Multi-accident reproduction vehicle speed fusion method and system based on fuzzy mathematics

Abstract

In order to solve the problem that it is difficult to ensure that a final result obeys normal distribution when a plurality of accident reproduction vehicle speeds are fused in an existing achievement, the invention provides a method and system for fusing the plurality of accident reproduction vehicle speeds based on fuzzy mathematics, and the method comprises the steps: firstly, determining a subinterval of a final fusion result according to the accident reproduction vehicle speeds; then determining a membership function corresponding to the accident reproduction vehicle speed, and converting the accident reproduction vehicle speed and the subintervals into a fuzzy set by using a Zadeh representation method by means of the membership function; calculating an evaluation index value of the fuzzy set, and combining the evaluation index value with the fuzzy set to obtain a final fusion result; and finally, giving a bar chart for the obtained final fusion result, and visually expressing the result. Compared with the prior art, the method has the beneficial effect that the final fusion result is ensured to obey normal distribution.

Description

Technical Field

[0001] The present invention relates to the field of accident reconstruction, and more specifically, to a method and system for fusing multiple accident reconstruction vehicle speeds based on fuzzy mathematics. Background Art

[0002] Accident reconstruction is to use the accident reconstruction method to reversely deduce the information such as the way and cause of the accident based on the various traces collected at the accident scene and the descriptions of the accident participants; in order to obtain a reliable reconstructed vehicle speed, scholars have proposed many methods, such as simulation software method, video image method, vehicle event data recorder method, theoretical and empirical formula method, etc. The basis of accident reconstruction is traces, which are affected by environmental and human factors, especially when the accident occurs at night or in bad weather. The traces at the accident scene are often destroyed and gradually disappear. Therefore, it is difficult to ensure the accuracy of the measured traces, which are bound to contain uncertain information, making the reconstructed vehicle speed obtained based on the traces uncertain. In order to objectively reflect the uncertainty of traces in the reconstructed vehicle speed, scholars have proposed a variety of solutions, including uncertainty assessment method, Monte Carlo method, Bayesian method, random perturbation method, upper and lower bounds method, and response surface method. The use of these methods improves the objectivity of the reconstructed vehicle speed, but cannot improve the accuracy of the vehicle speed. In order to obtain more accurate results of reproducing vehicle speed, as more accident reconstruction methods are available, scholars are more likely to choose multiple models to reproduce the same accident, thereby obtaining multiple accident reconstruction vehicle speeds. This is to use multiple tools to measure the same event, and the results obtained must obey the normal distribution. The normal distribution is also called the normal curve, which is bell-shaped, low at both ends and high in the middle. Therefore, the question of how to objectively integrate multiple vehicle speeds so that the final fusion result obeys the normal distribution arises.

[0003] There are some methods for describing multiple accident reconstruction speeds, which can be roughly divided into two categories. The first category deals with the situation where all speeds are normal, including methods such as evidence theory, ordered weighted average and Monte Carlo. They can all well fuse multiple reconstructed speeds or give reliability rankings of different speeds, but cannot handle potential risk speeds. The second category deals with the situation where there are potential risk speeds, including methods such as entropy method, clustering and priority diagram. They can reduce the proportion of potential risk speeds before fusion, thereby obtaining a result that is approximately normally distributed, but the final fusion result obtained by the entropy method does not completely obey the normal distribution, and the clustering and priority diagram methods are too cumbersome, so more exploration is needed to obtain new accident reconstruction speed fusion methods.

[0004] The essential reason why multiple accident reconstruction speeds need to be integrated is that the speed obtained by a single model is not a fixed value, while the speeds obtained by multiple models are inconsistent, that is, the speed is uncertain, or fuzzy, and fuzzy mathematics is to take uncertain things as the research object, and use precise mathematical means to describe and model fuzzy concepts and fuzzy phenomena in the real world. For this reason, fuzzy mathematics can be introduced to integrate multiple accident reconstruction speeds.

[0005] To this end, the present invention proposes a method and system for merging multiple accident reconstruction vehicle speeds based on fuzzy mathematics. Summary of the invention

[0006] In view of the fact that there are no or few methods in existing research results to deal with the situation where there are potential risk speeds among multiple accident reconstruction speeds, so that the final result obeys the normal probability distribution of the normal distribution, the present invention proposes a method for fusing multiple accident reconstruction speeds based on fuzzy mathematics. This method can fuse multiple accident reconstruction speeds to ensure that the final result obeys the normal distribution, and solves the problem of objective fusion when there are potential risk speeds among multiple accident reconstruction speeds; and a system for fusing multiple accident reconstruction speeds based on fuzzy mathematics is developed according to this method.

[0007] Preferably, the specific implementation steps of the method are as follows:

[0008] S11: Reconstruct vehicle speed B based on n accidents i , i = [1, n], determine the m sub-intervals of the final fusion result;

[0009] S12: Obtain the membership function A corresponding to the n accident reconstructed vehicle speeds according to the n accident reconstructed vehicle speeds and the m sub-intervals of the final fusion result obtained in step S11. i (x);

[0010] S13: converting the relationship between the n accident reconstructed vehicle speeds and the m sub-intervals of the final fusion result into a fuzzy set;

[0011] S14: Calculate the evaluation index value w of the fuzzy set i ;

[0012] S15: obtain the final fusion result;

[0013] S16: Output the membership of the sub-intervals in the final fusion result in a bar chart as the final result.

[0014] Preferably, the method for determining the m sub-intervals of the final fusion result in step S11 is: first, the minimum value e of all accident reconstruction vehicle speeds is used as the lower bound of the final fusion result, and the maximum value f of all accident reconstruction vehicle speeds is used as the upper bound of the final fusion result, thereby obtaining the final fusion result interval [e, f]; secondly, by using the specified interval method, m continuous sub-intervals are given in the interval [e, f].

[0015] Preferably, the membership function A corresponding to the n accident recurrence vehicle speeds in step S12 i(x) According to the assignment method, three commonly used membership function types are shown in formula (1), which are, from top to bottom, triangular membership function, rectangular membership function and trapezoidal membership function;

[0016]

[0017]

[0018]

[0019] In the triangle membership function, c=(b+d) / 2, and in the trapezoidal membership function, c=(3b+e) / 4, d=(b+3e) / 4.

[0020] Prior to obtaining the fuzzy set in step S13, the relationship between the accident reconstruction vehicle speed and the sub-interval of the final fusion result is converted into a fuzzy set using the Zadeh representation method, and the corresponding fuzzy set expression is written based on the membership function obtained in step S12;

[0021]

[0022] In the formula, A i The accident re-occurrence speed is B i The corresponding fuzzy set, a1…a m Represents the subinterval of the final fusion result, A i (a1)…A i (a m ) represents the membership of the subinterval of the final fusion result on the accident reconstruction speed, A i (a m ) represents the mth subinterval (a m ) is the membership degree of the vehicle speed at the i-th accident reappearance.

[0023] Preferably, the evaluation index value w of the fuzzy set in step S14 is i The solution is as follows:

[0024] S141 performs a fuzzy set product (·) operation on the fuzzy set obtained in step S13, and the formula is as follows:

[0025]

[0026] Where i, j = 1, 2...n, A ij =A ji , only needs to be calculated once;

[0027] S142 Calculate the evaluation result v ij with u ij ;

[0028] v ij=A i (a1)·A j (a1)+A i (a2)·A j (a2)+…+A i (a m )·A j (a m ) (4)

[0029] where v ij =v ji , which only needs to be calculated once

[0030]

[0031] where u ij =u ji , which only needs to be calculated once

[0032] S143 Calculate the evaluation index value w of the fuzzy set i ;

[0033]

[0034] Where i≠j.

[0035] Preferably, the steps of obtaining the final fusion result in step S15 are:

[0036] S151 first converts the evaluation index value w obtained in step S14 into i Multiply the corresponding fuzzy sets obtained in step S13 to obtain n new fuzzy set expressions;

[0037] S152 Secondly, the n new fuzzy set expressions are added together according to the membership degrees corresponding to the subintervals to form a fuzzy set expression;

[0038]

[0039] In the formula, A i The accident re-occurrence speed is B i The corresponding fuzzy set, w i ·A i (a1), ..., w i ·A i (a m ) represents the membership degree A i (a1)...A i (a m ) The evaluation index value w i The value obtained after processing, a1...a m The subinterval representing the final fusion result;

[0040] S153 Finally, the membership of all sub-intervals is normalized, and the membership of the obtained result can be regarded as the probability of the sub-interval of the final fusion result.

[0041] Preferably, a system for fusion of multiple accident reconstruction vehicle speeds based on fuzzy mathematics is developed according to the method, and the system consists of a data input module, a fuzzification module, a fuzzy decision module and a result output module; the data input module is used to input multiple accident reconstruction vehicle speeds, and transmit the data to the fuzzification module for processing; the fuzzification module is used to fuzzify the input multiple accident reconstruction vehicle speeds (corresponding to steps S11, S12, and S13 described in the specification); the fuzzy decision module is used to calculate the evaluation index value of the fuzzy set, and combine it with the fuzzy set in the fuzzification module, thereby reducing the proportion of potential risk speeds (corresponding to steps S14 and S15 described in the specification); the result output module is used to output the final result, and a bar chart is given for the final fusion result obtained to intuitively express the result (corresponding to step S16 described in the specification).

[0042] The present invention proposes a method and system for fusing multiple accident reconstruction vehicle speeds based on fuzzy mathematics. The method first determines the sub-interval of the final fusion result according to the accident reconstruction vehicle speed, then determines the membership function corresponding to the accident reconstruction vehicle speed, and converts the accident reconstruction vehicle speed and the sub-interval into a fuzzy set using the Zadeh representation method with the help of the membership function; then calculates the evaluation index value of the fuzzy set, and combines it with the fuzzy set to obtain the final fusion result; finally, a bar chart is given for the final fusion result to intuitively express the result. According to the method, a system for fusing multiple accident reconstruction vehicle speeds based on fuzzy mathematics is developed, which consists of a data input module, a fuzzification module, a fuzzy decision module and a result output module. The input module inputs multiple accident reconstruction speeds; the fuzzification module determines the sub-interval of the final fusion result according to the multiple accident reconstruction speeds, and then determines the membership function corresponding to the accident reconstruction speed, and uses the Zadeh representation method to convert the accident reconstruction speed and the final fusion result sub-interval into a fuzzy set; the fuzzy decision module is used to calculate the evaluation index value of the fuzzy set, and the evaluation index value of the obtained fuzzy set is combined with the fuzzy set to obtain the final fusion result; the result output module is used to give a bar chart for the obtained final fusion result to intuitively express the result. Compared with the prior art, the beneficial effect of the present invention is to ensure that the obtained final fusion result obeys the normal distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flowchart of the present invention.

[0044] Figure 2 It is a system block diagram of the present invention.

[0045] Figure 3 This is the fusion result obtained for a specific example of the present invention. DETAILED DESCRIPTION

[0046] The accompanying drawings are only used for exemplary description and should not be construed as limiting the present patent. The technical solution of the present invention will be further described below in conjunction with embodiments.

[0047] Embodiment 1

[0048] Assume that four accident reconstruction models are selected to obtain four vehicle speeds of a certain accident, namely B1 = [64, 66] km / h, B2 = [63, 65] km / h, B3 = [59, 69] km / h, and B4 = [65, 75] km / h. The method described in the present invention is used to fuse these four reproduced vehicle speeds.

[0049] Step S11: According to the four accident reconstruction vehicle speeds, the upper limit of the final fusion result is determined to be 75 and the lower limit is 59, and the final fusion result interval is [59, 75]. The specified interval method is used to determine the six sub-intervals of the final fusion result, which are a1 = [59, 63] km / h, a2 = [63, 64] km / h, a3 = [64, 65] km / h, a4 = [65, 66] km / h, a5 = [66, 69] km / h, and a6 = [69, 75] km / h.

[0050] Step S12: Then, according to the four accident re-creation speeds, the assignment method is used to determine the membership function A corresponding to the accident re-creation speed i (x), the membership functions of the four accident re-creation speeds are obtained according to formula (1), among which the membership functions corresponding to the accident re-creation speeds B1, B2, B3, and B4 are A1(x), A2(x), A3(x), and A4(x). The membership functions are determined according to formula (1), as shown below:

[0051]

[0052]

[0053] Step S13: Use Zadeh's method to convert the sub-intervals of the accident reconstruction vehicle speed and the final fusion result into fuzzy sets. Based on the membership function obtained in step S12, the corresponding fuzzy set expression is written in combination with equation (2) as follows:

[0054]

[0055]

[0056]

[0057]

[0058] Among them, A1, A2, A3, and A4 are the fuzzy sets corresponding to the accident reconstruction speeds B1, B2, B3, and B4, a1, a2, a3, a4, a5, and a6 represent the subintervals of the final fusion results, and the numerator on the right side of the equation represents the membership of the subinterval of the final fusion result on the accident reconstruction speed.

[0059] Step S14: Calculate the evaluation index value w of the fuzzy set i ;

[0060] S141 performs a fuzzy set product (·) operation on the fuzzy set obtained in step S13, and obtains the following equation (3):

[0061]

[0062]

[0063] …

[0064]

[0065] S142 Calculate evaluation result v ij with u ij ,

[0066] Table 1. Evaluation results

[0067]

[0068] where v ij =v ji ,u ij =u ji , only needs to be calculated once,

[0069] S143 According to the formula Calculate the evaluation index value w of the fuzzy set i ;

[0070] w1=0.292 w2=0.255 w3=0.261 w4=0.113

[0071] Step S15: obtaining the final fusion result;

[0072] S151 The evaluation index value w obtained in step S14 is i Multiplying the corresponding fuzzy sets obtained in step S13 to obtain four new fuzzy set expressions;

[0073]

[0074]

[0075]

[0076]

[0077] S152 adds the four new fuzzy set expressions according to the membership degrees corresponding to the subintervals to form a fuzzy set expression;

[0078]

[0079] S153 normalizes the membership of all sub-intervals, and the membership of the obtained result can be regarded as the probability of the sub-interval of the final fusion result.

[0080]

[0081] S16 gives a bar graph of the final fusion result obtained to express the result intuitively.

[0082] In the embodiment, the data input module inputs four accident reproduction speeds and transmits them to the fuzzification module for calculation; the fuzzification module receives the four accident reproduction speeds and performs fuzzification processing on the four speeds (corresponding to steps S11, S12, and S13); the fuzzy decision module calculates the evaluation index value of the fuzzy set, and combines it with the fuzzy set in the fuzzification module, thereby reducing the proportion of potential risk speeds (corresponding to steps S14 and S15); the result output module gives a bar chart of the final fusion result obtained to intuitively express the result (corresponding to step S16).

[0083] The above description is only a preferred example of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for fusion of multiple accident reconstruction vehicle speeds based on fuzzy mathematics, characterized by: The fusion of multiple accident reconstruction speeds ensures that the final result follows a normal distribution and solves the problem of objective fusion when there are potential risk speeds in multiple accident reconstruction speeds. The specific implementation steps are as follows: S11: Reconstruct vehicle speed B based on n accidents i , i = [1, n], determine the m sub-intervals of the final fusion result; S12: Obtain the membership function A corresponding to the n accident reconstructed vehicle speeds according to the n accident reconstructed vehicle speeds and the m sub-intervals of the final fusion result obtained in step S1. i (x); S13: converting the relationship between the n accident reconstructed vehicle speeds and the m sub-intervals of the final fusion result into a fuzzy set; S14: Calculate the evaluation index value w of the fuzzy set i ; S15: obtain the final fusion result; S16: Output the membership of the sub-intervals in the final fusion result in a bar chart as the final result.

2. The method for merging multiple accident reconstruction vehicle speeds based on fuzzy mathematics according to claim 1, characterized in that: The method for determining the m sub-intervals of the final fusion result in step S11 is as follows: first, the minimum value e of all accident-reconstructed vehicle speeds is used as the lower bound of the final fusion result, and the maximum value f of all accident-reconstructed vehicle speeds is used as the upper bound of the final fusion result, thereby obtaining the final fusion result interval [e, f]; secondly, by using the specified interval method, m continuous sub-intervals are given in the interval [e, f].

3. The method for merging multiple accident reconstruction vehicle speeds based on fuzzy mathematics according to claim 1, characterized in that: The membership function A corresponding to the n accident re-occurrence vehicle speeds in step S12 i (x) is obtained according to the assignment method; the three commonly used membership function types are shown in formula (1), from top to bottom, triangular membership function, rectangular membership function and trapezoidal membership function; In the triangular membership function, c=(b+d) / 2, and in the trapezoidal membership function, c=(3b+e) / 4, d=(b+3e) / 4.

4. The method for merging multiple accident reconstruction vehicle speeds based on fuzzy mathematics according to claim 1, characterized in that: In step S13, the fuzzy set is obtained by converting the relationship between the accident reconstruction vehicle speed and the sub-interval of the final fusion result into a fuzzy set using the Zadeh representation method, and the corresponding fuzzy set expression is written based on the membership function obtained in step S12; In the formula, A i The accident re-occurrence speed is B i The corresponding fuzzy set, a1…a m Represents the subinterval of the final fusion result, A i (a1)…A i (a m ) represents the membership degree of the subinterval of the final fusion result on the accident reconstruction speed, A i (a m ) represents the mth subinterval (a m ) is the membership degree of the vehicle speed at the i-th accident reproduction.

5. The method for merging multiple accident reconstruction vehicle speeds based on fuzzy mathematics according to claim 1, characterized in that: The evaluation index value w of the fuzzy set in step S14 i The solution is as follows: S141 performs a fuzzy set product (·) operation on the fuzzy set obtained in step S13, and the formula is as follows: Where i, j = 1, 2…n, A ij =A ji , only needs to be calculated once; S142 Calculate the evaluation result v ij with u ij ; v ij =A i (a1)·A j (a1)+A i (a2)·A j (a2)+…+A i (a m )·A j (a m ) (4) where v ij =v ji , only needs to be calculated once; where u ij =u ji , only needs to be calculated once; S143 Calculate the evaluation index value w of the fuzzy set i ; Where i≠j.

6. The method for merging multiple accident reconstruction vehicle speeds based on fuzzy mathematics according to claim 1, characterized in that: The steps to obtain the final fusion result in step S15 are: S151 The evaluation index value w obtained in step S14 is i Multiply the corresponding fuzzy sets obtained in step S13 to obtain n new fuzzy set expressions; In the formula, A i The accident re-occurrence speed is B i The corresponding fuzzy set, w i ·A i (a1),…,w i ·A i (a m ) represents the membership degree A i (a1)…A i (a m ) The evaluation index value w i The value obtained after processing, a1…a m The subinterval representing the final fusion result; S152 adds the n new fuzzy set expressions according to the membership degrees corresponding to the subintervals to form a fuzzy set expression; S153 normalizes the membership of all sub-intervals, and the membership of the obtained result can be regarded as the probability of the sub-interval of the final fusion result.

7. The method for merging multiple accident reconstruction vehicle speeds based on fuzzy mathematics according to claim 1 is characterized in that: According to the method, a fusion system of multiple accident reconstruction vehicle speeds based on fuzzy mathematics is developed, and the system consists of a data input module, a fuzzification module, a fuzzy decision module and a result output module; the data input module is used to input multiple accident reconstruction vehicle speeds, and transmit the data to the fuzzification module for processing; the fuzzification module is used to fuzzify the input multiple accident reconstruction vehicle speeds (corresponding to steps S11, S12, and S13 described in claim 1); the fuzzy decision module is used to calculate the evaluation index value of the fuzzy set, and combine it with the fuzzy set in the fuzzification module, thereby reducing the proportion of potential risk speeds (corresponding to steps S14 and S15 described in claim 1); the result output module is used to output the final result, and a bar chart is given for the final fusion result obtained to intuitively express the result (corresponding to step S16 described in claim 1).

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