CN113378397B - Basic map model of inland waterway ship traffic flow considering ship rudder efficiency - Google Patents

Basic map model of inland waterway ship traffic flow considering ship rudder efficiency Download PDF

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CN113378397B
CN113378397B CN202110692614.0A CN202110692614A CN113378397B CN 113378397 B CN113378397 B CN 113378397B CN 202110692614 A CN202110692614 A CN 202110692614A CN 113378397 B CN113378397 B CN 113378397B
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廖鹏
杨文章
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Abstract

The invention discloses a basic map model of inland waterway ship traffic flow considering ship rudder performance, and belongs to the technical field of ship traffic flow. Firstly, taking ship rudder efficiency into consideration, and providing a minimum navigational speed characteristic variable; correcting the blocking density characteristic variable, defining the blocking density characteristic variable as the maximum density, and giving a calculation method by deducing the minimum bow spacing; determining critical conditions of the ship traffic flow by referring to the vehicle traffic flow; and finally, deducing the speed-density relation of the ship traffic flow according to the speed-space relation of the ship, obtaining a basic diagram model of the ship traffic flow, and providing a calculation method of each characteristic variable. The traffic flow basic diagram model suitable for the inland ship provided by the invention not only takes into account the general rule of the traffic flow basic diagram model, but also has the characteristics of inland ship traffic flow, and the result is favorable for the development of traffic flow theory.

Description

Basic map model of inland waterway ship traffic flow considering ship rudder efficiency
Technical Field
The invention relates to a basic map model of inland waterway ship traffic flow considering ship rudder performance, belonging to the technical field of ship traffic flow.
Background
In recent years, the inland water transportation demand is vigorous, the ship is large, the gathering effect of transportation to a main channel is obvious, the phenomenon of serious ship crowding occurs in a local navigation section and a local period, and the contradiction of insufficient local channel passing capacity relative to traffic demand is highlighted. In order to effectively relieve channel congestion and reasonably organize ship traffic, it is highly desirable to grasp basic characteristics of inland channel ship traffic flow, particularly basic diagrams of ship traffic flow.
In the past, the basic diagram of the ship traffic flow is researched, the basic diagram model of the vehicle traffic flow is often directly adopted to fit the relationship among the speed, the density and the flow of the ship traffic flow, and a linear model of the speed-density relationship proposed by GREENSHIELDS, a logarithmic model of the speed-density relationship proposed by Greenberg and an exponential model of the speed-density relationship proposed by Underwood are more common. The expression of these models involves the characteristic variables of the traffic flow: maximum flow q m, critical speed v m, optimum density k m, blocking density k j, speed v f. The blocking density k j is defined as a density when the traffic is dense to the point where the vehicle cannot move, but this definition is not applicable to the ship traffic flow. For the ship traffic flow, the speed can be reduced to zero unlike the speed when the vehicle runs, the lowest speed can not be reduced to zero for keeping rudder performance when the ship is in normal voyage, so that the characteristic variable of the ship traffic flow is required to be redefined. It is not appropriate to directly apply the basic map model of the vehicle traffic flow to the study of the ship traffic flow, and a basic map model suitable for the ship traffic flow is required.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a basic map model of the traffic flow of the inland waterway ship considering the ship rudder performance through theoretical analysis, so as to promote the research of the traffic flow of the inland waterway ship.
The aim of the invention can be achieved by the following technical scheme:
a basic map model of a inland waterway ship traffic flow considering ship rudder performance, the method comprising the steps of:
S1, considering ship rudder effectiveness, and providing a minimum navigational speed characteristic variable, wherein the characteristic variable is v min;
S2, correcting the blocking density characteristic variable, defining the blocking density characteristic variable as the maximum density, wherein the expression of the maximum density is as follows:
kmax＝1000/smin (1)
Wherein: k max is the maximum density (Kkm -1);smin is the minimum bow spacing (m), L 0 is the ship length (m), mu is the ratio of the reaction distance to the safety spacing, and the upper limit is 42%;
S3, determining critical conditions of the ship traffic flow as follows: k=k max,v＝vmin;k＝0,v＝vf;k＝km,v＝vm;
Wherein k is the traffic density of the ship (Ikm -1); v is the traffic flow speed of the ship (km.h -1);vf is the speed in smooth going, i.e. the density tends to zero, the average speed when the ship can go in smooth going without resistance; k m is the optimal density, i.e. the density when the flow reaches the maximum; v m is the critical speed, i.e. the speed when the flow reaches the maximum);
S4, building a basic map model of the ship traffic flow through a speed-density logarithmic relation model, a speed-density linear relation model and a speed-density exponential relation model according to the lowest navigational speed characteristic variable v min in the step S1 and the maximum density k max defined in the step S2:
The speed-density logarithmic relation model in this model is as follows:
The velocity-density linear relationship model in this model is as follows:
the velocity-density index relationship model in this model is as follows:
wherein e is a natural constant having a value of about 2.718281828459045; the logarithmic and linear relationship models correspond to the Greenberg and GREENSHIELDS models in the vehicle traffic flow, respectively, but differ in form by correcting or redefining some characteristic variables; the exponential relationship model is consistent with Underwood model form in the vehicle traffic flow;
According to the relationship of speed and density, the basic diagram of ship traffic flow can be drawn by using density, speed, density, flow and speed-flow as horizontal-vertical axes.
The minimum bow spacing s min is derived by the above method as follows:
Minimum bow-to-bow spacing expression: s min＝Lmin+L0; wherein: l min is the minimum safety distance (m) between ships, namely the minimum distance from the stern of the front ship to the bow of the rear ship; l 0 is the captain (m). L min by considering the difference of the stopping safety distance, the reaction distance and the front and rear ship braking distance, the value can be reduced to 0.25L 0/(1-mu).
According to the above method, the critical condition of the ship traffic flow in step S3 is derived with reference to the critical condition of the vehicle traffic flow. And defining a minimum navigational speed characteristic variable v min; since the blocking density k j in the vehicle traffic is defined as the density when the traffic is dense to the point that the vehicle cannot move, but this definition is not applicable to the ship traffic, it should be corrected that k j is defined as the maximum density k max of the ship traffic when the ship speed is the lowest speed v min, so that the critical condition k=k j of the vehicle traffic, v=0 is replaced with k=k max,v＝vmin.
According to the method, in the step S4, a speed-density logarithmic relation model, a speed-density linear relation model and a speed-density exponential relation model are obtained through deduction according to the following formula:
Based on GM model, the following expression is used:
v(t)＝λln[s(t)]+C (4a)
Substituting critical conditions k=k max,v＝vmin and k=k m,v＝vm to obtain a speed-density logarithmic relation model;
By the following expression:
Substituting critical conditions k=0, v=v f and k=k max,v＝vmin, a linear relationship model of the speed-density of the ship traffic flow can be deduced;
By the following expression:
Wherein v (t) represents the speed of an individual ship at the time t, and the unit is km.h -1; s (t) represents the separation between the individual ship and the bow of the front ship at the moment t, the unit is km, and the conversion relation between the individual ship and the density k is s (t) =1/k; lambda is a positive constant; c is a constant. Substituting critical conditions k=0, v=v f and k=k m,v＝vm, an exponential relationship model of the speed-density of the ship traffic flow can be deduced;
According to the method, v m is a critical speed, which is defined as the speed when the flow reaches the maximum;
k m is the optimal density, defined as the optimal density variable;
v f is the speed of the free running, i.e. the average speed of the ship when the ship can go free is defined as the variable of the average speed of the free running;
v min is the lowest navigational speed characteristic variable, defined as the lowest navigational speed characteristic variable;
k max is the maximum density, defined as the maximum density characteristic variable;
the conversion of the above-mentioned variable values with parameters λ and C in the speed-space relationship of the formulae (4 a, 4b, 4C) is shown in the following table:
by adopting the technical scheme, the invention can produce the following technical effects:
The basic map model of the inland waterway ship traffic flow, which is provided by the invention, considers the rudder of the ship, redefines and corrects partial characteristic variables of the ship traffic flow, and further provides a basic map model of the inland waterway ship traffic flow on the basis of the classical basic map model of the vehicle traffic flow; the traffic flow basic diagram model suitable for the inland ship provided by the invention not only takes into account the general rule of the traffic flow basic diagram model, but also has the characteristics of inland ship traffic flow, and the result is favorable for the development of traffic flow theory.
Drawings
FIG. 1 is a flow chart of a basic diagram model of inland waterway ship traffic flow taking ship rudder efficiency into consideration;
FIG. 2 is a graph of a fit of the model of the present invention to the velocity-density relationship in experiment one;
FIG. 3 is a graph of a fit of the model of the present invention to the flow-density relationship in experiment one;
FIG. 4 is a graph of a fit of the model of the present invention to the flow-speed relationship in experiment one;
FIG. 5 is a graph of a fit of the model of the present invention to the velocity-density relationship in experiment two;
FIG. 6 is a graph of a fit of the model of the present invention to the flow-density relationship in experiment two;
FIG. 7 is a graph of a fit of the model of the present invention to the flow-velocity relationship in experiment two.
Detailed Description
In order to make the purpose and technical solutions of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. It will be apparent that the described embodiments are some, but not all, embodiments of the invention. All other embodiments, which can be made by a person skilled in the art without creative efforts, based on the described embodiments of the present invention fall within the protection scope of the present invention.
As shown in fig. 1: the invention provides a basic map model of inland waterway ship traffic flow considering ship rudder efficiency, which comprises the following steps:
s1, considering ship rudder performance, and providing a minimum navigational speed characteristic variable:
For the ship traffic flow, the speed can be reduced to zero when the vehicle runs, and the lowest navigational speed limit value related to factors such as ship performance, navigation environment and the like is used when the ship sails so as to maintain rudder efficiency. Because once the ship loses rudder efficiency, a pilot loses control over the course of the ship, the time and oil consumption are long when the ship is restarted again. Therefore, a characteristic variable v min is additionally defined in the ship traffic flow to represent the lowest speed of keeping rudder efficiency when the ship runs normally.
S2, correcting the blocking density characteristic variable, and defining the blocking density characteristic variable as the maximum density:
The blocking density k j in the vehicle traffic flow is defined as the density at which the traffic flow is dense to the point at which the vehicle cannot move, but this definition is not applicable to the ship traffic flow, and should be modified so that k j is defined as the lowest speed v min, the maximum density k max.kmax of the ship traffic flow is related to the minimum inter-ship bow space s min. Wherein:
smin＝Lmin+L0 (1)
wherein: s min is the minimum bow pitch (m); l 0 is the captain (m); l min is the minimum safe separation (m) between vessels, i.e. the minimum distance from the stern of the front vessel to the bow of the rear vessel. According to the literature: based on the ship field model research (Li Ying) of the ship stopping sight distance, L min is related to the ship stopping safety distance, the reaction distance and the front-rear ship braking distance difference between two ships, and the value can be simplified to be 0.25L 0/(1-mu), wherein mu is the ratio of the reaction distance to the safety distance, and the upper limit is 42% in general. Thus, the maximum density k max of the ship traffic flow is:
s3, determining critical conditions of ship traffic flow:
The critical conditions of the ship traffic flow are rewritten to k=k max,v＝vmin;k＝0,v＝vf;k＝km,v＝vm with reference to the critical conditions of the vehicle traffic flow. Wherein v f is the smooth speed, namely the average speed when the density tends to zero and the ship can be free from the smooth speed; k m is the optimal density, i.e. the density at which the flow reaches a maximum; v m is the critical speed, i.e. the speed at which the flow reaches a maximum.
S4, deducing a ship traffic flow speed-density relation to obtain a ship traffic flow basic diagram model:
Three relations between the speed and the distance of the traffic entity during the following movement can be deduced according to the GM model:
v(t)＝λln[s(t)]+C (3a)
Wherein v (t) represents the speed of the individual ship at the moment t, and the unit is km.h -1; s (t) represents the space between the individual ship and the bow of the front ship at the moment t, and the unit is km; lambda is a positive constant; c is a constant.
Considering that all the ship speeds are consistent under the condition of the ship traffic flow balance state and are equal to the macroscopic traffic flow speed, and the ship head distance is the reciprocal of the density, 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 microscopic level are converted into the macroscopic traffic flow speed v and the macroscopic traffic flow density k. Substituting the critical condition of the ship traffic flow, the speed-bow space relation can be converted into the ship traffic flow speed-density relation.
For equation (3 a), substituting the critical conditions k=k max,v＝vmin and k=k m,v＝vm, a logarithmic relationship model of the ship traffic flow speed-density can be derived:
For equation (3 b), substituting the critical conditions k=0, v=v f, and k=k max,v＝vmin, a linear relationship model of the ship traffic flow speed-density can be derived:
for equation (3 c), substituting the critical conditions k=0, v=v f, and k=k m,v＝vm, an exponential relationship model of the ship traffic flow speed-density can be derived:
Wherein the logarithmic and linear relationship models correspond to the Greenberg and GREENSHIELDS models in the vehicle traffic flow, respectively, but differ in form by correcting or redefining part of the characteristic variables; the exponential relationship model is consistent with the Underwood model form in the vehicle traffic flow.
The conversion relationships between the values of the respective characteristic variables and the parameters λ and C in the speed-space relationships of the formulae (3 a, 3b, 3C) are shown in table 1:
table 1 characteristic variables of three models
According to the relation between the speed and the density and the characteristic variable value, the basic diagram of the ship traffic flow is drawn by taking the density, the speed, the density, the flow and the speed and the flow as horizontal axis and vertical axis respectively.
And (3) selecting real ship heel-and-heel experimental data developed in Jiangsu tin Cheng canal Jiangyin North stage in 12 months and 20 days of 2019 to test the model. The field experiment organizes 7 cargo ships and 2 navigation boats to form an experiment fleet respectively, the cargo ships are 800-ton full-load, the performance is good, the ship length is about 45m, the navigation boat is 17m, and the ship is navigated by a driver according to habit. The navigation speed and the position of each ship are recorded in real time by a high-precision GNSS positioning instrument. The experimental period was about 20km long, and the experimental period amounted to about 4 hours. Figure 2 depicts the speed of each vessel and the bow pitch for different speeds, accelerations and decelerations of the lead vessel. The first experiment consists of seven cargo ships, wherein the maximum navigational speed of the ship is 10.7km/h, the minimum navigational speed of the ship is 1.9km/h, and the maximum spacing between the ship heads is 0.415km and the minimum spacing between the ship heads is 0.054km; the second experiment consists of two navigation boats, wherein the maximum navigational speed of the boats is 19.1km/h, the minimum navigational speed of the boats is 5.2km/h, and the maximum bow distance is 0.585km and the maximum bow distance is 0.042km.
The results of the model fitting to experimental data are shown in figures 2-7. The scattered point distribution map 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 graph model are calculated according to table 1 after fitting the velocity-pitch relationship. And only evaluating the fitting result of the speed-density relation in the fitting result analysis. Three models in the two experiments were evaluated using Mean Absolute Percentage Error (MAPE), root Mean Square Error (RMSE) and determinant coefficient R-square (R 2) as evaluation indexes, and the evaluation results are shown in Table 2. It can be seen that the fitting of the three models to the experimental data is excellent.
Table 2 evaluation index of two experiments
According to the invention, the rudderiness of the ship is considered, and part of characteristic variables of the ship traffic flow are redefined and corrected, so that a basic map model of the ship traffic flow of the inland waterway is provided on the basis of a classical basic map model of the ship traffic flow, the general rule of the basic map model of the traffic flow is considered, the characteristics of the ship traffic flow of the inland waterway are also considered, and the development of traffic flow theory is facilitated.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims (3)

1. The basic map model of inland waterway ship traffic flow considering ship rudder performance is characterized in that: it comprises the following steps:
S1, considering ship rudder effectiveness, and providing a minimum navigational speed characteristic variable, wherein the characteristic variable is v min;
S2, correcting the blocking density characteristic variable, defining the blocking density characteristic variable as the maximum density, wherein the expression of the maximum density is as follows:
kmax＝1000/smin (1)
Wherein: k max is the maximum density (Kkm -1);smin is the minimum bow spacing (m), L 0 is the ship length (m), mu is the ratio of the reaction distance to the safety spacing, and the upper limit is 42%;
The minimum bow spacing s min is derived by:
Minimum bow-to-bow spacing expression: s min＝Lmin+L0; wherein: l min is the minimum safety distance (m) between ships, namely the minimum distance from the stern of the front ship to the bow of the rear ship; l 0 is the captain (m); l min is simplified to 0.25L 0/(1-mu) by considering the difference of the ship stopping safety distance, the reaction distance and the front and rear ship braking distances;
S3, determining critical conditions of the ship traffic flow as follows: k=k max,v＝vmin;k＝0,v＝vf;k＝km,v＝vm;
Wherein k is the traffic density of the ship (Ikm -1); v is the traffic flow speed of the ship (km.h -1);vf is the speed in the free running, i.e. the average speed when the density is approaching zero and the ship is free from running; k m is the optimal density, i.e. the density when the flow rate is maximum; v m is the critical speed, i.e. the speed when the flow rate is maximum;
S4, building a basic map model of the ship traffic flow through a speed-density logarithmic relation model, a speed-density linear relation model and a speed-density exponential relation model according to the lowest navigational speed characteristic variable v min in the step S1 and the maximum density k max defined in the step S2:
The speed-density logarithmic relation model in this model is as follows:
The velocity-density linear relationship model in this model is as follows:
the velocity-density index relationship model in this model is as follows:
wherein the logarithmic and linear relationship models correspond to the Greenberg and GREENSHIELDS models in the vehicle traffic flow, respectively, but differ in form by correcting or redefining part of the characteristic variables; the exponential relationship model is consistent with Underwood model form in the vehicle traffic flow;
The speed-density logarithmic relation model, the speed-density linear relation model and the speed-density exponential relation model are obtained by deduction through the following formula:
Based on GM model, the following expression is used:
v(t)＝λln[s(t)]+C (4a)
Substituting critical conditions k=k max,v＝vmin and k=k m,v＝vm to obtain a speed-density logarithmic relation model;
By the following expression:
Substituting critical conditions k=0, v=v f and k=k max,v＝vmin to derive a linear relationship model of the speed-density of the ship traffic flow;
By the following expression:
substituting critical conditions k=0, v=v f and k=k m,v＝vm to derive an exponential relationship model of the speed-density of the ship traffic flow;
Wherein v (t) represents the speed of an individual ship at the time t, and the unit is km.h -1; s (t) represents the separation between the individual ship and the bow of the front ship at the moment t, the unit is km, and the conversion relation between the individual ship and the density k is s (t) =1/k; lambda is a positive constant; c is a constant;
According to the relationship of speed and density, respectively using density, speed, density, flow and speed-flow as horizontal-vertical axes to draw a basic diagram of ship traffic flow.
2. The model of a base map of inland waterway ship traffic flows taking into account ship rudder performance according to claim 1, wherein: the critical conditions of the ship traffic flow in step S3 are obtained by correcting the critical conditions of the vehicle traffic flow.
3. The model of a base map of inland waterway ship traffic flows taking into account ship rudder performance according to claim 1, wherein: the conversion relation between the values of the defined maximum critical speed variable, the optimal density variable, the average free speed variable, the minimum navigational speed characteristic variable and the maximum density characteristic variable and the parameters lambda and C in the speed-space relation of the above formulas 4a, 4b and 4C is as follows:
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