#### Abstract

In the petrochemical production system, the high-risk items malfunction may lead to major accidents so that the risk level of the items has become the highest focus of attention for the enterprises in petrochemical industry. Based on structural composition and risk relationship, a risk evaluation framework of the petrochemical production system can generally be divided into subsystems (SS), components and parts (CP), failure modes (FM), risk types, and risk factors. So it is a characteristic of multilevel, complex structure, and lack of evaluation criteria that the evaluated object has in the process of risk evaluation. However, there are few targeted modeling and calculation methods to carry out quantitative risk evaluation in the face of the evaluated object. In order to achieve risk quantitative evaluation of the complex structure hierarchical system, a multilevel Borda model (MLBM) is presented innovatively by us based on the traditional Borda method in this study. Moreover, the MLBM are applied to realize quantitative risk evaluation of the main structure system of truss type crane on the offshore platform. In this case study, the equivalent risk value (ERV) and risk priority number (RPN) of the evaluated object with multilevel, complex structure, and inadequate evaluation criteria are calculated and the risk ties in the RPN are effectively reduced. Then, the quantitative risk results can clarify the risk level and distribution of the high-risk items throughout the production system and provide data support for the development of risk control measures to better protect the production safety. Hence, the feasibility and practicability of the method are verified with the case study. The MLBM can be used to solve other comprehensive evaluation problems with a complex hierarchical structure as well.

#### 1. Introduction

In the petrochemical industry, there are many large-scale integrated and tandem production systems which have high risk, high cost, high technology, and other characteristics. Therefore, a safe and reliable operation has always been the focus of attention. The petrochemical production process has the characteristics of complex conditions such as flammable, explosive, high temperature and pressure, and strict process. The petrochemical production system is composed of hundreds of types of equipment and large-scale integrated systems, but also has a certain series of characteristics of the process of the production system. Statistical analysis on petrochemical industry in the explosion, fire, and other major causes in the world for nearly 30 years includes the following: equipment failure accounted for 41%, operating errors accounted for 20%, unknown reasons accounted for 18%, natural disasters accounted for 6%, design errors accounted 4%, and so on [1]. If the risk level and distribution of the equipment in the petrochemical production system are known, the high-risk items can be identified. This leads to develop risk control measures which can prevent nearly half of the major accidents. Especially in recent years, the global security and environmental issues are of great importance to the petrochemical industry, a major accident may lead to a business bankruptcy. Therefore, in order to achieve the purpose of reducing the probability of occurrence of major production accidents and controlling the operating costs of enterprises, petrochemical enterprises have an urgent need for effective quantitative assessment techniques for failure mode risk (FMR) [2].

In many industrial areas, quantitative risk evaluation methods have been developed to achieve quantitative management of various risks and more effective risk control. Li [3] proposed a quantitative risk evaluation method for long-distance pipeline based on fuzzy fault tree analysis. Xu [4] has proposed a petrochemical plant for the overall qualitative analysis and local quantitative analysis of the assessment method. Zhang [5] had carried out quantitative risk analysis (QRA) and its application in submarine pipeline integrity management. Zhao et al. [6] have demonstrated a quantitative risk analysis method for storage tanks based on the domino effect. C. R. Pitcher et al. [7] have illustrated a simple quantitative risk evaluation method for the limited capacity of the sustainability of the detection device on the impact of the habitat of the sea. Dan and Guix [8] have displayed a Monte Carlo simulation method based on the evaluation of human factors in quantitative risk evaluation. Collins and Davey et al. [9] have presented a new quantitative risk evaluation method to analyze the effects of microbial corrosion (MIC) carbon steel pipelines. However, the current quantitative risk evaluation methods are mostly pipelines, tanks, and other types of structural static equipment. At present, there have been still very a few relevant research oriented systems or equipment with multilevel and complex structure.

But a variety of comprehensive evaluation methods had been studied, including Analytic Hierarchy Process (AHP), Analytic Network Process (ANP), Borda, Delphi, and Rank Sum Ration (RSR) [10, 11]. Among them, the Borda method is a kind of classic postgroup evaluation method, proposed by C. de Borda in 1784, who is the first to solve the voting problem that has been widely used. It is now in the group decision-making, program demonstration, man-made economic evaluation, quality assessment, and many other areas [12]. The basic idea is that the Borda values of the* n* evaluated objects are determined by comparing the priority number of the* n* evaluated objects given by the* m* evaluators, that is, the Borda value of the group being evaluated and then sorted out according to the size of the group, Borda value which is the order of the object to be evaluated. Although the traditional Borda method can effectively solve the risk evaluation of multiple objects in the same one level, it cannot be directly used in the risk evaluation of the above-mentioned multilevel and complex structure problem [13]. Therefore, by analyzing the hierarchical structure and the interobject correlation in the risk evaluation process with the ideas, advantages of the traditional Borda method, an innovative approach should be presented to achieve a quantitative evaluation of multilevel complex structure hierarchical system in this study.

#### 2. Risk Hierarchy Analysis on the Complex Structural System

In the petrochemical industry, failure mode, effects, and criticality analysis (FMECA) is a common method for impact analysis and hazard analysis of system or equipment failure modes. According to the FMECA report (FR) of the petrochemical production system, the system or equipment contains a number of important functional items, including subsystems, equipment, components, and parts, and each of which has one or more failure modes. At the same time, in the risk evaluation, a failure mode will correspond to a variety of risk type, including safety risk (SR), environmental risk (ER), economic loss risk (ELR), and maintenance cost risk (MCR). Each risk type corresponds to multiple risk factors (RF), including Consequence Severity (CS) , Occurrence Frequency (OF) , and Detection Difficulty (DD) . As we know, different people or groups can produce different FMECA analysis reports. Finally, examples table for FMECA report data of the risk factors is shown in Table 1.

The corresponding qualitative description of the , , and is determined with some quantitative scale in Tables 2, 3, and 4.

In this study, the fuzzy linguistic of risk factors is eliminated based on the Tables 2, 3, and 4. Thus a quantization value of the risk factor is obtained with the calculation method as follows [14]:The membership function of each comment is showed in Figure 1. In the process of defuzzification, the values of and are always constant, namely, , . The values of and are the extreme points of the two ends of fuzzy linguistic description.

For example, the “Moderate” in the fuzzy linguistic in Table 3 is treated by defuzzification. The relevant parameter values are determined according to the membership function diagram, and then by substituting (1), the definite number of “Moderate" is calculated.And then, the quantitative transformation results of the fuzzy linguistics by defuzzification for , , and , and other fuzzy linguistic descriptions were obtained with this same way above, as shown in Table 5.

Based on the above anlysis and description with the system, subsystem, parts, failure modes risk types and risk factors, the risk evaluation problem of petrochemical production system or equipment is a comprehensive evaluation object with multilevel, complex structure and multicriteria evaluation, as shown in Figure 2.

As shown in the Figure 2, this is a huge problem of system evaluation of diversification, multilevel and complex structure with the relationship among failure mode, risk category, and risk factors and the structural composition of equipment, subsystem, and component. By taking full account of the actual situation and characteristics of the evaluated objects in the analogous structural system, it is summarized as a universal evaluation problem, a multilevel complex structure problem of evaluation object in this study. The undertaken problem can be described as follows. Under the known conditions of the basic evaluation criteria, there is a diversified, multilevel, and complex structure relationship between the target object and the basic evaluation criterion. The possibility of exploration is to establish a new mathematical model by using the basic evaluation criterion, hierarchical structure, and complex relationship to carry out quantitative representation of the evaluated objects and determine their priority number.

In Figure 2, the risk evaluation for system or equipment in the petrochemical industry is a multilevel and complex structure evaluation problem. In order to solve the problem of multilevel evaluation effectively, a novelty method is proposed to achieve the quantitative risk evaluation of petrochemical production system.

#### 3. Establishment of Mathematical Model of MLBM

The detailed algorithm of the MLBM is established as follows.

##### 3.1. Modeling Parameter Setting

There are some modeling parameters to be defined to describe calculation process and content of the MLBM [15]. : the total number of objects to be evaluated, . : the total number of objects to be evaluated in the Level* l*. : the total number of evaluation criteria in Level* l*. : the* i*-th object in Level* l* to be evaluated. : the* j*-th subobject to be evaluated in the Level* l-1* is associated with the* i*-th object in Level* l*. : the total number of objects to be evaluated in the lower level of the* i*-th object in Level* l*. : the evaluation criteria of Level* l*, = 1,2,...,. : the scoring of in Level* l *under the evaluation criteria . : the scoring of in Level* l-1* of the in Level* l*. : the total number of the evaluated objects whose score is higher than the in Level* l* under the evaluation criteria of . : the Borda value of the object to be evaluated in Level* l*. : the Borda value of the object to be evaluated in Level* l-1*. : the ranking value of the object to be evaluated in Level* l.* *l*=1,2,…;* i*=1,2,…,=1,2,…, =1,2,…, .

##### 3.2. Algorithm and Process

The MLBM is a bottom-up analysis and evaluation process. Therefore, in the whole evaluation process, it needs to be evaluated from the bottom to the up, and then the evaluation value of the target layer will be obtained. The steps and contents of the MLBM are listed as follows.

**(Calculating the Borda value and order of the evaluated objects in the first level)**

*Step 1. *Establish the hierarchical structure tree of the object to be evaluated. This step is based on the subordinate relationship, hierarchical relationship, and relevance of the object being evaluated.

*Step 2. *Determine the target number of Level ; determine the total number of the first level of evaluated objects and the total number of evaluation criterion .

*Step 3. *Determine the score of the first level evaluated object in the evaluation criterion , where* i*= 1, 2,…,; = 1, 2,…,.

*Step 4. *Calculate the total number of in all the evaluated objects in the first level, which is higher than the evaluated .

*Step 5. *Calculate the Borda value of evaluated in the first level.

**(Calculating the Borda value above the second level and sort)**

*Step 6. *Determine the objects to be evaluated and the total number in Level* l *and Level* l-1*, *(l≥2)*:

The total number of objects to be evaluated in Level* l *is .

The total number of subobjects is associated with the* i*-th evaluated object in the Level* l*; then the total number of subobjects in the Level* l-1* is

*Step 7. *Determining the evaluation criteria for Level* l *and its total number .

The method of determining the criteria for each level and its total number is as follows:

If the level specifies the evaluation criteria, the prescribed evaluation criteria are adopted, and the total number of evaluation criteria for the level is the actual number of the specified rules.

If the level does not specify the evaluation criteria, the evaluation criteria are constructed according to the hierarchical structure and the relevance of the object to be evaluated.

The specific method of constructing the evaluation criteria is as follows.

There are no evaluation criteria in Level* l;* then compare all the evaluated in Level* l* (measured or calculated Borda values), each object of comparison is one of the subobjects associated with the object in the Level* l-1.* The subobjects of all the objects in the Level* l *are sequentially compared with each other. That is, the object in the Level* l-1 *of the object to be evaluated in Level* l *is sorted out and combined in the above-described manner. One combination is an evaluation criterion of the Level* l*; the total number of evaluation criteria for Level* l* is the value of the combination of subobjects at Level* l-1.*

Assume the total number of objects to be evaluated in Level* l* is ; the number of subobjects corresponding to the* i*-th evaluated subobject is . There are a total of kinds of mixed combinations in the Level* l*; namely, the total number of evaluation criteria in the first level isNote: in the hierarchy structure tree, the bottom of the evaluation object must have established evaluation criteria.

*Step 8. *Determine the score of to be evaluated,

For the evaluation criteria of the regulation and construction, in the evaluation process, the evaluation method of the evaluated object is different; the specific difference is as follows:

If the Level* l* specifies the evaluation criteria, is the score of the evaluated object in Level* l* under the .

If the level does not specify the evaluation criteria, the number combination method in the evaluated objects that compared in Level* l* is , which iswhere . Therefore, is the score or Borda value of the* j*-th subobject in the Level* l-1 *of the* i*-th object of the combination in Level* l*, which is .

*Step 9. *Calculate the total number of all objects in the Level* l*, which is higher than the evaluated .

According to different criteria, the calculation method of is shown as follows:

If the level has the established criteria,

If the level does not have the criteria,where represents the number of collection elements.

*Step 10. *Calculate the Borda value, .

The Borda value of the evaluated object in Level* l *can be calculated, which is calculation formula as follows:

*Step 11. *Determine whether it reaches the target Level* L*.

If the target Level* L* is reached, the calculation will be stopped. If the target Level* L* is not reached, it will be cycled from Step 6 to Step 10 until the target Level* L* is executed.

*Step 12. *Output the evaluated object .

Determine the respective order of the object in the target Level* L*,* i *= 1, 2,…,, which is the order (Risk ranking or RPN) of the subject in the level.

Through the summary of the above calculation steps and contents, the computational flow chart of the MLBM is developed, as shown in Figure 3.

#### 4. Case Study

Taking the main structure system of the truss type crane (no. LIUHUA10-1PGC) as an example on the oil and gas production platform, the MLBM is used to evaluate the risk value and the priority relation of its failure modes, main parts, and subsystems. Firstly, the failure modes, risk types, and risk factors for the main structure system are analyzed by using FMECA [16], because different experts have certain differences in personnel composition, expertise, and on-site experience, which will lead to differences in the analysis reports of FMECA. In order to improve the objectivity of the analysis results, we organized 3 expert groups to perform FMECA separately and independently so that 3 FMECA reports were obtained. Secondly, the risk hierarchy structure tree (RHT) of the main structure system was established based on its structural diagrams of mechanical system, as shown in Figure 4.

In the* Level 1* of the RHT of the main structure system in Figure 4, there are three risk factors: Consequence Severity , Occurrence Frequency , and Detection Difficulty . In the* Level 2* of the RHT, there are four risk types relating to risk factors, including safety risk (SR), environmental risk (ER), economic loss risk (ELR), and maintenance cost risk (MCR). Based on semantic vagueness results of the risk factors in 3 FMECA reports, the quantization value of the risk factors corresponding to each failure mode is obtained by the Fuzzy Set Theory, as shown in Table 6 [17].

In Figure 4, the* Level 2 *of the RHT of the main structural system is the four risk types (SR, ER, ELR, and MCR) of each failure mode. Their risk evaluation criteria have been set in the* Level 2* based on 3 risk factors of , , and . And the quantitative value of the risk factors corresponding to each failure mode in the Table 6 is regarded as the risk score under the evaluation criterion above. In the MLBM, equivalent risk value (ERV) is Borda value and risk ranking that is obtain by comparing the Borda value is the RPN. And then, the ERV and RPN of the SR, ELR, and MCR for 13 failure modes are obtained by the MLBM in Figure 5, because the failure modes of the main structure system generally do not cause environmental consequences. The ERV and RPN of the ER of the failure modes were not considered in this case study.

According to the quantitative risk results about SR, ER, and MCR in the Figure 5, we can see that different failure modes might cause different types of risk consequent. We all know that the companies of different backgrounds and industries will focus on different types of risks. From the ERV and RPN of SR, ER, and MCR, the companies can focus directly on the type of risk they care about. F32: Weld failure has the highest SR, and the highest ELR and MCR are F31: structural failure.

In the Figure 4, there are 13 failure modes in the* Level 3* of the RHT of the main structural system. Because the ERV among the failure modes can be directly compared and sorted out when they are under same type of risk, the evaluation criteria in the* Level 3* can be identified as SR, ER, and MCR. So the total of the evaluation criteria is 3 in* Level 3*. Moreover, their ERV calculated in the last step can be taken as the risk scores under evaluation criterion of SR, ER, and MCR. Thus, the ERV and RPN of integrated risk of ach failure mode have been calculated by using traditional Borda method and the MLBM, respectively, in Figure 6 [18].

In the Figure 6, we can see that there are some risk ties of the failure modes with traditional Borda method, but few risks ties with the MLBM. From the Figure 6, F31: structural failure and F32: Weld failure have higher risk level than others according to the ERV and PRN of 13 failure modes. Therefore, in the system inspection process, these two failure modes should be excluded, which will be easier to avoid major failures and accidents in petrochemical production.

The* Level 4* of the RHT of the main structural system includes the “A”-shaped frame, Hinge pin, Truss boom, Joining flange, and Hinge pin. For the components or parts, the lower level displays a variety of different failure modes; it can not specify its evaluation criteria. According to the failure modes corresponding to the components or parts, the evaluation criteria are set in the* Level 4*. By arranging all the failure modes, the total number of evaluation criteria is 108 for calculating the* Level 4*. At the same time, the Borda value of each failure mode is calculated in the previous step taken as its risk score under each evaluation criterion in the current level. The ERV and RPN of the “A”-shaped frame, Hinge pin, Truss boom, Joining flange, and Hinge pin of the lifting arm are calculated as shown in Figure 7.

From Figure 7, we can know that there are not any risk ties for all of parts. The ERV and RPN about the Truss boom and Hinge pin are higher than the other parts. During their routine maintenance and inspection, the Truss boom and Hinge pin should be paid more attention to improve their reliability and security.

In Figure 4, the* Level 4* in the RHT of the main structural system is the “A”-shaped frame system and the Crane jib system. For the subsystems, their lower level objects are components or parts so that their respective ERV can be compared with each other. Therefore, the evaluation criteria of the* Level 4 *are the risk value of the components or parts. Through various permutations and combinations, there are six evaluation criteria in the* Level 4*. The Borda value of each component or part calculated in the previous step are taken as the risk score under six evaluation criteria. Quantitative risk evaluation results of the “A”-shaped frame system and the Crane jib system are calculated, as shown in Figure 8.

In Figure 8, the ERV of the “A”-shaped frame system is higher than the Crane jib system. During overhauling for the crane, the “A”-shaped frame system will be a key target, and the other systems are secondary. Therefore, quantitative risk evaluation results can better guarantee the safety of the whole system.

#### 5. Conclusion

The MLBM is a modified Borda method based on scoring and ranking among objects to be evaluated. This method is proposed to aim at solving the comprehensive evaluation problem which is multilevel, complex structure and lack of evaluation criteria of the middle level and achieving quantitative calculation results of the objects. In this study, the MLBM is applied to the quantitative risk evaluation of failure of the petrochemical production system. Not only are the risk value and risk ranking of the items, including subsystems, equipment, components, parts, and failure modes, in the petrochemical production system carried out, but also the risk tie of their RPN is reduced effectively to get a more accurate risk ranking. Based on the MLBM, the ERV and RPN of the failure modes are calculated in the overall system. And then, the high-risk failure modes can be selected according to their ERV and RPN. Thus, it can help the optimization of preventive maintenance program, evaluation of running status, and fault diagnosis of devices and equipment in the petrochemical production system. Moreover, the quantitative risk evaluation method based on the MLBM can be applied to analyze the ERV and RPN of each parts, components, and subsystem. And the quantitative risk evaluation results of these items can help to optimize their importance ranking and classification, in order for scientifically screening out important functional items to help the implementation of Reliability Centered Maintenance and asset integrity management (AIM) technology. Further, it is possible to clarify the risk level and distribution of the high-risk items throughout the production system and provide data support for the development of risk control measures to better protect the safety of production according to the quantification ERV and RPN of failure modes, components, parts, subsystems, and systems.

The MLBM can be used not only to solve the multilevel complex structure problem in the quantitative risk evaluation of petrochemical industry but also to provide a reference for other multilevel complex structure comprehensive evaluation problems. The MLBM is a method of fixed analysis and calculation process. In next study, it will be considered that the development of MLBM is carried out as computer program module in order to improve its computational efficiency and better promotion, and the application of the method is outreached and improved according to different objects to be evaluated in other fields.

#### Data Availability

The data of used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

#### Acknowledgments

This work is supported by the National Key Research and Development Program (2018YFC0310201), National Science and Technology Major Project (2016ZX05028-001-006), Key Research and Development Projects of Sichuan Science and Technology Department (2017GZ0386), Scientific Research Starting Project of SWPU (no. 2018QHZ017), and Open Fund of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University) (PLN201827).