Comprehensive Evaluation of Marine Ship Fires Risk Based on Fuzzy Broad Learning System

Abstract

Ship fires exhibit the main characteristics of a high possibility of occurrence, large load, fast spreading, high difficulty in extinguishing, and serious losses. Therefore, once a fire occurs, it will cause huge loss in terms of economic and personnel safety. Firstly, a ship fire risk evaluation indicator system was constructed based on the causes and severity of the fires. Secondly, a comprehensive evaluation method for the fuzzy broad learning system (FBLS) was proposed. The fuzzy system was used to implement feature mapping on the input data, and the extracted fuzzy features were further input into the BLS enhancement layer. A fuzzy broad learning neural network structure was constructed by combining fuzzy features, feature nodes, and enhancement nodes. The method was applied to the field of risk assessment for the first time, and is a reference for subsequent studies. Finally, the risk levels of ship fires were classified and compared with evaluation methods such as fuzzy support vector machine (FSVM) and Fuzzy BP neural network (FBPNN) to demonstrate effectiveness and accuracy. The proposed FBLS method was used to predict actual cases, and the results showed consistency with the level determined by the accident investigation report published by the Maritime Bureau Administration.

1. Introduction

In recent years, with the rise in economic globalization and the rapid development of maritime trade, the shipping industry, as an important pillar industry of economic development, has also achieved great development. The development level of the maritime transportation industry has become an important reference mark to measure the economic level and international status of a country. The rapid development of ports and shipping has led to the increase in scale, environmental protection, specialization, and intelligence of ships. The overall safety condition of ships has been widely improved, but statistical data do not show any significant improvement in ship fire accidents. The accident data of global ship fires with a total weight of over 3000 tons in the past decade are shown in Figure 1. In the first quarter of 2022, the shipping industry experienced total-loss accidents caused by ship fires on three ships with a total weight of over 3000 tons, including ro-ro ships, car ships, and oil tankers. In 2022, there was a total of 141 fires or explosion accidents on ships with a total weight of over 3000 tons, accounting for 7% of all ship traffic accidents in the year, which is the highest number of accidents in the past decade. Therefore, assessing the fire risk of ships has extremely high application and research value.

The main evaluation methods in the field of ship safety include gray correlation analysis, hierarchical analysis, a systematic risk assessment method, an artificial neural network method, and a fuzzy comprehensive evaluation method, as well as many other common methods for marine traffic risk assessment, among which the main methods for a ship fire risk assessment are fuzzy comprehensive evaluation method and neural network evaluation method. Liu et al. [1,2] proposed a method named ontology-based ship fires risk assessment. A ship fire ontology is constructed to obtain a seed ontology, and the seed ontology is converted into a two-dimensional evaluation form. Bayesian network inference is applied to the evaluation process. Ekaterina Savinykh et al. [3] studied the main fire causes of the ship from the perspective of equipment failure, human factors, electrical failure and ship battery compartment failure, established a fire risk evaluation model based on Bayesian network, and generated prior probability and conditional probability tables using statistical data and expert judgment to determine the fire risk level of the battery-powered ship. The risk analysis of fire and explosion accidents of bulk carriers is carried out based on fuzzy logic, fault tree analysis, and cut set importance measurement technology [4]. Since fault tree analysis provides a powerful graphical tool to explore the causes of system level faults, fuzzy sets deal with fuzziness in the decision-making process. A hybrid method combining human factors analysis and classification system (HFACS) and fuzzy fault tree analysis (FFTA) is used to analyze the fire explosion accident in the engine room of a ship. The HFACS method was used to classify the formation factors of cabin fires according to a hierarchical structure, and the FFTA method was used to calculate possible accident scenarios and probabilities [5,6]. A comprehensive evaluation model for ship fire risk was constructed, involving interpretive structural modeling, fuzzy analysis network processes, and evidence reasoning methods [7,8]. Kostas J. et al. [9] proposed a risk model for evaluating fire safety in the design phase of passenger ships, which was designed to enhance the probabilistic nature of performance-based ship fire evaluation. Safety management systems (SMS) are applied to ship management as a way to improve the risk management level of ships [10]. U. Bhardwaj [11] proposed a Bayesian network probability framework to quantify the fire and explosion events in floating production, storage, and unloading units (FPSOs). This framework comes from the systematic analysis of the unique contingencies and accidents of FPSOs, and discusses the potential accidents related to fire and explosion. A detailed risk analysis was conducted using the risk matrix method to screen and rank the main accidents that occurred in FPSOs. Then, based on the evidence obtained from accident reports and expert opinions, a Bayesian network model of high-risk fire and explosion scenarios is established [12,13]. Xu et al. [14] proposed a lightweight evaluation model based on convolutional neural networks to solve the problem of the excessive parameters of BP neural networks and assessed the fire hazard level of cruise ship fire compartments in real time. A dynamic evolutionary model is proposed to quantify the domino effect of ship cabin fires. Based on the spatial and temporal characteristics of fire incidents, the dynamic probability of the domino effect of multiple incident units is calculated using matrix calculations and Monte Carlo simulations [15]. In addition, deep learning networks have been used in the autonomous detection of ship fires to provide level warning of possible fires [16]. Wang et al. [17] established an evaluation method that can quantify the fire risk indicator of the building and scientifically calculate the fire risk value. Wei et al. [18] proposed a novel method for rapid fire risk evaluation based on fuzzy mathematics and support vector machine (SVM) algorithm, which establishes a flexible and operable fire risk evaluation indicator system, considering the comprehensiveness of building fire risk factors that improves the efficiency of building fire risk evaluation. A hierarchical task analysis (HTA) and human error assessment and reduction technique (HEART) approach is proposed to be applied to the risk assessment of fires on passenger ships [19]. A fire and explosion risk assessment model based on real-time computational fluid dynamics (CFD) and Bayesian networks is proposed using a fault tree/event tree (FT-ET) to describe accident scenarios, a Bayesian network (BN) to obtain initial probabilities for each outcome, and to describe the dependencies between safety barriers and evaluate various risk control measures and risk mitigation options [20,21]. Ji et al. [22] tested the structure of an integrated real-time situational risk assessment model for firefighting vessels based on fuzzy neural network principles and developed an integrated risk assessment model. The fire risk evaluation models of neural networks are becoming a mainstream assessment tool.

With the continuous optimization and development of neural networks, Philip Chen proposed a new type of neural network, namely the broad learning system (BLS) in 2018. C. L. P. Chen [23] studied the influence of feature nodes and enhancement nodes in the structure of BLS on the entire neural network, proposed a variant network of BLS, and applied it in the field of computer vision, achieving good results. Bai et al. [24] proposed a dynamic fuzzy inference system based on broad learning system (BL-DFIS), which improves the accuracy and interpretability of neural fuzzy models, and also solves the challenging problem of models being unable to autonomously determine the optimal architecture. Tian et al. [25] proposed that FBLS exhibits significant advantages in nonlinear and uncertain modeling, evaluating the performance of the proposed method by predicting surface roughness during actual slot milling processes, and outperforming traditional neural network models in terms of prediction accuracy. The FBLS proposed by Feng et al. [26] was evaluated using popular regression and classification criteria and compared them with some state-of-the-art non-fuzzy and neuro-fuzzy methods. The results indicate that FBLS outperforms other relevant models. Later, Jiao, X. et al. [27,28] comprehensively studied the training algorithm of FBLS and successfully applied it to nonlinear systems.

In this study, an FBLS network is applied to the field of risk assessment to make a comprehensive evaluation of ship fire risk. Firstly, the index system of ship fire safety evaluation is established, and the index system is scientifically and reasonably screened to establish a more complete and suitable evaluation index system for ship fire risk; the hierarchical analysis method is used to assign weights to the established evaluation index system and determine the influence size of each index on the evaluation results, and then the risk evaluation model of the FBLS network is trained and tested based on the data from the expert database. The risk evaluation model of FBLS network is trained and tested based on the data from the expert database, and an efficient, fast and accurate FBLS ship fire risk evaluation model is established. The model was compared with traditional fuzzy neural network evaluation methods (FSVM, FBPNN) in terms of MAE, MSE, and RMSE to prove the accuracy and feasibility of the model, and finally, the model was validated with real ship fire cases to achieve a quantitative evaluation of ship fire risk and provide technical support for ship risk management and decision-making. The main contributions of this article are outlined as follows:

(1)

This study presents a ship fire risk evaluation indicator system based on the causes and severity of fires. After scientific screening, the final evaluation index system and the weights of indicators at each level were determined by using analytic hierarchy process(AHP)

(2)

A comprehensive evaluation method for the fuzzy broad learning system (FBLS) is proposed. The fuzzy system is used to implement feature mapping on the input data, and the extracted fuzzy features are further input into the BLS enhancement layer. A fuzzy broad learning neural network structure is constructed by combining fuzzy features, feature nodes, and enhancement nodes.

(3)

To validate the effectiveness of the proposed method, a comprehensive evaluation of marine ship fire risk is compared to other existing state-of-the-art methods.

The rest of this paper is organized as follows. Section 2 initially establishes the evaluation index system of ship fire risk and determines the final evaluation index system after scientific screening, after which the weights of the indexes at each level are determined using an analytic hierarchy process (AHP). In Section 3, the FBLS network evaluation method is proposed and the new learning algorithm is discussed. Additionally, the method is applied to the assessment of ship fire risk in Section 4, and the advantages of FBLS are demonstrated through the comparison of experimental results. Section 5 demonstrates the feasibility of the assessment method by using a real case of ship fires. Finally, we conclude our work in Section 6.

2. Establishment of Evaluation Indicators for Ship Fires

The International Maritime Organization (IMO) clearly states in the International Management Code for the Safe Operation of Ships and for Pollution Prevention (ISM) Code that the vast majority of ship fires are caused by human factors, especially inadequate professional skills, weak fire prevention awareness, and negative work attitudes. These are potential risks that cause ship fires, which can be extended to include human and management factors. The human factor mainly includes the number and distribution of crew members, their awareness of accident prevention behavior, and their ability to self-rescue after an accident occurs. Management factor considers other factors, including policy, safety training, proficiency, and contingency deployment. Although most ship fires are caused by human factors, fires caused by electrical equipment and line problems on ships tend to cause a large number of casualties and greater economic losses. Fires from electrical equipment and line faults are usually accompanied by more intense fire sources and faster spreading characteristics. Compared with indicators of other factors, fires caused by risk source factors are more uncertain and difficult to prevent early. On the one hand, the gradual aging of electrical lines and a significant decrease in insulation resistance can easily lead to overload or short circuits; meanwhile, equipment (electrical or mechanical) malfunctions can also cause fires to occur. On the other hand, the International Convention for Safety of Life at Sea (SOLAS) Convention has low requirements for ship construction, and some ship fire protection measures have not been fully considered. Once a fire occurs, environmental factors often determine the scope, speed, casualties, and economic losses of the fire. In addition, the number and width of fire escape, as well as the condition of smoke extract facilities, play a crucial role in ensuring the smooth escape of crew numbers in the event of a fire. Therefore, the selection and screening of risk evaluation indicators for this paper will be carried out.

By investigating various typical cases of ship fire and analyzing the causes of fire, sorting out the relevant literature, and combining with the opinions of professionals, this paper summarizes the set of factors that may cause or affect ship fires, and classifies the influencing factors to establish a primary index consisting of four primary indicators, including human factor, risk source factor, environmental factor, and management factor. Moreover, 19 secondary indicators are shown in Figure 2.

2.1. Establishment of Evaluation Indicators Weights

Four primary indicators and nineteen secondary indicators are selected as a collection of evaluation indicators in this paper. For the weight part of the indicators, experts are chosen to score the evaluation indicators in pairs. The impact of indicators on the evaluation results varies at each level, so the weight of each evaluation indicator is determined by using an analytic hierarchy process (AHP). The decision judgments were quantified using the Saaty1–9 scale method (

Table 1. RI values of the judgment matrix of order 1 to 9.

n	1	2	3	4	5	6	7	8	9
RI	0	0	0.58	0.90	1.12	1.24	1.32	1.41	1.45

). When the two indicators are of equal importance, the score is 1; when one indicator is slightly important, important, highly important, or extremely important than the other, it is marked as 3, 5, 7, or 9, respectively. While the evaluation of importance is between the above two, the specific scoring table is shown in

Table 2. Importance comparison of a first-level indicator.

Indicator	Human Factor	Risk Source Factor	Environmental Factor	Management Factor	Consistency Check
Human Factor	1	1/2	1	3	CR = 0.03 < 0.1
Risk Source Factor	2	1	5	8
Environmental Factor	1	1/5	1	3
Management Factor	1/3	1/8	1/3	1

.

According to the above method, a judgment matrix is obtained by comparing the similar importance of the first-level index and the second-level index, and then the eigenvalues and eigenvectors of the obtained matrix are solved. The expert scoring method is used to evaluate the secondary indicators, and the corresponding scores are determined according to the indicator state set, and the average score is used as the final score of each secondary indicator. The specific calculation is as follows:

(1) The judgment matrix is normalized by column vectors as follows:

$$\widetilde{{\omega }_{ij}}=\frac{a_{ij}}{{\displaystyle {\sum }_{i=1}^n{a}_{ij}}}$$

(1)

where n is the dimension of the row vector and column vector of the judgment matrix, and i and j are the corner labels of the elements of the i-th row and j-th column of the matrix, respectively.

(2) Sum $\widetilde{{\omega }_{ij}}$ by row vector to obtain ${\omega }_i$:

$$\widetilde{{\omega }_i}={\displaystyle {\sum }_{j=1}^n\widetilde{{\omega }_{ij}}}$$

(2)

(3) Normalizing ${\omega }_i$ yields the approximate characteristic root:

$${\omega }_i=\frac{\widetilde{{\omega }_i}}{{\displaystyle {\sum }_{i=1}^n\widetilde{{\omega }_i}}}$$

(3)

$$\omega ={\left({\omega }_1,{\omega }_2,{\omega }_3,\dots ,{\omega }_n\right)}^{\mathrm{T}}$$

(4)

(4) Calculate the approximation of λ as the maximum characteristic root:

$$\lambda =\frac{1}{n}{\displaystyle {\sum }_{i=1}^n\frac{{\left(A\omega \right)}_i}{{\omega }_i}}$$

(5)

where A denotes judgment matrix.

During the risk evaluation of ship fires, the establishment of a scientific, reasonable, and complete evaluation indicator system is related to the accuracy and reliability of the evaluation results. However, there are still some problems in the selection and screening of risk indicators: first, in the pursuit of the completeness of the indicator system, new risk indicators are continuously added to increase the types and quantities of indicators in the evaluation system, and the effects of different indicators overlap, sharing the weight of important indicators. Secondly, due to the lack of scientific and effective indicator screening methods, most people only rely on experience to select indicators, or directly refer to the statistical data of ordinary fires to select indicators that they consider appropriate, without considering the characteristics of ship fires. This directly affects the accuracy and reliability of the risk evaluation of ship fires. Therefore, the four basic principles of completeness, subjectivity, independence, and pertinence of the evaluation system should be followed when screening indicators. The choice of indicators cannot be determined only by one aspect. The completeness of the evaluation indicator system includes not only the selection of indicators that can more fully reflect the risk sources of the evaluation objectives, but also the completeness of the evaluation index system based on the purpose and accuracy of the evaluation. The details are shown in Figure 3.

Finally, according to the flowchart in Figure 3, and considering the size of indicator weights, the indicators with extremely low weights in the evaluation process were removed, and the optimized risk evaluation indicator system of ship fires was analyzed and screened. The optimized evaluation indicator system is shown in Figure 4 and the weight of the indicators is shown in

Table 3. Weight of each indicator.

First-Level Indicator	Weight	Second-Level Indicator	Weight
Human Factor	0.21	Number and distribution of personnel	0.11
		Fire safety awareness	0.18
		Ability to seek refuge and self-rescue	0.42
		Fire emergency drill	0.29
Risk Source Factor	0.56	Electrical equipment failure	0.32
		Line fault	0.43
		Careless use of fire	0.25
Environmental Factor	0.17	Number and width of fire escape	0.11
		Integrity of smoke exhaust facility	0.12
		Automatic alarm system	0.19
		Flame retardant facility system	0.52
Management factor	0.06	Proficiency in firefighting facility	0.37
		Fire protection knowledge and skill	0.10
		Organizational skill	0.20
		Regular maintenance situation	0.33

.

2.2. Consistency Check

To ensure that the judgments and decisions made during the analysis hierarchy are reasonable and have a certain degree of credibility, it is necessary to perform consistency checks on the judgment matrix. If the consistency index is less than the preset threshold, it means that the judgment matrix has a certain consistency. On the contrary, the judgment matrix needs to be adjusted to ensure the accuracy and reliability of the decision results. In addition, the personal cognitive preferences of the judge and the relative importance of risk factors may lead to incorrect or inconsistent judgments. Therefore, consistency checking is important for the correct application of the analytical hierarchy process and the reliability of the decision results. It can effectively prevent deviations in the calculation of feature vectors due to inconsistencies in the judgment matrix, which can lead to incorrect judgment values of risk factor weights. After obtaining the risk judgment matrix, decision makers need to check whether each expert’s judgment is consistent. For this purpose, the maximum eigenvalue λ_max of the judgment matrix needs to be calculated.

CI (consistency index) is the indicator for measuring matrix inconsistency:

$$CI=\frac{{\lambda }_{max}-n}{n-1}$$

(6)

CR (consistency ratio) is the random consistency ratio:

$$CR=\frac{CI}{RI}$$

(7)

When CR < 0.1, it can be considered that the judgment matrix has satisfactory consistency. If CR > 0.1, it means that the consistency check of the judgment matrix does not meet the requirements. It is necessary to adjust the consistency again, and then update the weight calculation and consistency check until the consistency check of the judgment matrix is met.

3. Establishment of Evaluation Model Based on Fuzzy Broad Learning System

The fuzzy broad learning neural network system is composed of the fuzzy system and the broad learning system. Before inputting the neural network system, the fuzzy system preprocesses the data and transforms it into fuzzy input signal and weight value. Ultimately, the output of the neural network system is defuzzified, that is, the output result is quantified. The fuzzy system can imitate the fuzzy concept of human intelligent thinking behavior, as well as the way of receiving human language thinking and dealing with problems. The broad learning system has efficient learning ability, which is composed of executable neurons and imitates the information transmission between biological neurons. It can deal with the data with complex relationship or unclear mechanism between input and output, so as to achieve the purpose of prediction and simulation.

3.1. Fuzzy Systems

Fuzzy refers to the “either… or…” or “uncertainty” in objective things, for example, whether the risk level of fire is relatively safe or dangerous. It is generally qualitative for language description, but the degree of expression is vague. The evaluation index of emergency response capability for risk is fuzzy, and the width learning system is a method for processing quantitative data. Therefore, the qualitative evaluation results of the obtained index can be input into the fuzzy system for preprocessing. The function of the fuzzy system is to fuzzy the qualitative evaluation index, determine the index weight, index state set and its corresponding score, and calculate the index score and expected result at all levels.

The risk level of ship fires is divided into five grades, I, II, III, IV, and V, which correspond to five fire risk levels: very low, low, general, high, and very high. In the field of risk evaluation, the description of the safety level of the evaluation object is mostly related to the quantitative concept, and the fuzzy system can quantify the qualitative degree of adjective description.

When combining both fuzzy systems and width learning systems, the information stored in the mapped-to-feature and augmentation nodes needs to be fuzzified and weighted so that the information can remain fuzzy during transmission, and the expression of the fuzzy logic neuron function is as follows:

$$u_i=F_i(x_1,x_2,\dots ,x_n,v_{i1},v_{i2},\dots ,v_{in})$$

(8)

$$y_i=f_i(u_i)$$

(9)

where, $x_1,x_2,\dots ,x_n$ are the input of the fuzzy system; $v_{i1},v_{i2},\dots ,v_{in}$ are the weight of each neuron; $F_i$ is the fuzzy logic function; $u_i$ is the state of fuzzy neuron; $f_i$ is the output function of the fuzzy system; and $y_i$ is the output of the fuzzy system.

When the input to the fuzzy system is $x=(x_{11},x_{12},\dots ,x_{1j};x_{21},x_{22},\dots ,x_{2j};\dots ;x_{i1},x_{i2},\dots ,x_{ij})$, the set of linguistic variable values is as follows:

$$L(x_i)=\{A_i^1,A_i^2,\dots ,A_i^j\}$$

(10)

where, $x_i$ is the fuzzy linguistic variable.

Let $A_i^j$ be the j-th neuron variable of $x_i$, defined as the fuzzy set on $x_i$, then the affiliation function is as follows:

$$f={\mu }_{A_i^j}(x_i)$$

(11)

After changing the fuzzy weighting rules, the output of the fuzzy system can be obtained as:

$$\left\{\begin{array}{l}{y}_1=x_{11}{p}_1+x_{12}{p}_2+\dots +x_{1j}{p}_j\\ y_2=x_{21}{p}_1+x_{22}{p}_2+\dots +x_{2j}{p}_j\\ \dots \\ y_i=x_{i1}{p}_1+x_{i2}{p}_2+\dots +x_{ij}{p}_j\end{array}\right\}$$

(12)

$$y={(y_1,y_2,\dots ,y_i)}^T$$

(13)

3.2. Broad Learning System

The BLS is further optimized based on the random vector functional link network (RVFLN), while the BLS network retains the basic structure of RVFLN. The network structure of RVFLN is shown in Figure 5. RVFLN is composed of input layer, hidden layer (enhancement layer), and output layer, and has a strong approximation ability for any continuous function. However, when the input data have a large scale or the dimension of the input set is high, the effect of RVFLN is often unable to meet our training accuracy requirements.

The core of BLS is to find the pseudo-inverse matrix of feature and augmentation nodes to the target value, where the feature and augmentation nodes together form the input corresponding to the neural network, and the inverse matrix is equivalent to the weights and thresholds of the neural network. A significant advantage of BLS is the lateral scaling and incremental learning. When the prediction and evaluation performance of the model decreases, BLS uses the lateral expansion method to complete the tedious calculation by only adding new enhancement nodes and feature nodes to achieve the purpose of saving time and simplifying the network structure. In addition, the accuracy of BLS is more accurate and has achieved good performance on various task datasets. The network structure of BLS is shown in Figure 6. The most prominent characteristics of neural networks are self-learning and adaptability, which can learn according to the input sample data to acquire knowledge. In addition, they can adjust the parameters of new input data based on the established neural network model, change the mapping relationship between input and output, and achieve the function of self-learning adaptation. Compared to ordinary expert system modes, the impact of human subjective factors in the evaluation system is reduced. Therefore, the BLS model not only retains the self-learning and adaptability of the neural network, but also increases the network width to effectively shorten the training time and provide a good generalization ability in the case of an unknown system model’s recognition aspects.

In the process of risk evaluation, the indicator system is often complex, with mutual influence and strong fuzziness between indicators, resulting in the unsatisfactory effect of the fuzzy comprehensive evaluation method. The BLS model is designed to map input data to the feature nodes as the feature vector of the network. The enhancement nodes are obtained by random weighting the feature nodes. The enhancement nodes and feature nodes are merged together and connected to the output of the system, where the weights between the input and output can be solved directly by a pseudo-inverse algorithm based on ridge regression. Among them, N₁ and N₂ denote the number of feature nodes and feature node groups in each group, respectively, while N₃ denotes the number of enhancement nodes. The basic operational process of the BLS is as follows:

Determine the input set X and output set Y of the dataset, and assume that there are n groups of feature mappings, then the i-th feature mapping node can be expressed as:

$$Z_i=\varphi \left(X{W}_{ei}+{\beta }_{ei}\right),i=1,2,3,\dots ,n$$

(14)

where ф is the mapping function; W_ei is the weight of the output and feature layer; and β_ei is the bias; both the weight and bias are randomly generated.

The set of mapping feature nodes can be defined as:

$$Z^n=\left[Z_1,Z_2,Z_3,\dots ,Z_n\right]$$

(15)

Suppose there are m augmented nodes, then j enhancement nodes can be expressed as:

$$H_j=\xi \left(Z^n{W}_{h_j}+{\beta }_{h_j}\right),j=1,2,3,\dots ,n$$

(16)

where the connection weights $W_{h_j}$ and bias ${\beta }_{h_j}$ are also randomly generated, ξ is the activation function, and the set of total enhancement nodes can be expressed as:

$$H_m=\xi \left(Z^n{W}_h+{\beta }_h\right)$$

(17)

Thus, the output Y of the BLS is obtained, which can be expressed as:

$$Y=[Z_1,Z_2,\dots ,Z_n\left|\xi \left(Z^n{W}_{h_1}+{\beta }_{h_1}\right)\right.,\dots ,\xi \left(Z^n{W}_{h_j}+{\beta }_{h_j}\right)]W=[Z_1,Z_2,\dots ,Z_n\left|H_1,\dots ,H_M]W\right.$$

(18)

where W is the weight of the connection to the output layer.

Defining $A=\left[Z_n\left|H_m\right.\right]$, the parameter W can be solved by using ridge regression:

$$W={\left(A^{\mathrm{T}}A+\lambda I\right)}^{-1}{A}^{\mathrm{T}}Y$$

(19)

where I represents the unit matrix and $A^{\mathrm{T}}$ is the transpose of $A$.

The main parameters included in the BLS network model are the number of feature mapping groups, N₁, the number of feature mapping nodes contained in each group, N₂, and the number of enhancement layer nodes, N₃. Given the input ship fire risk indicator data x, the actual input matrix X is:

$$X={\left[x_1,x_2,\dots ,x_n,\beta \right]}^{\mathrm{T}}$$

(20)

where β is bias. The feature mapping nodes is:

$$Z_i=\phi \left(X{W}_{ei}+{\beta }_{ei}\right)$$

(21)

The matrix composed of feature nodes is a N₁ × N₂ matrix, which also serves as the input for the whole network. The coefficient matrix of the enhancement node is a random matrix after orthogonal normalization, which can be expressed as:

$$H=\xi \left(Z{W}_{h_j}+{\beta }_{h_j}\right)$$

(22)

where $W_{h_j}$ is the random initialization weight.

The activation function ξ(x) uses the tanh function to achieve the nonlinear transformation, which can be expressed as:

$$\xi \left(x\right)=\frac{e^x-e^{-x}}{e^x+e^{-x}}$$

(23)

3.3. Fuzzy Broad Learning System

Considering the strong fuzziness of risk evaluation indicators of ship fires, an FBLS network evaluation model is constructed by combining fuzzy system and broad learning system. There are multiple ways to combine fuzzy system with BLS. In this model, the fuzzy system and BLS are organically combined in series, and the data processed by the fuzzy system are directly output to the BLS. As shown in Figure 7, each node in the input layer of the fuzzy system represents a qualitative evaluation result of a secondary evaluation indicator, which is quantified and transmitted to the BLS. The number of nodes in the input layer of BLS is the same as the number of secondary indicators, and each node represents the quantitative simplified value of the indicators. The enhancement node layer is thinned through the weight matrix of the middle layer, and the enhancement layer is nonlinearly mapped to obtain the middle-layer training matrix, which can complete the mapping between the input value and the output value of the FBLS network. Its input and output are generally nonlinear functions, and nodes in the same layer do not interfere with each other. After inputting the training dataset into the network, the relevant parameters of the network are set and continuously adjusted to the optimal value. When the error between the training output and the expected output reaches the set standard after multiple iterations, the trained FBLS network evaluation model is obtained. Finally, the test data are input into the trained model, and the results and errors of the test output and the expected output are compared, including the average absolute error (MAE), mean squared error (MSE), and root-mean-squared error (RMSE), so as to determine whether the model can achieve the accuracy and reliability of the risk situation of the evaluation object.

4. Application of FBLS in Ship Fires Risk Evaluation

4.1. Fuzzy System Processing Data

By inviting experts in ship fire risk evaluation to score ship fire risk indicators as evaluation samples, the relative weight coefficients of evaluation indicators are established using analytic hierarchy process to obtain a hierarchical total ranking. Similarly, the evaluation of secondary indicators included in each primary indicator is continued, and the weight distribution of each level of primary and secondary indicators is ultimately obtained. Afterward, the evaluation data from the expert database are input into the fuzzy system, and the input of the whole network is simplified through fuzzy rules.

4.2. Determination of the FBLS Network Structure and Parameter Setting

The input nodes are based on the evaluation results of the indicator system, i.e., the results of 15 secondary evaluation indicators are quantified and input into the FBLS network. The final evaluation result is the ship fire risk level, so the number of output nodes is determined to be five. In addition, the number of feature mapping groups of the model is determined to be N₁ = 10, with each group containing N₂ = 10 feature mapping nodes and N₃ = 500 enhancement nodes.

After the FBLS network structure is designed, the shrinkage coefficient of the network is set to 0.8, the regularization parameters are 2⁻³⁰, the mapping function is the Sigmoid function, and the weights of all networks and the threshold values of neurons are randomly initialized. Using 30 sets of data from the expert pool processed by the fuzzy system as the training set, the global error meets the requirements after 10 iterations.

4.3. Evaluation Results

The output of the evaluation results is a 5 × 1 matrix, corresponding to the five levels of fire risk (I, II, III, IV, V), namely very low, low, average, high, and very high. According to the principle of maximum member, each value corresponds to the corresponding risk level, and the risk level corresponding to the maximum value of the output matrix is the fire risk evaluation level of the sample or test. For the characterization of the fire incident, the consequence level is usually also introduced together with the final risk evaluation, and the final risk index R is graded as follows:

R = P × C

where P is the risk level, C is the consequence level, which can be divided into five levels denoted by 1, 2, 3, 4, and 5. They are divided according to the consequences of the accident, as shown in

Table 4. Risk consequences guidelines.

C	Consequence Level	The Seriousness of the Consequences of the Accident
1	Slight	No personnel injury, ship damaged but not affecting mission completion, or negligible impact on schedule.
2	Mild	Minor injury to personnel, minor damage to the vessel, slight degradation of performance, or slight delay to the schedule.
3	Moderate	Moderate or severe injury to personnel, damage to ship functions, reduced performance, or significant delay to schedule.
4	Severe	Single fatality, severe damage to multiple functions of the ship, or severe schedule delay.
5	Catastrophic	More casualties or damage to critical systems and equipment.

. The risk matrix is designed to present and rank risks. It is a structured method for identifying the importance of risks, enabling an assessment of their potential impact, and is an easy-to-operate method that combines qualitative and quantitative analysis, as shown in

Table 5. Risk index distribution.

P	C
	1	2	3	4	5
Ⅴ	5	10	15	20	25
Ⅳ	4	8	12	16	20
Ⅲ	3	6	9	12	15
Ⅱ	2	4	6	8	10
Ⅰ	1	2	3	4	5

.

For risk classification level, when R ≤ 3, it can be judged as a lower risk level accident (Dark green); when 3 < R ≤ 6 is, it can be judged as a low risk level accident (Green); when 6 < R ≤ 12, it can be judged as a general risk level accident (Yellow); when 12 < R ≤ 16, it can be judged as a larger risk level accident (Orange); and when 16 < R ≤ 25, it can be judged as an extremely high risk level accident (Red).

Afterward, the trained FBLS network model is stored as a usable function and evaluated based on the research object. The error between the predicted output of the model and the expected comparison value of the sample, as well as the maximum membership degree, is shown in Figure 8, where each group of solid-line connected points of the same color represents the expected value, the dashed-line connected points represent the model predicted value, and the black square represents the error size of the maximum affiliation between the output of the five test sets and the expected value. The error size can be visualized by comparing the ups and downs of the black square deviating from the value 0 on the y-axis. The comparison between the evaluation results and the expected output results of the test set is shown in

Table 6. Comparison of evaluation results.

Evaluation Indicators	Evaluation Sample and Score
	x1	x2	x3	x4	x5
r11	0.112	0.200	0.128	0.152	0.240
r12	0.136	0.160	0.112	0.080	0.072
r13	0.120	0.208	0.184	0.208	0.184
r14	0.180	0.176	0.184	0.192	0.192
r21	0.136	0.104	0.200	0.208	0.192
r22	0.136	0.104	0.208	0.208	0.192
r23	0.216	0.248	0.208	0.152	0.112
r31	0.200	0.160	0.200	0.208	0.192
r32	0.200	0.144	0.200	0.224	0.208
r33	0.176	0.200	0.200	0.168	0.208
r34	0.176	0.120	0.180	0.168	0.160
r41	0.128	0.112	0.216	0.120	0.104
r42	0.120	0.128	0.136	0.136	0.072
r43	0.104	0.240	0.120	0.168	0.152
r44	0.104	0.112	0.224	0.272	0.256
Expectation results of test set output	0.000	0.100	0.070	0.070	0.100
	0.250	0.250	0.300	0.300	0.200
	0.300	0.250	0.430	0.430	0.430
	0.430	0.400	0.300	0.230	0.300
	0.150	0.400	0.150	0.200	0.250
Evaluation results of FBLS network	0.0940	−0.0333	−0.0771	−0.1078	0.0545
	0.2905	0.2313	0.2864	0.2465	0.2473
	0.2711	0.2298	0.4247	0.4150	0.4253
	0.4217	0.4450	0.2193	0.2727	0.2871
	0.2214	0.2251	0.1567	0.1300	0.1672

. The smaller the error of the maximum membership degree, the stronger the predictive evaluation ability of the model. In summary, it can be seen that the FBLS network model can effectively generalize knowledge and provide reasonable results for unknown input samples after learning the training samples.

To further verify the effectiveness and reliability of the proposed method in the ship fire risk evaluation, it was compared with the fuzzy support vector machine (FSVM) and fuzzy BP neural network. The standard deviation and penalty coefficient of SVM are set to 4 and 0.8, the training target minimum error of BP neural network is set to 1 × 10⁻⁵, the number of implicit layer nodes is set to 50, the learning rate is set to 0.01, and the iteration number is set to 1000. The predicted evaluation results are shown in Figure 9 and Figure 10. The FBPNN training error curve achieves a training accuracy of 1 × 10⁻⁷ after eight iterations, and the global error meets the requirements of the set value. The training error curve is shown in Figure 11.

As shown in Figure 12, the evaluation results of the FBLS, FSVM, and FBPNN are compared with the MAE, MSE, and RMSE. The errors of each evaluation result are shown in

Table 7. Error values of SVM, VPNN, and FBLS.

Model	Mean Absolute Error (MAE)	Mean Squared Error (MSE)	Root-Mean-Squared Error (RMSE)
FSVM	0.0268	0.0015	0.0386
FBPNN	0.0389	0.0021	0.0428
FBLS	0.0156	0.0005	0.0218

. The evaluation results of the FBLS network model and the expected values of the test set are better than the other two models, indicating that the simulation evaluation accuracy of this model is high, and proving that the proposed FBLS network model can meet the requirements of ship fire risk evaluation.

5. Risk Evaluation of Actual Cases of Ship Fires

5.1. Case Overview

On 22 July 2020, the “Fujian Fuzhou Oil 0010” vessel caught fire during the process of receiving oily wastewater of the “Fenghai 16” vessel at the outfitting dock water area of Mawei Shipyard (approximately 25°59.5′ N, 119°26.4′ E), resulting in the death of one person on board and constituting a general level of water traffic accident.

5.2. Safety Degree Evaluation Based on FBLS Network

In this accident investigation report, seven evaluation indicators, including ship information, ship condition, personnel situation, environmental factors, management factors, pollution situation, and site investigation situation, are given, respectively, in which the good or bad situation of each indicator is detailed. Based on the accident report, a score was given according to the evaluation indicator table in this article, and the accident was evaluated using the ship fire risk evaluation of the FBLS prediction model. The evaluation matrix is (

Table 8. Score table of ship fire risk evaluation indicators.

Index	Best	Better	Fair	Poor	Very Poor
Number and distribution of personnel	0	0	0.5	0.5	0
Fire safety awareness	0	0	0	0.4	0.6
Ability to seek refuge and self-rescue	0	0.2	0.5	0.2	0.1
Fire emergency drill	0	0.1	0.4	0.4	0.1
Electrical equipment failure	0	0.4	0.4	0.2	0
Line fault	0	0.25	0.5	0.25	0
Careless use of fire	0	0	0.6	0.4	0
Number and width of fire escape	0	0.2	0.6	0.2	0
Integrity of smoke exhaust facility	0	0.2	0.6	0.2	0
Automatic alarm system	0	0	0.5	0.3	0.2
Flame retardant facility system	0	0.3	0.4	0.3	0
Proficiency in firefighting facility	0	0	0.3	0.4	0.3
Fire protection knowledge and skill	0	0	0.2	0.3	0.5
Organizational skill	0	0.1	0.4	0.4	0.1
Regular maintenance situation	0.2	0.4	0.4	0	0

):

The evaluation matrix input to the fuzzy system after simplification will result in the actual input to the FBLS network:

Input = [0.16 0.072 0.184 0.16 0.216 0.2 0.168 0.2 0.2 0.144 0.2 0.12 0.096 0.16 0.264]

Upon running the model, the output unit of the model is the risk probability level of the accident:

Output = [−0.0303 0.3408 0.4136 0.2699 0.1617]

According to the principle of maximum membership, the fire risk level of the accident can be determined as level 3. Due to the death of one crew member caused by this accident, the consequence level is therefore level 4, and the final accident risk indicator is 12, indicating that the accident can be classified as a general level accident. This result is consistent with the level given in the accident investigation report issued by the Maritime Bureau Administration, proving that the model can effectively evaluate the fire risk level, making the results more practical.

In the field of ship fire risk assessment, many researchers have used various assessment tools to assess the probability of the occurrence of ship fire risk, and all of them can provide more reasonable risk levels when assessing the risk of actual cases; while this study introduces a risk matrix combining the probability of occurrence and the consequence level given the risk level, and proves the feasibility of this assessment method in reverse.

5.3. Measures to Deal with the Risk of Fire in an Actual Case

Regarding the accident report, it is presumed that the direct cause of the accident was that the vessel “Fujian Fuzhou Oil 0010” received naphtha-containing wash water from the vessel “Fenghai 16” when the operating compartment did not have safe operation requirements, and the volatilization of naphtha contained in the wash water caused a fire in the forward deck area of the bridge of the vessel “Min Fuzhou Oil 0010”. The naphtha volatilized in the bilge water and accumulated in the deck area in front of the bridge of the vessel “Min Fuzhou Oil 0010” and reached the flash ignition limit, which caused a fire in case of open flame and high heat. Indirectly, the fire was caused by the ship’s operation personnel, who did not have professional fire-fighting skills and operated in violation of regulations. The measures to deal with the risks according to the importance level of risk factors influence are as follows:

(1)

The ship should inspect the site before carrying out receiving and discharging operations, and should not blindly carry out operations if the operating compartment does not have safe operation requirements.

(2)

When the receiving operation is carried out, the channel door shall be opened to access the discharge pipe and the hatch shall be closed according to the requirements to meet the requirements needed for the operation.

(3)

Improve the management system, strengthen the management level of the crew, improve the overall team’s business quality, as well as the firefighting technology, and the safety awareness of the crew to ensure the safety of personnel and eliminate ship accidents.

6. Conclusions

Considering the lack of risk evaluation systems in the field of ship fire prevention, a more reasonable ship fire evaluation indicator system has been proposed by combining multiple methods. After screening, the indicator system retains a complete evaluation indicator system, including four primary indicators and fifteen secondary indicators. Based on this, a ship fire risk evaluation model based on FBLS network was established. The model randomly initializes weights and adjusts them through its adaptive function, avoiding the subjective influence of human factors. Additionally, the model was applied to the accuracy testing of actual cases, and the results showed that the predicted evaluation results of the model had the smallest error compared to the output results of the test set, and the convergence speed was fast and the operation was simple, overcoming the shortcomings of the ordinary single neural network evaluation method in terms of computational complexity and low efficiency. With regard to the application of scientific principles and technologies to the field of ship fire risk evaluation, the proposed model has a high accuracy, small human factors, and a simple operation, providing a reference for ship fire risk evaluation. In generally, the study of ship fire risk level evaluation by the FBLS method is still experimental. The complementary features of the fuzzy system and width learning system deals with the problem of the uncertainty of events and incomplete data in ship fire accident risk evaluation. Future work will concentrate on the consideration of real-time fires risk monitoring, using dynamic network monitoring and facility layout based on real-time risk results to optimize real-time fire risks. There remains some shortcomings for improvement in the research on this issue; however, due to personal inexperience and other problems, some details may still be poorly considered, and the ship itself is relatively complex and involves a large number of influencing factors. The construction of the system of evaluation indexes is the basis of the whole ship fire accident risk evaluation. Although the influencing factors of ship fire accident risk are screened and determined by studying the literature and with the help of expert judgment, it is impossible to consider all possible situations in this paper. We also have to be flexible toward certain special situations that appear in the actual operation of ships to further improve and update this research.