Method for predicting maximum wave height of ship in restricted waterway

Abstract

The present application relates to the prediction method of the maximum wave height of ship wave in restricted waterway, comprising: based on the waterway condition of the restricted waterway, establishing the waterway section flume physical model and the ship model according to the scale; designing the experimental water level working condition, the ship speed working condition, and arranging the ship wave height measuring point at different heights; based on the experimental results, carrying out the dimensionless analysis on the influence factors of the maximum wave height of ship wave, establishing the maximum wave height prediction equation; constructing the residual sum of squares function for the maximum wave height prediction formula, and solving the undetermined coefficient in the prediction equation by using the particle swarm optimization algorithm; constructing the fitting curve of the undetermined coefficient and the water depth, determining the value of the undetermined coefficient according to the water depth, substituting into the maximum wave height prediction equation, and obtaining the maximum wave height prediction equation under the corresponding scene. The present application provides a prediction method of the maximum wave height of ship wave in the restricted waterway, which is suitable for any section shape and ship type, and the prediction precision is greatly increased compared with the existing ship wave empirical formula.

Description

Technical Field

[0001] This invention relates to the field of ship navigation and ship wave prediction technology, specifically to a method for predicting the maximum wave height of ship waves in restricted waterways. Background Technology

[0002] Restricted waterways are characterized by shallow water depth and narrow channel width. Ship waves generated during navigation erode the riverbanks, and the maximum wave height determines the maximum energy generated during these waves and the degree of erosion. Especially in recent years, the rapid development of shipping in restricted waterways, the trend towards larger ships, and the significant increase in traffic density have exacerbated riverbank erosion. Predicting the maximum wave height remains a challenge in assessing navigation safety and the extent of riverbank erosion in restricted waterways. Summary of the Invention

[0003] The purpose of this invention is to provide a method for predicting the maximum wave height of ship traveling waves in a restricted channel, which can predict the maximum wave height of ship traveling waves under any channel cross-section and ship type combination in a restricted channel.

[0004] To achieve the above technical objectives, the present invention adopts the following solution:

[0005] A method for predicting the maximum wave height of a ship's traveling wave in a restricted channel includes:

[0006] Based on the waterway conditions of the restricted waterway, a physical model of the waterway cross-section and a ship model are established at scale.

[0007] Design experimental water level conditions and ship speed conditions, and set up ship wave height measuring points at different heights to measure the maximum wave height of the ship under different experimental conditions; at least two experimental water levels and ship model speeds should be set.

[0008] Based on the experimental results, a dimensionless analysis was conducted on the influencing factors of the maximum wave height of ship waves, and a prediction equation for the maximum wave height was established.

[0009] A residual sum of squares function is constructed for the maximum wave height prediction formula, and the undetermined coefficients in the prediction equation are solved using the particle swarm optimization algorithm.

[0010] Construct a fitting curve between the undetermined coefficients and the water depth, determine the value of the undetermined coefficients based on the water depth, and substitute them into the maximum wave height prediction equation to obtain the maximum wave height prediction equation for the corresponding scenario.

[0011] As a preferred embodiment, the water tank is provided with a first-length ship model acceleration area, a second-length channel cross-section test area, and a third-length buffer area.

[0012] The wave height measurement points are set up on both banks of the test area of ​​the waterway section.

[0013] As a preferred implementation, the model scale is selected to satisfy the following conditions: the channel depth in the physical model of the water tank is greater than 10 cm, and the total length of the water tank is greater than 14 times the ship length. The physical model of the water tank is a normal distribution model, and the larger the model scale, the more it conforms to the actual situation. The actual water depth varies between the lowest and highest navigable water levels. Considering the maneuverability of the ship model, the geometric scale λ is determined based on a water depth greater than 10 cm at the lowest navigable water level in the model. L1 The geometric scale λ is determined based on the premise that the length of the site in the model is greater than 14 times the length of the ship model. L2 Choose λ L1 , λ L2 The minimum value is determined as the geometric scale λ of the model. L This allows for the determination of the flow velocity and ship speed ratio λ. v =λ L 0.5 Water flow resistance ratio λ n =λ L 1 / 6 Time ratio λ t =λ L 0.5 Wave height ratio λ H =λ L .

[0014] In a preferred embodiment, the second length is not less than 4 times the ship's length, and the third length is greater than 5 times the ship's length.

[0015] As a preferred implementation, 6 to 8 wave height meters are arranged at the same channel cross-section to measure the wave height of ships. The spacing between the wave height meters is determined according to the degree of wave height change; the spacing is increased in flat terrain and decreased when the terrain changes drastically. In restricted channels, the terrain changes drastically at the bank slope, resulting in corresponding drastic wave height changes. Therefore, 8 wave height meters are set at unequal intervals at the bank slope according to the degree of terrain change to measure the cross-sectional wave height and obtain the maximum wave height.

[0016] As a preferred implementation method, the experimental design includes the minimum navigable level, normal level, and maximum navigable level; the ship speeds include low speed, normal speed, and high speed. The normal operating level of the restricted channel should be between the minimum and maximum navigable levels, and under normal circumstances, the channel's operating level should be the normal level. Therefore, the experimental design should cover the entire channel's operating level; hence, this experimental condition uses the minimum, normal, and maximum navigable levels. Ships travel at relatively slow speeds in restricted channels, especially at the minimum navigable level. At the same speed, the ship's resistance is much greater than at the normal and maximum navigable levels. Therefore, in the experimental condition, three ship speeds are set for each water depth: low speed, normal navigation speed, and high speed.

[0017] As a preferred implementation method, only low speeds are tested at the lowest navigable water level, while all speeds are tested at other navigable water levels.

[0018] As a preferred embodiment, the influencing factors include ship speed, water depth, distance of the measuring point from the center of the channel, gravitational acceleration, and water density.

[0019] As a preferred implementation method, the maximum wave height prediction equation is established as follows:

[0020]

[0021] Where V c For ship speed, h c For water depth, S c The distance from the measuring point to the center of the channel is given by , g is the acceleration due to gravity, and Fr is the acceleration due to gravity. h For the depth of the water, Froude number, k1 and k2 are undetermined coefficients.

[0022] As a preferred implementation, a residual sum of squares function is constructed for the maximum wave height prediction formula. Combined with the measured maximum wave height value, the minimum value of the residual sum of squares function is found using the particle swarm optimization algorithm, thereby determining the unknown coefficients in the maximum wave height prediction formula for ship waves under a certain water depth condition.

[0023] Common waterway cross-sections include trapezoidal, vertical wall, and vertical wall-trapezoidal composite cross-sections. Ship types are classified as 500-ton, 1000-ton, and 2000-ton. Under different cross-section forms and ship type combinations, the maximum wave height prediction results vary. This application establishes a waterway cross-section water tank physical model and a ship model for waterway conditions, designs different experimental water level conditions and ship speed conditions, and arranges ship wave height measuring points at different heights to measure experimental parameters. Dimensionless analysis is used to establish the maximum wave height prediction equation, and particle swarm optimization algorithm is used to solve the undetermined coefficients in the prediction equation. Finally, the maximum wave height prediction equation for the corresponding scenario is obtained.

[0024] This invention provides a method for predicting the maximum wave height of ship waves in restricted waterways. This method is applicable to any cross-sectional shape and ship type, and its prediction accuracy is significantly improved compared to existing empirical formulas for ship waves. Attached Figure Description

[0025] Figure 1 A cross-sectional view of the restricted waterway is shown.

[0026] Figure 2 The layout and physical model diagram of the water tank are shown.

[0027] Figure 3 A schematic diagram of the wave height meter arrangement is shown.

[0028] Figure 4 The diagram shows the relationship after dimensionless measurement of the maximum wave height of the ship's traveling wave.

[0029] Figure 5 The diagram shows the particle swarm optimization algorithm for solving the values ​​of k1 and k2, as well as the error between the actual and predicted values.

[0030] Figure 6 The graph shows the relationship between k1, k2 and water depth. Detailed Implementation

[0031] To better understand this invention, this application uses the Xiaqing River Class III restricted waterway in Jinan area of ​​Shandong Province as an example, and explains the invention in conjunction with the accompanying drawings and specific implementation inferences.

[0032] The method of the present invention includes the following steps:

[0033] (1) Based on the waterway conditions of the restricted waterway, establish the physical model of the waterway cross section and the ship model according to the scale.

[0034] The Xiaqing River is planned as a Class III restricted waterway with a trapezoidal double cross-section. The channel bottom width is 45.0m, and the channel banks are connected by 1:3 slopes via ramps. The design minimum water depth is 3.8m, the normal navigable water depth is 5.8m, and the maximum navigable water depth is 7.8m. Currently, the most common vessel type on the channel is the 500-ton inland cargo ship. Therefore, this application selects this trapezoidal cross-section and the 500-ton vessel type based on the actual conditions of the Xiaqing River area. The vessel dimensions are 46.0m × 8.8m × 3.0m (length × width × height). Figure 1 As shown.

[0035] The lowest water level in the actual waterway is 3.8m. Considering the portability and maneuverability of the model, the water depth in the waterway needs to be greater than 10cm. Therefore, the model's scale λ L ≤30; The actual ship dimensions are 46.0m × 8.8m × 3.0m (length × width × height), and the ship model dimensions are 2.30m × 0.44m × 0.15m (length × width × height). The test tank length of the model is 40m, and the test tank length in the model is greater than 17 times the ship length. λ L ≤20. In summary, we choose λ. L =20, and then determine the corresponding current velocity and ship speed ratio λ. v =λ L 0.5 =4.47, water flow resistance ratio λ n =λ L 1 / 6 =1.65, wave height ratio λ H =λ L =20, time ratio λ t =λ L0.5 =4.47.

[0036] Based on this similarity scale, a model of the water tank and its cross-sectional structure was constructed in the laboratory, such as... Figure 2 As shown, the water tank includes a 15m acceleration area for the ship model, a 10m channel cross-section test area, and a 15m buffer area. The ship model is also scaled down according to the scale and made by a professional manufacturer according to the selected ship type. The ship model size is 2.30m×0.44m×0.15m (length×width×height). The ship model has self-propulsion capability and can be remotely controlled to control its navigation trajectory.

[0037] (2) Design experimental water level conditions, including the lowest navigable water level, normal water level, and highest navigable water level; design experimental ship model speed conditions, including low speed, normal speed, and high speed; arrange ship wave height measurement points and carry out the measurement of the maximum wave height of ship waves under different experimental conditions.

[0038] The water depths for this experiment were 0.19m, 0.29m, and 0.39m, corresponding to the lowest navigable water level, normal water level, and highest navigable water level, respectively. The boat speeds were 1.06m / s, 1.25cm / s, and 1.42cm / s, corresponding to low, normal, and high speeds, respectively. Because the resistance experienced by a vessel varies at different water depths during navigation in a restricted channel, with lower speeds at lower depths, only one speed was designed for the low water depths, as shown in Table 1, for a total of 7 operating conditions. Eight wave height meters were deployed at fixed locations on the channel bank. Figure 3 As shown, when the water depth h c When h = 0.19m, wave height meters W1 to W5 can be used; when h c When h = 0.29m, wave height meters W1 to W6 can be used; when h c When the wave height is 0.39m, wave height meters W1 to W8 can be used.

[0039] Table 1 Experimental Condition Design

[0040]

[0041] (3) Dimensionless analysis of the factors affecting ship waves was conducted, and the maximum wave height prediction equation model was derived.

[0042] For the maximum wave height and ship speed V of the restricted channel c water depth h c Distance S of the measuring point from the center of the waterway c The relationship between the physical quantities of gravitational acceleration g and water density ρ is as follows: Figure 4 As shown, it can be expressed as:

[0043] H m =f(V c ,S c ,hc ,g,ρ) (1)

[0044] Its dimensional exponents are shown in Table 2:

[0045] Table 2. Dimensions of variables in the prediction of maximum wave height of ship sailing waves: power exponents

[0046]

[0047] According to the π theorem, S c h c One of the two independent variables is selected as the reference physical quantity, V. c Two of the following quantities, g and ρ, need to be selected as physical reference quantities. In this study, S is selected. c V c If the three independent variables ρ are used as reference physical quantities, then the above quantities are classified and sorted as shown in Table 3:

[0048] Table 3. Power exponents of variables after row transformation in the problem of predicting the maximum wave height of ship sailing waves.

[0049]

[0050] Then three dimensionless quantities are given:

[0051]

[0052] The above problem can then be described as:

[0053]

[0054] By making the measured data dimensionless, we can obtain... and Since the distribution follows a power-law exponential pattern, the formula for predicting the maximum wave height of a ship's waves can be written as:

[0055]

[0056] Where Fr h For the depth of the water, Froude number, k1 and k2 are the undetermined coefficients of the prediction formula.

[0057] (4) Construct the residual sum of squares function for the prediction formula.

[0058] Figure 5 To solve for the values ​​of k1 and k2 using a particle swarm optimization algorithm.

[0059] Based on the maximum wave height prediction formula (4), construct the target residual sum of squares function F(H) m ) SSE , can be represented as:

[0060]

[0061] Where Y i f(S) represents the measured maximum wave height of a ship's traveling wave at a certain measuring point. ci ,Fr hi V ci |k1,k2...) represents the calculated maximum wave height at that point, and N represents the total number of measurement points under all experimental conditions at a certain water depth. Assuming that k1 and k2 take a specific value, the residual sum of squares function can be obtained based on the overall measured values ​​and the prediction formula curve. When the residual sum of squares function reaches its minimum value, k1 and k2 are the desired parameter values.

[0062] (5) Use the particle swarm optimization algorithm to solve for the minimum value of the residual sum of squares function of the prediction formula, and obtain the unknown parameters in the prediction formula at a certain water depth.

[0063] Particle swarm optimization (PSO) is an algorithm that finds the optimal solution through cooperation and information sharing between the swarm and individuals. This method is used to solve the residual sum of squares function F(H) at a certain water depth. m ) SSE When the minimum value is obtained, the values ​​of k1 and k2 are less likely to get trapped in local optima compared to the traditional least squares method.

[0064] The basic principle of the particle swarm optimization algorithm is as follows:

[0065] v ij (t+1)=wv ij (t)+c1r1(t)[p ij (t)-x ij (t)]+c2r2(t)[p gj (t)-x ij (t)] (6)

[0066] x ij (t+1)=x ij (t)+v ij (t+1) (7)

[0067] Where v ij (t) represents the initial velocity t, and w is the inertial weight; c1r1(t)[p ij (t)-x ij [p(t)] represents the step size of an individual moving towards the global optimal solution, [p ij (t)-x ij [c2r2(t)] represents the step size forward to the individual's optimal solution position, where c1 is the individual's learning coefficient; c2r2(t)[p gj (t)-x ij [p(t)] represents the step size for moving towards the global optimum, [p gj (t)-x ij[(t)] represents the optimal position of the group, and c2 is the group learning coefficient; x ij (t+1) represents the coordinate position of the next generation (t+1), determined by x. ij (t) represents the position at time t and the velocity at time t+1. ij (t+1) determines the value. After multiple iterations, the values ​​of k1 and k2 are obtained when the sum of squared residuals of the target are minimized. For a certain water depth, the corresponding k1 and k2 are calculated respectively, thus obtaining the maximum wave height prediction formula under different water depth conditions.

[0068] Based on the particle swarm optimization algorithm, the residual sum of squares function F(H) of the maximum wave height measurement point is applied. m ) SSE Perform iterative calculations when F(H) m ) SSE When the value reaches its minimum, the values ​​of k1 and k2 are used to calculate the coefficients. In this algorithm, since all parameters are positive, k1 > 0. Therefore, the upper and lower limits of k1 and k2 can be set as: 0 ≤ k1 ≤ 6, -5 ≤ k2 ≤ 5. The acceleration constants c1 and c2 are both 2. The target residual sum of squares function F(H) can be obtained through iterative calculation. m ) SSE Minimum value. Measured maximum wave height H of the ship's traveling wave. m The fitted values ​​are in good agreement with those based on the particle swarm optimization algorithm, h. c When h = 0.19m, k1 = 1.52, k2 = -2.04; c When h = 0.29m, k1 = 5.30, k2 = -2.94; c When the value is 0.39m, k1 = 1.08 and k2 = -2.50.

[0069] Fit the correlation curves between k1, k2 and water depth ( Figure 6 The particle swarm optimization algorithm was used to solve the prediction equation for the maximum wave height of ship waves in shallow water. The goodness of fit of the prediction formulas under different water depth conditions all met R0. 2 ≥0.88, the predicted result is close to the measured value, and the values ​​of k1 and k2 under different water depth conditions can be obtained from... Figure 6 The query determines the value of the undetermined coefficient based on the water depth, and substitutes it into formula (4) to obtain the maximum wave height prediction equation for the corresponding scenario.

Claims

1. A method of predicting the maximum wave height of a ship in a restricted waterway, characterized by, The method comprises the following steps: Based on the channel condition of the restricted channel, a channel section flume physical model and a ship model are established according to a scale; An experimental water level condition and a ship speed condition are designed, and ship wave height measuring points are arranged at different heights to measure the maximum ship wave height under different experimental conditions; the experimental water level and the ship model speed are each set to be at least two or more; Based on the experimental results, the influence factors of the maximum ship wave height are analyzed in a dimensionless manner, and a maximum wave height prediction equation is established, including: The relationship between the physical quantities of the maximum wave height of the restricted channel, the ship speed V c , the water depth h c , the distance S of the measuring point from the center of the channel c , the gravitational acceleration g, and the water density p is expressed as follows: ； The dimensionless parameters obtained through the dimensionless analysis are as follows: ； The physical quantity relationship is described according to the dimensionless parameters as follows: ； The dimensionless determination by the measured data With In the form of power index, the final construction of the ship wave maximum wave height prediction formula is as follows: ； where Fr h is the water depth Froude number, k1, k2 are undetermined coefficients of the prediction formula; A residual sum of squares function is constructed for the maximum wave height prediction formula, and a particle swarm optimization algorithm is used to solve the undetermined coefficients in the prediction equation; A fitting curve of the undetermined coefficients and the water depth is constructed, the value of the undetermined coefficient is determined according to the water depth, and the maximum wave height prediction equation under the corresponding scenario is obtained by substituting the value into the maximum wave height prediction equation.

2. The method of claim 1, wherein, A first length of a ship model acceleration area, a second length of a channel section experimental area, and a third length of a buffer area are arranged in the flume. The ship wave height measuring points are arranged at both sides of the channel section experimental area.

3. The method of claim 1, wherein, The model scale is selected to satisfy that the channel water depth in the flume physical model is greater than 10 cm, and the total length of the flume is greater than 14 times the length of the ship.

4. The method of claim 2, wherein, The second length is not less than 4 times the length of the ship, and the third length is greater than 5 times the length of the ship.

5. The method of claim 1, wherein, Six to eight wave height meters are arranged at the same channel section to measure the ship wave height, and the distance between the wave height meters is determined according to the degree of change of the wave height; the distance between the wave height meters is increased at a flat terrain, and the distance between the wave height meters is decreased at a sharply changing terrain.

6. The method of claim 1, wherein, The water level designed in the experiment includes the lowest navigable water level, the normal water level, and the highest navigable water level; the ship speed includes the low speed, the normal speed, and the high speed.

7. The method of claim 6, wherein, Only the low speed is experimented at the lowest navigable water level, and all speeds are experimented at the other navigable water levels.

8. The method of claim 1, wherein, A residual sum of squares function is constructed for the maximum wave height prediction formula, and the particle swarm optimization algorithm is used to find the minimum value of the residual sum of squares function in combination with the measured maximum wave height value, so as to determine the unknown coefficient in the maximum ship wave height prediction formula under a certain water depth condition.

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