WO2020140318A1 - 基于最小二乘法的铸造车间安全评价综合权重计算方法 - Google Patents

基于最小二乘法的铸造车间安全评价综合权重计算方法 Download PDF

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WO2020140318A1
WO2020140318A1 PCT/CN2019/076220 CN2019076220W WO2020140318A1 WO 2020140318 A1 WO2020140318 A1 WO 2020140318A1 CN 2019076220 W CN2019076220 W CN 2019076220W WO 2020140318 A1 WO2020140318 A1 WO 2020140318A1
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evaluation
safety
weight
foundry
subjective
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徐青伟
许开立
葛及
陈守坤
徐晓虎
郑欣
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东北大学
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  • the invention relates to the technical field of safety assessment for foundry workshops, in particular to a method for calculating the comprehensive weight of safety assessment for foundry workshops based on least squares.
  • Safety assessment is aimed at achieving safety, applying the principles and methods of safety system engineering, identifying and analyzing dangerous and harmful factors in system, engineering, and production management activities, predicting the possibility and severity of accidents or occupational hazards, and Activities that propose scientific, reasonable, and feasible safety countermeasures and measures to make evaluation conclusions.
  • safety evaluation is an important means to prevent accidents.
  • Safety evaluation is not only widely used in the safety production of production and operation units, but also in different safety fields such as emergency management and accident investigation. Among them, in the casting field, the safety evaluation of the foundry is of great significance to the safe production of the foundry.
  • evaluation index weight In the process of implementing safety evaluation, the calculation of evaluation index weight is a very important part.
  • evaluation index weight There are three main calculation methods for existing evaluation index weights: subjective weighting method, objective weighting method and comprehensive weighting method.
  • the subjective weighting method relies on the subjective judgment of experts rather than actual data. It mainly includes the analytic hierarchy process and Delphi method, which can make full use of the knowledge that has been mastered, but different experts may get different evaluation results.
  • the objective weight method is based on actual data rather than the subjective judgment of experts. It mainly includes principal component analysis, entropy weight method, and coefficient of variation method. It can make full use of actual data, but the evaluation results may not be consistent with the actual situation.
  • the comprehensive weighting method combines the subjective weighting method and the objective weighting method, taking into account the subjective judgment of experts and the objectivity of actual data, and can more fully reflect the actual situation of the evaluated object; however, regarding the preference coefficient of comprehensive weighting, The physical meaning of most calculation methods is unclear, and there is no unified calculation method, which leads to low accuracy and reliability of the evaluation results.
  • the present invention provides a method for calculating the comprehensive weight of the safety evaluation of the foundry workshop based on the least square method, which can improve the accuracy and reliability of the safety evaluation results.
  • a method for calculating the comprehensive weight of safety evaluation of foundry workshop based on least square method which is characterized by the following steps:
  • Step 1 Analyze the safety management status of the foundry and find n factors ⁇ R 1 , R 2 , R 3 ,..., R n ⁇ that affect the safety management of the foundry, these n factors are the safety of the foundry Evaluation index of evaluation;
  • Step 2 Based on the analytic hierarchy process, determine the subjective weight vector for the safety evaluation of the foundry:
  • Step 2.3 Perform consistency check on the subjective judgment matrix: calculate the consistency index of the subjective judgment matrix as The consistency index ratio of the subjective judgment matrix is Among them, RI is the random consistency index of the subjective judgment matrix. RI is related to the order n of the subjective judgment matrix; if CR ⁇ 0.1, the consistency of the subjective judgment matrix is acceptable, so that the subjective judgment matrix passes the consistency test and enters the step 2.4; If CR ⁇ 0.1, the subjective judgment matrix fails the consistency check, and return to step 2.1, adjust the value of the subjective judgment matrix until CR ⁇ 0.1;
  • Step 2.4 Normalize the feature vector W to obtain the subjective weight vector for the safety assessment of the foundry as Among them, W j S is the subjective weight of the jth evaluation index R j ,
  • Step 3 Based on the entropy weight method, determine the objective weight vector for the safety evaluation of the foundry:
  • Step 3.2 Calculate the proportion of the kth evaluation level under the jth evaluation index R j as
  • Step 3.3 Calculate the entropy of the jth evaluation index R j as
  • Step 3.4 Calculate the entropy weight of the jth evaluation index R j as W j O is the objective weight of the j-th evaluation index R j , and the objective weight vector that constitutes the safety evaluation of the foundry is
  • Step 4 Based on the least square method, determine the comprehensive weight vector for the safety evaluation of the foundry:
  • Step 4.2 Calculate the sum of squared errors between comprehensive weight, subjective weight and objective weight as
  • Step 4.3 Establish the minimum square error model as
  • the present invention calculates the comprehensive weight of the safety evaluation of the foundry workshop based on the least square method, so that the comprehensive weight has a clear physical meaning, that is, the sum of the square of the error between the comprehensive weight, the subjective weight, and the objective weight is the smallest. Carrying out safety evaluation can improve the accuracy and reliability of the safety evaluation results of the foundry.
  • FIG. 1 is a flow chart of the method for calculating the comprehensive weight of safety evaluation of a foundry workshop based on the least square method of the present invention.
  • the object of the present invention is to provide a method for calculating the comprehensive weight of safety evaluation of foundry workshops based on least squares, which can improve the accuracy and reliability of safety evaluation results.
  • FIG. 1 it is a flow chart of the method for calculating the comprehensive weight of the safety evaluation of the foundry workshop based on the least square method of the present invention.
  • the method for calculating the comprehensive weight of the safety evaluation of the foundry workshop based on the least square method of the present invention includes the following steps:
  • Step 1 Analyze the safety management status of the foundry and find n factors ⁇ R 1 , R 2 , R 3 ,..., R n ⁇ that affect the safety management of the foundry, these n factors are the safety of the foundry Evaluation index for evaluation.
  • n 5
  • the n factors affecting the safety management of the foundry workshop ⁇ R 1 , R 2 , R 3 ,..., R n ⁇ are safety education and training, safety investment, risk source management, and hidden trouble investigation Governance and safety management system.
  • Step 2 Based on the analytic hierarchy process, determine the subjective weight vector for the safety evaluation of the foundry:
  • Step 2.3 Perform consistency check on the subjective judgment matrix: calculate the consistency index of the subjective judgment matrix as The consistency index ratio of the subjective judgment matrix is Among them, RI is the random consistency index of the subjective judgment matrix. RI is related to the order n of the subjective judgment matrix. The specific relationship is shown in Table 1. If CR ⁇ 0.1, the consistency of the subjective judgment matrix is acceptable, so that the subjective judgment The matrix passes the consistency test and enters step 2.4; if CR ⁇ 0.1, the subjective judgment matrix fails the consistency test, and returns to step 2.1 to adjust the value of the subjective judgment matrix until CR ⁇ 0.1;
  • Step 2.4 Normalize the feature vector W to obtain the subjective weight vector for the safety assessment of the foundry as Among them, W j S is the subjective weight of the jth evaluation index R j ,
  • the expert method is used to compare the importance of each evaluation index to the evaluation result, and the subjective judgment matrix is obtained as
  • Step 3 Based on the entropy weight method, determine the objective weight vector for the safety evaluation of the foundry:
  • Step 3.2 Calculate the proportion of the kth evaluation level under the jth evaluation index R j as
  • Step 3.3 Calculate the entropy of the jth evaluation index R j as
  • Step 3.4 Calculate the entropy weight of the jth evaluation index R j as W j O is the objective weight of the j-th evaluation index R j , and the objective weight vector that constitutes the safety evaluation of the foundry is
  • Step 4 Based on the least square method, determine the comprehensive weight vector for the safety evaluation of the foundry:
  • Step 4.2 Calculate the sum of squared errors between comprehensive weight, subjective weight and objective weight as
  • Step 4.3 Establish the minimum square error model as

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Abstract

一种基于最小二乘法的铸造车间安全评价综合权重计算方法，首先确定影响铸造车间安全管理的评价指标，然后基于层次分析法，通过专家法得到主观判断矩阵，计算该矩阵的最大特征值及特征向量并对其进行一致性检验，若通过检验，则归一化特征向量，得到主观权重向量；然后基于熵权法，组织专家对每个评价指标的评价等级进行投票，得到投票比例评价矩阵，计算熵与熵权，得到客观权重向量；最后基于最小二乘法，建立综合权重与主观权重、客观权重间的误差平方和最小模型，求解该模型，得到偏好系数，最终得到铸造车间安全评价的综合权重向量。本方法能够提高铸造车间安全评价结果的准确性及可靠性。

Description

基于最小二乘法的铸造车间安全评价综合权重计算方法 技术领域
本发明涉及铸造车间安全评价技术领域，特别是涉及一种基于最小二乘法的铸造车间安全评价综合权重计算方法。
背景技术
安全评价是以实现安全为目的，应用安全系统工程的原理和方法，辨识与分析系统、工程、生产管理活动中的危险有害因素，预测发生事故或造成职业危害的可能性及其严重程度，并提出科学、合理、可行的安全对策措施建议，从而做出评价结论的活动。安全评价作为现代安全管理的重要组成部分，是预防事故的重要手段。安全评价不仅广泛应用于生产经营单位的安全生产，还应用于应急管理、事故调查等不同的安全领域。其中，在铸造领域，铸造车间的安全评价对铸造厂的安全生产具有重要意义。
在实施安全评价的过程中，评价指标权重的计算是非常重要的一环。现有的评价指标权重的计算方法主要有三种：主观权重法、客观权重法与综合权重法。其中，主观权重法是依靠专家的主观判断而不是实际数据，主要包括层次分析法、德尔菲法，其能够充分利用已经掌握的知识，但是不同的专家可能得到不同的评价结果。客观权重法是依据实际数据而不是专家的主观判断，主要包括主成分分析法、熵权法、变异系数法，其能够充分利用实际数据，但评价结果可能与实际情况不符合。综合权重法结合了主观权重法和客观权重法，将专家的主观判断和实际数据的客观性都考虑在内，能较为全面地反映被评价对象的实际情况；然而，关于综合权重的偏好系数，大多数的计算方法中物理意义不明确，而且没有统一的计算方法，导致评价结果的准确性和可靠性都比较低。
发明内容
针对现有技术存在的问题，本发明提供一种基于最小二乘法的铸造车间安全评价综合权重计算方法，能够提高安全评价结果的准确性及可靠性。
本发明的技术方案为：
一种基于最小二乘法的铸造车间安全评价综合权重计算方法，其特征在于，包括下述步骤：
步骤1：分析铸造车间的安全管理状况，找出影响铸造车间安全管理的n个因素{R 1,R 2,R 3,...,R n}，这n个因素即为进行铸造车间安全评价的评价指标；
步骤2：基于层次分析法，确定铸造车间安全评价的主观权重向量：
步骤2.1：采用专家法两两比较各评价指标对评价结果的重要性，得到评价指标R i与评价指标R j对评价结果的相对重要性s ij，构成主观判断矩阵S＝(s ij) n×n，i,j＝1,2,...,n；
步骤2.2：计算主观判断矩阵的最大特征值为λ max及对应的特征向量为W＝[W 1,W 2,...,W j,...,W n]；
步骤2.3：对主观判断矩阵进行一致性检验：计算主观判断矩阵的一致性指标为
Figure PCTCN2019076220-appb-000001
得到主观判断矩阵的一致性指标比率为
Figure PCTCN2019076220-appb-000002
其中，RI为主观判断矩阵的随机一致性指标，RI与主观判断矩阵的阶数n有关；若CR＜0.1，则主观判断矩阵的一致性可以接受，从而主观判断矩阵通过一致性检验，进入步骤2.4；若CR≥0.1，则主观判断矩阵未通过一致性检验，返回步骤2.1，对主观判断矩阵的值进行调整，直到CR＜0.1；
步骤2.4：对特征向量W进行归一化处理，得到铸造车间安全评价的主观权重向量为
Figure PCTCN2019076220-appb-000003
其中，W j S为第j个评价指标R j的主观权重，
Figure PCTCN2019076220-appb-000004
步骤3：基于熵权法，确定铸造车间安全评价的客观权重向量：
步骤3.1：设定m个评价等级为{安全，较安全，一般，危险，极度危险}，组织专家对每个评价指标进行评价，通过专家对每个评价指标的评价等级进行投票，计算每个评价指标下每个评价等级获得的票数占总票数的比例，得到投票比例评价矩阵O＝(o kj) m×n，k＝1,2,...,m，j＝1,2,...,n；
步骤3.2：计算第j个评价指标R j下第k个评价等级的比重为
Figure PCTCN2019076220-appb-000005
步骤3.3：计算第j个评价指标R j的熵为
Figure PCTCN2019076220-appb-000006
步骤3.4：计算第j个评价指标R j的熵权为
Figure PCTCN2019076220-appb-000007
W j O即为第j个评价指标R j的客观权重，构成铸造车间安全评价的客观权重向量为
Figure PCTCN2019076220-appb-000008
步骤4：基于最小二乘法，确定铸造车间安全评价的综合权重向量：
步骤4.1：确定第j个评价指标R j的综合权重为W j I＝δW j S+(1-δ)W j O，j＝1,2,...,n；其中，δ为偏好系数，δ∈[0,1]；
步骤4.2：计算综合权重与主观权重、客观权重之间的误差平方和为
Figure PCTCN2019076220-appb-000009
步骤4.3：建立误差平方和最小模型为
Figure PCTCN2019076220-appb-000010
步骤4.4：求解误差平方和最小模型：对步骤4.2中的公式求关于偏好系数δ的导数，并令导数为0，得到
Figure PCTCN2019076220-appb-000011
求解该等式，得到δ＝0.5，从而第j个评价指标R j的综合权重为
Figure PCTCN2019076220-appb-000012
构成铸造车间安全评价的综合权重向量为
Figure PCTCN2019076220-appb-000013
所述步骤1中，n＝5，影响铸造车间安全管理的n个因素{R 1,R 2,R 3,...,R n}分别为安全教育培训、安全投入、危险源管理、隐患排查治理、安全管理制度；步骤2.3中，RI＝1.12。
本发明的有益效果为：
本发明基于最小二乘法对铸造车间安全评价的综合权重进行计算，使得综合权重有了明确的物理意义，即综合权重与主观权重、客观权重之间的误差平方和最小，采用综合权重对铸造车间进行安全评价，能够提高铸造车间安全评价结果的准确性及可靠性。
附图说明
图1为本发明的基于最小二乘法的铸造车间安全评价综合权重计算方法的流程图。
具体实施方式
下面将结合附图和具体实施方式，对本发明作进一步描述。
本发明的目的是提供一种基于最小二乘法的铸造车间安全评价综合权重计算方法，能够提高安全评价结果的准确性及可靠性。
如图1所示，为本发明的基于最小二乘法的铸造车间安全评价综合权重计算方法的流程图。本发明的基于最小二乘法的铸造车间安全评价综合权重计算方法，包括下述步骤：
步骤1：分析铸造车间的安全管理状况，找出影响铸造车间安全管理的n个因素 {R 1,R 2,R 3,...,R n}，这n个因素即为进行铸造车间安全评价的评价指标。
本实施例中，n＝5，影响铸造车间安全管理的n个因素{R 1,R 2,R 3,...,R n}分别为安全教育培训、安全投入、危险源管理、隐患排查治理、安全管理制度。
步骤2：基于层次分析法，确定铸造车间安全评价的主观权重向量：
步骤2.1：采用专家法两两比较各评价指标对评价结果的重要性，得到评价指标R i与评价指标R j对评价结果的相对重要性s ij，构成主观判断矩阵S＝(s ij) n×n，i,j＝1,2,...,n；
步骤2.2：计算主观判断矩阵的最大特征值为λ max及对应的特征向量为W＝[W 1,W 2,...,W j,...,W n]；
步骤2.3：对主观判断矩阵进行一致性检验：计算主观判断矩阵的一致性指标为
Figure PCTCN2019076220-appb-000014
得到主观判断矩阵的一致性指标比率为
Figure PCTCN2019076220-appb-000015
其中，RI为主观判断矩阵的随机一致性指标，RI与主观判断矩阵的阶数n有关，具体关系如表1所示；若CR＜0.1，则主观判断矩阵的一致性可以接受，从而主观判断矩阵通过一致性检验，进入步骤2.4；若CR≥0.1，则主观判断矩阵未通过一致性检验，返回步骤2.1，对主观判断矩阵的值进行调整，直到CR＜0.1；
步骤2.4：对特征向量W进行归一化处理，得到铸造车间安全评价的主观权重向量为
Figure PCTCN2019076220-appb-000016
其中，W j S为第j个评价指标R j的主观权重，
Figure PCTCN2019076220-appb-000017
表1
矩阵阶数 3 4 5 6 7 8 9 10 11 12 13 14
RI 0.52 0.89 1.12 1.26 1.36 1.41 1.46 1.49 1.52 1.54 1.56 1.58
本实施例中，
Figure PCTCN2019076220-appb-000018
这里采用1-9标度法，来比较第i个评价指标与第j个评价指标对评价结果的重要性：当s ij＝1时，表示第i个评价指标与第j个评价指标对评价结果同等重要；当s ij＝3时，表示第i个评价指标比第j个评价指标对评价结果稍重要；当s ij＝5时，表示第i个评价指标比第j个评价指标对评价结果明显重要；当s ij＝7时，表示第i个评价指标比第j个评价指标对评价结果强烈重要；当s ij＝9时，表示第i个评价指标比第j个评价指标对评价结果极端重要；当s ij为大于1的其他值时，表示第i个评价指标与第j个评价指标对评价结 果的重要性的比较结果介于与s ij相邻的两个整数对应的比较结果之间；当s ij为小于1的值时，表示第i个评价指标与第j个评价指标对评价结果的重要性的反比较。
本实施例中，通过专家法对各评价指标对评价结果的重要性的两两比较，得到主观判断矩阵为
Figure PCTCN2019076220-appb-000019
计算主观判断矩阵的最大特征值为λ max＝5.1947，对应的特征向量为W＝[0.2933,0.5107,0.387,0.6738,0.2223]；计算一致性指标为CI＝0.0487，由表1可知，n＝5时，RI＝1.12，从而得到一致性指标比率为CR＝0.0435<0.1，从而主观判断矩阵通过一致性检验；对特征向量W进行归一化处理，得到铸造车间安全评价的主观权重向量为W S＝[0.141,0.245,0.185,0.323,0.106]。
步骤3：基于熵权法，确定铸造车间安全评价的客观权重向量：
步骤3.1：设定m个评价等级为{安全，较安全，一般，危险，极度危险}，组织专家对每个评价指标进行评价，通过专家对每个评价指标的评价等级进行投票，计算每个评价指标下每个评价等级获得的票数占总票数的比例，得到投票比例评价矩阵O＝(o kj) m×n，k＝1,2,...,m，j＝1,2,...,n；
步骤3.2：计算第j个评价指标R j下第k个评价等级的比重为
Figure PCTCN2019076220-appb-000020
步骤3.3：计算第j个评价指标R j的熵为
Figure PCTCN2019076220-appb-000021
步骤3.4：计算第j个评价指标R j的熵权为
Figure PCTCN2019076220-appb-000022
W j O即为第j个评价指标R j的客观权重，构成铸造车间安全评价的客观权重向量为
Figure PCTCN2019076220-appb-000023
本实施例中，通过专家对每个评价指标的评价等级进行投票，得到投票比例评价矩阵为
Figure PCTCN2019076220-appb-000024
计算得到铸造车间安全评价的客观权重向量为W O＝[0.12,0.202,0.281,0.244,0.153]。
步骤4：基于最小二乘法，确定铸造车间安全评价的综合权重向量：
步骤4.1：确定第j个评价指标R j的综合权重为W j I＝δW j S+(1-δ)W j O，j＝1,2,...,n；其中，δ为偏好系数，δ∈[0,1]；
步骤4.2：计算综合权重与主观权重、客观权重之间的误差平方和为
Figure PCTCN2019076220-appb-000025
步骤4.3：建立误差平方和最小模型为
Figure PCTCN2019076220-appb-000026
步骤4.4：求解误差平方和最小模型：对步骤4.2中的公式求关于偏好系数δ的导数，并令导数为0，得到
Figure PCTCN2019076220-appb-000027
求解该等式，得到δ＝0.5，从而第j个评价指标R j的综合权重为
Figure PCTCN2019076220-appb-000028
构成铸造车间安全评价的综合权重向量为
Figure PCTCN2019076220-appb-000029
本实施例中，通过计算，得到铸造车间安全评价的综合权重向量为W I＝[0.133,0.2315,0.231,0.2745,0.13]。
显然，上述实施例仅仅是本发明的一部分实施例，而不是全部的实施例。上述实施例仅用于解释本发明，并不构成对本发明保护范围的限定。基于上述实施例，本领域技术人员在没有做出创造性劳动的前提下所获得的所有其他实施例，也即凡在本申请的精神和原理之内所作的所有修改、等同替换和改进等，均落在本发明要求的保护范围内。

Claims (2)

  1. 一种基于最小二乘法的铸造车间安全评价综合权重计算方法，其特征在于，包括下述步骤：
    步骤1：分析铸造车间的安全管理状况，找出影响铸造车间安全管理的n个因素{R 1,R 2,R 3,...,R n}，这n个因素即为进行铸造车间安全评价的评价指标；
    步骤2：基于层次分析法，确定铸造车间安全评价的主观权重向量：
    步骤2.1：采用专家法两两比较各评价指标对评价结果的重要性，得到评价指标R i与评价指标R j对评价结果的相对重要性s ij，构成主观判断矩阵S＝(s ij) n×n，i,j＝1,2,...,n；
    步骤2.2：计算主观判断矩阵的最大特征值为λ max及对应的特征向量为W＝[W 1,W 2,...,W j,...,W n]；
    步骤2.3：对主观判断矩阵进行一致性检验：计算主观判断矩阵的一致性指标为
    Figure PCTCN2019076220-appb-100001
    得到主观判断矩阵的一致性指标比率为
    Figure PCTCN2019076220-appb-100002
    其中，RI为主观判断矩阵的随机一致性指标，RI与主观判断矩阵的阶数n有关；若CR＜0.1，则主观判断矩阵的一致性可以接受，从而主观判断矩阵通过一致性检验，进入步骤2.4；若CR≥0.1，则主观判断矩阵未通过一致性检验，返回步骤2.1，对主观判断矩阵的值进行调整，直到CR＜0.1；
    步骤2.4：对特征向量W进行归一化处理，得到铸造车间安全评价的主观权重向量为
    Figure PCTCN2019076220-appb-100003
    其中，W j S为第j个评价指标R j的主观权重，
    Figure PCTCN2019076220-appb-100004
    步骤3：基于熵权法，确定铸造车间安全评价的客观权重向量：
    步骤3.1：设定m个评价等级为{安全，较安全，一般，危险，极度危险}，组织专家对每个评价指标进行评价，通过专家对每个评价指标的评价等级进行投票，计算每个评价指标下每个评价等级获得的票数占总票数的比例，得到投票比例评价矩阵O＝(o kj) m×n，k＝1,2,...,m，j＝1,2,...,n；
    步骤3.2：计算第j个评价指标R j下第k个评价等级的比重为
    Figure PCTCN2019076220-appb-100005
    步骤3.3：计算第j个评价指标R j的熵为
    Figure PCTCN2019076220-appb-100006
    步骤3.4：计算第j个评价指标R j的熵权为
    Figure PCTCN2019076220-appb-100007
    W j O即为第j个评价指标R j的客观权重，构成铸造车间安全评价的客观权重向量为
    Figure PCTCN2019076220-appb-100008
    步骤4：基于最小二乘法，确定铸造车间安全评价的综合权重向量：
    步骤4.1：确定第j个评价指标R j的综合权重为W j I＝δW j S+(1-δ)W j O，j＝1,2,...,n；其中，δ为偏好系数，δ∈[0,1]；
    步骤4.2：计算综合权重与主观权重、客观权重之间的误差平方和为
    Figure PCTCN2019076220-appb-100009
    步骤4.3：建立误差平方和最小模型为
    Figure PCTCN2019076220-appb-100010
    步骤4.4：求解误差平方和最小模型：对步骤4.2中的公式求关于偏好系数δ的导数，并令导数为0，得到
    Figure PCTCN2019076220-appb-100011
    求解该等式，得到δ＝0.5，从而第j个评价指标R j的综合权重为
    Figure PCTCN2019076220-appb-100012
    构成铸造车间安全评价的综合权重向量为
    Figure PCTCN2019076220-appb-100013
  2. 根据权利要求1所述的基于最小二乘法的铸造车间安全评价综合权重计算方法，其特征在于，所述步骤1中，n＝5，影响铸造车间安全管理的n个因素{R 1,R 2,R 3,...,R n}分别为安全教育培训、安全投入、危险源管理、隐患排查治理、安全管理制度；步骤2.3中，RI＝1.12。
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