Risk analysis of bridge ship collision based on AIS data model and nonlinear finite element

1.1 Theoretical significance

This article proposes a risk research method that combines AIS data, collision history accident data, and water traffic simulation to analyze the risk and characteristics of ship collision accidents in estuarine waters, in response to the characteristics of incomplete data, numerous causal factors, and mutual coupling of ship collision accidents. The research methods adopted and the designed models have reference significance for similar research.

1.2 Use value

This article uses AIS data to obtain the number, situation, and spatiotemporal characteristics of potential collision hazards and supplement the analysis results of actual data; it is of great guiding significance to analyze the risk level and spatiotemporal characteristics of water bodies, identify sensitive factors that affect collision accidents, and provide decision-making support for ship traffic safety management in water bodies.

3.1 Ship AIS system

The methods of bridge ship collision risk assessment mainly include four statistical methods and mathematical model methods. The statistical method is to calculate the collision probability of a ship bridge by statistical analysis of a ship bridge collision accident. The mathematical model method refers to the establishment of ship bridge collision probability calculation models, such as AASHTO canonical model 7, KUNZI model I8, and three-parameter path integral model. However, the values of relevant parameters in the model are different from the actual situation, so more real data are needed to ensure the validity of the collision probability calculation. Since the AIS data record various static and dynamic information of the ship, it is widely used in water traffic safety and ship dynamic analysis. Based on AIS data, this study calculated the probability of ship collision with pier by the mathematical model method and analyzed the difference of ship collision risk with pier and before and after the revision of the AASHTO normative model.

The ship AIS system is mainly composed of three parts: receiver, information processor, and transceiver. The main function of onboard AIS equipment is to broadcast the navigation data of the ship through specific channels. The onboard AIS is mainly divided into three categories: class A, class B, and AIS receivers, the functions of the three types of AIS equipment are shown in Table 1. So far, most of the ships are installed with class A AIS, while the shore affairs system is installed with AIS receivers to receive AIS data from passing ships. There are three working modes of Class A AIS system, namely autonomous continuous mode, distribution mode, and polling mode. Generally, the onboard AIS system is in the autonomous mode. In this mode, the system automatically sends the relevant information of the ship to the surrounding at the specified time [8].

AIS information is mainly divided into four types: static information, dynamic information, navigation-related information, and concise safety information. Through these information, the ship can well understand the static and dynamic information of other ships around the ship. However, the onboard AIS equipment only transmits one type of information content at a time. The following are the specific contents of the four types of information:

1. Static information includes IMO number, ship name (call sign), captain and width, ship category, and the location of AIS locator antenna on the ship;

2. Dynamic information includes: accurate and complete ship position, UTC time, route to the ground, speed to the ground, bow direction, navigation status, turning speed, etc.;

3. Information related to navigation includes: ship draft, dangerous goods, destination, planned navigation route, etc.;

4. SMS related to safety includes important navigation warnings or important meteorological warnings. At the same time, there are differences in the update time of the four kinds of information, that is, the time interval when the AIS system sends such information. Static information is sent every 6 min or according to the request of relevant parts; The navigation-related information is also sent every 6 min, at the same time, if the relevant data changes or there are relevant requests, such information will also be sent; safety-related information is sent as required; and the update time of ship dynamic information is related to the navigation status of the ship, as shown in Table 2.

3.2 Discussion on collision probability model

The KUNZI model is similar to the three-parameter path integral model, which is mainly based on the collision principle to calculate the collision probability of the ship bridge according to the failure path during the collision of the ship bridge. KUNZI model only considers the single track line of the ship, and the three-parameter path integral model adds the transverse distribution of the ship track line. Among them, for the calculation of ship stopping distance, most scholars estimate the ship stopping distance through the ship stopping stroke, but this is difficult to combine with the different navigation environment in each region. Therefore, the author selects the AASHTO model, which is widely used and has strong practicability, to calculate the collision probability of ship bridge [9].

The calculation of collision probability in the AASHTO model mainly considers two probabilities, geometric probability, and yaw probability. However, there are some problems worth discussing about the calculation methods of these two main probabilities: first, the geometric probability in the AASHTO model (hereinafter referred to as “PG”) is mainly determined by the transverse distribution of ships passing through the bridge area. The transverse distribution of ships in the bridge area can be approximately and reasonably fitted with the normal distribution, the mean value of the normal distribution is the centerline of the channel, and the standard deviation is the characteristic length of the channel representing the ship type; however, in actual navigation, the parameter values of the transverse distribution of ships in the bridge area are very different. For example, the previous chapter analyzed the ship traffic flow near Tongling Yangtze River Highway Bridge, as for the navigation track of ships on the ground, due to the water level and the navigation habits of the crew, some ships did not navigate according to the designed waterway, leading to the collision risk of piers far away from the designed waterway. At the same time, for launching ships, the mean value of the ship’s track band also deviates from the design channel centerline. Therefore, if the geometric probability of ships calculated based on the theory of the AASHTO model is different from the actual situation, it is necessary to use real-time AIS data of ships to calculate the lateral distribution of ships, so that the obtained geometric probability will be more realistic. Second, the most reasonable method to determine the yaw probability (hereinafter referred to as “PA”) is to obtain it through long-term accident statistics. When data are scarce, it can be estimated through empirical formula. In the AASHTO model, P4 is estimated through yaw datum probability, bridge location correction coefficient, water flow correction coefficient, etc. When determining the water flow correction coefficient, AASHTO uses a constant flow velocity for calculation; however, the flow velocity in the bridge area varies throughout the year, especially in the dry season, flood season, rising tide, falling tide, and other periods in the inland river basin. At the same time, when the ship is sailing in the bridge area, other factors, such as wind and climate, will also affect the ship’s yaw, in addition to the current. If the influence of water velocity, wind, climate, etc., can be introduced into the calculation of yaw probability of the target basin, in which the influence of water flow is the main part, the result will be more reasonable, the effect of these factors is reflected in the change of ship speed and yaw angle. Therefore, the influence of the external environment on yaw probability can be estimated by analyzing the change in ship speed and yaw angle [10].

The most reasonable method to get ship drift probability is to make statistics on long-term accidents. In the case of lack of data, it can be estimated by empirical formula. However, due to the lack of measured data on ship lateral distribution in the AASHTO standard model, the geometric probability is obtained by using the channel center line as the mean distribution and the variance as the standard normal distribution of ship length, which is different from the actual situation. In addition, Px is estimated in the AASHTO standard model through yaw reference probability, bridge position correction coefficient, and flow correction coefficient. When determining the flow correction coefficient, the AASHTO standard model adopts a constant flow velocity, while the flow velocity in the bridge area changes in a year. There are great differences in river velocity in different periods such as low water season, flood season, high tide, and low tide. If the influence of water velocity can be introduced into the calculation of yaw probability of target watershed, the calculation results will be more reasonable.

1. Pier: the risk can be reduced by enhancing the resistance of the pier itself, such as the steel sheath, which increases the collision resistance without increasing the probability of geometric collision. The increase of large-scale buffer collision prevention measures will reduce the probability of pier collapse but also increase the probability of bridge geometric collision, which needs comprehensive consideration. It is recommended to use large-scale buffer anti-collision measures for bridges in large river basins, and it is recommended to directly wrap steel protection tubes in small river basins.

2. Ships: traffic and tonnage restrictions can be adopted to reduce the probability of bridge failure by limiting ship flow and illegal entry of large tonnage ships into the channel; another measure is to install an early warning system on the ship, regulate the operation of the pilot, and reduce the error rate per unit of sailing distance.

3. Waterway: regulate the traffic order of waterway, especially in special bad weather. Timely dredging of the waterway is conducive to easing the traffic volume.

Therefore, the transverse distribution of ships in the bridge area is obtained by statistical analysis of real-time AIS data of ships, so as to calculate the geometric probability of ships colliding with piers in the bridge area, at the same time, the author will acquire the up and down navigation speed of actual ships by collecting AIS data and obtain the actual transverse bridge speed Vr of environmental factors in the target basin every month, which is referred to as the transverse bridge speed and the along bridge speed Vx of environmental factors, which is referred to as the long bridge speed, at the same time, the calculation formula of yaw probability is revised as follows, as shown in the following formula:

3.3 Finite element model

SHELL163 shell element is used to simulate the hull, solid164 hexahedral element is used for bridge piers, bearing platforms, and foundation piles, and COMBI165 is used to simulate the constraint effect of soil on piles. The total plan is to divide it into 1.17 million units. During the analysis process, the influence of water flow force is included based on the kinetic energy of the fluid.

3.4 Determination of conditional probability

The conditional probability of network nodes is an important part of quantitative reasoning in a Bayesian network. It gives the strength of a causal relationship between variables and their parent nodes in the form of probability. From the perspective of probability acquisition methods, there are mainly three categories: input from expert knowledge, parameter learning, and combining expert and parameter learning.

In terms of eliciting expert knowledge and manually entering variable conditional probability tables, the commonly used methods include analytic hierarchy process, Delphi method, etc. The main ideas of these methods are similar, which are used to design indicators and questionnaires and then ask experts to give the probability of variables in different states in the form of interviews. Generally speaking, the conditional probability obtained in this way is called subjective probability, because it contains the subjectivity and uncertainty of the evaluation experts themselves. However, in the case of insufficient and incomplete available data, subjective probability is still an important way to obtain conditional probability. In recent years, with the continuous development of data mining technology, data-driven conditional probability determination methods have been further studied and popularized. The representative algorithms include the expectation maximum algorithm and Bayesian Learning.

The method of parameter learning is not applicable in this study due to its large training data sample size. Therefore, in the determination of conditional probability of network variables, this study mainly adopts the idea of combining accident data with reference to existing literature.

4.1 AIS data statistics and analysis

The main purpose of the navigation route model is to mine the main navigation channels from a large number of actual navigation data of ships, so as to build the virtual navigation route in the simulation system. This part mainly involves the trajectory clustering of ships and statistical analysis of the clustering results, to obtain the outline of the main navigation route and other data. The route model is an abstract and topological representation of the actual route of a ship's water area. In the design process of ship traffic simulation systems, traditional route models mainly rely on chart data of water bodies to complete. However, as these data typically only include routes in the main water bodies, observing AIS data from actual ships reveals that some ships do not strictly follow the routes. AIS data can be used to obtain the impact parameters of bridge ship collision, including ship weight, trajectory, yaw, and speed distribution. The weight distribution of navigable ships passing the navigation area of the Second Yangtze River Bridge in Wuhan from November to December 2019 obtained by the author based on AIS data is shown in Figure 2. It can be seen from Figure 2 that the average weight of the ship is 3,038 t, which is close to 2,000 t of the representative ship type for Class I waterway navigation specified by the inland waterway navigation standard port; the maximum ship weight has exceeded 10,000 t; the exceedance probability of 6,000 and 4,000 t ships is 95 and 90% respectively. According to the 10% criterion, the author determines to use a 5,000 t ship as the representative ship type for bridge anti-collision and anti-collision analyses [11–13]. In this article, the general nonlinear dynamic response analysis program ANSYS/LS-DYNA is used to simulate the ship-protection device collision of the Second Yangtze River Bridge. LS-DYNA adopts explicit time integration, which does not need to solve linear simultaneous equations, nor does it need to integrate the total stiffness matrix and total mass matrix. It avoids the formation of stiffness matrix and related matrix operations, saves storage space and solution time, and allows large-scale finite element problem analysis with less computer capacity. It has obvious advantages for solving short-term strong nonlinear problems of large structures. However, it is necessary to pay attention to the selection of the time step, because the central difference method is conditionally stable, and its time step cannot exceed the critical time step.

Figure 2

Weight distribution of ships in the bridge area.

The cumulative distribution of yaw angle of navigable ships in the bridge area when going down and up is shown in Figure 3. It can be seen from Figure 3 that the yaw angle of upgoing ships is obviously greater than that of downgoing ships; 91% of the downgoing ships have a yaw angle of 0–6°, while only 65.8% of the upgoing ships are within this range; in the cumulative distribution function of the ship’s yaw angle, the yaw angle with 95% probability of exceedance when the ship goes down and up is 8″ and 22°, respectively; whether the ship goes up or down, the yaw angle is 22° or less, which is close to the 20° specified in the railway code [14,15].

Figure 3

Cumulative distribution of ship yaw angle.

The speed distribution of navigation vessels in the bridge area when going down and up is shown in Figure 4a and b. It can be seen from Figure 4 that the average speed of down and up ships is 3.28 and 1.91 m/s, respectively; in the cumulative distribution function of ship speed, the speed of downward and upward ships with 95% probability of exceedance is 5.5 and 3.5 m/s, respectively; The average down speed is obviously higher than the average up speed, because the ship’s sailing direction is in line with the current flow direction during the down direction, and the current pushes the ship to move, thus increasing the ship’s speed. For the ship impacting the bridge pier, the larger the yaw angle is, the greater the velocity component of the ship along the bridge direction is. From the perspective of bridge safety, the author takes the maximum upstream yaw angle as 22″ and the maximum downstream yaw angle as 8° for analysis. The collision speed of ships is the main factor affecting the collision force, considering that there is a certain distance between the bridge pier and the centerline of the channel, the collision speed between navigable ships and the bridge pier is smaller than the ship speed at the centerline of the channel; therefore, the author takes the average speed (1.91 m/s upward and 3.28 m/s downward) as the speed of ship collision force calculation of bridge piers [16–18].

Figure 4

Speed of navigation vessels in bridge area when going down and going up. (a) The downside and (b) the upside.

4.2 Ship collision response analysis of bridge pier anti-ship collision device

As the ship impact force is greater than the collision resistance force of the pier itself, anti-collision facilities need to be set to protect the pier. Considering the large drop of water level in the bridge area, a self-floating anti-collision structure is designed for the main pier of the Second Wuhan Yangtze River Bridge. Referring to relevant literature, the internal structure of a ship collision prevention device adopts sandwich structure similar to honeycomb to improve energy absorption capacity. The designed anti-collision structure size is 38.3 m × 12.2 m × 4 m, the thickness of the inner and outer wall plates is 10 mm, and the thickness of the middle X-shaped sandwich plate is 8 mm. In the anti-collision device, steel fenders are set on both sides of the outside for buffering, the finite element model of the X-shaped sandwich structure anti-collision device is established with the spacing of the inner trapezoidal fenders of 2.25 m, and the dynamic analysis of the ship impact anti-collision device is carried out. The plate is simulated by the Sel163 element, and the truss and circumferential reinforcement are simulated by the Beam161 element. As the main body of the anti-collision device is a steel structure, its material properties are the same as those of the hull, and the grid size is set as 100 mm × 100 mm [19].

4.3 Ship collision response analysis of anti-collision device

The time history curve of the collision force of the ship impacting the anti-collision device is shown in Figure 5. It can be seen from Figure 5 that: (i) Compared with the direct impact of the ship on the pier, the anti-collision facilities can extend the collision time, and the impact time under the frontal collision condition is extended from 1.2 to 2.0 s. (ii) The peak value of collision force can be effectively reduced when the initial momentum is consistent. After the anti-collision device is installed, the ship collision force under working conditions 1–2 is, respectively, 16.53, 16.29, and 12.11 MN, and the anti-collision structure can reduce the ship collision force by 30–40%. (iii) When the ship impacts the anti-collision facilities at an angle of 8° yaw, the collision force along the bridge direction transmitted to the pier is slightly greater than that before fortification. This is because, before the fortification, when the ship collides with the pier, there is a large relative slip along the bridge direction, after the anti-collision device is added, the deformed anti-collision device restricts the ship slip to a certain extent, resulting in an increase in the collision force along the bridge direction. Since the reduction effect of the collision force in the transverse direction is obvious, and the increase in the collision force in the longitudinal direction is small, the anti-collision device can play a better anti-collision effect. (4) Before and after the fortification, the integration of collision force in time is basically the same, it can be seen from the conservation of momentum that the anti-collision device reduces the peak value of collision force by extending the collision course.

Figure 5

Time history curve of impact force of impact system.

Under all working conditions, the moment when the maximum lateral displacement of the anti-collision device occurs is about 1.5 s, which shows that the collision force continuously drops to 0 from this moment on the collision force time history. In the collision process, the anti-collision device absorbs part of the collision energy through its own deformation, under the premise of a certain initial kinetic energy, the deformation of the ship due to collision energy absorption will be reduced after the fortification. The anti-collision device has local permanent deformation under the impact of a 5,000 t ship, but there is no damage and failure, which will not cause water ingress and sinking.

4.4 Discuss

1. According to AIS statistics, the average weight of navigable ships in the Second bridge area of the Yangtze River is 3,038 t, which is close to the requirement of 4,000 t ships in the first class waterway. However, according to the 10% criterion of probabilistic statistical analysis in the collision avoidance code, it is suggested to use the 5,000 t class ship as the representative ship type to analyze the collision resistance and collision avoidance of Bridges.

2. The upward drift angle of navigable ships in the bridge area is 22°, which is close to the recommended value of the railway code, and the recommended value of the railway code can be adopted in the case of lack of data. There is a big difference between the yaw angle and the average speed of the upper and lower ships, so it is recommended to consider the difference between the collision energy of the upper and lower ships separately in the design of the anti-collision device, and design appropriate anti-collision devices for the areas where the upper and lower ships may collide, so as to improve the economy of the anti-collision design while ensuring safety.