Fuzzy Evaluation of Inland Ship Lock Service Condition Based on Combination Weighting and Matter-Element Extension Cloud Model

Abstract

Ship lock as a typical hydraulic structure has become an important node in waterway transportation. Due to the long operating life and high demand of throughput, many locks are under the overloaded operation situation. However, the service condition assessment of ship locks has rarely been directly studied, and there is a lack of an efficient and standardized method owing to the complex structure of the ship lock system. In this paper, a multi-level hierarchical system including 36 indexes was constructed based on the engineering breakdown structure theory. The synthetic weights of indexes were determined by the order relation method and entropy weight method combining subjectivity and objectivity. The extension cloud model combining the extension theory and cloud model was put forward, aiming to deal with the uncertainty of fuzziness and randomness in the evaluation process. Then, two typical locks were investigated, and the numerical scores indicated that their states belong to Level III and Level IV, respectively. The proposed method reveals the structural condition and provides theoretical reference for the maintenance of ship locks, which can be applied with generalizability and operability.

1. Introduction

The waterway network has the obvious advantages of large freight volume, low cost, and low pollution [1], which has brought great benefits to the development of the social economy. Hydraulic buildings have become an indispensable large infrastructure system to form the waterway network and promote development of shipping. As a typical hydraulic structure, ship lock has become an important node in the inland waterway transportation network that plays a vital role in the safe operation of shipping. The construction of ship lock is often accompanied by large-scale investment and the consumption of a large number of resources, while damage and aging problems occur with the expanse of service life and lack of maintenance [2], which affect effectiveness and become a security risk for major problems. Maintaining and tracking the service condition of ship lock can be instrumental in realizing the whole life-cycle management of infrastructure performance under uncertainty. It is of great significance in promoting the healthy and sustainable development of facility operation and ensuring investment benefits. Ship locks are long-term infrastructure assets with a great possibility of risk. Due to their long operating life and degradation, many of the lock systems are in need of repair [3]. It is likely to lead to unscheduled delay and even the interruption of the lock, followed by huge losses if maintenance of the ship lock is ignored. Twenty-six years ago, the United States Army Corps of Engineers (USACE) found from their studies that the economic cost of a delay was about USD 300–400 per hours, based on a 15-barge tow pushed by a 2200–4400 horsepower towboat [2]. It can be seen that the losses that incurred many years ago are so huge that they are even more incalculable today.

Since the 1930s and 1970s were the prosperous periods for the construction of hydraulic structures in the world, this means that some of these structures are now nearly 100 years old [4]. The water conservancy projects that were built made great contributions to the national economy and the people’s livelihood. However, the structures are so old that their safety performances are unable to be guaranteed. Due to the changing environment and aging, condition assessment of the structures is becoming increasingly important for their safety [5]. The emerging safety issues may lead to potential accidents and further cause adverse impacts on life. If the misbehaviors are not detected and resolved in time, they will cause huge losses and shipping inconvenience. The efficiency of the inland waterway and locks face enormous challenges, such as Saint Lawrence Seaway [6], Panama Canal [7], Antwerp Kieldrecht lock, and Beijing-Hangzhou Grand Canal [8], due to their busy traffic conditions. Therefore, it is urgent to carry out monitoring and evaluation activities to sustain and enhance the beneficial economic impacts of the locks. In order to find out the dangerous position of ship lock in time and prevent possible accidents, timely monitoring, assessment, and maintenance of ship locks is required. The Beijing-Hangzhou Grand Canal runs through the Jiangsu Province from north to south. The waterway of the Grand Canal in northern Jiangsu is called the Subei canal. There are 11 steps in the canal, with a total of 28 ship locks. With the continuous development of large-scale ships and the shipping industry, most ship locks are expanding in scale. Due to the comprehensive effect of external factors during the operation of the ship lock facility system, the shape and size of large-scale leads to the change of material properties in the structure [9]. The health performance gradually decreases over time. The actual throughput of most ship locks of the Subei canal exceeds the design throughput, resulting in overload operation for a long time. Therefore, it is of great significance to carry out efficient life-cycle management for the ship locks on the Subei canal and to assess the structural conditions.

Foreign countries pay more attention to the safety research of ship locks and have achieved many results in the research of aging diseases and reliability of hydraulic structures. The research focus shifted from the mechanism of disease and the repair method of dangerous parts to the detection and evaluation of structural members, and then developed to the research of evaluation standards. With the improvement of risk prevention awareness in the field of ship locks, some studies have revealed the necessity of evaluating ship locks to promote life-cycle management [10]. The assessment of ship lock can be summarized into two aspects: (1) Most research focused on analyzing or evaluating the technical status of a single structure, such as lock gate fatigue, damage, seals, or strength evaluation [11,12,13,14,15]. (2) Other researchers analyzed or evaluated the shipping benefits of the entire ship lock to achieve the purpose of optimization, including relieving congestion and optimizing scheduling to improve capacity [16,17,18,19]. Few studies evaluated the service condition of the ship lock from the perspective of the ship lock system and overall function. Therefore, the comprehensive evaluation method has not been formed and there is a lack of an index system that can reflect the abstractness of the evaluation index of ship lock service condition and the fuzziness of the evaluation grade classification.

In order to characterize the degree of the certain properties of the objects, the commonly used methods mainly include the fuzzy mathematics method [20,21,22] and extension method [23,24,25]. Compared with the former, the extension method fully considers the relationship between the evaluation object, index, and index range. It can effectively clarify the incompatibility and qualitative and quantitative coexistence between various indicators. On the other hand, the cloud model as a cognitive model can simultaneously describe the fuzziness, randomness, and discreteness of concepts and implement the uncertain transformation between qualitative concepts and quantitative description [26,27]. Thus, the combination of extension theory and cloud model can realize the reasonable transformation of quantity and quality. Rare investigations are devoted to modelling both fuzziness and randomness in the ship lock system for routine general inspection. In this regard, this paper proposes a service condition evaluation method of ship lock based on an extension cloud model to take both fuzziness and randomness into consideration.

The service condition evaluation of ship lock is conducive to auxiliary information decision-making. The uncertainty in the operation of the ship lock is specific to each component of the system. Diversified data sources screen, extract, and locate the hidden parts of danger, so as to determine the quality of service status. The decision-makers can thus quickly and accurately carry out the safety appraisal and specify the risk elimination and reinforcement scheme. The approach realizes the continuous assessment, which can present the general trend of the ship lock service condition and prevent the severe consequences that happen during the operation and maintenance stages. It is applicable to ship locks on inland rivers, but it also has certain reference significance for the evaluation criteria of offshore navigation buildings. It will provide a theoretical support for the maintenance of ship locks.

2. Materials and Methods

2.1. Analysis of the Service Status Evaluation Factors

Large and complex engineering project management should first analyze the structure and the characteristics of the engineering system, and further take the structural decomposition of the engineering system as the basis of project planning control. Referring to the project breakdown structure (PBS) and work breakdown structure (WBS) [28] commonly used in construction projects, Cheng and Cheng [29] proposed the engineering breakdown structure (EBS). EBS decomposes the system into various engineering subsystems based on function analysis, and can be viewed as the basis and premise of WBS. Figure 1 indicates the principle of EBS. Firstly, the functional areas are decomposed by dividing the space of buildings from the perspective of function. The second layer is divided into engineering systems according to professional characteristics in each functional area. It can provide a reference for engineering management based on the regularity of the function of the entity structure for similar engineering systems.

The ship locks belonging to the hydraulic structure have a number of systems to support function implementation. Using EBS is an effective approach to accomplish the ship locks’ operation in the life-cycle management process. On this basis, the function systems are divided into independent project units in sequence of decomposition from the perspective of engineering. The elements are extracted from different subsystems of ship locks, such as hydraulic construction, metal structure, hydraulic pressure system, electrical system, and hydraulic characteristics. They possess different configurations along with fault characteristics and service status. The operations of these subsystems realize the abstracted service functions, including water retaining and supervision function together with the navigation and berthing function. During the operation of the ship lock, the service functions are implemented by interaction between the subsystems, which can be observed directly from the fixed physical structure. Therefore, exploring the subsystems of ship locks and analyzing the technological indexes by EBS contribute to mapping relationships with service functions.

According to relevant research and field investigations, an evaluation indexes set can be proposed according to service functions and the related physical structure. Based on previous research experience [30], the multi-indexes system has been improved. From the view of space division, the functional areas of the ship lock system are decomposed into water retaining function, berthing function, navigation function, and supervision function. The supporting structures of each function are then defined, more specifically as the gate metal structure, gate valve open-close, and the electrical system, which can determine the water retaining function, and the berthing function is decided by the lock chamber structure. Similarly, the navigation function is directly related to the state of the approach channel and the supervision function is mainly concentrated in the office area. According to the corresponding technical indicators included in each professional structure, the index system is formed. Different from the previous index set, some indicators have been integrated or deleted to promote optimization of the indicator system. For instance, the equipment aging index and the failure rate of components index, which have been integrated since they are relevant and inseparable, both reflect function loss in the later stage of equipment operation. The indexes of filling and emptying time are removed because they can be embodied from the other indexes, such as piston rod deformation, operating speed, and hoisting capacity related to the valve opening and closing. The energy dissipation effect index has been deleted because it can be reflected by the fluctuation of approach channels. Finally, the complete level index set of the service condition of the ship lock is presented in Figure 2.

2.2. Service Condition Level Gradation

Failure or incomplete functioning of each indicator implies risk during the service process. This assessment of risk is the determination of the quantitative or qualitative value of risk related to a concrete situation and a recognized hazard [31]. Several specifications or standards regarding the evaluation indicators of the ship locks have been put forward by numerous monitoring tests and experimental studies. Grading the indicators and quantifying their service status is favorable to the final assessment of ship lock service condition. According to guiding documents, such as ‘Technical code for maintenance of navigable buildings (JTS 320-2-2018)’ and ‘Technical code for inspection and evaluation of hydraulic structures in water transportation engineering (JTS 304-2019)’, the sluices are classified as four grades. With reference to these standards, the service status of the ship lock structural components can subsequently be quantitatively classified into four equidistant intervals [32,33,34]. The specific meaning of each service status level is elucidated in

Table 1. The description of the service condition levels.

Level	Definition	Description
I	Dangerous	Major structural components are unsafety, resulting in the totally failure of the ship lock operation.
II	Fatigue	The structure cannot satisfy the requirement of normal serviceability. Some structural components are unsafety, leading to partially endangered building system.
III	Sub-health	The structure can generally satisfy the requirement of normal serviceability. Some defects exist in the service condition of ship lock and danger hides.
IV	Health	The structure can totally satisfy the requirement of normal serviceability. It is safe and reliable without any serious defects or dangerous indicators.

.

2.3. Quantification and Gradation of Indicators

The quantification of each indicator and taking the specific values of indicators into the corresponding rank intervals is very complicated. Since there are 36 indicators in the evaluation system, the quantification of every indicator could occupy a large space. The indicators can be distinguished qualitatively and quantitatively [25,35]. By combining qualitative and quantitative indicators, the service state of indicators is divided into four intervals. Through establishing relationships between the indicators’ values with the unified intervals, this is instrumental to the construction of the multi-index evaluation system. The qualitative indicators can be assessed by means of specific conditions and quantitative indicators can fall into the range according to concrete values.

(1) The qualitative indicator of A12 (Deformation) is taken as an example. The deformation of the lock gate is attributed to the impact of water flow and ships along with incorrect maintenance during the operation of the ship lock. The degree of the service condition can be judged by observing the deformation of the gate plate on site. The scoring criteria are as follows [36,37]: (a) Level I: If the lock gate has severe deformity or damage, the score of deformation can be selected from [0, 25), (b) Level II: If the lock gate has medium deformity or damage, the score of deformation can be selected from [25, 50), (c) Level III: If the lock gate has slight deformity or damage, the score of deformation can be selected from [50, 75), and (d) Level IV: If the lock gate has no deformity or damage, the score of deformation can be selected from [75, 100].

(2) The quantitative indicator A25 (Hoisting capacity of gate) is taken as an example. According to the ratio between the detection result of gate hoisting force and the designed value, the service status and corresponding scoring rules are as follows [38]: (a) if $A25\in [0,0.18)$, the service state is judged as level I. (b) The condition will be regarded as Level II if $A25\in [0.18,0.62)$. (c) If $A25\in [0.62,0.78)$, the index state belongs to the rank of Level III. (d) If $A25\in [0.78,1]$, the condition of the index can be viewed as Level IV.

On the other hand, the value range of the indicators decides whether to continue through the evaluation process. If the value of index exceeds the defined interval range, this indicates that the indicator is in a sudden situation with danger. At this time, the whole ship lock system automatically judges it as Level I with extreme risk, and no further evaluation process is needed. In index A25, for instance, if the ratio exceeds 1, this indicates that it is in the limit state of overload operation. If an emergency occurs to the ship lock or the ships in the lock operation have an uncontrolled situation, such as a sudden failure of the propulsion system [39] or auxiliary power plant, the ship lock suddenly fails to operate normally. The entire evaluation process will stop, and the results of the evaluation of the service condition of the inland river ship locks will be Level I, which indicates danger.

2.4. Weight Assignment of Indicators

2.4.1. Subjective Weight by Order Relation Method

The order relation method is a widely used subjective weighting method that avoids overcomplicated calculation. It can reflect the order relationship between indicators and arrange them according to certain principles without the consistency test process. The order relation method is described as follows [40]:

(1) For the evaluation criteria set $(x_1,x_2,\dots ,x_m)$, the most important indicator is chosen and marked as $x_1{}^{*}$; Then, choose the most important indicator in the retaining (m − 1) indicators and mark as $x_2{}^{*}$; The process will be repeated (m − 1) times until the indicator is marked as $x_m{}^{*}$. Finally, the order nation can be expressed as:

$$x_1{}^{*}>x_2{}^{*}>\dots >x_m{}^{*}(or{x}_1>x_2>\dots >x_m)$$

(1)

(2) It is assumed that the important degree ratio $w_{k-1}/w_k$ of the evaluation index $x_{k-1}$ and $x_k$ can be judged rationally, valued as $r_k=w_{k-1}/w_k$, $k=m,m-1,\dots ,2$.

(3) The corresponding weight $w_k$ of the evaluation index $x_k$ can be calculated by Equation (2):

$$w_k={(1+{\displaystyle {\sum }_{k=2}^m{\displaystyle {\prod }_{j=k}^m{r}_k}})}^{-1}$$

(2)

In the equation, the value range of $r_k$ can be referred to Wang, et al. [41] and Ma, Lyu and Zhang [36]. The subjective weight value of each indicator ($w_{subjective}$) can be calculated according to the $r_k$ of the adjacent indicators.

2.4.2. Objective Weight by Entropy Weight Method

Entropy was used to describe the irreversible phenomenon of the movement course at first, and gradually expressed the uncertainty of parameters in information theory [42]. The entropy weight method (EWM) is a widely used weighting method in assessment and it assigns weights on the basis of the dipartite degree principle [43].

It is assumed that there are $n$ items to be evaluated and they are refined into $m$ indicators. The observation data vector of the $jth$ indicator is denoted as $x_j=\{x_{1j},x_{2j},\dots ,x_i{}_j,\dots ,x_{nj}\}$, and $x_i{}_j$ is the monitoring value of the $jth$ indicator in the $i_{th}$ item. The normalization process is indispensable because of the different dimensions of the indicators. The observation data vector $x_j$ is converted into a normalized data vector $p_j=\{p_{1j},p_{2j},\dots ,p_i{}_j,\dots ,p_{nj}\}$:

$$p_i{}_j=\frac{x_{ij}}{{\displaystyle {\sum }_{i=1}^n{x}_{ij}}}$$

(3)

In the EWM, the entropy value $E_i$ of the $i_{th}$ indicator is defined as [44]:

$$E_i=\frac{{\displaystyle {\sum }_{j=1}^n{p}_{ij}\cdot \ln p_{ij}}}{\ln n}$$

(4)

When $p_i{}_j=0$, the value of $p_i{}_j\cdot \ln p_{ij}$ equals to 0.

The value range of $E_i$ is [0, 1]. A smaller $E_i$ indicates a higher indicator’s dipartite degree, hence, the efficiency information provided by the indicator is more and the weight should be larger. Finally, the calculation method of weight $w_i$ can be expressed as Equation (5) and the objective weight ($w_{objective}$) can be obtained.

$$w_i=\frac{1-E_i}{{\displaystyle {\sum }_{i=1}^m(1-E_i)}}$$

(5)

2.4.3. Objective Weight by Entropy Weight Method

In order to effectively reflect the subjective and objective information and make the weight assignment more illustrative, the comprehensive integration weighting method combining the order relation method and EWM were adopted [41]. The weights of the indicators were decided by the additive integration method and the formula was as follows:

$$w_i=\alpha w_{subjective}+(1-\alpha )w_{objective}(0\le \alpha \le 1)$$

(6)

The value of $\alpha$ was taken as 0.5 [35,36] in this paper, which meant the subjectivity and objective factors both have equal weight, and the combined weights of indicators are presented in

Table 2. Multi-indexes system of service condition of ship locks.

Service Functions	Physical Structures	Characteristics	Unit	${\mathit{w}}_{\mathit{s}\mathit{u}\mathit{b}\mathit{j}\mathit{e}\mathit{c}\mathit{t}\mathit{i}\mathit{v}\mathit{e}}$	${\mathit{w}}_{\mathit{o}\mathit{b}\mathit{j}\mathit{e}\mathit{c}\mathit{t}\mathit{i}\mathit{v}\mathit{e}}$	${\mathit{w}}_{\mathit{i}}$
A. Water Retaining Function	A1. Gate metal structure	A11. Run-out	mm	0.0135	0.0163	0.0149
		A12. Deformation	Score	0.0306	0.0437	0.0371
		A13. Crack	Score	0.0202	0.0423	0.0313
		A14. Abrasion	Score	0.0090	0.0204	0.0147
		A15. Vibration	Score	0.0060	0.0386	0.0223
		A16. Drift	mm	0.0040	0.0155	0.0098
		A17. Seal	Score	0.0027	0.0360	0.0194
		A18. Gate thickness	mm/mm	0.0691	0.0187	0.0439
		A19. Centering	mm	0.0456	0.0190	0.0323
	A2. Gate valve open-close	A21. Systematic pressure	kN/kN	0.0301	0.0177	0.0239
		A22. Operating speed	Unit = 1	0.0201	0.0170	0.0186
		A23. Piston rod deformation	Score	0.0452	0.0315	0.0384
		A24. Oil quality	Score	0.0027	0.0333	0.0180
		A25. Hoisting capacity of gate	Mpa/Mpa	0.0136	0.0184	0.0160
		A26. Hoisting capacity of valve	Mpa/Mpa	0.0090	0.0393	0.0241
		A27. Leakage of gate valve	Score	0.0061	0.0140	0.0100
		A28. Pipeline aging	Score	0.0040	0.0334	0.0187
		A29. Synchronism	s	0.0018	0.0509	0.0264
	A3. Electrical system	A31. Aging and failure	Score	0.0335	0.0348	0.0342
		A32. Power supply	Score	0.0223	0.0211	0.0217
		A33. Grounding	unit = 1	0.0101	0.0325	0.0213
		A34. Term stability	Score	0.0149	0.0245	0.0197
		A35. Insulation	unit = 1	0.0070	0.0398	0.0234
B. Berthing Function	B1. Lock chamber structure	B11. Deformation of lock wall	mm	0.0658	0.0513	0.0585
		B12. Lock wall rack	unit = 1	0.0442	0.0375	0.0409
		B13. Spoilage of chamber	Score	0.0296	0.0208	0.0252
		B14. Seepage of chamber	Score	0.0198	0.0187	0.0193
		B15. Carbonization of lock wall	mm	0.0135	0.0330	0.0232
		B16. Lock wall intensity	Mpa/Mpa	0.0092	0.0266	0.0179
C. Navigation Function	C1. Approach channel status	C11. Deposition of approach channels	Score	0.1299	0.0283	0.0791
		C12. Fluctuation of approach channels	m	0.0872	0.0150	0.0511
		C13. Flow regime of approach channels	Score	0.0596	0.0352	0.0474
D. Supervision Function	D1. Office area	D11. Video surveillance	Score	0.0226	0.0172	0.0199
		D12. Communication system stability	Score	0.0333	0.0151	0.0242
		D13. Navigation signal	unit = 1	0.0151	0.0175	0.0163
		D14. operation scheduling management	Score	0.0490	0.0251	0.0371

.

2.5. Construction of an Extension Cloud Evaluation Model

The cloud model has been used in various fields, such as intelligent control, decision making, and data mining. It is also often successfully used in the evaluation field, which verifies the effect of the cloud model in practical applications. This paper improves the matter-element extension cloud model to better assess ship lock performance.

2.5.1. Cloud Model of Evaluation Factors

There are three approaches to performing the reasonable transformation between qualitative concepts and quantitative values, including cantor set, fuzzy set, and extension set [45]. Only the extension set with a range of $(-\infty ,+\infty )$ allows for solving contradictory problems which cannot be handled by the cantor set or fuzzy set. In extension theory, matter elements can be defined as three fundamental aspects, that is, $R=(N,C,V)$, where $N$ is the matter name, $C$ means the matter characteristics, and $V$ is the values of the matter characteristics. The classical domain matter element matrix is composed of the matter characteristics and the range of standard values. The classical domain matter element can be defined as [46]:

$$R_0=(N_j,C_i,V_{ij})=\left[\begin{array}{ccc}\begin{array}{c}{N}_j\\ \\ \\ \end{array}& \begin{array}{c}{C}_1\\ C_2\\ \dots \\ C_n\end{array}& \begin{array}{c}{v}_{j1}\\ v_{j2}\\ \dots \\ v_{jn}\end{array}\end{array}\right]=\left[\begin{array}{ccc}\begin{array}{c}{N}_j\\ \\ \\ \end{array}& \begin{array}{c}{C}_1\\ C_2\\ \dots \\ C_n\end{array}& \begin{array}{c}<a_{j1},b_{j1}>\\ <a_{j2},b_{j2}>\\ \dots \\ <a_{jn},b_{jn}>\end{array}\end{array}\right]$$

(7)

In the equation, $N_j$ represents the divided $j$ evaluation grades and $C_i$ means the $i_{th}$ evaluation indicator. $v_{ij}=<a_{ji},b_{ji}>$ indicates a range of classical intervals by $N_j$ with the respect of $C_i$; It is the value range of each evaluation grade of the matter element that is to be evaluated. Matter element extension evaluation firstly calculated the coincidence level between the measuring indicator and the demanding of the research object by the correlation function, that is, establishing the correlation degree, and then decided the relative importance of each indicator, which means determining the weight coefficient according to the principle of maximum correlation degree, and selecting the result corresponding to the optimal values in the comprehensive correlation as the final evaluation outcome.

The cloud model was proposed to represent the fuzziness and randomness of things. It is an uncertain transformation model from qualitative to quantitative based on fuzzy theory and probability theory [47]. The cloud model has three digital features to express qualitative concepts, such as expectation ($E_x$), entropy ($E_n$) and hyper-entropy ($H_e$). The expected value ($E_x$) represents the center value of the membership cloud, which reflects the service condition classification grade; $E_n$ is the measure of uncertainty, a larger $E_n$ means the more ambiguous the qualitative concept is; $H_e$ is the hyper-entropy, which reflects the uncertainty measurement of entropy and the discrete degree of cloud [48]. For dealing with the uncertainty of fuzziness and the randomness of the evaluation process, the extension cloud model that combines extension theory and the cloud model was set up. The $v_{ij}=<a_{ji},b_{ji}>$ of extension theory was replaced by the normal cloud model $(E_x,E_n,H_e)$ as follows:

$$R_0=(N_j,C_i,V_{ij})=\left[\begin{array}{ccc}\begin{array}{c}{N}_j\\ \\ \\ \end{array}& \begin{array}{c}{C}_1\\ C_2\\ \dots \\ C_n\end{array}& \begin{array}{c}{v}_{j1}\\ v_{j2}\\ \dots \\ v_{jn}\end{array}\end{array}\right]=\left[\begin{array}{ccc}\begin{array}{c}{N}_j\\ \\ \\ \end{array}& \begin{array}{c}{C}_1\\ C_2\\ \dots \\ C_n\end{array}& \begin{array}{c}(E_{x1},E_{n1},H_{e1})\\ (E_{x2},E_{n2},H_{e2})\\ \dots \\ (E_{xn},E_{nn},H_{en})\end{array}\end{array}\right]$$

(8)

Specific values of the limit interval $<a_{ji},b_{ji}>$ can be obtained by the threshold classification of evaluating the service condition of ship locks. The cloud parameters can be calculated by Equations (9)–(11):

$$E_x=\frac{a_{ji}+b_{ji}}{2}$$

(9)

$$E_n=\frac{b_{ji}-a_{ji}}{6}$$

(10)

$$H_e=s$$

(11)

While $s$ is a constant, which can be adjusted by the estimation of the decision-maker according to the uncertainties of corresponding evaluation objects existing in actual conditions. In this research, it is defined as a constant equal to 0.001.

2.5.2. Correlation Calculation

The membership degree between the matter element to be evaluated and the matter element represented by the cloud model can be determined by the cloud certainty degree of the corresponding value. Based on the cloud model forward generator, the steps of calculating the correlation degree are as follows:

(1) Generate a normal random number $E_n{}^{\prime }$ with $E_n$ as the expectation and $H_e$ as the variance;

(2) Generate the normal random number $x_i$ with $E_x$ as the expectation and $E_n{}^{\prime }$ as the variance, and thus the cloud droplets $(x_i,{\mu }_k(x_i))$ can be formed;

(3) Calculate the membership degree of each grade corresponding to cloud droplets by Equation (12):

$${\mu }_k(x_i)=\exp \left[-\frac{{(x_i-E_x)}^2}{2{(E_n{}^{\prime })}^2}\right]$$

(12)

(4) Repeat the above steps n times with the average of all results as the final membership value. In an effort to satisfy the demand for real-time data processing and analysis, the value of $n$ is chosen to be 1000 in practical applications.

2.5.3. Evaluation Results

The comprehensive evaluation vector $D$ of the service state of inland river ship lock can be decided based on the weight matrix $W$ and correlation matrix $Z$ by Equation (13). The rating was estimated following the principle of maximum membership.

$$D=WZ=(d_1,d_2,d_3,d_4)$$

(13)

In the process of calculating cloud correlation degree, the determination of the core value of hyper-entropy ($H_e$) and normal random numbers $E_n{}^{\prime }$ and $x_i$ have key impacts on the evaluation results and have strong randomness. To reduce the influence of randomness on the accuracy of evaluation results, it is necessary to repeatedly calculate in order to obtain the comprehensive evaluation characteristic expectation denoted by $E_{rx}$ and standard deviation denoted by $E_{rn}$. The two values can be calculated by Equations (14) and (15).

$$Erx=\frac{{\displaystyle {\sum }_{i=1}^n{r}_i(x)}}{n}$$

(14)

$$E_{rn}=\sqrt{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{\left[r_i(x)-E_{rx}\right]}^2}}$$

(15)

where $r_i(x)$ means the comprehensive evaluation results in the $ith$ calculation, and $n$, which is taken as 1000, represents the number of repeated calculations.

The confidence level factor $\phi$ is put forward to measure the reliability of the evaluation result. $\phi$ is zero when the evaluation result is perfectly reliable. The closer the value of $\phi$ when it approaches zero, the smaller the dispersion and the more significant the predominant tendency of the evaluation results [25]. It can be calculated by Equation (16):

$$\phi =\frac{E_{rn}}{E_{rx}}$$

(16)

According to the principle of the extension cloud model and the evaluation process, the flow chart of the comprehensive evaluation for the service condition of inland river ship locks is shown in Figure 3.

3. Results

Subei Canal is the busiest segment of the Grand Canal and has the best comprehensive benefit, except for the Yangtze River. Heavy traffic demand increased pressure on the ship lock, and many new locks have been built to alleviate the blockage of ship traffic flow. Liulaojian locks and Shiqiao locks are typical third-line locks. As a representative of the old ship lock, Liulaojian No. 2 ship lock (note as #1 lock) was built in 1987 and has been in service for 35 years. The average daily throughput of the Liulaojian lock was maintained at about 500,000 tons and the cumulative opening times reached 40,891 in 2020. On the other hand, the average daily throughput of the Shiqiao lock was more than 800,000 tons and the cumulative opening times reached 41,066 in 2020. The Shiqiao No. 3 ship lock (note as lock #2 lock) was put into operation in 2012 to relieve ship congestion and improve shipping efficiency. Hence, the critical state of strong working pressure leads to many ship lock challenges, and this overload increases uncertainty in the operation. It is meaningful to take measures to evaluate the technical state of these challenges and improve service condition. Through the quantification and gradation of indicators, the threshold range for service condition evaluation of indicators of inland river locks can be concluded in

Table 3. Threshold rating for service condition evaluation of inland river locks indicators.

Indexes	Value Range	Service Condition Level
		I	II	III	IV
A11. Run-out	[0, 6]	(4, 6]	(3, 4]	(2, 3]	[0, 2]
A12. Deformation	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
A13. Crack	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
A14. Abrasion	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
A15. Vibration	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
A16. Drift	[0, 300]	(200, 300]	(175, 200]	(150, 175]	[0, 150]
A17. Seal	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
A18. Gate thickness	[0, 2]	[0, 0.85)	[0.85, 0.9)	[0.9, 0.95)	[0.95, 2]
A19. Centering	[0, 60]	(40, 60]	(35, 40]	(30, 35]	[0, 30]
A21. Systematic pressure	[0, 1]	(0.075, 1]	(0.05, 0.075]	(0.02, 0.05]	[0, 0.02]
A22. Operating speed	[0, 1]	[0, 0.5)	[0.5, 0.7)	[0.7, 0.9)	[0.9, 1]
A23. Piston rod deformation	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
A24. Oil quality	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
A25. Hoisting capacity of gate	[0, 1]	[0, 0.18)	[0.18, 0.62)	[0.62, 0.78)	[0.78, 1]
A26. Hoisting capacity of valve	[0, 1]	[0, 0.18)	[0.18, 0.62)	[0.62, 0.78)	[0.78, 1]
A27. Leakage of gate valve	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
A28. Pipeline aging	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
A29. Synchronism	[0, 30]	[25, 30]	[15, 25)	[5, 15)	[0, 5)
A31. Aging and failure	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
A32. Power supply	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
A33. Grounding	[0, 1]	[0, 0.85)	[0.85, 0.9)	[0.9, 0.95)	[0.95, 1]
A34. Term stability	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
A35. Insulation	[0, 1]	[0, 0.85)	[0.85, 0.9)	[0.9, 0.95)	[0.95, 1]
B11. Deformation of lock wall	[0, 15]	(10, 15]	(8, 10]	(5, 8]	[0, 5]
B12. Lock wall crack	[0, 10]	(8, 10]	(5, 8]	(2, 5]	[0, 2]
B13. Spoilage of chamber	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
B14. Seepage of chamber	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
B15. Carbonization of lock wall	[0, 20]	[15, 20]	[10, 15)	[5, 10)	[0, 5)
B16. Lock wall intensity	[0, 2]	[0, 1)	[1, 1.2)	[1.2, 1.5)	[1.5, 2]
C11. Deposition of approach channels	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
C12. Fluctuation of approach channels	[0, 3]	(1.5, 3]	(1, 1.5]	(0.5, 1]	[0, 0.5]
C13. Flow regime of approach channels	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
D11. Video surveillance	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
D12. Communication system stability	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]
D13. navigation signal	[0, 1]	[0, 0.5)	[0.5, 0.75)	[0.75, 0.9)	[0.9, 1]
D14. operation scheduling management	[0, 100]	[0, 25)	[25, 50)	[50, 75)	[75, 100]

.

The 36 indicators are ranged into four intervals denoted as level I, II, III, and IV in terms of their values. Each indicator has its own value range, and if the measured data is out of the boundary, the service condition of the ship lock will be Level I. Correspondingly, each indicator can determine the evaluation status according to the measured value. For instance, A11 lies in the [0, 6] domain; if the runout of the evaluation object is seven, exceeding the range, the evaluation is suspended, and the service condition of the ship lock is considered to be dangerous. If it equals to three, the A11 index of the object belongs to Level III (sub-health). Through the interval threshold $<a_{ji},b_{ji}>$, the standard normal cloud model of each assessment index can be obtained according to Equations (9)–(11), through which 200 cloud droplets of each index were simulated. The indicator level cloud map can be drawn, as shown in Figure 4, by combining the extension cloud model generation algorithm and the indicators’ data. The figure takes the value of the evaluation indicator as the abscissa and the membership degree as the ordinate. The four clouds represent the standard connection cloud of the four grades, and the connection cloud is more superior on the assumption of indicator distribution.

To verify the reasonableness and feasibility of the method for service condition evaluation, ship locks #1 and #2 are taken as the examples. The data used in the case are all from detection of the ship locks in 2022. These data are brought into the model established for calculation. According to the comprehensive test result, the states of the indicators are within the threshold range. Then, the cloud parameters and membership matrix of the service condition evaluation system for #1 lock can be calculated.

Table 4. The membership degree of service condition level of #1 lock.

Indexes	Value	Weight	I	II	III	IV
A11. Run-out	0.815	0.0149	0.0000	0.0000	0.0000	0.8572
A12. Deformation	60.000	0.0371	0.0000	0.0000	0.8353	0.0000
A13. Crack	75.000	0.0313	0.0000	0.0000	0.0111	0.0111
A14. Abrasion	60.000	0.0147	0.0000	0.0000	0.8353	0.0000
A15. Vibration	70.000	0.0223	0.0000	0.0000	0.1979	0.0001
A16. Drift	80.000	0.0098	0.0000	0.0000	0.0000	0.9802
A17. Seal	50.000	0.0194	0.0000	0.0111	0.0111	0.0000
A18. Gate thickness	2.000	0.0439	0.0000	0.0000	0.0000	0.0111
A19. Centering	30.000	0.0323	0.0000	0.0000	0.0111	0.0111
A21. Systematic pressure	0.020	0.0239	0.0036	0.0000	0.0209	0.0325
A22. Operating speed	0.600	0.0186	0.0002	1.0000	0.0000	0.0000
A23. Piston rod deformation	75.000	0.0384	0.0000	0.0000	0.0111	0.0111
A24. Oil quality	75.000	0.0180	0.0000	0.0000	0.0111	0.0111
A25. Hoisting capacity of gate	0.700	0.0160	0.0000	0.0002	1.0000	0.0000
A26. Hoisting capacity of valve	0.700	0.0241	0.0000	0.0002	1.0000	0.0000
A27. Leakage of gate valve	50.000	0.0100	0.0000	0.0111	0.0111	0.0000
A28. Pipeline aging	70.000	0.0187	0.0000	0.0000	0.1979	0.0001
A29. Synchronism	10.000	0.0264	0.0000	0.0000	1.0000	0.0000
A31. Aging and failure	60.000	0.0342	0.0000	0.0000	0.8353	0.0000
A32.Power supply	75.000	0.0217	0.0000	0.0000	0.0111	0.0111
A33. Grounding	0.950	0.0213	0.0010	0.0000	0.0148	0.0151
A34. Term stability	75.000	0.0197	0.0000	0.0000	0.0111	0.0111
A35. Insulation	1.000	0.0234	0.0003	0.0000	0.0000	0.0152
B11. Deformation of lock wall	2.900	0.0585	0.0000	0.0000	0.0000	0.8912
B12. Lock wall crack	8.000	0.0409	0.0111	0.0111	0.0000	0.0000
B13. Spoilage of chamber	20.000	0.0252	0.1979	0.0001	0.0000	0.0000
B14. Seepage of chamber	45.000	0.0193	0.0000	0.1979	0.0001	0.0000
B15. Carbonization of lock wall	3.700	0.0232	0.0000	0.0000	0.0000	0.3545
B16. Lock wall intensity	1.300	0.0179	0.0000	0.0000	0.6062	0.0000
C11. Deposition of approach channels	75.000	0.0791	0.0000	0.0000	0.0111	0.0111
C12. Fluctuation of approach channels	0.400	0.0511	0.0000	0.0000	0.0002	0.1976
C13. Flow regime of approach channels	75.000	0.0474	0.0000	0.0000	0.0111	0.0111
D11. Video surveillance	80.000	0.0199	0.0000	0.0000	0.0001	0.1979
D12. Communication system stability	80.000	0.0242	0.0000	0.0000	0.0001	0.1979
D13. navigation signal	0.900	0.0163	0.0000	0.0000	0.0117	0.0118
D14. operation scheduling management	70.000	0.0371	0.0000	0.0000	0.1979	0.0001

shows the third-level evaluation indexes and the membership degree of the service condition level of #1 lock calculated by 1000 times. Subsequently, the comprehensive evaluation vector of the ship lock service condition can be worked out using Equation (13). $D=WZ=(0.0056,0.0232,0.1683,0.1070)$.

It can be seen that the maximum comprehensive cloud association degree is 0.1683, indicating that the grade of the service condition level of #1 lock is grade III. The indexes related to the chamber structure of #1 lock are mostly in the state of fatigue, and the long-term operation makes it unable to give full play to its role. The comprehensive evaluation characteristic expectation $E_{rx}$ is calculated based on Equation (14) with the values of 3.2382. The confidence level factor $\phi$ is accordingly obtained to be approaching zero, which indicates that the dispersion is small and that the result is reliable.

The status of indicators also follows the principle of maximum membership, so whether each indicator is in a healthy state can be obtained from the table. For #1 lock, the index B13 is subordinate to Level I, which means that it is in a dangerous state. The damage degree of the lock chamber is large, which seriously affects the safety of the lock operation. Similarly, the membership degree of the service condition level of #2lock is calculated by 1000 times (

Table 5. The membership degree of service condition level of #2 lock.

Indexes	Value	Weight	I	II	III	IV
A11. Run-out	3.000	0.0149	0.0000	0.0111	0.0111	0.0000
A12. Deformation	25.000	0.0371	0.0111	0.0111	0.0000	0.0000
A13. Crack	75.000	0.0313	0.0000	0.0000	0.0111	0.0111
A14. Abrasion	70.000	0.0147	0.0000	0.0000	0.1979	0.0001
A15. Vibration	70.000	0.0223	0.0000	0.0000	0.1979	0.0001
A16. Drift	80.000	0.0098	0.0000	0.0000	0.0000	0.9802
A17. Seal	70.000	0.0194	0.0000	0.0000	0.1979	0.0001
A18. Gate thickness	1.630	0.0439	0.0000	0.0000	0.0000	0.6754
A19. Centering	30.000	0.0323	0.0000	0.0000	0.0111	0.0111
A21. Systematic pressure	0.020	0.0239	0.0036	0.0000	0.0219	0.0315
A22. Operating speed	0.700	0.0186	0.0000	0.0114	0.0113	0.0000
A23. Piston rod deformation	75.000	0.0384	0.0000	0.0000	0.0111	0.0111
A24. Oil quality	30.000	0.0180	0.0001	0.1979	0.0000	0.0000
A25. Hoisting capacity of gate	0.700	0.0160	0.0000	0.0002	1.0000	0.0000
A26. Hoisting capacity of valve	0.700	0.0241	0.0000	0.0002	1.0000	0.0000
A27. Leakage of gate valve	40.000	0.0100	0.0000	0.8353	0.0000	0.0000
A28. Pipeline aging	70.000	0.0187	0.0000	0.0000	0.1979	0.0001
A29. Synchronism	20.000	0.0264	0.0000	1.0000	0.0000	0.0000
A31. Aging and failure	70.000	0.0342	0.0000	0.0000	0.1979	0.0001
A32. Power supply	75.000	0.0217	0.0000	0.0000	0.0111	0.0111
A33. Grounding	1.000	0.0213	0.0003	0.0000	0.0000	0.0155
A34. Term stability	75.000	0.0197	0.0000	0.0000	0.0111	0.0111
A35. Insulation	1.000	0.0234	0.0003	0.0000	0.0000	0.0158
B11. Deformation of lock wall	1.900	0.0585	0.0000	0.0000	0.0000	0.7717
B12. Lock wall crack	0.000	0.0409	0.0000	0.0000	0.0000	0.0111
B13. Spoilage of chamber	40.000	0.0252	0.0000	0.8353	0.0000	0.0000
B14. Seepage of chamber	70.000	0.0193	0.0000	0.0000	0.1979	0.0001
B15. Carbonization of lock wall	2.800	0.0232	0.0000	0.0000	0.0000	0.9373
B16. Lock wall intensity	1.500	0.0179	0.0000	0.0000	0.0111	0.0111
C11. Deposition of approach channels	75.000	0.0791	0.0000	0.0000	0.0111	0.0111
C12. Fluctuation of approach channels	0.300	0.0511	0.0000	0.0000	0.0000	0.8352
C13. Flow regime of approach channels	75.000	0.0474	0.0000	0.0000	0.0111	0.0111
D11. Video surveillance	80.000	0.0199	0.0000	0.0000	0.0001	0.1979
D12. Communication system stability	80.000	0.0242	0.0000	0.0000	0.0001	0.1979
D13. navigation signal	0.900	0.0163	0.0000	0.0000	0.0116	0.0122
D14. operation scheduling management	75.000	0.0371	0.0000	0.0000	0.0111	0.0111

). Unlike #1 lock, #2 lock has no dangerous indicators and most indicators are in the sub-health and health states.

It can be seen from the table that the indexes of #2 lock mostly belong to healthy or sub-healthy states and there are no indexes in dangerous condition. The comprehensive evaluation vector can be worked out using Equation (13). $D=WZ=(0.0005,0.0602,0.0698,0.1624)$. According to the maximum membership degree principle,#2 lock is judged to be grade IV, which represents that the service level is healthy. The service level eigenvalue ($E_{rx}=3.3471$) is calculated using Equation (14) and the confidence level factor $\phi$ is obtained to be approaching zero. In regard to the evaluation of two locks, since the $E_{rx}$ of #2 lock is larger than #1 lock, this indicates that the function exertion degree and comprehensive service state of #2 lock are better than those of #1 lock.

4. Discussion

To further clarify the differences, a comparison between the membership degrees of the indexes of the two ship locks is shown in Figure 5. The picture helps to understand the service condition of the indexes at one ship lock and compares them with the others. The distribution of the service condition of each index can be clearly displayed on the basis of the principle of maximum membership. The service condition distribution of various indexes of the ship lock can find out which indexes are not healthy or cannot fully play the roles, which is instrumental in taking measures to improve. It can be seen from the figure that the indexes of #1 and #2 lock mostly belong to the level III or IV interval ranges, embodying fairly good service status. Each ship lock index presents different service state distribution according to the state. For #1 lock, there is an index (B13) of danger, which implies that the damages related to the lock chamber have seriously threatened the operation safety of the ship lock. The indexes belonging to the lock chamber structure are mostly unhealthy, thus, the civil engineering status of the lock chamber of #1 lock is less than satisfactory. On the other hand, there is, apparently, no danger condition index for #2 lock, but it has several indicators in a state of fatigue. Although its service status belongs to level IV, to a certain extent, it is close to grade III, which indicates sub-health. It can be seen from Figure 5 that the equipment added in the later stage of the ship lock operation is in good condition and mostly in a healthy state. However, the relevant indicators of the infrastructure with slow replacement frequency and difficult replacement, such as gate metal structure and chamber, are mostly in unhealthy condition. More attention should be given to the indexes that do not belong to Level IV and have a large membership degree. Therefore, the two ship locks need to immediately repair and maintain the weak indexes for the sake of production safety.

After 1000 calculations of the model, the membership degree of the index to the four evaluation intervals can be obtained. With four intervals as abscissa and the membership degree [0, 1] as ordinate, the distribution of indexes can be obtained as shown in Figure 6. With regard to the indicators considering four intervals, it can be seen from Figure 6a,b that the indicators of #1 and #2 have a similar distribution. The number of index points gather in the intervals of grade III and IV, and the membership degrees concentrate near the value of one. The scatter in grade IV of #2 lock seems more concentrated. On the contrary, the membership degrees of others are concentrated around zero, and most of the index points belonging to the grade I interval are not shown in the graph because their values approximate to zero. It can be seen from this distribution diagram that, if a large number of scattered indicators are concentrated in the upper right corner of the diagram, the service condition of the ship lock is much healthier.

As shown in Equation (11), the hyper-entropy is taken as 0.001, which can be adjusted by the estimation of the decision-maker, according to the uncertainties of corresponding evaluation objects existing in actual conditions. In this research, in order to further study the influence of $H_e$ on the evaluation results, it is taken from the set $H_e=\left[0.001,0.005,0.01,0.05,0.1,0.5\right]$. To calculate the rule of the service condition evaluation grade, the comprehensive evaluation characteristic expectation $E_{rx}$, and confidence level factor $\phi$, comparison of the results is shown in Figure 7.

As shown in the figure, $E_{rx}$ gradually increases before $H_e\le 0.01$, resulting in improvement of the evaluation. However, when $H_e$ increases from 0.01 to 0.5, the $E_{rx}$ decreases significantly, and the increasing trend of $\phi$ becomes larger, which means that the confidence level reduces. For both ship locks, regardless of the change of $H_e$, the $E_{rx}$ of #2 is greater than that of #1, which means that the average value of the evaluation results of #2 in 1000 calculations is higher. Since the hyper-entropy $H_e$ represents the discrete degree of cloud droplets, the cloud thickness together with the dispersion of cloud droplets magnifies and the confidence level weakens with the increase of $H_e$. This once again confirms the superiority of #2 ship lock. As a matter of fact, #2 ship lock has been in service for 10 years and has never been overhauled. While #1 lockhas been in service for 35 years and has undergone three overhauls in 1995, 2002, and 2012; it has been 10 years since the last overhaul. There is a gap in service life as both ship locks have fatigue indicators and even danger indicators, which should be repaired in time. The evaluation results are helpful for ship lock management to improve the maintenance scheme and carry out the maintenance plan in time. It is also conducive to the mutual comparison between multiple ship locks or development analysis on the time span.

5. Conclusions

Ship locks occupy an important position in waterway transportation and brings huge benefits. It is of great significance to carry out life-cycle management because of its long service life and high risk. Maintaining or improving the service status of the ship lock and ensuring the smooth navigation of the ship are conducive to improving the safety and reliability of the ship lock. It will also be helpful to increase the passing speed and the number of ships passing. The operation and maintenance of ship locks are inseparable from evaluation of service condition. However, a systematic and unified evaluation has not been formed. To assist with the management and maintenance of ship locks, a comprehensive evaluation of service condition is proposed in this paper. The evaluation method will reveal the actual structural condition and provide a theoretical reference for the maintenance of ship locks.

The ship lock involves a wide range of professional fields and complex functional systems. The multi-indexes evaluation system is established by analyzing the function and structure of the ship lock based on EBS. The indexes are quantitatively calculated and divided into four evaluation intervals. The synthetic weight is adopted based on the order relation method and the entropy weight method combining subjectivity and objectivity. For dealing with the uncertainty of fuzziness and the randomness of the evaluation process, the extension cloud model that combines extension theory and the cloud model is set up. Eventually, two typical cases are studied to investigate the service condition to verify the feasibility of the proposed evaluation method in this research. The evaluation results demonstrate that #1 lock is in the sub-health state and #2 lock is healthy. This approach realizes continuous assessment which can present the general trend of the ship lock service condition and prevent the severe consequences that happen during the operation and maintenance stages.

Although the proposed comprehensive evaluation can realize the continuous assessment of ship lock service condition, there are still some existing limitations. More monitoring data should be collected to analyze the correlations between each indicator and the index system could be further improved. Additionally, more ship locks could be assessed to support the evaluation method. Overcoming the limitations and improving the evaluation index system will be a topic of further study.