Electrostatic sensitivity test method for industrial explosives and pyrotechnic agents with maximum response probability

Abstract

The present invention discloses a method for testing the electrostatic sensitivity of industrial explosives and pyrotechnic agents with a maximum response probability in the field of safety technology of the civilian explosives industry, which specifically includes the following steps: first, a series of electrostatic spark discharge ignition tests are carried out as preliminary tests based on the quartile convergence method; second, a series of electrostatic spark discharge ignition tests are formally carried out based on the optimal weighted information matrix method; third, all test electrostatic characterization parameters and response conditions are statistically analyzed, and the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agent samples is calculated based on the maximum likelihood method; fourth, the electrostatic sensitivity distribution of samples and the measurement error and confidence interval of related test results are calculated based on the Fisher information matrix method. This method has the characteristics of accurate measurement, less dependence on the initial parameter selection, and the ability to calculate the test result error and confidence interval, and provides a more standardized and standardized test method for the electrostatic sensitivity test of industrial explosives and pyrotechnic agents.

Description

Technical Field

[0001] The invention relates to the field of safety technology in the civilian explosives industry, to electrostatic sensitivity testing of industrial explosives and pyrotechnic agents, and in particular to an electrostatic sensitivity testing method of industrial explosives and pyrotechnic agents with a maximum response probability. Background Art

[0002] Electrostatic sensitivity is a sensitivity index that characterizes the combustion and explosion characteristics of industrial explosives and pyrotechnics, and is also an important data for analyzing their ignition reliability. The electrostatic sensitivity test for industrial explosives and pyrotechnics requires a series of electrostatic spark discharge ignition tests to be carried out in sequence based on a mathematical and statistical model, and finally the ignition probability of industrial explosives and pyrotechnics under different electrostatic stimulation amounts is calculated, that is, the electrostatic sensitivity distribution of the sample. Among them, the critical electrostatic stimulation amount corresponding to the maximum ignition probability can characterize the electrostatic initiation reliability threshold, which is the basic data for evaluating the reliability of electric ignition and initiation of industrial explosives and pyrotechnics, and is an important basis for increasing the reliability, stability and safety of initiation operations in the civil explosives industry. Setting the discharge energy of the electric bridge ignition initiator to be greater than the electrostatic initiation threshold can ensure that industrial explosives and pyrotechnics can complete initiation / ignition reliably, stably and safely.

[0003] The electrostatic sensitivity test of industrial explosives and pyrotechnic agents refers to the relationship between the applied electrostatic stimulation amount and the response probability of industrial explosives and pyrotechnic agents obtained through the test, which is a very complicated problem. Existing studies have shown that the minimum electrostatic ignition stimulation amount of a single sample cannot be obtained through the test. The reason is that the electrostatic spark discharge ignition test of industrial explosives and pyrotechnic agents is an extremely special destructive test. For a specific sample, only one test can be carried out to determine the electrostatic stimulation amount, and the result of its response (ignition) or non-response (non-ignition) can be observed, and the test cannot be repeated. Therefore, it is impossible to accurately measure the electrostatic stimulation amount of a single industrial explosive and pyrotechnic agent sample through the test, and only a series of similar industrial explosives and pyrotechnic agent samples can be subjected to electrostatic spark discharge ignition tests, and finally the response probability distribution of the industrial explosive and pyrotechnic agent sample under different electrostatic stimulation amounts, that is, its electrostatic sensitivity distribution, can be calculated. However, the true value of the probability distribution cannot be obtained through a limited number of tests, and only a calculated value close to its true value can be obtained, that is, there will always be errors in the results of the electrostatic sensitivity test of industrial explosives and pyrotechnic agents.

[0004] The current domestic standards for electrostatic sensitivity test of industrial explosives and pyrotechnics mainly include Part 3 of the test method for industrial pyrotechnics: electrostatic spark sensitivity test (WJ / T9038.3-2004), the electrostatic sensitivity test method for industrial electric detonators (WJ / T9042-2004), the national military standard for explosive test standards (GJB772A-1997), and the national military standard for electrostatic sensitivity test of insensitive explosive safety test methods (GJB 8142-2013). The methods specified in these electrostatic sensitivity test standards are all based on the "lifting method" and "Langley method" test methods in the national military recommended standard for mathematical methods for sensitivity test (GJB / Z 377A-1994), which belong to the sequential electrostatic sensitivity test method as the present invention.

[0005] The "lift and drop method" was first proposed by WJ Dixon and AM Wood in 1948 and is currently the most commonly used test method for electrostatic sensitivity of industrial explosives and pyrotechnic agents. Its execution steps are simple: take a fixed step length d, if the electrostatic stimulation amount x is set i If the result of the test is a response, the electrostatic stimulation amount will be reduced by one step in the next test. Otherwise, if there is no response, it will be increased by one step. The test based on the "lift and lower method" can effectively obtain the mean of the electrostatic sensitivity distribution, but the measurement error of the variance of the sensitivity distribution is large. Moreover, the accuracy of the sensitivity distribution obtained by the "lift and lower method" is related to the selection of the initial stimulation amount x0 and the step length d. If the initial electrostatic stimulation amount can be set near the mean of the sensitivity distribution and the step length can be set near the variance of the sensitivity distribution, better test results can be obtained. However, the selection of initial parameters can only be roughly estimated based on existing experience, and the error is large. Therefore, the "lift and lower method" cannot guarantee the reliability and accuracy of the test.

[0006] The Langley method was proposed by HJ Langlie in 1963. It is a variable step-length lifting method. Its efficiency as an electrostatic sensitivity test method is better than the lifting method. Before the Langley method test, the full non-response electrostatic stimulation amount x must be set. L As the lower limit of the test, and the full response electrostatic stimulus x U As the upper limit of the test, the average value of the upper and lower limits of the test is calculated in the first test as the initial electrostatic stimulation amount x0. The rising and falling direction of the new stimulation amount selected in the test is the same as the "rising and falling method", but its change step is calculated based on the existing test records. Finally, the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agent samples is calculated based on the "maximum likelihood method". The electrostatic sensitivity test of industrial explosives and pyrotechnic agents based on the "Langley method" can quickly converge the test electrostatic stimulation amount selection to 50% response probability, so the mean value of the electrostatic sensitivity distribution can be obtained more accurately, but the measurement error of its distribution variance is large, and the measurement error of the maximum probability response point is also large.

[0007] In 1994, Barry T.Neyer proposed an electrostatic sensitivity test method based on Fisher information, which is called "Neyer-D method". It consists of two parts. The first step is to quickly obtain the mixed result area through the binary search method; the second step is to select new test points according to the optimal criterion of the determinant. Before the binary search method is performed, it is necessary to estimate a full-response electrostatic stimulation amount as the upper limit of the test and a full-unresponsive electrostatic stimulation amount as the lower limit of the test, and the variance of the electrostatic sensitivity distribution as the initial step length of the test. After a series of electrostatic spark discharge ignition tests are carried out by this method, the rough estimate of the electrostatic sensitivity distribution parameters of industrial explosives and pyrotechnic agents can be calculated. Subsequently, based on the rough estimate, the electrostatic sensitivity test is carried out based on the "optimal determinant method", and the electrostatic stimulation amount in each test is selected to maximize the determinant of the Fisher information matrix. Finally, the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents is calculated based on the "maximum likelihood method".

[0008] The above three methods for testing the electrostatic sensitivity of industrial explosives and pyrotechnic agents are only accurate in calculating the electrostatic sensitivity of 50% response probability, but not accurate in calculating the response point with a high probability (99.99% in this article). The accuracy of the test results is highly dependent on the selection of initial parameters. The error and confidence interval of the test results cannot be calculated after the test, and the test process is not standardized and detailed for the electrostatic sensitivity test of industrial explosives and pyrotechnic agents. The following are four specific shortcomings and deficiencies:

[0009] (I) The accuracy of the calculation of the maximum probability response point is not high

[0010] When the electrostatic sensitivity test of industrial explosives and pyrotechnics is conducted based on the "lifting and lowering method", the electrostatic stimulation amount will be concentrated near the 50% probability response point, so the 50% probability response point of the sample can be measured more accurately, but the maximum probability response point cannot be accurately measured. When the electrostatic sensitivity test of industrial explosives and pyrotechnics is conducted based on the "Langley method", the electrostatic stimulation amount will converge more quickly to its 50% probability response point, so it can quickly and accurately measure the 50% probability response point of industrial explosives and pyrotechnic samples, but the variance of the sensitivity distribution cannot be effectively measured, so the error of the maximum probability response point in the final test result is large. When the electrostatic sensitivity test of industrial explosives and pyrotechnics is conducted based on the "Neyer-D method", although the mean and variance of the electrostatic sensitivity distribution can be more accurately measured at the same time, the accuracy of the maximum probability response point result is more dependent on the variance of the electrostatic sensitivity distribution, so the "Neyer-D method" can further improve the accuracy of the measurement of the maximum probability response point.

[0011] (II) The accuracy of the test results is highly dependent on the selection of initial parameters

[0012] When conducting electrostatic sensitivity tests on industrial explosives and pyrotechnic agents based on the "lift and drop method", it is necessary to estimate the variance and mean of the electrostatic sensitivity distribution of the samples in advance. Inaccurate estimates will seriously affect the test results. If the electrostatic sensitivity distribution of an industrial explosive or pyrotechnic agent sample is known in advance, the lift and drop method can be used to measure it more accurately. However, if it is not known in advance, it is difficult to accurately measure its electrostatic sensitivity distribution through the lift and drop method, that is, the accuracy of the "lift and drop method" depends on the setting of the initial parameters before the test. In addition, before conducting a test based on the "Neyer-D method", it is also necessary to accurately estimate the variance of the electrostatic sensitivity of industrial explosives and pyrotechnic agent samples. If the variance is not estimated accurately, the accuracy of the test results may be reduced, and the test efficiency may be reduced.

[0013] (III) Unable to calculate the error and confidence interval of the test results

[0014] The current electrostatic sensitivity test methods for industrial explosives and pyrotechnic agents at home and abroad do not specify the error analysis method of the test results and the calculation method of the confidence interval. Therefore, there is no scientific and reasonable evaluation standard for the accuracy of the test results. When using the electrostatic initiation reliability threshold represented by the maximum response probability response point, there is also a lack of standards for evaluating its effectiveness and reserved margin.

[0015] (IV) Failure to standardize and refine the electrostatic sensitivity test process for industrial explosives and pyrotechnics

[0016] The above three methods are general sensitivity test methods. When the current domestic and international standards formulate the electrostatic sensitivity test standards for industrial explosives and pyrotechnic agents based on the above three methods, they do not formulate standardized and detailed test procedures based on the particularity of the electrostatic sensitivity test of industrial explosives and pyrotechnic agents, and do not stipulate the preset probability distribution form, nor specify the selection form of the electrostatic stimulation amount, which is not conducive to the specific operation of the test.

[0017] In view of the above-mentioned related technologies, the present invention provides a method for testing the electrostatic sensitivity of industrial explosives and pyrotechnic agents with a maximum response probability. Based on the electrostatic sensitivity test, the electrostatic sensitivity distribution of the sample can be accurately calculated within a relatively small number of tests, especially the critical electrostatic stimulation amount corresponding to the maximum ignition probability (such as 99.99%), which can characterize the reliable detonation threshold of industrial explosives and pyrotechnic agents during electrical ignition. The method has the characteristics of accurate measurement, less dependence on the selection of initial parameters, and the ability to calculate the error and confidence interval of the test results, and provides a more standardized and standardized test method for the electrostatic sensitivity of industrial explosives and pyrotechnic agents. Summary of the invention

[0018] The purpose of the present invention is to improve the accuracy and standardization of the electrostatic sensitivity test method, to solve the problems of large measurement error, low test efficiency, serious dependence of test results on initial values, inability to obtain test result errors, non-standard test procedures, and especially inability to accurately measure the reliable threshold of electric ignition detonation characterized by a maximum response probability (99.99%), and the like in the existing electrostatic sensitivity test method for industrial explosives and pyrotechnic agents. A method for systematically carrying out electrostatic sensitivity tests of industrial explosives and pyrotechnic agents is proposed, which guides the test process based on an "optimal weighted information matrix method" for a maximum probability response point, analyzes the uncertainty of test data and its results, improves test efficiency and result accuracy, and carries out electrostatic sensitivity tests of industrial explosives and pyrotechnic agents.

[0019] The present invention provides a method for testing the electrostatic sensitivity of industrial explosives and pyrotechnic agents with a maximum response probability. The method is based on an optimized weighted information matrix method, which can accurately calculate the maximum response probability point, has a low dependence on the selection of initial parameters, and can calculate the test result error and confidence interval. The method specifically includes the following steps:

[0020] Step 1: Prepare the electrostatic spark discharge ignition test device and the industrial explosives and pyrotechnic agent samples for the test, set the electrostatic sensitivity characterization parameters, ensure that the electrostatic charging energy can be adjusted before each test, and the selected electrostatic sensitivity characterization parameters can be measured after each test;

[0021] Step 2: Setting the upper and lower limits of the electrostatic charging energy of the electrostatic spark discharge ignition test device;

[0022] Step 3: Based on the quartile convergence method, a series of electrostatic spark discharge ignition tests are carried out on industrial explosives and pyrotechnic agent samples as preliminary experiments. In the preliminary experiments, the electrostatic stimulation amount is taken as the logarithm of the charging energy. Each preliminary experiment needs to measure and record the electrostatic sensitivity characterization parameters. When the preliminary experiment results show a mixed result area, that is, the minimum response charging energy is less than the maximum non-response charging energy, the preliminary experiment is stopped and the formal experiment is started;

[0023] Step 4: Based on the maximum likelihood method, the charging energy and response (ignition) of the pre-test are statistically analyzed, and the preliminary results of the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents are calculated. Assuming that the electrostatic sensitivity distribution obeys the log-normal distribution, the mean μ and variance σ of the electrostatic sensitivity distribution are solved to maximize the probability P of the pre-test results.

[0024] Step 5: Based on the "optimal weighted information matrix method", a series of electrostatic spark discharge ignition tests are carried out, and the test is officially carried out according to steps 6 to 10;

[0025] Step 6: Set the maximum number of tests N for the formal test, and count the charging energy and response of all tests including the pre-test, and calculate the electrostatic sensitivity distribution parameters μ, σ according to the method in step 4;

[0026] Step 7: Select M+1 calculation points evenly between the upper and lower limits of the electrostatic stimulation amount set in step 2:

[0027] y i =[(Mi)x L +ix U ] / M (1)

[0028] Where: M is the number of calculation points minus one; y i is the value of the selected calculation point; i is the number of different calculation points; x L is the lower limit of electrostatic stimulation, which is the logarithm of the minimum charging energy; x U The upper limit of electrostatic stimulation is taken as the logarithm of the maximum charging energy;

[0029] Step 8: Calculate the weighted information entropy S(y) of the above selected calculation point according to equations (2)-(6) i ):

[0030]

[0031] w i (y i )=(y i -μ) / σ,u j =(x j -μ) / σ (6)

[0032] Where: S is the weighted information entropy; α p is the weighting constant, corresponding to a 99.99% response probability; I ij is the matrix element of the Fisher matrix in row i and column j; n is the number of trials currently performed; y i is the value of the i-th calculation point; x j is the logarithm of electrostatic charging energy in the jth test; w i ,u j is the normal distribution quantile corresponding to the electrostatic stimulation amount; μ is the mean value of the electrostatic sensitivity distribution calculated from the results of the previous n tests; σ is the variance of the electrostatic sensitivity distribution calculated from the results of the previous n tests; Φ(u) is the probability distribution function of the electrostatic sensitivity calculated from the results of the previous n tests; Φ′(u) is the derivative of the probability distribution function of the electrostatic sensitivity calculated from the results of the previous n tests;

[0033] Step 9: Select the corresponding S(y i )The smallest calculation point y i The electrostatic stimulation amount x for the next formal test n+1 , set the electrostatic charging energy according to its natural logarithm, carry out the electrostatic spark discharge ignition test, and measure and record the electrostatic sensitivity characterization parameters after each test;

[0034] Step 10: Determine whether the number of tests and the test measurement error meet the requirements. If not, repeat steps 6 to 9. If they meet the requirements, continue with the following steps;

[0035] Step 11: According to step 4, the electrostatic sensitivity characterization parameters and responses (ignition) of all tests are statistically analyzed based on the maximum likelihood method, and the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agent samples characterized by the selected parameters is calculated;

[0036] Step 12: Based on the Fisher information matrix method, calculate the measurement errors V(μ), V(σ) of the electrostatic sensitivity distribution parameters μ, σ of industrial explosives and pyrotechnic agents, and further calculate the measurement errors and confidence intervals of the critical electrostatic stimulation quantities with different response probabilities;

[0037] Step 13: Set the maximum response probability that characterizes the electrostatic detonation reliability threshold, calculate the electrostatic detonation reliability threshold characterized by the selected response probability and the selected parameters for industrial explosives and pyrotechnic agent samples, and obtain its confidence interval.

[0038] Optionally, in step 2, the upper limit of the charging energy is set to carry out 10 electrostatic spark discharge ignition tests to ensure that all test samples respond (ignite); the lower limit of the charging energy is set to carry out 10 electrostatic spark discharge ignition tests to ensure that none of the test samples respond (do not ignite), otherwise the range of the electrostatic spark discharge test device needs to be adjusted to meet the above requirements.

[0039] Optionally, in step three, the amount of electrostatic stimulation in the first test is taken as the average of the upper and lower limits; the amount of electrostatic stimulation in each subsequent test is taken as the average of the set value of the previous test and the intermediate variable, and the intermediate variable can be calculated based on the charging energy of the conducted test based on the quartile convergence method; the natural exponent of the electrostatic stimulation amount is set as the charging energy in each test.

[0040] Optionally, in step 4, the Newton method is used to iteratively solve the maximum point of the function P as the electrostatic sensitivity distribution parameter.

[0041] Optionally, in step 12, based on the Fisher information matrix method, the error of the test result is calculated according to equations (7)-(11):

[0042]

[0043]

[0044] u j =(x j -μ) / σ (11)

[0045] Where: V is the error variance of the measured quantity; Cov is the error covariance of the measured quantity; I ijis the matrix element of the Fisher matrix in row i and column j; n is the number of trials currently performed; x j u is the logarithm of electrostatic charging energy (i.e. electrostatic stimulation) in the jth test; i is the normal distribution quantile corresponding to the electrostatic stimulation amount in the jth test; μ is the normal distribution mean; σ is the normal distribution variance.

[0046] Optionally, the critical electrostatic stimulation amount corresponding to different response probabilities is:

[0047] x(p)=μ+α p σ (12)

[0048] Where: p is the probability of response (firing); x(p) is the critical stimulus; α p is the quantile of probability p, that is, the horizontal axis value of the standard normal distribution corresponding to probability p.

[0049] Optionally, the measurement error of the critical electrostatic stimulation amount is calculated by the three parameters in formula (7):

[0050]

[0051] Where: V(x) is the error variance of the critical stimulus of probability p.

[0052] Optionally, by substituting the parameter expression in formula (7) into formula (14) and taking the response probability as 99.99%, formula (2) can be obtained, which means that the selection of the electrostatic stimulation amount each time in the formal test can minimize the measurement error of the response point with the maximum response probability (99.99%).

[0053] In summary, the present invention includes at least one of the following beneficial effects: the present invention provides a relatively standardized and normalized test method for the electrostatic sensitivity of industrial explosives and pyrotechnic agents. Experiments based on the present invention can accurately measure the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents, especially their maximum response probability points. The accuracy of the test results is less dependent on the selection of initial setting parameters, and the error and confidence interval of the test results can also be calculated. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0055] Figure 1 This is the overall flow chart of the electrostatic sensitivity test of industrial explosives and pyrotechnic agents of the present invention;

[0056] Figure 2 This is a flow chart of a single electrostatic spark discharge ignition test of the present invention;

[0057] Figure 3 This is a flow chart of the preliminary test based on the quartile convergence method of the present invention;

[0058] Figure 4 The present invention is a flow chart of calculating the electrostatic sensitivity distribution based on the maximum likelihood method;

[0059] Figure 5 This is a formal test flow chart for the present invention based on the optimized weighted information matrix method. DETAILED DESCRIPTION

[0060] The following is combined with Figure 1-5 The present invention is described in further detail.

[0061] Reference Figure 1 The present invention discloses a method for testing the electrostatic sensitivity of industrial explosives and pyrotechnic agents with a maximum response probability. The specific implementation scheme is as follows:

[0062] Step 1: Prepare the electrostatic spark discharge ignition test method, equipment and industrial explosives and pyrotechnic agent samples for the test, set the electrostatic sensitivity characterization parameters (such as the actual spark discharge energy), ensure that the electrostatic charging energy can be adjusted before each test, and the selected electrostatic sensitivity characterization parameters can be measured after each test. The process of each electrostatic spark discharge ignition test is as follows: Figure 2 shown.

[0063] Step 2. Set the upper and lower limits of the electrostatic charging energy of the electrostatic spark discharge ignition test device. Set the charging energy as the upper limit to perform 10 electrostatic spark discharge ignition tests to ensure that all test samples respond (ignite); set the charging energy as the lower limit to perform 10 electrostatic spark discharge ignition tests to ensure that all test samples do not respond (do not ignite). Otherwise, the range of the electrostatic spark discharge test device needs to be adjusted to meet the above requirements.

[0064] Step 3. Based on the “quartile convergence method”, a series of electrostatic spark discharge ignition tests are carried out on industrial explosives and pyrotechnic agent samples as preliminary tests. In the preliminary test, the electrostatic stimulation amount is taken as the logarithm of the charging energy. After each preliminary test, the electrostatic sensitivity characterization parameters need to be measured and recorded: the electrostatic stimulation amount of the first test is taken as the average of the upper and lower limits, and the electrostatic stimulation amount of each subsequent test is taken as the average of the previous test set value and the intermediate variable. The intermediate variable can be calculated based on the “quartile convergence method” according to the existing test data; the charging energy of each test is set to the natural exponent of the electrostatic stimulation amount; when the test results show a mixed result area, the preliminary test is stopped and the formal test is started (that is, the minimum response charging energy is less than the maximum non-response charging energy). The preliminary test process is as follows: Figure 3 shown.

[0065] Step 4: Based on the "maximum likelihood method", the charging energy and response of the pre-test are statistically analyzed, and the preliminary results of the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents are calculated. Assuming that the electrostatic sensitivity distribution obeys the log-normal distribution, the mean μ and variance σ of the electrostatic sensitivity distribution are solved to maximize the probability P of the pre-test results. The Newton method can be used to iteratively solve the function maximum point. The specific calculation process is as follows: Figure 4 shown.

[0066] Step 5: Based on the "optimal weighted information matrix method", a series of electrostatic spark discharge ignition tests are carried out. According to steps 6 to 10, the test is formally carried out. The charging energy is set in each test so that the weighted information entropy S(x k ) is the smallest, such as Figure 5 shown.

[0067] Step 6: Set the maximum number of tests N for the formal test, and count the charging energy and response of all tests including the pre-test, and calculate the electrostatic sensitivity distribution parameters μ, σ according to the method in step 4.

[0068] Step 7: Select M+1 different calculation points evenly between the upper and lower limits of the electrostatic stimulation amount set in step 2:

[0069] y i =[(Mi)x L +ix U ] / M, (1)

[0070] Where: M is the number of calculation points minus one; y i is the value of the selected calculation point; i is the number of different calculation points; x L is the lower limit of electrostatic stimulation, which is the logarithm of the minimum charging energy; x U The upper limit of electrostatic stimulation is taken as the logarithm of the maximum charging energy;

[0071] Step 8: Calculate the weighted information entropy S(y) of the above selected calculation point according to equations (2)-(6) i ):

[0072]

[0073] w i (y i )=(y i -μ) / σ,u j =(x j -μ) / σ (6)

[0074] Where: S is the weighted information entropy; α p is the weighting constant, corresponding to a 99.99% response probability; I ijis the matrix element of the Fisher matrix in row i and column j; n is the number of trials currently performed; y i is the value of the i-th calculation point; x j is the logarithm of electrostatic charging energy in the jth test; w i ,u j is the normal distribution quantile corresponding to the electrostatic stimulation amount; μ is the mean value of the electrostatic sensitivity distribution calculated from the results of the previous n tests; σ is the variance of the electrostatic sensitivity distribution calculated from the results of the previous n tests; Φ(u) is the probability distribution function of the electrostatic sensitivity calculated from the results of the previous n tests; Φ′(u) is the derivative of the probability distribution function of the electrostatic sensitivity calculated from the results of the previous n tests;

[0075] Step 9. Select the corresponding S(y i )The smallest calculation point y i The electrostatic stimulation amount x for the next formal test n+1 , set the electrostatic charging energy according to its natural logarithm, carry out the electrostatic spark discharge ignition test, and measure and record the electrostatic sensitivity characterization parameters after each test.

[0076] Step 10: Determine whether the number of tests and the test measurement error meet the requirements. If not, repeat steps 6 to 9. If they do, continue with the following steps.

[0077] Step 11: According to step 4, the electrostatic sensitivity characterization parameters and responses (ignition) of all tests are statistically analyzed based on the "maximum likelihood method", and the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agent samples characterized by the selected parameters is calculated.

[0078] Step 12: Based on the "Fisher information matrix method", calculate the measurement errors V(μ) and V(σ) of the electrostatic sensitivity distribution parameters μ and σ of industrial explosives and pyrotechnic agents, and obtain the measurement errors and confidence intervals of the critical electrostatic stimulation quantities with different response probabilities.

[0079] Step 13: Set the maximum response probability that characterizes the electrostatic detonation reliability threshold, calculate the electrostatic detonation reliability threshold characterized by the selected response probability and the selected parameters for industrial explosives and pyrotechnic agent samples, and obtain its confidence interval.

[0080] Since then, electrostatic sensitivity tests of industrial explosives and pyrotechnic agents based on maximum response probability have been completed.

[0081] The method of the present invention can more accurately measure the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents, especially the maximum probability response point, and the accuracy of the test results is less dependent on the selection of initial setting parameters, and the error and confidence interval of the test results can be calculated. The present invention also provides a more standardized and standardized test method for the electrostatic sensitivity of industrial explosives and pyrotechnic agents by clarifying the specific operation process. Therefore, the present invention solves the four defects of the existing electrostatic sensitivity test method for industrial explosives and pyrotechnic agents mentioned in the technical background:

[0082] (1) The calculation of the maximum response probability response point is more accurate

[0083] First, in the formal test, the "optimal weighted information matrix" method is used to set the electrostatic charging energy of each electrostatic spark discharge ignition test. The most accurate electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents can be calculated within the least number of tests. In particular, the variance of the electrostatic sensitivity distribution can be accurately calculated. Therefore, the calculation accuracy of the maximum response probability point in the test results is very high.

[0084] Based on the "maximum likelihood method", the most likely electrostatic sensitivity distribution can be fitted from a limited number of test results. It obeys the normal distribution and can be determined by two key parameters: mean μ and variance σ. The measurement errors of these two parameters can be calculated according to the "Fisher information matrix method":

[0085]

[0086] u j =(x j -μ) / σ (11)

[0087] Where: V is the error variance of the measured quantity; Cov is the error covariance of the measured quantity; I ij is the matrix element of the Fisher matrix in row i and column j; n is the number of trials currently performed; x j u is the logarithm of electrostatic charging energy (i.e. electrostatic stimulation) in the jth test; i is the normal distribution quantile corresponding to the electrostatic stimulation amount in the jth test; μ is the normal distribution mean; σ is the normal distribution variance.

[0088] Since the normal distribution is completely determined by these two parameters, the critical electrostatic stimulation amount corresponding to different response probabilities can also be expressed by:

[0089] x(p)=μ+α p σ (12)

[0090] Where: p is the response (firing) probability; x(p) is the critical electrostatic stimulus; α p is the quantile of probability p, that is, the horizontal axis value of the standard normal distribution corresponding to probability p.

[0091] The calculation error of critical electrostatic stimulation amount with different response probabilities can be obtained by the three parameters in formula (7):

[0092] Number calculation:

[0093]

[0094] Where: V(x) is the error variance of the critical electrostatic stimulation with probability p.

[0095] Substituting the parameter expression in formula (7) into formula (14) and taking the response probability as 99.99%, we can obtain formula (2) used in the present invention. Therefore, the selection of the electrostatic stimulation amount for each test by the "optimal weighted information matrix method" can minimize the measurement error of the critical electrostatic stimulation amount corresponding to the 99.99% response probability, thereby ensuring that the test efficiently obtains the most accurate electrostatic sensitivity test results corresponding to the maximum response probability (99.99% in this article).

[0096] Secondly, the present invention sets the electrostatic stimulation amount of each test to the logarithm of the charging energy, which essentially assumes that the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents obeys the lognormal distribution, which is more in line with the actual situation than the normal distribution or logistic distribution used in the traditional method. This is because no matter what kind of industrial explosives and pyrotechnic agent samples are, the charging energy during the electrostatic spark discharge ignition test can only be positive, and when the electrostatic charging energy is 0, no electrostatic spark discharge will occur, so the probability of sample response should be strictly equal to 0. The normal distribution and logistic distribution only have a corresponding probability of 0 when the charging energy is negative infinity, which cannot meet the above requirements; while the lognormal distribution is a normal distribution with a logarithmic transformation of the horizontal coordinate, which ensures that the charging energy can only be positive, and the corresponding probability when the charging energy is 0 is strictly 0, which is more in line with the actual situation of the electrostatic sensitivity of industrial explosives and pyrotechnic agents. Choosing a more practical form of electrostatic sensitivity distribution can not only set the charging energy for each test more scientifically and effectively when conducting formal tests based on the "optimal weighted information matrix method", but also calculate a more accurate electrostatic sensitivity distribution based on the "maximum likelihood method" when processing test data. Therefore, the maximum response probability response points of industrial explosives and pyrotechnic agents can be more accurately measured.

[0097] In summary, the present invention can more accurately calculate the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents, especially their maximum probability response points, within a smaller number of tests than the existing test methods.

[0098] (2) The accuracy of the test results is less dependent on the initial setting parameter selection

[0099] First, the pre-test of the present invention is carried out based on the "quartile convergence method". Before the test begins, it is only necessary to provide the upper and lower limits of the electrostatic spark discharge ignition test device, and there is no need to estimate the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agent samples. When conducting the pre-test, it is necessary to start from the last test result before each test. When the number of responses (ignition) and non-responses (non-ignition) is equal, it can be considered that the stimulus amount of this test approximately corresponds to the 50% probability response point. Therefore, no matter how the stimulus amount of the initial test is set, the 50% probability response point of the test sample can be quickly locked after several pre-tests. Moreover, the "quartile convergence method" is different from the "Langley method". After convergence and locking, the electrostatic stimulus amount of each test will not be selected at the 50% probability response point, but will be scattered near the 25% and 75% probability response points. Therefore, the mean and variance of the electrostatic sensitivity distribution can be more accurately pre-tested. Calculation.

[0100] Secondly, the formal test was carried out based on the "optimal weighted information matrix method". The initial input parameters were provided by the preliminary test, which had a certain experimental basis and was independent of the initial test parameters (the upper and lower limits of the electrostatic stimulation amount). Moreover, during the formal experiment, the selection of the stimulation amount for each ignition test needed to solve the optimization equation based on all the existing test records, so it was less dependent on the selection of the initial setting parameters.

[0101] In summary, the accuracy of the test results of the present invention is less dependent on the selection of initial setting parameters.

[0102] (3) The error and confidence interval of the test results can be calculated

[0103] The present invention can not only calculate the electrostatic sensitivity distribution of the sample from the test record based on the "maximum likelihood method", but also calculate the measurement error of the electrostatic sensitivity distribution based on the "Fisher information matrix method". In fact, in the formal test stage, the present invention needs to calculate the measurement error of the electrostatic sensitivity distribution before each test based on the "optimal weighted information matrix method". The calculation method is shown in formula (2), and the measurement error of the electrostatic critical stimulation amount corresponding to different response probabilities can be calculated. Combined with the measurement error of the test results and the total number of tests, the confidence interval (such as 95% confidence interval) of each measurement result under different confidence probabilities can also be estimated according to the t distribution principle to evaluate the accuracy of the results such as the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents obtained by the test. When the reliable threshold of electrostatic initiation of industrial explosives and pyrotechnic agents characterized by the maximum response probability is actually used, a certain margin can be reserved according to the confidence interval to prevent the reduction of initiation reliability caused by the test measurement error.

[0104] (4) Standardize and refine the electrostatic sensitivity test process for industrial explosives and pyrotechnic agents

[0105] The present invention is different from the existing standards for the electrostatic sensitivity test methods of industrial explosives and pyrotechnic agents, and standardizes and refines the test process of the electrostatic sensitivity test of industrial explosives and pyrotechnic agents. The electrostatic sensitivity test of industrial explosives and pyrotechnic agents is a process based on a mathematical and statistical model to carry out a series of electrostatic spark discharge ignition tests, and finally calculate the electrostatic sensitivity of industrial explosives and pyrotechnic agents. The present invention clarifies the requirements of the electrostatic spark discharge ignition test in the steps, distinguishes the controllable electrostatic charging energy and the electrostatic sensitivity characterization parameters to be measured in the test, and requires the calculation of the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents according to the log-normal distribution. Therefore, it can guide the electrostatic sensitivity test of industrial explosives and pyrotechnic agents in a more standardized and systematic manner, and facilitate the specific operation of the test.

[0106] Example:

[0107] 0. Static spark discharge ignition test (such as Figure 2 shown):

[0108] 0.1. Set the electrostatic stimulation amount x;

[0109] 0.2. Take the electrostatic charging energy as the natural index E of the electrostatic stimulation amount C = exp(x);

[0110] 0.3. According to E C =CU 2 / 2, select the appropriate charging capacitor C and charging voltage U within the adjustable range of the electrostatic spark discharge ignition test device;

[0111] 0.4. Use capacitor C as charging capacitor and charge it with voltage U;

[0112] 0.5. Release the static electricity in the charging capacitor to form static spark discharge, and let the discharge spark pass through the industrial explosives and pyrotechnic agent samples;

[0113] 0.6. Observe and record the sample response v. If the sample responds (ignites), v = 1, otherwise v = 0;

[0114] 0.7.Measure, calculate and record the actual spark energy E during electrostatic discharge S , as a parameter to characterize the electrostatic sensitivity of industrial explosives and pyrotechnic agents;

[0115] 1. Preparation before the test:

[0116] 1.1. Set the control parameters of the electrostatic spark discharge ignition test. This scheme takes the charging capacitor and voltage as an example;

[0117] 1.2. Set the electrostatic sensitivity characterization parameters of industrial explosives and pyrotechnic agents. This scheme takes the real spark energy as an example;

[0118] 1.3. Prepare the electrostatic spark discharge ignition test method, device and industrial explosives and pyrotechnic agent samples for the test according to step 0, ensure that the charging capacitance and voltage can be adjusted before each test, and the actual discharge spark energy can be measured after the test;

[0119] 2. Conduct a test to find out the upper and lower limits of electrostatic stimulation:

[0120] 2.1. Setting the electrostatic spark discharge ignition test device can adjust the upper and lower limits of the electrostatic charging capacitance and voltage;

[0121] 2.2. Set the maximum charging capacitance and voltage, and conduct 10 electrostatic spark discharge ignition tests on the test sample;

[0122] 2.3. If the sample does not respond (does not ignite), it is necessary to increase the upper limit of the range of the electrostatic spark discharge ignition test device and repeat step 2.2. If the sample responds (ignites), continue with the following steps;

[0123] 2.4. Set the minimum charging capacitance and voltage, and conduct 10 electrostatic spark discharge ignition tests on the test sample;

[0124] 2.5. If the sample responds (ignites), it is necessary to lower the lower limit of the range of the electrostatic spark discharge ignition test device and repeat step 2.4. If the sample does not respond (does not ignite), continue with the following steps;

[0125] 2.6. Using E=CU 2 / 2, calculate the upper limit of the test charging energy E based on the maximum charging capacitance and voltage U , calculate the lower limit of the test charging energy E according to the minimum charging capacitance and voltage L , and calculate their natural logarithms as the upper and lower limits of the electrostatic stimulation x U =log(E U ),x L =log(E L );

[0126] 3. Conduct a pilot test based on the “quartile convergence method” (e.g. Figure 2 shown):

[0127] 3.1. Set the initial electrostatic stimulation amount to the average value of the upper and lower limits x0 = x L +x U ;

[0128] 3.2. Carry out the electrostatic spark discharge ignition test according to step 0;

[0129] 3.3. Record the number of responses (firings) and non-responses (non-firings) from the last test forward, and Figure 2 The logical calculation intermediate variable x′;

[0130] 3.4. Determine whether the pre-test results show a mixed result area, that is, the minimum non-response (non-ignition) charging energy is less than the maximum response (ignition) charging energy;

[0131] 3.5. If no mixed result area appears, the electrostatic stimulation amount of the next test is taken as the sum of the electrostatic stimulation amount of the previous test and the intermediate variable, and steps 3.2 to 3.4 are repeated. If a mixed result area appears, continue with the following steps;

[0132] 4. Based on the "maximum likelihood method", calculate the electrostatic sensitivity distribution represented by charging energy (such as Figure 5 shown):

[0133] 4.1. Statistics of charging energy E of all k trials Ci And its corresponding response (firing) situation v i , and calculate the natural logarithm of the charging energy as the electrostatic stimulation amount x i =log(E Ci );

[0134] 4.2. Set the allowable error ε for calculating the electrostatic sensitivity distribution parameters (generally set to ε = 10 -3 ), and began to iteratively solve the maximum probability point of the test results based on the "Newton method";

[0135] 4.3. Find the corresponding v i =1 is denoted as x 1L , find the corresponding v i =0 is denoted as x 0U , x 1L and x 0U The number of electrostatic stimulations between m , and thus determine the initial value of the iterative calculation:

[0136]

[0137] Where: μ (0) is the initial value of the iteration of the mean value of electrostatic sensitivity; σ (0) is the iterative initial value of the electrostatic sensitivity variance;

[0138] k is the total number of trials;

[0139] x 1L It is the minimum response (firing) stimulus amount;

[0140] x 0U is the maximum non-response (non-firing) stimulus amount;

[0141] n m is the number of stimulus amounts in the mixed result area;

[0142] 4.4. Calculate the following intermediate variables in sequence:

[0143]

[0144] Where: t is the number of iteration steps;

[0145] i is the number of different tests;

[0146] u is the coordination number of normal distribution;

[0147] p is the probability of electrostatic sensitivity response;

[0148] Other parameters are calculated intermediate variables;

[0149] 4.5. Solve the binary equations in equation (23) to obtain the change in the electrostatic sensitivity distribution parameter:

[0150]

[0151] Where: Δμ (t) Iterative increase of the mean value of sensitivity distribution;

[0152] Δσ (t) -------Iterative increase in sensitivity distribution variance;

[0153] 4.6. Determine and suppress excessive changes: Ensure |Δμ (t) |<σ (t-1)

[0154] And σ (t-1) / 2<Δσ (t) <2σ (t-1) If it is not satisfied, the change should be limited to this range;

[0155] 4.7. Add the mean and variance of the electrostatic sensitivity distribution to the change amount to complete one iteration;

[0156] 4.8. Determine whether the sum of the absolute values ​​of the changes of the two parameters is less than the allowable error ε. If so, continue with the following steps; otherwise, repeat steps 4.4 to 4.7;

[0157] 5. Carry out formal experiments based on the "optimal weighted information matrix method" (such as Figure 3 shown):

[0158] 5.1. Set the maximum number of tests N, which can generally be 100;

[0159] 5.2. Collect the existing test data (including pre-test data) and calculate the electrostatic sensitivity distribution parameters μ, σ according to the method in step 4;

[0160] 5.3. Select M+1 different calculation points (10000 points can be taken) evenly between the upper and lower limits of the electrostatic stimulation amount:

[0161] y i =[(Mi)x L +ix U ] / M, (24)

[0162] Where: M is the number of calculation points minus one;

[0163] y i Take values ​​for the selected calculation points;

[0164] i is the number of different calculation points;

[0165] x L is the lower limit of electrostatic stimulation, which is taken as the logarithm of the minimum charging energy;

[0166] x U is the upper limit of electrostatic stimulation, which is taken as the logarithm of the maximum charging energy;

[0167] 5.4. Calculate the weighted information entropy S(y) of the selected points according to equations (2)-(6) i );

[0168] 5.5. Select S(y i )The calculation point corresponding to the smallest point is y i As the electrostatic stimulus x for the next test n+1 , and carry out the electrostatic spark discharge ignition test according to the method of step 0;

[0169] 5.6. Determine whether the number of tests and test error meet the requirements. If not, repeat steps 5.2 to 5.5. Otherwise, continue with the following steps;

[0170] 6. Calculate the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents characterized by real spark energy based on the "maximum likelihood method":

[0171] 6.1. Calculate the actual spark energy E of electrostatic discharge in each test Si and the corresponding response (firing) situation v i , calculate the natural logarithm of the real spark energy and record it as the electrostatic stimulation amount x i ;

[0172] 6.2. According to the method in step 4, fitting the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents characterized by real spark energy;

[0173] 7. Calculation of electrostatic sensitivity measurement error of industrial explosives and pyrotechnic agents based on the "Fisher information matrix method":

[0174] 7.1. Calculate the measurement error of the electrostatic sensitivity distribution parameter according to formula (7);

[0175] 7.2. Calculate the measurement error of the critical electrostatic stimulation amount corresponding to different response probabilities according to formula (14);

[0176] 8. Calculate the test results such as the electrostatic initiation reliability threshold, set the maximum response probability (such as 99.99%) that characterizes the initiation reliability threshold, and calculate the sample's initiation reliability threshold and its confidence interval based on the above test results.

[0177] The above are all preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Therefore, any equivalent changes made based on the structure, shape, and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for testing the electrostatic sensitivity of industrial explosives and pyrotechnic agents with a maximum response probability, characterized in that: The specific steps include: Step 1: Prepare the electrostatic spark discharge ignition test device and industrial explosives and pyrotechnic agent samples, set the electrostatic sensitivity characterization parameters, ensure that the electrostatic charging energy can be adjusted before each test, and the selected electrostatic sensitivity characterization parameters can be measured after each test; Step 2: Setting the upper and lower limits of the electrostatic charging energy of the electrostatic spark discharge ignition test device; Step 3: Based on the quartile convergence method, a series of electrostatic spark discharge ignition tests are carried out on industrial explosives and pyrotechnic agent samples as preliminary tests. In the preliminary tests, the electrostatic stimulation amount is taken as the logarithm of the charging energy. Each preliminary test needs to measure and record the electrostatic sensitivity characterization parameters. When the preliminary test results show a mixed result area, that is, the minimum response charging energy is less than the maximum non-response charging energy, the preliminary test is stopped and the formal test is started; Step 4: Based on the maximum likelihood method, the charging energy and response ignition of the pre-test are statistically analyzed, and the preliminary results of the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agents are calculated. Assuming that the electrostatic sensitivity distribution obeys the log-normal distribution, the mean μ and variance σ of the electrostatic sensitivity distribution are solved to maximize the probability P of the pre-test results. Step 5: Based on the optimized weighted information matrix method, a series of electrostatic spark discharge ignition tests are carried out, and the test is officially carried out according to steps 6 to 10; Step 6: Set the maximum number of tests N for the formal test, and count the charging energy and response firing of all tests including the pre-test, and calculate the electrostatic sensitivity distribution parameters μ, σ according to the method of step 4; Step 7: Select M+1 calculation points between the upper limit and lower limit of the electrostatic stimulation amount set in step 2: the i =[(M)x L +ix U ] / M (1) Where: M is the number of calculation points minus one; y i is the value of the selected calculation point; i is the number of different calculation points; x L is the lower limit of electrostatic stimulation, the logarithm of the minimum charging energy; x U The upper limit of electrostatic stimulation, the logarithm of the maximum charging energy; Step 8: Calculate the weighted information entropy S(y) of the above selected calculation point according to equations (2)-(6) i ): w i (y i )=(y i -μ) / σ,u j =(x j -m) / s (6) Where: S is the weighted information entropy; α p is the weighting constant, corresponding to a 99.99% response probability; I ij is the matrix element of the Fisher matrix in row i and column j; n is the number of trials currently performed; y i is the value of the i-th calculation point; x j is the logarithm of electrostatic charging energy in the jth test; w i ,u j is the quantile of normal distribution; μ is the mean value of electrostatic sensitivity distribution calculated from the results of the previous n tests; σ is the variance of electrostatic sensitivity distribution calculated from the results of the previous n tests; Φ(u) is the probability distribution function of electrostatic sensitivity calculated from the results of the previous n tests; Φ′(u) is the derivative of the probability distribution function of electrostatic sensitivity calculated from the results of the previous n tests; Step 9: Select the corresponding S(y i )The smallest calculation point y i The electrostatic stimulation amount x for the next formal test n+1 , carry out electrostatic spark discharge ignition test according to the set electrostatic charging energy, and measure and record the electrostatic sensitivity characterization parameters after each test; Step 10: Determine whether the number of tests and the test measurement error meet the requirements. If not, repeat steps 6 to 9. If they meet the requirements, continue with the following steps; Step 11: According to step 4, all test electrostatic sensitivity characterization parameters and response ignition are statistically analyzed based on the maximum likelihood method, and the electrostatic sensitivity distribution of industrial explosives and pyrotechnic agent samples characterized by the selected parameters is calculated; Step 12: Based on the Fisher information matrix method, the measurement errors V(μ) and V(σ) of the electrostatic sensitivity distribution parameters μ and σ of industrial explosives and pyrotechnic agents are calculated, and the measurement errors and confidence intervals of the critical electrostatic stimulation quantities with different response probabilities are further obtained; Step 13: Set the maximum response probability that characterizes the electrostatic detonation reliability threshold, calculate the electrostatic detonation reliability threshold characterized by the selected response probability and the selected parameters for industrial explosives and pyrotechnic agent samples, and obtain its confidence interval.

2. The electrostatic sensitivity test method for industrial explosives and pyrotechnic agents with a maximum response probability according to claim 1, characterized in that: In the step 2, the upper limit of the charging energy is set to carry out 10 electrostatic spark discharge ignition tests to ensure that all test samples respond and ignite; the lower limit of the charging energy is set to carry out 10 electrostatic spark discharge ignition tests to ensure that none of the test samples respond and do not ignite, otherwise the range of the electrostatic spark discharge test device needs to be adjusted to meet the above requirements.

3. The electrostatic sensitivity test method for industrial explosives and pyrotechnic agents with a maximum response probability according to claim 1, characterized in that: In the step three, the electrostatic stimulation amount in the first test is taken as the average of the upper and lower limits; the electrostatic stimulation amount in each subsequent test is taken as the average of the set value of the previous test and the intermediate variable, and the intermediate variable can be calculated based on the charging energy of the conducted test based on the quartile convergence method; the natural exponent of the electrostatic stimulation amount is set as the charging energy in each test.

4. The electrostatic sensitivity test method for industrial explosives and pyrotechnic agents with a maximum response probability according to claim 1, characterized in that: In the step 4, the Newton method is used to iteratively solve the maximum point of the function P as the electrostatic sensitivity distribution parameter.

5. The electrostatic sensitivity test method for industrial explosives and pyrotechnic agents with a maximum response probability according to claim 1, characterized in that: In step 12, based on the Fisher information matrix method, the error of the test result is calculated according to equations (7)-(11): you j =(x j -m) / s (11) Where: V is the error variance of the measured quantity; Cov is the error covariance of the measured quantity; I ij is the matrix element of the Fisher matrix in row i and column j; n is the number of trials currently performed; x j u is the logarithm of the electrostatic charging energy in the jth test, i.e., the electrostatic stimulation amount; j is the normal distribution quantile corresponding to the electrostatic stimulation amount in the jth test; μ is the normal distribution mean; σ is the normal distribution variance.

6. The electrostatic sensitivity test method for industrial explosives and pyrotechnic agents with a maximum response probability according to claim 5, characterized in that: The critical electrostatic stimulation amount corresponding to different response probabilities is expressed as: x(p)=μ+α p p (12) Where: p is the probability of response firing; x(p) is the critical stimulus; α p is the quantile of probability p, that is, the horizontal coordinate of the standard normal distribution corresponding to probability p.

7. The electrostatic sensitivity test method for industrial explosives and pyrotechnic agents with a maximum response probability according to claim 1, characterized in that: The measurement error of the critical electrostatic stimulation amount is calculated by the three parameters in formula (7): Where: V(x) is the error variance of the critical stimulus of probability p.

8. The electrostatic sensitivity test method for industrial explosives and pyrotechnic agents with a maximum response probability according to claim 7, characterized in that: Substituting the parameter expression in equation (7) into equation (14) and taking the response probability as 99.99%, we can obtain equation (2).

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