1. Introduction
The floating crane (FC) is widely used for rescue, salvage and large-scale offshore installation projects, which plays an important role in ocean engineering. Considering the complexity and heavy-duty of offshore engineering operations, the application of the FC tends to involve large-scale, deep-sea, multi-ship collaborative operation and intelligent automation [
1]. The lifting operation can lead to the heel and trim of the FC. As the FC becomes larger, the problem becomes more prominent and important. The overturning moment generated by lifting cargo can make the heel angle reach 7–8° or even greater, which seriously affects the operation safety [
2]. The ballast system can adjust draught and longitudinal and transverse balance, and offset heel and trim moments by transferring ballast water between ballast tanks, which can ensure the operation safety of ships. Therefore, the ballast system and ballast water allocation between ballast tanks are important to ensure the operation safety of the FC. Offshore operations are often affected by the marine environment, and the time suitable for offshore operations is short. In addition, the FC needs to carry out lifting operations quickly under safe conditions. Thus, the research on an efficient solving algorithm for the allocation scheme of the FC has become an urgent task at present. It can not only ensure the safety of offshore operations of the FC, but also improve the automation of offshore operations. In a word, the ballast water dynamic allocation optimization model and an efficient solving algorithm are the core issues of the automatic or intelligent ballast system.
In recent years, some researchers have studied the mathematical modeling of the ship ballast process, the algorithm for solving the ballast water allocation and the optimization design method.
For the optimization modeling and solving algorithm, Pan et al. [
3] proposed a mathematical model of ballast water adjustment for the FC, which calculates the ballast water allocation mass when the crane arm rotates at each unit angle. Combining the influence of ballast tank mass, inertia and moment, Samyn et al. [
4] proposed a six-degree-of-freedom dynamic ballast water control system for semi-submersible platforms. Chen et al. [
5] proposed a hover control based on LI adaptive theory for the submarine, and established the ballast tank and submarine dynamics model. Meng et al. [
6] solved the established ballast water allocation model based on a multi-objective genetic algorithm, and proposed to use the TOPSIS method to rank the Pareto optimal solutions, in which the inclination of the hull during the allocation process was greatly reduced. Zhou et al. [
7] proposed to apply the multi-objective optimization algorithm based on decomposition technology to optimize ballast water allocation. Liu et al. [
8,
9,
10] built the ballast water allocation optimization models for the FC with different ballast systems, and proposed a dynamic programming strategy and intelligent algorithms, and a numerical simulation combined with case analysis showed that the optimal scheme can effectively reduce the mass of ballast water allocation and improve the operation efficiency. Zheng et al. [
11] proposed an improved PSO algorithm to optimize the hull form of an engineering vessel to reduce the wave-making resistance coefficient under static constraints.
In addition to optimization modeling and solving algorithms, relevant studies on ballast control systems have also been receiving wide attentions nowadays, aiming to improve the operation efficiency of the FC. Based on virtual reality technology and online analysis, Xu et al. [
12] established a human–machine interactive simulation system for FCs, which can improve the feasibility of the design scheme and the safety of actual operation. Wu et al. [
13] designed a FC visualization system, which integrates crane motion information collection, status monitoring, fault diagnosis and other functions to monitor the performance of ship deck cranes. Nam and Kim [
14] introduced a ballast simulation system that predicts the ballasting and deballasting processes using a computer model. Liu et al. [
15] and Zhao et al. [
16] proposed a new ballast system that changes the speed of the servo motor and the opening time of the solenoid valve to improve the hovering performance of an AUV. Jesse et al. [
17] proposed a PID control system that can realize the free flow of seawater into and out of an AUV ballast tank.
The influencing factors of ballast water dynamic allocation involve lifting cargo state, the marine environmental load, the ballast system and the ship hull state. The ballast system state includes the ballasting method, the layout of ballast tank and the ballast tank water level. Thus, from the perspective of engineering optimization, ballast dynamic allocation optimization is a complex engineering optimization problem with constraints, which has multiple difficulties such as engineering complexity, modeling and solving complexity, and practicality. Previous studies have shown that the solving efficiency and the quality of scheme made it difficult to meet engineering needs if only relying on an optimization model and general solving algorithm. For example, the optimal allocation scheme generally used all ballast tanks, which increased the response difficulty of hardware and made the optimal scheme difficult to apply in the engineering.
Domain knowledge plays an important role in solving complex engineering problems, such as human intelligence, expert experience rule and field data. At present, some researchers have incorporated domain knowledge into engineering problems. Zhu et al. [
18] proposed a decision-making model based on artificial experience to locate the ECG boundary. Mohammad et al. [
19] applied domain knowledge to the optimization of the grinding process. Rogulj et al. [
20] applied domain knowledge to road and bridge condition assessment. Mahbub et al. [
21] proposed to introduce domain knowledge related to energy systems into the different stages of the Multi-Objective Evolutionary Algorithm (MOEA) operation, in which experiments were conducted on the energy system problem in Aalborg, Denmark, and the results showed that the method incorporating domain knowledge provided significant improvements over conventional methods in terms of solving quality and optimal speed. More studies [
22,
23,
24] indicated that the introduction of domain knowledge was of great significance for solving complex engineering problems. In addition, some hybrid algorithms are presented to improve the solving quality, for example references [
25,
26,
27].
In order to improve the solving efficiency and quality, this paper proposes an optimization design method for a ballast water dynamic allocation scheme based on domain knowledge and particle swarm optimization (PSO). The domain knowledge in ballast water allocation is extracted to establish an expert experience rule base, and the expert experience rule is introduced into the algorithm solving process through fuzzy logic inference. The introduction of domain knowledge can obtain an optimal allocation scheme that conforms to practical engineering. The combination of domain knowledge and PSO can effectively optimize the mode of population initialization, which can improve the solving efficiency, solving quality and engineering practicability of the allocation scheme.
This paper is organized as follows. In
Section 2, the lifting operation process of the RFC is introduced, and the multi-stage decision-making optimization model for ballast water allocation is built. In
Section 3, based on dynamic programming and PSO algorithms, the FPSO algorithm is proposed. In
Section 4, the model and algorithm proposed in this paper are verified by experiment and applied to two ships with different ballast configurations.