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The evaluation indicators are the scoring points to evaluate potential safety management risks in the production process. They are the inducement set of accident risks.
The enterprise may ignore some crucial potential risk factors in the production process if they use an evaluation indicator system with unreasonable weights. In addition, due to the changes in industry characteristics, production level, environmental factors, policy guidance, and other factors, the weights of the evaluation indicators need to be dynamically adjusted.
Therefore, how to scientifically optimize the evaluation indicator weights has become a hot research issue. A chemical safety evaluation system is used to characterize the possible safety hazards which may lead to accident risks in the chemical production process Huang et al.
The goal of indicator weight optimization is to find the potential hazards and improve the safety management level of chemical enterprises. We need to fully consider the influence of chemical safety accidents and the indicator importance evaluated by the experts in the weight optimization.
However, the existing comprehensive weighting methods usually linearly weight the contribution of subjective and objective elements. These methods lack a good sampling and fusion mechanism of subjective and objective elements.
Due to the above problems, we propose an indicator weight optimization method combining subjective and objective factors in this paper. Similar to the multi-objective optimization problem Deng et al.
A random walk is used to sample and fuse subjective and objective elements and finally realize the optimization of the existing indicator weights. The main contributions of this paper are as follows:. A comprehensive weighting method to optimize indicator weights in the chemical safety evaluation system is proposed.
The bipartite graph model is employed to integrate subjective and objective evaluation factors related to the weight optimization. It can sample and fuse the subjective and objective factors on the bipartite graph model, similarly to Brownian motion, and effectively improve the accuracy of global indicator weight deduction in limited sample space.
A new method to measure the weight optimization performance for a safety evaluation system is put forward. It evaluates the optimized indicator weights from order ranking and curve fitting.
Experiments verify the effectiveness of our indicator weight optimization method. The remainder of this paper is organized as follows. Section 2 reviews the related work.
Section 3 presents a calculation method for the accident influence and correlation intensity between accident nodes and indicator nodes based on the association bipartite graph ABG. A weight optimization method based on the improved PersonalRank algorithm is designed in Section 4.
How to evaluate the proposed method is detailed in Section 5. Section 6 offers experiments and the performance of the proposed method. Section 7 concludes this paper and throws light on future work. The existing indicator weight setting methods of the safety evaluation system can be divided into subjective weighting, objective weighting, and comprehensive weighting methods.
The objective evaluation method, represented by the entropy weight method EWM and scatter degree method SDM , quantifies the indicator weight based on the distribution characteristics of the sample data, such as discrimination, credibility, and information amount.
The EWM is the most widely used objective weighting method. Liu et al. He determined the weight of each indicator by using the structural EWM. Huang et al. He pointed out that EWM aimed at reflecting relative intensities among the evaluation indicators; however, SDM reflected the projection factor that maximizes the overall difference among the evaluated objects.
To get a dynamic solution based on multi-factor variable weight, Zavalishina adjusted the process of obtaining more objective data by reducing or increasing the number of self-evaluation indicators.
He established a Rasch model to optimize the self-evaluation indicator system, and proved the superiority of the model. Yang and Li used the fuzzy analytic hierarchy process AHP and entropy to determine the indicator weights for evaluating the usefulness of negative online reviews.
The usefulness ranking results of negative online reviews are obtained through the improved TOPSIS method. The objective methods can effectively distinguish the objects based on the distribution characteristics or differences of the data; however, they lack of consideration on the contribution of evaluation indicators to management objectives.
Therefore, the simple objective weighting method is not suitable to quantify the weights of the chemical safety evaluation indicators. The frequently used subjective weighting methods include AHP, ANP, and Delphi. AHP is the most widely used method in weight optimization. To evaluate the overall performance of the Internet of things system, Wang chose the system performance as the evaluation indicator.
He set the indicator weight by the AHP and presented a performance indicator model of the Internet of things based on the cloud model. Wu and Tu proposed the optimization models to obtain transitive preferences for solving individual consistency and group consensus problems. The proposed models provide an optimal way to minimize modifications in deriving transitive preferences.
Lv et al. Arsic et al. Delphi method adopts multi-round anonymous feedback mechanism. It can reduce the influence of authoritative experts on decision-making objectives.
Zhang et al. Some intelligent optimization methods were employed to find fault diagnosis or fatigue indicators. For example, Cui et al. Wu et al. He extracted four fatigue indicators by performing the ensemble wavelet transform and Hilbert transform. Cui et al.
The method was designed based on the variational mode decomposition and maximum correlation kurtosis deconvolution. It can effectively diagnose the rolling element fault of rolling bearings and obtain better fault accuracy.
The subjective weighting method can sufficiently express the intention of decision makers and cater to the policy orientation. The subjective methods quantify the weight by indicator evaluation from experts. They can well reflect the intention of decision makers.
However, the scores are based on the subjective experience of experts. It is easy to produce artificial single value evaluation error and difficult to construct the consistency evaluation matrix once facing many comparison indicators.
Researchers used different weighting methods in combination to obtain more reasonable weights of evaluation indicators. For example, Altintas et al. Li et al. Yuan et al. The evaluation criteria system was designed based on a combined analytic network process-entropy method.
It could help the investors avoid too risky countries and facilitate the government to take measures to attract more investors. Shen et al. Pishyar et al. Hu et al. He used the entropy model to evaluate the objective weights.
Meanwhile, he calculated the subjective weights by the fuzzy AHP expert scoring method. The subjective and objective weights were coupled to generate the final risk weights. Koulinas et al. It formed a quantitative evaluation of the safety risk of the Greek construction work environment by weighted fusion.
The existing comprehensive weighting methods can be divided into two categories. One is to introduce various weight measurement techniques into a single subjective or objective way.
The other is to integrate subjective and objective factors for weight calculation. The comprehensive methods can consider the subjective decision-making factors and the distribution characteristics of objective data. However, these methods still lack an effective fusion and sampling mechanism of subjective and objective factors.
In addition, how to deduce the reasonable weight value in the limited sample space is also a complex problem faced by this kind of method. The differences in the existing work are shown in Table 1.
As we can see, the current weighting methods are not suitable for the weight optimization of the chemical safety evaluation system, which aims to find potential safety hazards in production and improve the safety management level of enterprises.
We propose an indicator weight optimization method combining subjective and objective factors. The method comprehensively considers the indicator importance evaluated by the experts and the influence of the factors such as the time of the accident, accident hazard, and the revised contribution degree.
A random walk is used to sample and fuse subjective and objective factors and finally realize the optimization of the existing indicator weights. The enterprise will carry out an accident safety assessment once an accident has occurred or a safety hazard is discovered.
Experts will present an accident case report after they finish the safety assessment. In the accident report, safety analysts analyze the root cause of the accident with the evaluation indicators and evaluate the importance of these indicators.
Therefore, the enterprises have accumulated many accident analysis reports in the daily safety production and management process.
We can obtain the correlation between accident case and evaluation indicators after safety analysts have performed the root cause analysis. As shown in Fig. The nodes in the bipartite graph are divided into accident case nodes and evaluation indicator nodes.
The connecting arcs between the two types of nodes indicate the correlation relationship between the accident cases and the evaluation indicators. For example, the accident case node d 3 is associated with the evaluation indicator nodes l 1 , l 4 , and l n , which means that the root cause of the accident node d 3 contains the content corresponding to evaluation indicator nodes l 1 , l 4 , and l n.
The following factors are mainly considered when measuring the correction influence between accident cases and evaluation indicators:. Occurrence time and hazard degree of the accident.
The safety management deficiencies of the accident feedback are time-sensitive. Compared with the recent accidents, earlier accidents are less closely related to the weight optimization.
Some accidents with high hazard degrees have more influence on weight optimization than accidents with small hazard degrees. That is to say, accident cases with different occurrence times and hazard degrees have different feedback influences on safety management defects.
Their contributions to the weight optimization of evaluation indicators are diverse in nature. Therefore, the occurrence time and hazard degree are essential factors to calculate the influences of the accidents in weight optimization.
Analysis credibility of the accident root cause. The root cause analysis of the accident is carried out by the accident analyst. It is subject to individual factors such as the domain knowledge and working experience of the accident analyst. Some accident root cause analysis may be incomplete and biased.
This situation can lead to inaccurate and incomplete correlation analysis between accident cases and evaluation indicators. So, the analysis credibility of accident root cause is an important factor for computing the influence of an accident.
Evaluation of importance of correlation between evaluation indicators and accident root cause. Accident analysts usually choose natural language to evaluate the importance of evaluation indicators.
There are many evaluation indicators in a safety evaluation system. Analysts may present different granular evaluations for the same indicator in an accident based on their expertise.
Conversely, expert B will present an evaluation with a finer granularity once he has a good understanding of the correlation between the indicator and the accident root cause.
We know that the finer granularity evaluation means more accurately describing the correlations. Therefore, how to quantify the correlation importance based on fuzzy natural language is another important factor to calculate the influence of accidents.
To accurately optimize the weight of evaluation indicators, the above factors need to be considered. A bipartite graph of accident cases and evaluation indicators is proposed in this study. We integrate the quantitative constraint information into the bipartite graph. Then the weights of evaluation indicators are optimized by an improved random walk algorithm.
Two concepts, accident node influence and correlation intensity, are introduced in the bipartite graph of accident cases and evaluation indicators. Accident node influence is used to describe the contribution of the accident case in the optimization of indicator weights.
The accident node influence for the node v i is denoted as InF v i. The greater the correlation intensity, the higher the contribution of evaluation indicator v j to the accident node v i. The correlation intensity between node v i and v j is symbolized as CI v i , v j. In this study, InF v i is determined by the occurrence time, hazard degree, and the analysis credibility of the accident in the aforementioned factors 1 and 2.
CI v i , v j is determined by the factor 3. Accident node influence and correlation intensity are employed to compute the random walk probability in the indicator weight optimization.
Accident analysts need to assess the importance of each evaluation indicator that may cause the accident when they analyze the cause of an accident Koulinas et al.
It is difficult to quantitatively measure the importance of various potential evaluation indicators. Analysts usually choose natural language to evaluate these indicators. There are many indicators in an evaluation system. The accident analysts may be from different fields and they are not very familiar with all the evaluation indicators.
Normally, the analysts may give different granular evaluations based on their expertise and experiences. Therefore, how to obtain the correlation intensity between the evaluation indicators and accident cases from different granularities language evaluations is a key issue to be resolved.
Various methods such as two-tuple linguistic representation and interval-valued intuitionistic fuzzy set can be used to deal with uncertainty in evaluation Wu et al. For most experts, it is difficult to give the specific interval value in the metric of affiliation or non-affiliation between the accident and each evaluation indicator.
So the relatively simple two-tuple linguistic method is employed to perform uncertainty evaluation in this study. The two-tuple linguistic representation is based on the concept of symbol transfer Qi et al. It adopts a two-tuple s i , α i to represent language evaluation information.
It indicates the deviation between the calculated evaluation result and the nearest phrase in S. For example, the triangular fuzzy value for the granularity of five is shown in Table 2. For the s i and s j , the size between them is determined by the following rules:. The matrix is denoted as Z.
Algorithm 1 provides the method to obtain the matrix Z. The accident influences in weight optimization of evaluation indicators are mainly affected by factors such as the occurrence time, the hazard degree, and the revised contribution degree.
The method to quantify these factors is presented in this section. The hazard degree of an accident is the quantitative analysis score of the influence of the accident damage. Different industries or fields are involved in different factors of accident hazards.
The indicators of each level are different. Generally, the following four elements are used to describe the accident hazards in the chemical industry, which are personal injury, property loss, environmental influence, and social influence. For example, Table 3 is a common quantitative scoring table for the accidents in Sinopec, which gives different scores for different levels of the hazards.
The hazard degree of accident is the score obtained after the hazard evaluation for an accident according to Table 3. DEL is used to denote the direct economic loss. Each accident sample is assigned an evaluation score of hazard degree from the above four aspects.
The highest one is selected as the quantified value of the accident hazard. The hazard degree of accident for the i -th sample is symbolized as h i. The correlation intensity matrix Z is obtained by linguistic weighting from the correlation evaluation.
The correlation between an accident and evaluation indicators may be evaluated as a diversified importance due to the differences of knowledge and perspective of accident analysts. The greater the difference between the correlation importance of an accident and each evaluation indicator, the higher the revised contribution degree of the accident to distinguish each evaluation indicator from all the others, and vice versa.
Therefore, the revised contribution degree is determined by the dispersion degree of correlation importance. In Section 3 , we have presented the definition of the bipartite graph of accident cases and evaluation indicators. How to obtain the influence of the accident node and correlation intensity between the accident nodes and the evaluation indicators are also investigated.
To use a random walk way to optimize the weights of evaluation indicators, we add weight values to the nodes and edges of our proposed bipartite graph. The initial weight of evaluation indicator node is set as zero, i. We obtain a new weight value for the evaluation indicator node by a random walk method.
PersonalRank, a random walk algorithm based on bipartite graph, is one of the frequently used algorithms to compute node correlations Hu et al.
It is often used in personalized recommendation of various commodities based on the network structure Li et al. Commodity recommendation to users can be understood as the redistribution of the commodity resources Wei et al.
The idea of commodity recommendation can be transferred to the optimization of indicator weight. The access probability of node v j in the PersonalRank algorithm is shown in Equation Here, r j represents the access probability of node v j , and λ is the probability of random walk.
The parameter p j is assigned as 1 if the node v j is an evaluation indicator node, otherwise it is set as 0. out k represents the number of all outgoing edges of node v k , and in v j represents the set of incoming edges pointing to node v j.
m 0 is the number of samples while T t 0 is the time weight of the original indicator system. Here, the algorithm 2 presents the proposed indicator weight optimization method based on the improved PersonalRank algorithm. We present two ways to verify the effectiveness of the proposed method.
The first one is a ranking evaluation method. It does not consider the accuracy of indicator weights. We only test whether the ranking distribution of the optimized indicator weights are consistent with the ranking of the indicator weights given by the experts.
The second one is an evaluation method of distribution fitness. It evaluates the accuracy of weight assignment by verifying which indicator system fits better with the acknowledged excellent indicator system.
The correlation similarity is greater if their correlation coefficient is with a high absolute value. The computing method of the correlation coefficients is shown in Equation 16 — The distribution fitness method is used to evaluate the assignment accuracy of indicator weights.
K-L divergence is introduced to evaluate distribution fitness between two indicator systems. K-L divergence is a method to describe the difference between two probability distributions.
The evaluation indicators are regarded as random variables while indicator weights are regarded as different values of these random variables. In this way, K-L divergence can be used to measure the fitting degree between two evaluation indicator systems.
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