CN113378397A - Inland waterway ship traffic flow basic graph model considering ship rudder effect - Google Patents
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Abstract
The invention discloses a basic graph model of inland waterway ship traffic flow considering ship rudder effect, and belongs to the technical field of ship traffic flow. The model firstly considers the rudder effect of a ship and provides a minimum speed characteristic variable; correcting a characteristic variable of the blocking density, defining the characteristic variable as the maximum density, and giving a calculation method by deducing the minimum bow interval; then referring to the vehicle traffic flow, determining the critical condition of the ship traffic flow; and finally, deducing a ship traffic flow speed-density relation according to the ship speed-space relation to obtain a ship traffic flow basic graph model, and providing a calculation method of each characteristic variable. The basic graph model of the traffic flow suitable for inland ships, which is provided by the invention, not only considers the general rule of the basic graph model of the traffic flow, but also has the characteristics of the inland ship traffic flow, and the achievement of the basic graph model of the traffic flow is beneficial to the development of the traffic flow theory.
Description
Technical Field
The invention relates to a basic graph model of inland waterway ship traffic flow considering ship rudder effect, and belongs to the technical field of ship traffic flow.
Background
In recent years, inland river water transportation demands are vigorous, ships are large in size, the gathering effect of transportation to a main line channel is obvious, severe ship crowding phenomena occur in local navigation sections and local time periods, and the contradiction of local channel passing capacity relative to insufficient traffic demands is highlighted. In order to effectively relieve channel congestion and reasonably organize ship traffic, the basic characteristics of the ship traffic flow of inland channel, especially the basic diagram of the ship traffic flow, are urgently needed to be mastered.
In the past, the research on a basic graph of ship traffic flow is related, and a basic graph model of vehicle traffic flow is often directly adopted to fit the relation among the speed, the density and the flow of the ship traffic flow, so that a speed-density relation linear model proposed by Greenshirds, a speed-density relation logarithmic model proposed by Greenberg and a speed-density relation exponential model proposed by Underwood are common. The expression of these models relates to the characteristic variables of the traffic flow: maximum flow qmCritical velocity vmOptimum density kmBlocking density kjFree speed vf. Wherein the blocking density kjDefined as the density at which the flow is so dense that the vehicle cannot move, but this definition is not applicable to marine traffic flow. For the ship traffic flow, the speed can be reduced to zero, unlike the speed when the vehicle runs, the lowest speed of the ship does not reduce to zero in order to maintain the steering effect when the ship normally runs, and therefore, the characteristic variable of the ship traffic flow needs to be redefined. Then, it is not appropriate to directly apply the basic graph model of the vehicle traffic flow to the research of the ship traffic flow, and a basic graph model suitable for the ship traffic flow is required.
Disclosure of Invention
The invention aims to solve the technical problem of providing a basic graph model of the inland waterway ship traffic flow by considering ship rudder effect through theoretical analysis, and promoting the research of the inland waterway ship traffic flow.
The purpose of the invention can be realized by the following technical scheme:
an inland waterway ship traffic flow basic graph model considering ship rudder effect, which comprises the following steps:
s1, taking the rudder effect of the ship into consideration, and providing a minimum speed characteristic variable, wherein the characteristic variable is vmin；
S2, correcting a characteristic variable of the blocking density, and defining the characteristic variable as the maximum density, wherein the expression of the maximum density is as follows:
kmax＝1000/smin (1)
in the formula: k is a radical ofmaxIs maximum density (i.km)-1)；sminIs the minimum bow spacing (m); l is0Is the ship length (m); mu is the ratio of the reaction distance to the safety distance, and the upper limit is 42%;
s3, determining the critical conditions of the ship traffic flow as follows: k is kmax，v＝vmin；k＝0，v＝vf；k＝km，v＝vm；
Wherein k is ship traffic flow density (e.g., km)-1) (ii) a v is the ship traffic flow speed (km.h)-1)；vfThe average speed of the ship can be smooth, namely the density tends to zero; k is a radical ofmThe optimum density, i.e. the density at which the flow rate reaches a maximum; v. ofmThe critical speed is the speed at which the flow rate reaches the maximum;
s4, passing through the lowest speed characteristic variable v in the step S1minThe maximum density k defined in step S2maxEstablishing a ship traffic flow basic graph model through a speed-density logarithmic relation model, a speed-density linear relation model and a speed-density exponential relation model:
the logarithmic velocity-density relationship model in the model is as follows:
the linear relation model of velocity-density in the model is as follows:
the speed-density exponential relation model in the model is as follows:
wherein e is a natural constant having a value of about 2.718281828459045; the logarithmic relation model and the linear relation model respectively correspond to a Greenberg model and a Greenshirds model in the vehicle traffic flow, but are different in form because part of characteristic variables are corrected or redefined; the exponential relation model is consistent with an Underwood model in the vehicle traffic flow in form;
according to the speed-density relationship, a ship traffic flow basic diagram can be drawn by respectively taking density-speed, density-flow and speed-flow as horizontal and vertical axes.
In the above-mentioned manner, the minimum bow spacing sminDerived from the following process:
minimum bow spacing expression: smin＝Lmin+L0(ii) a In the formula: l isminThe minimum safe distance (m) between the ships is the minimum distance from the stern of the front ship to the bow of the rear ship; l is0The length of the ship (m). L isminBy considering the safe stopping distance, the reaction distance and the difference between the braking distance of the front ship and the braking distance of the rear ship, the value can be reduced to 0.25L0/(1-μ)。
In the above method, the critical condition of the ship traffic flow is referred to the critical condition of the vehicle traffic flow in step S3. And defining a minimum speed characteristic variable vmin(ii) a Due to the blocking density k in the traffic flowjDefined as the density of the dense traffic flow to the point where the vehicle cannot move, but this definition is not applicable to the ship traffic flow, and should be corrected byjDefined as the speed of the ship as the lowest speed vminMaximum density k of ship traffic flowmaxSo that the critical condition k of the vehicle traffic flow is kjV-0 replacement for k-kmax，v＝vmin。
According to the above method, the speed-density logarithmic relation model, the speed-density linear relation model and the speed-density exponential relation model in step S4 are derived by the following equations:
based on the GM model, by the following expression:
v(t)＝λln[s(t)]+C (4a)
substituting the critical condition k ═ kmax，v＝vminAnd k is km，v＝vmObtaining a speed-density logarithmic relation model;
by the following expression:
substituting the critical condition k to 0 and v to vfAnd k is kmax，v＝vminA linear relation model of ship traffic flow speed-density can be deduced;
by the following expression:
wherein v (t) represents the speed of the individual ship at time t, in km.h-1(ii) a s (t) represents the distance between the individual ship and the front ship bow at the time t, the unit is km, and the conversion relation of the km and the density k is that s (t) is 1/k; λ is a normal number; c is a constant. Substituting the critical condition k to 0 and v to vfAnd k is km，v＝vmAn exponential relation model of ship traffic flow speed-density can be deduced;
in the above-mentioned manner, for vmCritical speed, defined as the speed at which the flow reaches maximum;
kmdefining as an optimal density variable for optimal density;
vfthe average speed of the ship when the ship can run smoothly is the smooth speed, namely the density tends to zero, and is defined as an average smooth speed variable;
vmindefining the characteristic variable as the lowest speed characteristic variable;
kmaxthe maximum density is defined as a characteristic variable of the maximum density;
the conversion of the variable values to the parameters λ and C in the speed-pitch relationship of equations (4a, 4b, 4C) is shown in the following table:
by adopting the technical scheme, the invention can produce the following technical effects:
the invention provides a basic graph model of inland waterway ship traffic flow considering ship rudder effect, which redefines and corrects partial characteristic variables of the ship traffic flow considering the rudder effect of ships, and further provides a basic graph model of the inland waterway ship traffic flow on the basis of a classical basic graph model of vehicle traffic flow; the basic graph model of the traffic flow suitable for inland ships, which is provided by the invention, not only considers the general rule of the basic graph model of the traffic flow, but also has the characteristics of the inland ship traffic flow, and the achievement of the basic graph model of the traffic flow is beneficial to the development of the traffic flow theory.
Drawings
FIG. 1 is a basic graphical model flow chart of inland waterway ship traffic flow considering ship rudder effect according to the present invention;
FIG. 2 is a plot of a fit of the model of the present invention to a velocity-density relationship in experiment one;
FIG. 3 is a plot of a fit of the model of the present invention to the flow-density relationship in experiment one;
FIG. 4 is a plot of a fit of the model of the present invention to the flow-velocity relationship in experiment one;
FIG. 5 is a plot of the velocity-density relationship fit of the model of the present invention to experiment two;
FIG. 6 is a plot of a fit of the model of the present invention to the flow-density relationship of experiment two;
FIG. 7 is a plot of the fit of the model of the present invention to the flow-velocity relationship of experiment two.
Detailed Description
In order to make the purpose and technical solution of the embodiments of the present invention clearer, the technical solution of the embodiments of the present invention will be clearly and completely described below with reference to the drawings of the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the described embodiments of the invention without any inventive step, are within the scope of protection of the invention.
As shown in fig. 1: the invention provides a basic graph model of inland waterway ship traffic flow considering ship rudder effect, which comprises the following steps:
s1, taking the rudder effect of the ship into consideration, and providing a minimum speed characteristic variable:
for ship traffic flow, the speed can be reduced to zero different from that when the vehicle runs, and when the ship runs, a lowest speed limit value related to ship performance, navigation environment and other factors is used for keeping the steering effect. Once the ship loses the rudder effect, the driver loses the control on the ship course, and the ship is long in time and high in oil consumption when restarted again. Therefore, a characteristic variable v needs to be additionally defined in ship traffic flowminThe minimum speed at which the rudder effect is maintained when the ship is normally running is represented.
S2, correcting a blockage density characteristic variable, and defining the variable as the maximum density:
jam density k in vehicular traffic flowjDefined as the density of the dense traffic flow to the point where the vehicle cannot move, but this definition is not applicable to the ship traffic flow, and should be corrected byjDefined as the speed of the ship as the lowest speed vminMaximum density k of ship traffic flowmax。kmaxMinimum bow spacing s from shipminIt is related. Wherein:
smin＝Lmin+L0 (1)
in the formula: sminIs the minimum bow spacing (m); l is0Is the ship length (m); l isminThe minimum safe distance (m) between the ships, i.e. the minimum distance from the stern of the forward ship to the bow of the aft ship. According to the literature: ship field model research (LiYing), L based on ship stopping sight distanceminThe safe distance between two ships, the reaction distance and the difference between the braking distance of the front ship and the braking distance of the rear ship can be reduced to 0.25L0V (1-. mu.), where. mu.is the ratio of the reaction distance to the safety margin, the upper limit is usually 42%. Thus, maximum density k of marine traffic flowmaxComprises the following steps:
s3, determining the critical conditions of the ship traffic flow:
referring to the critical condition of the vehicle traffic flow, the critical condition of the ship traffic flow is rewritten into k ═ kmax，v＝vmin；k＝0，v＝vf；k＝km，v＝vm. Wherein v isfThe average speed of the ship can be smooth, namely the density tends to zero; k is a radical ofmThe optimum density, i.e. the density at which the flow rate reaches a maximum; v. ofmIs the critical velocity, i.e., the velocity at which the flow rate reaches a maximum.
S4, deducing a ship traffic flow speed-density relation to obtain a ship traffic flow basic graph model:
according to the GM model, three relations between the speed and the distance when the traffic entity moves with the galloping can be deduced:
v(t)＝λln[s(t)]+C (3a)
wherein v (t) represents the speed of the individual vessel at time t, in km.h-1(ii) a s (t) represents the distance between the individual ship and the front ship bow at the time t, and the unit is km; λ is a normal number; c is a constant.
Considering that all ship speeds are consistent under the condition of ship traffic flow balance state and are equal to the macro traffic flow speed, the distance between the ship heads is the reciprocal of the density, so the time factor (t) of the traffic state parameter can be omitted, and the individual ship speed v (t) and the ship head distance s (t) at the micro level are converted into the macro traffic flow speed v and the density k. The speed-bow spacing relation can be converted into a ship traffic flow speed-density relation by substituting the ship traffic flow critical condition.
For formula (3a), the critical condition k ═ k is substitutedmax，v＝vminAnd k is km，v＝vmThe ship traffic flow speed-density logarithmic relation model can be deduced:
for formula (3b), the critical condition k is substituted by 0, and v is substituted by vfAnd k is kmax，v＝vminThe linear relation model of ship traffic flow speed-density can be deduced:
for formula (3c), the critical condition k is substituted by 0, and v is substituted by vfAnd k is km，v＝vmAn exponential relation model of ship traffic flow speed-density can be deduced:
the logarithmic relation model and the linear relation model respectively correspond to a Greenberg model and a Greenshirds model in the vehicle traffic flow, but are different in form because part of characteristic variables are corrected or redefined; the exponential relationship model is consistent with the Underwood model form in vehicular traffic flow.
The values of the characteristic variables are converted into the parameters λ and C in the speed-pitch relationship of the equations (3a, 3b, 3C) as shown in table 1:
TABLE 1 characteristic variables of the three models
The ship traffic flow basic diagram can be drawn according to the speed-density relation and the characteristic variable value by respectively taking the density-speed, the density-flow and the speed-flow as the horizontal and vertical axes.
And (3) selecting actual ship following experiment data developed in the northwest segment of the river of the Xicheng river of Jiangsu in 2019, 12 months and 20 days to test the model. On-site experiments organize 7 cargo ships and 2 administrative boats to form an experiment fleet respectively, the cargo ships are 800 tons in full load and have good performance, the captain is about 45m, the administrative boat captain is 17m, and the ships are navigated by a driver according to habits. And recording the speed and the position of each ship in real time by a high-precision GNSS locator. The length of the experimental section was about 20km, and the total length of the experiment was about 4 h. Fig. 2 depicts the speed and bow spacing of each vessel at different speeds, accelerations and decelerations of the lead vessel. The first experiment comprises seven cargo ships, the maximum navigational speed of the ship is 10.7km/h, the minimum navigational speed of the ship is 1.9km/h, and the distance between the ship heads is 0.415km at most and 0.054km at least; and the second experiment consists of two administrative boats, the maximum speed of the ship is 19.1km/h, the minimum speed of the ship is 5.2km/h, and the distance between the ship heads is 0.585km and 0.042km at most.
The results of the model fit to the experimental data are shown in figures 2-7. Wherein the scatter distribution chart of the experimental data is derived from the position and speed information of the ship in the experimental data; the characteristic variables in the basic map model were calculated as shown in table 1 after fitting the velocity-spacing relationship. And only evaluating the speed-density relation fitting result when analyzing the fitting result. Using Mean Absolute Percent Error (MAPE), Root Mean Square Error (RMSE) and coefficient of determination R-square (R)2) Three models of the two experiments were evaluated as evaluation indexes, and the evaluation results are shown in table 2. Therefore, the fitting conditions of the three models to experimental data are good.
TABLE 2 evaluation indexes of two experiments
The invention takes the rudder effect of the ship into consideration, redefines and corrects partial characteristic variables of the ship traffic flow, and further provides a inland waterway ship traffic flow basic graph model on the basis of a classic basic graph model of the vehicle traffic flow, which not only considers the general rule of the traffic flow basic graph model, but also has the characteristics of the inland waterway ship traffic flow, and the achievement of the invention is beneficial to the development of the traffic flow theory.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (5)
1. A basic graph model of inland waterway ship traffic flow considering ship rudder effect is characterized in that: it comprises the following steps:
s1, taking the rudder effect of the ship into consideration, and providing a minimum speed characteristic variable, wherein the characteristic variable is vmin；
S2, correcting a characteristic variable of the blocking density, and defining the characteristic variable as the maximum density, wherein the expression of the maximum density is as follows:
kmax＝1000/smin (1)
in the formula: k is a radical ofmaxIs maximum density (i.km)-1)；sminIs the minimum bow spacing (m); l is0Is the ship length (m); mu is the ratio of the reaction distance to the safety distance, and the upper limit is 42%;
s3, determining the critical conditions of the ship traffic flow as follows: k is kmax，v＝vmin；k＝0，v＝vf；k＝km，v＝vm；
Wherein k is ship traffic flow density (e.g., km)-1) (ii) a v is the ship traffic flow speed (km.h)-1)；vfThe average speed of the ship can be smooth, namely the density tends to zero; k is a radical ofmThe optimum density, i.e. the density at which the flow rate reaches a maximum; v. ofmIs coming toThe boundary speed, i.e. the speed at which the flow reaches maximum;
s4, passing through the lowest speed characteristic variable v in the step S1minThe maximum density k defined in step S2maxEstablishing a ship traffic flow basic graph model through a speed-density logarithmic relation model, a speed-density linear relation model and a speed-density exponential relation model:
the logarithmic velocity-density relationship model in the model is as follows:
the linear relation model of velocity-density in the model is as follows:
the speed-density exponential relation model in the model is as follows:
the logarithmic relation model and the linear relation model respectively correspond to a Greenberg model and a Greenshirds model in the vehicle traffic flow, but are different in form because part of characteristic variables are corrected or redefined; the exponential relation model is consistent with an Underwood model in the vehicle traffic flow in form;
according to the speed-density relationship, a ship traffic flow basic diagram can be drawn by respectively taking density-speed, density-flow and speed-flow as horizontal and vertical axes.
2. The basic graphic model of inland waterway ship traffic flow considering ship rudder effect according to claim 1, wherein: minimum bow spacing sminDerived from the following process:
minimum bow spacing expression：smin＝Lmin+L0(ii) a In the formula: l isminThe minimum safe distance (m) between the ships is the minimum distance from the stern of the front ship to the bow of the rear ship; l is0The length of the ship (m). L isminBy considering the safe stopping distance, the reaction distance and the difference between the braking distance of the front ship and the braking distance of the rear ship, the value can be reduced to 0.25L0/(1-μ)。
3. The basic graphic model of inland waterway ship traffic flow considering ship rudder effect according to claim 1, wherein: the critical condition of the ship traffic flow in step S3 is obtained by correcting the critical condition of the vehicular traffic flow.
4. The basic graphic model of inland waterway ship traffic flow considering ship rudder effect according to claim 1, wherein: in step S4, the speed-density logarithmic relation model, the speed-density linear relation model, and the speed-density exponential relation model are derived by the following equations:
based on the GM model, by the following expression:
v(t)＝λln[s(t)]+C (4a)
substituting the critical condition k ═ kmax，v＝vminAnd k is km，v＝vmObtaining a speed-density logarithmic relation model;
by the following expression:
substituting the critical condition k to 0 and v to vfAnd k is kmax，v＝vminA linear relation model of ship traffic flow speed-density can be deduced;
by the following expression:
substituted into clinicalBoundary conditions k-0 and v-vfAnd k is km，v＝vmAn exponential relation model of ship traffic flow speed-density can be deduced;
wherein v (t) represents the speed of the individual ship at time t, in km.h-1(ii) a s (t) represents the distance between the individual ship and the front ship bow at the time t, the unit is km, and the conversion relation of the km and the density k is that s (t) is 1/k; λ is a normal number; c is a constant.
5. The basic graphic model of inland waterway ship traffic flow considering ship rudder effect according to claim 4, wherein: the conversion relationship between the defined values of the flow maximum critical speed variable, the optimum density variable, the average smooth speed variable, the lowest speed characteristic variable and the maximum density characteristic variable and the parameters lambda and C in the speed-spacing relationship of the above equations 4a, 4b and 4C is as follows:
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