WO2021000061A1 - 一种基于改进证据融合算法的燃气管网泄露等级判断方法 - Google Patents

一种基于改进证据融合算法的燃气管网泄露等级判断方法 Download PDF

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WO2021000061A1
WO2021000061A1 PCT/CN2019/000150 CN2019000150W WO2021000061A1 WO 2021000061 A1 WO2021000061 A1 WO 2021000061A1 CN 2019000150 W CN2019000150 W CN 2019000150W WO 2021000061 A1 WO2021000061 A1 WO 2021000061A1
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evidence
focal element
focal
average
decision
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PCT/CN2019/000150
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French (fr)
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王博
贾婧媛
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北京理工大学
王博
贾婧媛
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M3/00—Investigating fluid-tightness of structures
    • G01M3/02—Investigating fluid-tightness of structures by using fluid or vacuum
    • G01M3/04—Investigating fluid-tightness of structures by using fluid or vacuum by detecting the presence of fluid at the leakage point
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/25—Fusion techniques
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/25—Fusion techniques
    • G06F18/257—Belief theory, e.g. Dempster-Shafer

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  • the invention relates to the technical field of decision evidence fusion, in particular to a gas pipeline network leakage level judgment method based on an improved evidence fusion algorithm.
  • Evidence fusion method can be adopted to judge the leakage level of gas pipeline network.
  • This solution uses the leakage information extracted by multiple types of sensors such as pressure and flow on the gas pipeline to construct evidence sources; these evidence sources are redundant, complementary, and conflicting, and require effective fusion processing to improve the gas pipeline network Accuracy of leak diagnosis.
  • the fusion of evidence sources can be realized by using Dempster-Shafer (DS) evidence theory for uncertainty reasoning.
  • Evidence theory focuses on using Dempster synthesis rules to fuse multi-source information and provide decision support.
  • Conflicting evidence is common in practical applications. When the information between the evidences is highly conflicted, due to the normalization factor used in the evidence combination formula, the combination result often contradicts the facts.
  • the problems with the DS algorithm are:
  • the elements in the gas pipeline leakage level identification framework ⁇ correspond to different leakage levels.
  • each piece of evidence has three propositions A, B, and C, and A, B, and C correspond to the leak levels A, B, and C respectively level.
  • the basic probability distribution function value (BPA) or mass value of these three propositions is:
  • evidence 1 and 2 support A
  • evidence 3 supports B
  • the difference between the largest trusted focal element A and the second largest trusted focal element B of evidence 1 and 2 is small.
  • the view of correcting the evidence source believes that the fusion result that is contrary to intuition is caused by the unreliability of the evidence source.
  • the evidence source should be corrected before synthesis.
  • the main research method is to correct the evidence by estimating the weight of evidence.
  • Murphy proposed a weighted average method to solve the problem of evidence failure. The method first averages the basic probabilities of n pieces of evidence, and then uses the DS formula to synthesize n-1 times to obtain the composite result. Inadequate consideration of the correlation between.
  • the viewpoint of modifying the synthesis rules believes that the fusion result is contrary to intuition due to the imperfection of DS synthesis rules, and how to redistribute evidence conflicts should be considered.
  • Such research methods mainly focus on how to redistribute global or local conflicting evidence. Yager believes that all conflicting evidence is unavailable, so the normalization factor in the DS combination rule is removed and all conflict probabilities are assigned to uncertain propositions. However, all conflicting evidences are rejected, which increases the uncertainty of the composite result.
  • the present invention addresses the problem of insufficient consideration of the influence of weak decision evidence on decision results in the prior art, and comprehensively considers the relationship between focal elements and Jousselme distance, and proposes a new evidence modification method. Apply it to the gas pipeline network leakage level judgment, thereby improving the accuracy of decision-making.
  • the present invention provides a gas pipeline network leakage level judgment method based on an improved evidence fusion algorithm, which can effectively expand the difference between the maximum trust focal element and other focal elements, so that the evidence fusion result is more reliable and the convergence speed is faster , To improve the accuracy of the decision-making on the leakage level of the gas pipeline network.
  • the present invention is implemented as follows:
  • a method for judging gas pipeline network leakage levels based on improved evidence fusion algorithm including:
  • Step 1 Use the gas pipeline network information measured by the sensors to obtain multiple sources of evidence for judging gas pipeline network leakage; each focal element in the evidence corresponds to a leakage level;
  • Step 2. Judge and deal with conflict evidence
  • Step 3 For weak decision evidence, take the focal element weight of the focal element with the highest mass value as 1, and multiply the other focal elements by their respective focal element weights, and then normalize a single piece of evidence; among them, the jth in the weak decision evidence
  • the focal element weight of each focal element is: the average value of the focal element for obtaining weak decision evidence, calculate the distance of the j-th focal element relative to the average of all focal elements in this evidence, and the standard for obtaining all focal elements in the weak decision evidence Difference, using the ratio between the distance and the standard deviation as the focal element weight of the j-th focal element;
  • Step 4 Use the weight of evidence to correct the evidence processed in Step 3;
  • Step 5 The revised evidence is fused according to the Dempster synthesis rule, and the leakage level of the gas pipeline network is determined according to the fusion result.
  • the method for judging the weak decision evidence is: judging the difference between the focal element with the largest mass value and the focal element with the second largest mass value in a single piece of evidence, and if the difference is less than the selected threshold, it is a weak decision. evidence.
  • the method for determining the threshold is: obtaining the average evidence of the evidence obtained after processing in step 2, and taking the difference between the focal element with the largest mass value and the focal element with the second largest mass value in the average evidence as the threshold.
  • the method further sets a lower threshold; if the difference between the focal element with the largest mass value and the focal element with the second largest mass value in the average evidence is less than the lower threshold, the lower threshold is used as the threshold.
  • the step 2 includes:
  • conflicting evidence judge whether the average evidence is conflict evidence, if it is, remove the conflict evidence source and recalculate the average evidence, and replace the conflict evidence source with the average evidence; if the average evidence is not conflict evidence, there is no need to recalculate the average Evidence, replace the source of conflicting evidence with average evidence.
  • the present invention takes the ratio of the distance of the focal element relative to the average to the degree of dispersion of all focal elements in the evidence relative to the average as the focal element weight of a single focal element, and separately considers the relationship between the focal elements in any piece of evidence , Without being affected by other evidence, reflects the individual differences of Jiao Yuan.
  • This method effectively measures the distribution of the mass values of each focal element in the evidence, that is, the focal element with the largest mass value deviates from the average value more, while the deviation of the second largest focal element is smaller, the greater the deviation , The larger the weight, and the calculated weight will not cause data distortion because it is too large or too small.
  • the existing algorithms measure the difference between the evidence from the perspective of decision distance, and there is no clear indication of the specific scope of the difference that can be regarded as weak decision evidence.
  • the present invention defines the difference between the focal element with the largest mass function value and the focal element with the second largest value in the average evidence as the threshold, and modifies the threshold according to the identification accuracy. This method can set the threshold according to the accuracy requirements of different engineering environments, and has a better recognition of weak decision evidence.
  • Fig. 1 is a flow chart of the method for judging the gas pipeline network leakage level based on the improved evidence fusion algorithm of the present invention.
  • the present invention provides a gas pipeline network leakage level judgment method based on an improved evidence fusion algorithm.
  • the basic idea is: in view of the problem of weak decision evidence in the evidence fusion process that affects the final fusion effect, the present invention focuses on weak decision evidence.
  • the weighting process of the focal element retains the decision-making position of the most trusted focal element and reduces the influence of other focal elements.
  • each focal element with weak decision evidence is restricted by the weight of the focal element, which reduces the occurrence of evidence distortion and obtains more accurate, Reliable fusion results.
  • ⁇ ⁇ 1 , ⁇ 2 ,..., ⁇ N ⁇ is the identification frame, the elements are mutually exclusive and finite, the number of elements is N, ⁇ i (1 ⁇ i ⁇ N) is one of the identification frames Element or event, a finite set consisting of all subsets of the recognition frame is called the power set, denoted as
  • the initial trust level distribution of evidence can be represented by the basic probability distribution (BPA) value.
  • the basic probability distribution function m is the mapping of the set 2 ⁇ ⁇ [0, 1], A is any subset of the power set, and satisfies the empty set
  • the mass value is 0, that is m(A) is the value of the basic probability distribution function of proposition A, which also becomes the value of mass function, which represents the credibility of the proposition.
  • A is called the focal element of the evidence.
  • the subscript of m indicates the serial number of the evidence.
  • m 1 , m 2 ,..., m n are n pieces of evidence under the same identification frame.
  • the distance between m 1 and m 2 is defined as:
  • M 1 [m 1 (A 1 ), m 1 (A 2 ), m 1 (A 3 ),..., m 1 (A N )] T
  • M 2 [m 2 (A 1 ), m 2 (A 2 ), m 2 (A 3 ),..., m 2 (A N )] T
  • D (D ij ) is an N ⁇ N order matrix,
  • the focal element weight of the j-th focal element in evidence i is defined as: Calculate the distance between the focal element j of evidence i and the average of all focal elements of this evidence, and calculate the degree of dispersion of all focal elements in this evidence i relative to the average (ie Standard deviation), the ratio of the distance to the standard deviation is used as the weight of a single focal element.
  • the source of evidence is corrected and then fused according to DS synthesis rules.
  • the focal element with the highest mass value does not change its assignment, that is, the weight. Take 1, and the other focal elements are respectively multiplied by the weight ⁇ ij .
  • m i (A j ) is the j-th focal element in evidence i
  • max(m i (A)) is the mass value of the largest focal element in evidence i
  • each piece of evidence is assigned a weight of evidence ⁇ i , as shown in formula (5).
  • m′′ i [ ⁇ ] represents the uncertainty of this piece of evidence i. Since the weight of evidence ⁇ i is used to modify the evidence, the sum of the mass values of the focal elements in the evidence is less than 1, so a representative is added after each piece of evidence The uncertainty of the focal element m" i [ ⁇ ], the part less than 1 is assigned to this focal element. This ensures that the sum of the mass values of all focal elements in the evidence is 1.
  • Fig. 1 is a flow chart of the gas pipeline network leakage level judgment method based on the improved evidence fusion algorithm of the present invention. As shown in Figure 1, the method includes the following steps:
  • Step 1 Use sensors to measure gas pipeline network information to obtain multiple sources of evidence.
  • the pressure, concentration, flow and other information on the gas pipeline can be collected through sensors, and then multiple sources of evidence can be given by means of expert scoring, and each focal element in the evidence corresponds to a leakage level.
  • Step 2 Calculate the average evidence of the evidence source.
  • Step 3 Based on the Jousselme distance model and the focal element attributes, the evidence weight and the focal element weight are calculated according to equations (2) and (3).
  • Step 4. Judge and deal with conflict evidence.
  • step 5 first judge whether there is conflict evidence. If the focal element with the largest mass value in each piece of evidence is the same proposition, that is, whether the evidence supports the same decision, then it is mutually supporting evidence. There is no conflict, and then go to step 5; otherwise, there is Conflict evidence.
  • conflict evidence it is necessary to first judge whether the average evidence is conflict evidence. If it is conflict evidence, it means that the abnormal evidence in the original evidence source seriously affects the decision result. To facilitate decision-making, remove the conflict evidence source, recalculate the average evidence, and then The conflict evidence source is replaced by the average evidence; if the average evidence is not conflict evidence, there is no need to recalculate the average evidence, and the conflict evidence source is directly replaced by the average evidence.
  • Step 5 Determine the threshold for weak decision evidence processing.
  • the difference between the focal element with the largest mass function value in the average evidence and the focal element with the second largest value is used as the threshold.
  • the threshold is still used If the difference between the maximum mass value of the average evidence and the second-largest mass value, some evidence may be judged as non-weak decision-making evidence. Therefore, a minimum value (lower limit) needs to be set for the threshold, that is, the maximum mass value of the average evidence and the second-largest mass value If the difference between is less than this minimum value, the threshold is selected as the minimum value.
  • the lower limit of the threshold can be selected according to the discrimination accuracy used in the final decision.
  • the lower limit of the threshold is 0.1, even if the difference between the maximum value of the average evidence focal element and the second largest value is less than 0.1, the threshold is set to 0.1.
  • Step 6 Judgment and processing of weak decision evidence.
  • the difference between the focal element with the largest mass function value and the focal element with the second largest value in a single piece of evidence is judged. If the difference is less than the threshold, it is a weak decision evidence.
  • the focal element is assigned a corresponding weight according to formula (4), that is, the focal element with the largest mass function value is multiplied by the focal element weight 1, and the other focal elements are multiplied by their respective focal element weights, and then a single piece of evidence is classified One treatment. If there is no weak decision evidence, proceed directly to the next step.
  • Step 7 use the weight of evidence to correct the evidence source processed in step 6. Using the weight of evidence to modify evidence is a conventional technique and will not be detailed here.
  • Step 8 Fuse the revised evidence according to the Dempster synthesis rule.
  • the leakage level corresponding to the focal element with the largest mass function value in the fusion evidence is the judgment result.

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Abstract

一种基于改进证据融合算法的燃气管网泄露等级判断方法，该方法利用传感器测量的燃气管网信息获得用于判断燃气管网泄露的多条证据源；对于弱决策证据，将mass值最高焦元的焦元权值取l，其他焦元分别乘以各自的焦元权值，从而有效扩大最大信任焦元与其他焦元之间的差异，使得证据融合结果更加可靠，收敛速度快。对于冲突证据，采用平均证据对冲突证据进行代替，并用证据距离权值对此冲突证据进行限制，降低其对证据合成结果的影响，使弱决策证据能发挥其决策作用。使用本方法能够提高燃气管网泄露等级决策的准确性。

Description

一种基于改进证据融合算法的燃气管网泄露等级判断方法 技术领域
本发明涉及决策证据融合技术领域，尤其涉及一种基于改进证据融合算法的燃气管网泄露等级判断方法。
背景技术
对于燃气管网泄露等级判断可以采用证据融合的方式。该方案利用燃气管线上的压力、流量等多类传感器提取的泄漏信息，构建证据源；这些证据源具有冗余性、互补性和冲突性，需要进行有效的融合处理，从而可提高燃气管网泄漏诊断准确率。
对证据源的融合可以采用Dempster-Shafer(DS)证据理论进行不确定性推理实现。证据理论重点在于利用Dempster合成规则融合多源信息，提供决策支持。在实际应用中冲突证据是普遍存在的，当证据间信息高度冲突时，由于证据组合公式中采用了归一化因子，组合结果经常与事实相违背。DS算法存在的问题有：
(1)当证据完全冲突时，算法中合成规则的分母为0，无法使用DS合成公式。
(2)当证据间高冲突时，可能得到与直观不符的结果。如，燃气管道泄漏等级的辨识框架Θ中的元素对应于不同的泄露等级。假设在辨识框架Θ＝{A，B，C}下有2条证据，每条证据中具有三个命题A、B、C，且A，B，C分别对应泄露等级A级、B级、C级。这三个命题的基本概率分配函数值(BPA)或者称为mass值为：
m 1(A)＝0.9，m 1(B)＝0.1，m 1(C)＝0；
m 2(A)＝0，m 2(B)＝0.1，m 2(C)＝0.9。
其中，证据1支持命题A，证据2支持命题C，2条证据对命题B的支持度均不高，然而通过DS组合公式合成后，得到m(A)＝m(C)＝0，m(B)＝1，结果是支持命题B，即可信度最小的命题在合成后反而可信度最高，明显与事实相悖。
(3)证据间低冲突时仍可能得到与直观相违背的融合结果。如，在辨识框架Θ＝{A，B，C}，A下有3条证据，mass值为：
m 1(A)＝0.46，m 1(B)＝0.41，m 1(C)＝0.13
m 2(A)＝0.46，m 2(B)＝0.41，m 2(C)＝0.13
m 3(A)＝0.10，m 3(B)＝0.80，m 3(C)＝0.10
其中，证据1、2支持A，证据3支持B，且证据1、2的最大信任焦元A和次大信任焦元B之间差值较小。服从多数原则，直观上三条证据的合成结果应为命题A，然而根据DS合成规则得到合成结果为：m(A)＝0.1345，m(B)＝0.8548，m(C)＝0.0107，结果支持命题B，与事实不符。
国内外学者针对冲突问题进行了大量研究改进工作，目前，主要的证据融合算法改进研究可分为修正证据源和改进合成规则两个方向。
修正证据源的观点认为产生与直觉相悖的融合结果是由于证据源不可靠导致的，在合成之前应对证据源进行修正，主要研究手段是通过估算证据权值对证据进行修正。Murphy提出了一种加权平均方法用以解决证据失效问题，该方法首先将n个证据的基本概率进行平均，然后用DS公式进行n-1次合成，即可得到合成结果，但此方法对证据间的相关性考虑不足。为此，部分学者通过一些方法对证据之间的联系、冲突进行衡量：刘海燕等人针对高度冲突证据合成问题，通过使用证据间的距离权值对证据源做出修正，获得新的证据基本可信度分配模型；胡海亮提出了基于迭代合成的算法，用以削弱证据间的冲突程度； 孟媛媛采用了信任度和虚假度结合，对冲突进行衡量与修正；毕文豪等人在Pignistic概率距离的基础上，通过引入冲突系数等方法来修正证据源；严志军等人基于Jousselme距离和信度熵对证据源做出修正；以上这些方法均可有效衡量证据间联系，但对于在合成过程中存在的弱决策证据对决策结果的影响考虑不足。
修改合成规则的观点认为由于DS合成规则的不完善造成了融合结果与直观相悖，应考虑如何重新分配证据冲突，此类研究方法主要关注如何对全局或局部冲突证据的再分配。Yager认为全部冲突证据都不可用，因此去除了DS组合规则中的归一化因子，将所有的冲突概率分配给不确定命题，但是由于证据冲突全部被否定，增大了合成结果的不确定性；与此相反的是，Smets认为全部冲突均可用，通过集合理论保留了冲突证据，但高可信度聚集在并集焦元，与决策不利；孙全等人认为全局冲突部分可用，使用证据可信度将冲突再分配；Dubois等人不再研究全局冲突问题，而是考虑如何解决局部冲突问题，将局部冲突分配给冲突焦元的交并集，并以一定比例融合，降低不可靠证据对融合结果的影响。从局部冲突的角度进行算法改进方法虽然简单有效，但新的合成规则往往会破坏DS合成规则的良好特性，并且其合成结果通常会受到证据组合次序的影响。
因此，本发明在修改证据源观点基础上，针对现有技术存在的弱决策证据对决策结果的影响考虑不足的问题，综合考虑焦元间联系和Jousselme距离，提出一种新的证据修正方法，将其应用于燃气管网泄露等级判断，从而提高决策的准确性。
发明内容
有鉴于此，本发明提供了一种基于改进证据融合算法的燃气管网泄露等级 判断方法，能够有效扩大最大信任焦元与其他焦元之间的差异，使得证据融合结果更加可靠，收敛速度快，提高燃气管网泄露等级决策的准确性。
为了解决上述技术问题，本发明是这样实现的：
一种基于改进证据融合算法的燃气管网泄露等级判断方法，包括：
步骤1、利用传感器测量的燃气管网信息，获得用于判断燃气管网泄露的多条证据源；证据中每个焦元对应一个泄露等级；
步骤2、进行冲突证据的判断和处理；
步骤3、对于弱决策证据，将mass值最高的焦元的焦元权值取1，其他焦元分别乘以各自的焦元权值，然后对单条证据进行归一化处理；其中，弱决策证据中第j个焦元的焦元权值为：获得弱决策证据的焦元的平均值，计算此证据中第j个焦元相对于所有焦元的平均值的距离，以及获得弱决策证据中所有焦元的标准差，将所述距离与所述标准差之间的比值作为第j个焦元的焦元权值；
步骤4、利用证据权值对步骤3处理后的证据进行修正；
步骤5、根据采用Dempster合成规则对修正后的证据进行融合，根据融合结果判定燃气管网的泄露等级。
优选地，所述弱决策证据的判断方式为：判断单条证据中mass值最大的焦元和mass值次大的焦元之间的差值，如果差值小于选定的阈值，则为弱决策证据。
优选地，所述阈值的确定方式为：获得经步骤2处理后所得证据的平均证据，将平均证据中mass值最大的焦元和mass值次大的焦元之间的差值作为阈值。
优选地，该方法进一步设置阈值下限；如果平均证据中mass值最大的焦元和mass值次大的焦元之间的差值小于所述阈值下限，则用阈值下限作为所述阈值。
优选地，所述步骤2包括：
判断各条证据中mass值最大的焦元是否为同一命题：如果是，则不存在冲突证据，转入步骤3；反之，则确定存在冲突证据；
在存在冲突证据情况下，判断平均证据是否为冲突证据，如果是，则去除冲突证据源后重新计算平均证据，将冲突证据源用平均证据代替；如果平均证据不是冲突证据，则无需重新计算平均证据，将冲突证据源用平均证据代替。
有益效果：
(1)针对证据融合过程中存在弱决策证据，影响最终融合效果的问题我们提出了一种新的证据权值确定方法。对弱决策证据各个焦元进行加权处理，按各个焦元的相对平均值的距离的占比取值，保留了最大信任焦元的决策地位，减弱其他焦元的影响，同时，弱决策证据的各个焦元由于受到焦元权值的限制，减小发生证据失真的情况，得到更准确、可靠的融合结果。尤其是对于临界点数据的判断更加准确，从而提高燃气管网泄露等级的区分精确度。
(2)本发明将焦元相对于平均值的距离与证据中所有焦元相对于平均数的离散程度的比值作为单个焦元的焦元权值，单独考虑了任意一条证据中焦元之间的关系，而不受其他证据的影响，体现了焦元的个体间差异。此方法有效地衡量了证据中各个焦元mass值之间的分配情况，即mass值最大的焦元偏离平均值的程度较大，而次大的焦元的偏离程度稍小，偏离度越大，权值越大，并且计算得到的权值不会因为过大或过小而引起数据失真。
(3)在确定弱决策证据时，现有算法从决策距离角度衡量证据间的差异，没有明确的指明具体什么范围的差异可认定为弱决策证据。本发明定义平均证据中mass函数值最大的焦元和数值次大的焦元之间的差值作为阈值，并且根据辨识精度对阈值进行修改。这种方法可根据不同工程环境对精度的要求来设定阈值，且对于弱决策证据的识别度较好。
(4)本发明弱决策证据和冲突证据同时存在情形下，通过采用平均证据对冲突证据进行代替，并用证据距离权值对此冲突证据进行限制，降低其对证据合成结果的影响，使弱决策证据能发挥其决策作用。
通过数值实验表明，本发明算法融合结果收敛速度更快，具有更高的决策正确性，优于现有的修正证据源改进算法。
附图说明
图1为本发明基于改进证据融合算法的燃气管网泄露等级判断方法的流程图。
具体实施方式
本发明提供了一种基于改进证据融合算法的燃气管网泄露等级判断方法，其基本思想是：针对证据融合过程中存在弱决策证据，影响最终融合效果的问题，本发明对弱决策证据各个焦元进行加权处理，保留了最大信任焦元的决策地位，减弱其他焦元的影响，同时，弱决策证据的各个焦元由于受到焦元权值的限制，减小发生证据失真的情况，得到更准确、可靠的融合结果。
下面结合附图并举实施例，对本发明进行详细描述。
定义：Θ＝{θ 1，θ 2，...，θ N}为辨识框架，元素间互斥且有穷，元素个数为N，θ i(1＜i＜N)为识别框架的一个元素或事件，由识别框架的所有子集构成的一个有限集合称为的幂集合，记作
Figure PCTCN2019000150-appb-000001
其中
Figure PCTCN2019000150-appb-000002
表示空集，Θ表示全集，幂集合2 Θ中的每一个子集都表示一个命题，即问题的答案，共有2 N个元素。在燃气管道泄漏等级判断的应用中，由于不存在发 生的泄露处于不同等级的情况，因此，此时的幂集合中仅有N个元素。
证据的初始信任程度分配，可用基本概率分配(BPA)值来表示，基本概率分配函数m是集合2 Θ→[0，1]的映射，A为幂集合的任一子集，并且满足空集的mass值为0，即
Figure PCTCN2019000150-appb-000003
m(A)为命题A的基本概率分配函数值，也成为mass函数值，表征命题的可信度。对于辨识框架的任意命题(子集)A，若满足m(A)＞0，则称A为证据的焦元。
设m 1，m 2是同一个辨识框架上的2条证据基本概率分配函数，则DS合成规则如式(1)：
Figure PCTCN2019000150-appb-000004
其中A，A i，B j∈2 Θ，
Figure PCTCN2019000150-appb-000005
为冲突系数，表示证据m 1，m 2之间的冲突程度。m的下角标表示证据的序号。设n为证据的个数，那么n条证据组合可通过两条证据的组合公式组合n-1次得到，其结果与组合的次序无关。
本发明对证据进行修正时，用到了两个权值，一个是常用的证据权值，另一个是本发明提出的用于处理弱决策证据的焦元权值。
1)证据权值
m 1，m 2，…，m n是同一辨识框架下的n条证据，定义m 1，m 2之间的距离表示为：
Figure PCTCN2019000150-appb-000006
其中，M 1＝[m 1(A 1)，m 1(A 2)，m 1(A 3)，...，m 1(A N)] T
M 2＝[m 2(A 1)，m 2(A 2)，m 2(A 3)，...，m 2(A N)] T
D＝(D ij)为N×N阶矩阵，
Figure PCTCN2019000150-appb-000007
|·|表示集合中元素的个数。
m 1、m 2的距离的具体计算方法为：
Figure PCTCN2019000150-appb-000008
其中，
Figure PCTCN2019000150-appb-000009
m 1、m 2的相近程度表示为：s(m 1，m 2)＝1-d(m 1，m 2)，两个证据间的距离越小，则相近程度越大。
证据相对于最可信证据的证据权重表示为式子(2)：
Figure PCTCN2019000150-appb-000010
2)焦元权值
设共有n条证据，每条证据均包含f个焦元。证据i中第j个焦元的焦元权值定义为：计算证据i的焦元j与此证据的所有焦元平均值的距离，计算此证据i中所有焦元相对于平均数的离散程度(即标准差)，将距离于标准差的比值作为单个焦元的权值。其中，i＝1，2，…，n；j＝1，2，…，f。
第i条证据中焦元的标准差为
Figure PCTCN2019000150-appb-000011
第i条证据中焦元的标准差为
Figure PCTCN2019000150-appb-000012
Figure PCTCN2019000150-appb-000013
综上，第i条证据的第j个焦元的权值为式(3)：
Figure PCTCN2019000150-appb-000014
3)利用上述两个权值修正证据源
获得证据权重和焦元权重后，对证据源进行修正，然后再根据DS合成规则进行融合。
为扩大最大可信焦元和次大可信焦元之间的基本概率分配值的差异，对于被确定为弱决策证据的证据，其中mass值最高的焦元，不改变其赋值，即权值取1，而其他的焦元分别乘权值ω ij。如式(4)所示。m i(A j)为证据i的第j个焦元，max(m i(A))为证据i中最大的焦元mass值
Figure PCTCN2019000150-appb-000015
上述对各个焦元加权处理后，对每条证据的mass值进行归一化处理。
然后，利用证据权值对步骤3处理后的证据进行修正。具体来说，将每一条证据分别赋予证据权值β i，如式(5)所示。
Figure PCTCN2019000150-appb-000016
其中，m″ i[Θ]表示这条证据i的不确定度。由于使用证据权值β i修改证据后，证据内的焦元mass值之和小于1，因此在每条证据之后增加一个代表不确定度的焦元m″ i[Θ]，将小于1的部分赋值给此焦元。从而保证证据所有焦元mass值的和为1。
图1为本发明基于改进证据融合算法的燃气管网泄露等级判断方法的流程。如图1所示，该方法包括如下步骤：
步骤1、利用传感器测量燃气管网信息，获得多条证据源。
这里可以通过传感器采集燃气管线上的压力、浓度、流量等信息，然后采用专家打分等方式给出多条证据源，证据中每个焦元对应一个泄露等级。
步骤2、计算证据源的平均证据。
将所有证据中相同焦元相加，获得平均证据。
步骤3、基于Jousselme距离模型和焦元属性，根据式(2)和式(3)计算证据权值和焦元权值。
步骤4、进行冲突证据的判断和处理。
本步骤首先判断是否存在冲突证据，如果各条证据中mass值最大的焦元同一命题，即证据是否支持同一决策，则为相互支持的证据，不存在冲突，转入步骤5；反之，则存在冲突证据。
如存在冲突证据，需要先判断平均证据是否为冲突证据，如为冲突证据，则说明原证据源中的异常证据严重影响决策结果，为利于决策，去除冲突证据源，重新计算平均证据，然后将冲突证据源用平均证据代替；如果平均证据不是冲突证据，则无需重新计算平均证据，直接将冲突证据源用平均证据代替。
步骤5、确定用于弱决策证据处理的阈值。
本步骤中，平均证据中mass函数值最大的焦元和数值次大的焦元之间的差值作为阈值，考虑到如果进行融合的证据的焦元间差值均很小，如阈值仍用平均证据最大mass值与次大mass值的差值，则可能存在部分证据被判定为非弱决策证据，因此需要对阈值制定最小值(下限)，即如平均证据最大mass值与次大mass值的差值小于此最小值，则将阈值选定为最小值。阈值的下限可根据最终决策时采用的区分精度来选取。
例如阈值的下限定为0.1，即使平均证据焦元的最大值与次大值的差值小于0.1，也将阈值定为0.1。
步骤6、弱决策证据的判断和处理。
本步骤中，判断单条证据中mass函数值最大的焦元和数值次大的焦元之间的差值，如差值小于阈值，则为弱决策证据。
如存在弱决策证据，则根据式(4)对焦元赋予对应权值，即将mass函数值最大的焦元乘以焦元权值1，其他焦元分别乘以各自的焦元权值，然后对单条证据进行归一化处理。如不存在弱决策证据，则直接进行下一步。
步骤7、根据式(5)，利用证据权值对步骤6处理后的证据源进行修正。利用证据权值进行证据修正是常规技术，这里不详述。
步骤8、根据采用Dempster合成规则对修正后的证据进行融合。融合证据中mass函数值最大的焦元对应的泄露等级为判定结果。
至此，本流程结束。
综上所述，以上仅为本发明的较佳实施例而已，并非用于限定本发明的保护范围。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

Claims (5)

  1. 一种基于改进证据融合算法的燃气管网泄露等级判断方法，其特征在于，包括：
    步骤1、利用传感器测量的燃气管网信息，获得用于判断燃气管网泄露的多条证据源；证据中每个焦元对应一个泄露等级；
    步骤2、进行冲突证据的判断和处理；
    步骤3、对于弱决策证据，将mass值最高的焦元的焦元权值取1，其他焦元分别乘以各自的焦元权值，然后对单条证据进行归一化处理；其中，弱决策证据中第j个焦元的焦元权值为：获得弱决策证据的焦元的平均值，计算此证据中第j个焦元相对于所有焦元的平均值的距离，以及获得弱决策证据中所有焦元的标准差，将所述距离与所述标准差之间的比值作为第j个焦元的焦元权值；
    步骤4、利用证据权值对步骤3处理后的证据进行修正；
    步骤5、根据采用Dempster合成规则对修正后的证据进行融合，根据融合结果判定燃气管网的泄露等级。
  2. 如权利要求1所述的方法，其特征在于，所述弱决策证据的判断方式为：判断单条证据中mass值最大的焦元和mass值次大的焦元之间的差值，如果差值小于选定的阈值，则为弱决策证据。
  3. 如权利要求2所述的方法，其特征在于，所述阈值的确定方式为：获得经步骤2处理后所得证据的平均证据，将平均证据中mass值最大的焦元和mass值次大的焦元之间的差值作为阈值。
  4. 如权利要求3所述的方法，其特征在于，进一步设置阈值下限；如果平均证据中mass值最大的焦元和mass值次大的焦元之间的差值小于所述阈值下限，则用阈值下限作为所述阈值。
  5. 如权利要求1所述的方法，其特征在于，所述步骤2包括：
    判断各条证据中mass值最大的焦元是否为同一命题：如果是，则不存在冲突证据，转入步骤3；反之，则确定存在冲突证据；
    在存在冲突证据情况下，判断平均证据是否为冲突证据，如果是，则去除冲突证据源后重新计算平均证据，将冲突证据源用平均证据代替；如果平均证据不是冲突证据，则无需重新计算平均证据，将冲突证据源用平均证据代替。
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