(UP ik -LW ik ) / 4.

[0070] This step describes the inversion process of the i-th generation, Q ik Take LW ik +(UP ik -LW ik ) / 4 or LW ik +(UP ik -LW ik )×3 / 4 reflects that the value of this column should be in the upper half or in the lower half. Let's assume that the result shows that Q ik It should be in the lower half, so the upper and lower limits of the next generation column are constructed with the upper and lower limits of the lower half to continue the inversion of the i+1 generation.

[0071] (5) Let i = i + 1, and repeat the inversion steps of step (4) until Min(σ i )<1%×f i * (1), stop the iteration and record the rough transfer function solution at this time as f P * , record the population standard deviation at this time as σ P * , that is, f is obtained in the step of “rough transfer function inversion” in the flowchart shown in Figure 2 P * and σ P * .

[0072] Furthermore, as shown in FIG2 , the steps of changing the rough transfer function are:

[0073] Let P = P + 1, repeat the rough transfer function inversion R times, and get fP+0 * 、f P+1 * ,…,f P+R * and σ P+0 * , σ P+1 * ,…,σ P+R * .

[0074] Furthermore, the inversion step of the fine transfer function is: let f ave This is the final desired fine transfer function, i.e., the final solution obtained by the inversion algorithm of the present invention.

[0075] The following describes the effects of the method of the present invention in conjunction with the scanning result diagram. First, a scanning result shown in Figure 4 is obtained through a TDMA experiment. This result is used to invert the DMA transfer function using the traditional triangle assumption method to obtain the transfer function result shown in Figure 5. However, when the TDMA scanning result is simulated using the transfer function shown in Figure 5, a different height from the experimental result is obtained, as shown in Figure 6. The DMA transfer function is inverted using the method of the present invention to obtain the transfer function result shown in Figure 7. The TDMA scanning result is simulated using the transfer function shown in Figure 7 to obtain the result shown in Figure 8. The experimental results and the verification results are almost identical. This example shows that in some cases, the traditional triangle transfer function inversion method is not applicable.

[0076] The above-described embodiments are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined 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 comprises the following steps: S1. Calibrate the DMA using the TDMA calibration platform and obtain the experimental scanning results of the TDMA calibration platform; S2. Obtaining a coarse transfer function of the DMA according to the experimental scanning results of the TDMA calibration platform; S3, adjusting the parameters of the DMA coarse transfer function, updating the DMA coarse transfer function, and obtaining a set of changes in the coarse transfer function; S4. According to the variation set of the coarse transfer function, perform weighted averaging on each coarse transfer function in the variation set of the coarse transfer function to determine a fine transfer function of the DMA.

2. The DMA transfer function inversion method based on the TDMA calibration platform according to claim 1, characterized in that: In step S2, obtaining the coarse transfer function of DMA includes: The transfer function of the DMA to be calibrated is assumed to be P bars of a histogram. According to the experimental scanning results of the TDMA calibration platform, the rough transfer function of the DMA is solved by the bisection method.

3. The DMA transfer function inversion method based on the TDMA calibration platform according to claim 2, characterized in that: In step S3, adjusting the parameters of the DMA coarse transfer function, updating the DMA coarse transfer function, and obtaining a set of changes in the coarse transfer function include: The P columns assumed in the process of obtaining the rough transfer function are changed to P+1, P+2, ..., P+R, and step S2 is repeated to obtain a total of R+1 rough transfer functions. The R+1 rough transfer functions are used to construct a variation set of the rough transfer function.

4. The DMA transfer function inversion method based on the TDMA calibration platform according to claim 3, characterized in that: In step S4, performing weighted averaging on each coarse transfer function in the coarse transfer function variation set according to the coarse transfer function variation set to determine the fine transfer function of the DMA includes: The R+1 coarse transfer functions in the variation set of the transfer function are weighted 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.

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

6. The DMA transfer function inversion method based on the TDMA calibration platform according to claim 1, characterized in that: The experimental scanning results of the TDMA calibration platform are the input of the inversion algorithm. The experimental scanning results of the TDMA calibration platform are N / N * =f scan (Z p / Z p * ) need to meet the following requirements: The horizontal axis is Z p / Z p * , no unit, the vertical coordinate is N / N * , no unit; among them, Z p is the scanned electrical mobility, Z p * is the center mobility, Z p / Z p * The scanning range is (0,2], N is the scanning mobility Z p The corresponding particle number concentration, N * is the central mobility Z p * The corresponding particle number concentration, N / N * The range of is [0,1); The experimental scanning results of the TDMA calibration platform show the middle (Z p / Z p * =1) is the highest, and the lowest on both sides (N / N * =0).

7. A DMA transfer function inversion device based on a TDMA calibration platform, characterized in that: The device comprises: 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 result acquisition module is used to calibrate the DMA using the TDMA calibration platform and obtain the experimental scanning results of the TDMA calibration platform; The coarse transfer function acquisition module is used to acquire the coarse transfer function of DMA according to the experimental scanning results of the TDMA calibration platform; The transfer function change set acquisition module is used to adjust the parameters of the DMA coarse transfer function, update the DMA coarse transfer function, and acquire the change set of the coarse transfer function; The fine function acquisition module is configured to perform weighted averaging on each coarse transfer function in the coarse transfer function variation set according to the coarse transfer function variation set, so as to determine the fine transfer function of the DMA.

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