CN101739822A - Sensor network configuring method for regional traffic state acquisition - Google Patents

Abstract

The invention relates to a sensor network configuring method for regional traffic state acquisition. The method comprises the following steps of: optimizing the sensor network from the aspect of acquiring traffic information; putting forward an information density function on the basis of relativity with the sensor acquiring the traffic information; establishing information value maximum models of two stages by the information density function and through considering the comprehensive cost for configuring the sensors, wherein the model of the first stage is modeled on the basis of road sections, and the shortest road algorithm of model solution is put forward (see figure 1 for algorithm executing flowchart); the model of the second stage is modeled on the basis of road networks or regions, and the relativity between the road sections is considered (see figure 2 for algorithm executing flowchart).

Description

The sensor network configuring method that regional traffic state obtains

Technical field

The present invention relates to the sensor network configuring method that a kind of regional traffic state obtains, the invention belongs to traffic behavior detecting sensor technical field, relate in particular to sensor placement optimization and network optimized approach.

Background technology

It is the important prerequisite of carrying out traffic flow control and traffic administration such as inducing that road traffic state obtains, be the necessary basis of formulating traffic insurance measures such as traffic safety management strategy, traffic hazard detection, the analysis of traffic hazard reason, be the traffic infrastructure management, monitor and safeguard the indispensable firsthand information.Therefore to obtain be the basic major issue that traffic administration, traffic insurance and traffic infrastructure monitoring are safeguarded to traffic behavior.

Sensor placement Study on optimized meaning has some, and whether the traffic data that traffic sensor collects can correct response traffic flow running rate at that time, with the space density and the particular location of sensor very big relation is arranged.Because traffic sensor that generally adopts both at home and abroad such as collections such as toroid winding, microwave radar and video sensor is the traffic flow parameter data of fixed location at present, have only when abundant sensor is arranged in the road network, the information that can obtain sufficiently complete is described road network traffic circulation state.

In order better to obtain traffic characteristics, grasp road traffic state in real time, traffic sensor is being brought into play more and more important effect.Obtain transport information by traffic sensor,, instruct traffic administration person to make a strategic decision for control of traffic and road person provides reliable traffic network information.Under the situation of given road information, lay sensor as how less cost, obtain the transport information of maximum value.From but the transport information that obtains is reliable as much as possible, real-time, complete, for vehicle supervision department provides transport information as much as possible, instruct communications policy.

Summary of the invention

In order to overcome the deficiency of prior art structure, the invention provides the sensor network configuring method that a kind of regional traffic state obtains, this method has universality, comprehensive, dirigibility.The present invention has provided based on the transport information of obtaining and has been worth maximum road network sensor placement optimization method.

The technical solution adopted for the present invention to solve the technical problems is:

The sensor network configuring method that a kind of regional traffic state obtains, contain following steps:

At set sensor place, obtain the step of the information of maximum road section traffic volume characteristic; According to obtaining the information density function of the correlativity of transport information for the basis with sensor, the comprehensive cost of placement sensor has been set up the step of the maximum model of two stage information value.

The step that the angle of the transport information of obtaining from sensor is optimized transducer arrangements; Describe the feature of relevance function, utilized the relevance function of path sensor to obtain the step of information density function.

The Layout Problem of sensor is converted into the step of digraph problem; Proposed the cum rights matrix of sensor digraph, and the stage expense of sensor has been converted into the step of highway section expense; Road section information is worth the step that finding the solution of maximum model is converted into critical path problem.

Set up the step of the maximum model of two stage information value: its phase one is that modeling is carried out on the basis with the highway section, utilizes shortest path algorithm to find the solution; Subordinate phase is that modeling is carried out on the basis with road network or zone, considers the correlativity between the highway section in the road network.

Foundation is based on the step of the maximum model of information value in highway section; Foundation is based on the step of the maximum model of information value of road network; Divide two steps that level is optimized sensor, from the line to the face, from the part to integral body, carry out the step that modeling is optimized again from the face to the line, from the part to integral body.

The shortest path of the dual graph by finding the solution the sensor digraph is tried to achieve the step of the arrangement of this highway section sensor; The correlativity and the scale of investment of section traffic information have been considered, the step that whole road network is optimized.

Beneficial effect of the present invention:

The present invention is optimized the path sensor layout from the angle of information value, can provide the laying scheme of information value maximum according to the integrated cost of laying sensor, can lay the variation of spacing simultaneously according to the case study of integrated cost, provide comparatively reasonably distribution method at last.

Description of drawings

Fig. 1 is the information density functional arrangement in common highway section;

Fig. 2 is sensor digraph G;

Fig. 3 is the dual graph G ' of sensor digraph;

Fig. 4 lays for the highway section sensor and optimizes process flow diagram;

Fig. 5 lays for area sensor and optimizes process flow diagram;

The sensor that Fig. 6 chooses for the match relevance function;

Fig. 7 is two sensors flow waveform figure;

Fig. 8 is a two sensors occupation rate oscillogram;

Fig. 9 is two sensors velocity wave form figure;

Figure 10 is each sensor velocity wave form figure;

Figure 11 is the fitting result of correlativity curve r (x);

Figure 12 is that initial sensor is laid synoptic diagram;

Figure 13 is g ₁₂(x) functional arrangement a;

Figure 14 is g ₁₂(x) functional arrangement b;

Figure 15 lays figure as a result for sensor.

Embodiment

Embodiment 1:

The sensor network configuring method that a kind of regional traffic state obtains, contain following steps:

(1) utilize the relevance function of path sensor to obtain the step of information density function; At set sensor place, obtain the step of the information of maximum road section traffic volume characteristic; Set up the step of the maximum model of information value for the information density function on basis and the comprehensive cost of laying sensor according to the correlativity of obtaining transport information with sensor;

Step 1: at first, at the sensor place that is disposed, can farthest represent section traffic information, far away more apart from this sensor, the quantity of information of the traffic characteristics in the highway section that this sensor can be represented will reduce.Here, the information density function of definition sensor is h (x), and h (x) expression is the traffic characteristics information of center unit distance with this sensor.If to establish the sensor place is initial point, h on the one-dimensional space (x) is for being the one dimension function at center with the initial point, on two-dimensional space for being the toroidal function at center with the initial point.Because we generally only detect the transport information on the linear highway section, so mainly study information density function property on the one-dimensional space here.

Step 2: the information density function can be represented according to the relevance function of the transport information of different distance on the highway section, can represent transport information completely herein at the sensor place, if the related coefficient with the information of sensing station is 1 herein, increase along with distance, the transport information of sensor can be represented herein, and the correlativity of information can reduce, during to ± ∞, be reduced to 0.With r (x) expression relevance function, then the pass of h (x) and r (x) is h (x)=a * r (x), and wherein a is a conversion factor, can demarcate according to different highway section situations.

Relevance function r (x) on the highway section between known sensor and other sensors can carry out following description:

(a) r (x) is about the continuous function on the field of definition, and field of definition is the segment distance on the linear highway section of being studied, and r (0)=1.

(b) according to different road surface characteristic, r (x) can have the different forms of expression, and (Fig. 1) such as triangle distribution, normal distribution, negative exponent distributions generally arranged, and some is symmetrical, and some is asymmetric.

(c) r (x) can be on the basis of the traffic environment of studying the highway section and highway section situation, utilize computer simulation technique, by intensive laying sensor, the transport information of pick-up transducers (as speed, density, flow) asks the related coefficient of each sensor to demarcate; The also transport information that can gather by the sensor that certain urban road has been laid, obtain with a certain distance from other sensors of this sensor correlativity of sensor transport information therewith, simulate r (x), here point out different categories of roads and road surface situation, its r (x) can be different, and the present invention adopts the method to demarcate.

Step 3: by demarcating the relevance function of road upper sensor, utilize conversion factor a, can try to achieve the road grid traffic information of this sensor representative in tenure of use in the highway section upper integral to this function in the hope of the information density function of each sensor.Set up model from the angle of information, each sensor can both be caught certain telecommunication flow information, when not having sensor, can make traffic flow lose certain information, the present invention's hypothesis is laid sensor thick and fast with identical distance, like this, it is exactly just to be converted into that the sensor placement problem is optimized in the highway section of length-specific: how on the basis of the information value of taking all factors into consideration traffic characteristics and sensor comprehensive cost, determine the sensor density on the certain distance highway section, and provide the sensor distribution method.

(2) foundation is based on the step of the maximum model of information value in highway section.

Step 1: unified for standard, be located at sensor in tenure of use, the transport information that folk prescription is upwards detected when sensor is a unit distance (getting 1km) is 1, promptly ${\∫}_0^{1}h\left(x\right)=1,$ For the road of being studied, establishing the density function of laying the whole road section information that obtains behind the sensor at a certain distance is g (x), and then the quantity of information that whole sensor obtained is $I=\underset{D}{\∫}g\left(x\right)\mathrm{dx},$ Wherein, D is the union of all the sensors field of definition, generally speaking for studying the distance in highway section.Density function after adjacent two sensors stack may be defined as into $g_{\mathrm{ij}}\left(x\right)=h_i\left(x\right)\⊕h_j\left(x\right),$ Wherein

Represent the information density stack operational symbol of two functions, wherein superpositing function can be expressed as follows:

$g_{\mathrm{ij}}\left(x\right)=h_i\left(x\right)\⊕h_j\left(x\right)=\left\{\begin{array}{cc}{h}_i\left(x\right)& D_i-D_i\∩D_j\\ h_j\left(x\right)& D_j-D_i\∩D_j\\ \mathrm{hh}(h_i\left(x\right),h_j\left(x\right))& D_i\∩D_j\end{array}\right.$

Wherein:

D _i, D _j--h _i(x), h _j(x) field of definition;

Hh (h _i, h _j)--i, the superpositing function of the information density function of j sensor remains further research about the stack of information density function, and the present invention gets max (h _i, h _j).

Step 2: suppose can lay sensor equably on research highway section, the sensor number of establishing laying is n, and the position of each sensor note is made i (1≤i≤n), and to establish the comprehensive cost of laying i sensor on this highway section be C _i, then according to above-mentioned foundation as drag:

$\max W=\mathrm{kI}-f=k{\∫}_0^{D}g\left(x\right)\mathrm{dx}-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{X}_i\·C_i$

$s.t.\left\{\begin{array}{c}g\left(x\right)=\underset{i=1}{\overset{n}{\⊕}}{h}_i\left(x\right)\\ X_i=0\mathrm{or}1\end{array}\right.$

Wherein:

W--comprehensive value, the road section traffic volume characteristic information of sensor representative are worth the expense of laying sensor that deducts.

K--represents on this highway section that in tenure of use, the value of 1 unit information, different road parameters have different k values at sensor.

C _i--lay the needed comprehensive cost of sensor (real cost of sensor installation in the highway section) at the i place, owing to be subjected to the influence of road environment, traffic environment, the highway section sensor installation inconvenience that has, as installation process difficulty, use, maintenance process inconvenience etc., therefore, the cost of these highway section sensors configured is than general highway section height, so different road parameters has different C values, for same section road, generally get identical C value, promptly get C _i=C;

X _i--0 or 1,0 is illustrated in the i place and does not lay sensor, and 1 is illustrated in the i place lays sensor;

h _i(x)--lay the information density function of sensor at the i place, different road parameters has different h _i(x), for same section road, generally get identical h _i(x) value is promptly got h _i(x)=h (x).

(3) Layout Problem of sensor is converted into the step of digraph problem; Proposed the cum rights matrix of sensor digraph, and the stage expense of sensor has been converted into the step of highway section expense; Road section information is worth the step that finding the solution of maximum model is converted into critical path problem; The shortest path of the dual graph by finding the solution the sensor digraph is tried to achieve the step (carry out flow process and see Fig. 4) of the arrangement of this highway section sensor.

Step 1: some parameters of model or function can utilize experimental formula or historical data match to obtain, and the known conditions that obtains at last has: the unit information expense k of the i place placement sensor on the highway section of studying _i, information density function h _i(x), the integrated cost C of placement sensor _i, the parameter that needs to set is n, promptly studies the highway section and initially lays number of sensors, the laying that can be converted into sensor is apart from d, if study the long L in highway section, then like this $d=\frac{L}{n-1}$ (sensor that L lays from the two ends, highway section is counted) can determine n according to the sensor distance that initial desire is laid like this.

Step 2: according to the information density function of each sensor and utilize superpositing function $g_{12}\left(x\right)=h_1\left(x\right)\⊕h_2\left(x\right)$ Calculate the overlapped information between any two sensors, obtain the information matrix I between following each sensor _Ij

Can be constructed as follows digraph G (Fig. 2), wherein 1,2 ..., k, ..., n is respectively the numbering of placement sensor on the highway section, also can represent the position of each sensor, and wherein any 2 all have an oriented circuit from the low grade to the high grade, the weights of each circuit are that value corresponding multiply by its corresponding unit information expense, i.e. information value between these 2 in the information matrix.Be w _Ij=k _IjI _Ij,

K wherein _IjGet average, promptly $k_{\mathrm{ij}}=\frac{k_i+{\mathrm{<figure-callout\; id="2"\; label="k\; j"\; filenames="DEST\_PATH\_HA20171172200910079438201E00012.png,DEST\_PATH\_HA20171172200910079438201E00031.png"\; state="\{\{state\}\}">k</figure-callout>}}_j}{2}.$

Finding the solution exactly of model looked for a paths from No. 1 sensor to the n sensor in this digraph, make the information value maximum on the path.

Step 3: consider the influence of each sensor comprehensive cost, whenever how will increase corresponding cost in the path through a sensor.If the position of each sensor is seen the node of mapping G, we can transfer to the node expense on the path so, because will increase the expense of this node, so can divide the expense of node on former and later two paths of this node of process equally through a node.Definable sensor i thus, the weight between the j is

$w_{\mathrm{ij}}=k_{\mathrm{ij}}{I}_{\mathrm{ij}}-\frac{1}{2}{C}_i-\frac{1}{2}{C}_j,$

Thereby can obtain the cum rights matrix of following digraph G:

Finding the solution road section information is worth maximum model and just is converted into the longest path problem of asking this digraph, owing to formed a lot of classic algorithm in the graph theory about shortest path, so each weights is asked its opposite number, get another digraph, this digraph of definable is the dual graph of former figure, note is made G ' (Fig. 3), so the cum rights matrix of this dual graph G ' is:

So just can because negative value may appear in weights, can find the solution in the hope of the shortest path of Fig. 3 with the Floyed algorithm.

Step 4: by trying to achieve the shortest path of G ', we can find a longest path according to the path of G ' on former figure G, and the highway section maximum information that obtain this moment is worth and is W=∑ w _Ij, w _IjBe each the cum rights value on the highway section, W the node of process be the disaggregation of model, i.e. sensing station and the number that will lay of this highway section, the laying maximum information that can obtain the highway section is worth like this.

(4) foundation is based on the step of the maximum model of information value of road network; Divide two steps that level is optimized sensor, from the line to the face, from the part to integral body, carry out the step that modeling is optimized again from the face to the line, from the part to integral body.The correlativity and the scale of investment of section traffic information have been considered, the step that whole road network is optimized (carry out flow process and see Fig. 5).

Step 1: demarcate each parameter according to expressway, through street, trunk roads, branch road etc., unit information expense k is arranged _i, information density function parameter b _i, the comprehensive cost C of laying sensor _iDeng.

Step 2: analyze each crossing,, each crossing is laid in advance according to the arrangement principle of crossing.

Step 3: if zone bigger (as considering the sensor placement of entire city), can be divided into some each zonules, each zone comprises that 20-30 highway section is (because of the increase along with distance, the correlativity of transport information can very fast attenuating), analyze the correlativity in each highway section, the highway section that each correlativity is strong is divided in groups;

Step 4: to each group, requirement must be provided with the highway section of sensor, then must lay; For the highway section that does not have particular requirement, guaranteeing at least in every group has a highway section to be laid, and can choose according to importance.Obtain needing in the road network to lay the highway section of sensor.

Step 5: if do not consider to drop into, can get suitable laying, utilize the highway section of phase one to be worth maximum Model Calculation apart from d.In order to improve precision, can lay by every 1m, result calculated is that the best under each highway section parameter is laid distance, counts thereby obtain best the laying, lays, and calculates and finishes; Drop into as if considering, do not consider to drop into calculating with above-mentioned earlier, obtain best the laying and count, always calculate and drop into,, then stop to calculate, otherwise enter step 6 as if dropping into less than estimating.

Step 6: Δ d is set, and constantly laying in the best in each highway section increases Δ d under the distance, recomputate, and drops into less than estimating up to total input, stops to calculate.

Embodiment 2:

With Beijing's road network is foundation, at different highway section situations the model application has been carried out in the highway section of plan placement sensor, utilize Beijing's sensing data that Beijing Traffic Administration Bureau provides as historical data, and done the parameter selection at the situation in actual highway section and the problem that will study, then utilize the model in the literary composition to provide computation process and result of calculation.

(1) highway section chooses

For layout optimization is carried out in through street, Beijing, choose one section through street of West 3rd Ring Road, Beijing, from the Zizhu Flyover to Feng Yiqiao, to 11 sensors (S1, S2, S3 on it, S4, S5, S6, S7, S8, S9, S10, S11) traffic flow data on April 10th, 2008 is analyzed, and sampling interval is 2 minutes, sees Fig. 6.

The particular location of each sensor is between following website, and is as shown in table 1:

Table 1 sensor particular location

Why select this section highway section to be because there is not the crossing before this section highway section, wagon flow is more satisfactory, be subjected to interference less, and a large-scale crossing is arranged in Feng Yi bridge back, the wagon flow of its back can be subjected to the influence of this crossing, the correlativity of back car flow information must be lower significantly, so we have selected these nine car flow information that sensor obtained to carry out correlation analysis.

(2) factor of selection correlation analysis

Car flow information mainly contains three part factors and constitutes: vehicle flowrate, vehicle density (occupation rate is represented), wagon flow speed.Select which factor to carry out correlation analysis experimental result is had direct influence.Below from the Zizhu Flyover to the bridge of garden and the space flight bridge carry out the correlation analysis of flow, occupation rate and speed respectively to the data of these two sensors the Yuyuan Lake Park.

A). the correlation analysis of flow

With the detected data on flows of two sensors its oscillogram (seeing 7) of drawing respectively: the correlativity of flow is bigger as seen from the figure, is 0.907 by calculating the correlativity that can obtain them.

B). the correlation analysis of occupation rate

With the detected occupation rate data of two sensors its oscillogram (seeing 8) of drawing respectively: the correlativity of comparing occupation rate as seen from the figure with flow is smaller, is 0.668 by calculating the correlativity that can obtain them.

C). the correlation analysis of speed

With the detected wagon flow speed data of two sensors its oscillogram (seeing 9) of drawing respectively: the display speed correlativity is minimum among the figure, and calculating its correlativity is 0.366.

The correlativity of information is more little on the highway section, needs the number of sensors of laying just many more, so just can obtain comprehensive car flow information.The correlativity minimum of speed in these three factors, if be research object with other two factors, the result of laying just can't reflect comprehensive transport information.Therefore this research with speed as the research factor.

(3) correlation analysis

By the sampling period between April 10 0:00 to 24:00 be 2 minutes the traffic flow speed data as can be known, night from 22:00 to morning next day the 6:00 magnitude of traffic flow less, night, vehicle flowrate reduced, representativeness is not strong, relevance is also relatively poor, and daytime, vehicle flowrate was more, and data dependence is stronger, was easier to find out the correlativity rule between each dot information on the highway section.

Figure 10 is 6:00 to 22:00 vehicle flowrate velocity wave form figure.Therefore, by this relevance, be that reference point removes to simulate the relevance function between the road section information with certain sensor installation position, and then draw the information density function of sensor.

(4) match of relevance function r (x)

With S1 is reference point, by to the calculating of the data dependence (being mainly speed here) of check point S1 and S1, S2, S3, S4, S5, S6, S7, S8, S9 and carry out the transport information relevance function r (x) that match just can draw this highway section.Yet the transport information of each point has space and time difference on the highway section, the information correlativity of synchronization each point is not very strong, can't embody the correlativity rule of each point on the highway section, therefore when carrying out correlation calculations, need and will the information data of difference be offsetted, the method of taking is to offset at a certain time interval, and constantly calculate its correlativity, get maximum correlativity at last and be correlativity between this point and the reference point.

By calculating the correlativity between each point and the S1, it is carried out match, see Figure 11, the expression formula that draws r (x) at last is:

r(x)＝e ^-0.2632x。

This is a negative exponential function, and it can embody the relevance between the information on the highway section, but what need to prove that this function chooses is that unidirectional track data on the through street are carried out match, and it can only be applied to the sensor placement on the city expressway.

(5) layout optimization calculates

A). example is chosen

The formula that match obtains above utilizing applies it in the similar through street, is chosen in Haidian bridge and lays sensor with Zhong Guan-cun San Qiao to the sensor of Zhong Guan-cun San Qiao between the sensor of opening up spring two bridge, between them apart 1000 meters.At first with 100 meters intensive laying sensors, just laid 9 sensors (amounting to 11) between the two sensors, with these sensors be numbered respectively S1, S2 ..., S11 (as Figure 12).

B). the computing information matrix

Owing to be the through street all, directly take top fitting result, r (x)=e ^-0.2632x, the traffic parameter of selected road is basic identical, and can establish each point sensor has identical information density function, and then the information density function is: h (x)=a * r (x)=a * e ^-0.2632x,

Again ${\&Integral;}_0^{1}h\left(x\right)=1,$ Get a=1.1374, so h (x)=a * r (x)=1.1374 * e ^-0.2632x

Distance is from certain sensor x like this ₁, x ₂Between transport information be:

$I(x_1\&RightArrow;x_2)={\&Integral;}_{x_1}^{x_2}h\left(x\right)=1.1374{\&Integral;}_{x_1}^{x_2}{e}^{-0.2632x}=\frac{1.1374}{-0.2632}{e}^{-0.2632x}{|}_{x_1}^{x_2}$

$=1.1374\&times;\frac{1}{0.2632}(e^{-0.2632x_1}-e^{-0.2632x_2})=4.3241(e^{-0.2632x_1}-e^{-0.2632x_2})$

For two sensor information stacks is to adopt function $g_{\mathrm{ij}}\left(x\right)=h_i\left(x\right)\&CirclePlus;h_j\left(x\right),$ Define by last joint:

$g_{\mathrm{ij}}\left(x\right)=h_i\left(x\right)\&CirclePlus;h_j\left(x\right)=\left\{\begin{array}{cc}{h}_i\left(x\right)& x\&le;0\\ h_i\left(x\right)& x\&GreaterEqual;d\\ \mathrm{hh}(h_i\left(x\right),h_i\left(x\right))& 0<x<d\end{array}\right.$

Wherein: d--sensor i, the distance between the j.

Here d gets 0.1km, this function g ₁₂(x) shape such as Figure 13.

Hh (h wherein _i(x), h _j(x)) get max (h _i(x), h _j(x)), g so ₁₂(x) form just becomes:

$g_{12}\left(x\right)=h_1\left(x\right)\&CirclePlus;h_2\left(x\right)=\left\{\begin{array}{cc}{h}_1\left(x\right)& x<0.05\\ h_2\left(x\right)& x\&GreaterEqual;0.05\end{array}\right.$

See Figure 14.

Overlapped information between S1 and the S2 is:

$I_{12}={\&Integral;}_0^{0.05}h\left(x\right)+{\&Integral;}_0^{0.05}h\left(x\right)=2\&times;{4.3214e}^{-0.2632x}{|}_0^{0.05}=2\&times;4.3214(1-e^{-02632\&times;0.05})=0.1132.$

In like manner can release $I_{\mathrm{ij}}=8.6428\left({1-e}^{0.2632\&times;\frac{|i-j|}{2}d}\right),$ Can obtain 11 overlapped information matrix I between the sensor thus _Ij:

C). calculate the cum rights matrix

Information value w between the i, 2 of j _Ij=k _IjI _Ij, wherein $k_{\mathrm{ij}}=\frac{k_i+{\mathrm{<figure-callout\; id="2"\; label="k\; j"\; filenames="DEST\_PATH\_HA20171172200910079438201E00012.png,DEST\_PATH\_HA20171172200910079438201E00031.png"\; state="\{\{state\}\}">k</figure-callout>}}_j}{2}.$ Because the highway section of selecting in the example is the through street, promptly road conditions and natural conditions are basic identical, so unit information is worth k _IjDeployment cost C with each sensor _iAll equal substantially, replace with k and C respectively below.

According to market survey, at present the most expensive sensor is a microwave remote sensor, lays the expense that engineering spent in addition and comprises maintenance cost, system cost, process information expense, external action expense and time cost etc.And the information value that sensor brings after laying comprises the minimizing resident trip time, reduces traffic congestion, avoids traffic accident, reduces value such as environmental pollution and reduction traffic administration expense.As seen, generally speaking, sensor information is worth and will be far longer than its laying total cost, promptly

$k\underset{D}{\&Integral;}h\left(x\right)\mathrm{dx}>>C_{\max }$

The factor of comprehensive each side, getting k is 150000.

And this research institute is approximately 2000 yuan with the total cost of geomagnetic sensor, if consider comprehensive cost, C value may be higher, discussion specially in this analysis afterwards, and here, tentative C is 2000.

Definable sensor i thus, the weights between the j are

$w_{\mathrm{ij}}=k_{\mathrm{ij}}{I}_{\mathrm{ij}}-\frac{1}{2}{C}_i-\frac{1}{2}{C}_j,$

After the simplification

w _ij＝kI _ij-C，

That is:

$w_{\mathrm{ij}}=8.6428\&times;k\&times;(1-e^{-\frac{0.02632\&times;|i-j|}{2}d})=-C=8.6428\&times;150000\&times;(1-e^{-\frac{0.02632|i-j|}{2}\&times;0.05})-2000.$

Thereby can obtain following digraph cum rights matrix:

Each weights is got opposite number, obtain the cum rights matrix w ' of dual graph G ' _Ij

The cum rights matrix that calculates G ' is (this is digraph, and MAX replaces with a big number, gets 100000000 here):

??0	??-14949.229	??-31676.868	??-48185.814	??-64478.924	??-80559.023	??-96428.893	??-112091.28	??-127548.91	??-142804.44	??-157860.53
											??100000000	??0	??-14949.229	??-31676.868	??-48185.814	??-64478.924	??-80559.023	??-96428.893	??-112091.28	??-127548.91	??-142804.44
??100000000	??100000000	??0	??-14949.229	??-31676.868	??-48185.814	??-64478.924	??-80559.023	??-96428.893	??-112091.28	??-127548.91
											??100000000	??100000000	??100000000	??0	??-14949.229	??-31676.868	??-48185.814	??-64478.924	??-80559.023	??-96428.893	??-112091.28
??100000000	??100000000	??100000000	??100000000	??0	??-14949.229	??-31676.868	??-48185.814	??-64478.924	??-80559.023	??-96428.893
											??100000000	??100000000	??100000000	??100000000	??100000000	??0	??-14949.229	??-31676.868	??-48185.814	??-64478.924	??-80559.023
??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??0	??-14949.229	??-31676.868	??-48185.814	??-64478.924
											??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??0	??-14949.229	??-31676.868	??-48185.814

??0	??-14949.229	??-31676.868	??-48185.814	??-64478.924	??-80559.023	??-96428.893	??-112091.28	??-127548.91	??-142804.44	??-157860.53
											??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??0	??-14949.229	??-31676.868
??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??0	??-14949.229
											??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??100000000	??0

D). result of calculation

Utilization Floyd algorithm obtains shortest path and is:

1→6→11。

Final arrangement plan is seen Figure 15.

Therefore as if lay the comprehensive value maximum that sensor can make the Traffic Information of acquisition again at the S6 place.

Claims (6)

1. sensor network configuring method that regional traffic state obtains is characterized in that containing following steps:

At set sensor place, obtain the step of the information of maximum road section traffic volume characteristic; According to obtaining the information density function of the correlativity of transport information for the basis with sensor, the comprehensive cost of placement sensor has been set up the step of the maximum model of two stage information value; Set up the step of the maximum model of two stage information value: its phase one is that modeling is carried out on the basis with the highway section, utilizes shortest path algorithm to find the solution; Subordinate phase is that modeling is carried out on the basis with road network or zone, considers the correlativity between the highway section in the road network; The step that the angle of the transport information of obtaining from sensor is optimized transducer arrangements.

2. the sensor network configuring method that regional traffic state as claimed in claim 1 obtains is characterized in that utilizing the relevance function of path sensor to obtain the step of information density function; And on this basis the feature of relevance function has been described, provided the information density function.

3. the sensor network configuring method that regional traffic state as claimed in claim 1 obtains is characterized in that the step that two levels of branch are optimized sensor; From the line to the face, from the part to integral body, carry out the step that modeling is optimized again from the face to the line, from the part to integral body.

4. the sensor network configuring method that regional traffic state as claimed in claim 1 obtains is characterized in that setting up the step based on the maximum model of information value in highway section; Foundation is based on the step of the maximum model of information value of road network;

Step 1: set up based on the maximum model of the information value in highway section;

Lay sensor on the highway section equably, the sensor number of establishing laying is n, and the position of each sensor note is made i (1≤i≤n), and to establish the comprehensive cost of laying i sensor on this highway section be C _i, then according to above-mentioned foundation as drag:

$\max W=\mathrm{kI}-f=k{\&Integral;}_0^{D}g\left(x\right)\mathrm{dx}-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{X}_i\&CenterDot;C_i$

$s.t.\left\{\begin{array}{c}g\left(x\right)=\underset{i=1}{\overset{n}{\&CirclePlus;}}{h}_i\left(x\right)\\ X_i=0\mathrm{or}1\end{array}\right.$

Wherein:

W---comprehensive value, the road section traffic volume characteristic information of sensor representative are worth the expense of laying sensor that deducts;

K---represent on this highway section that in tenure of use, the value of 1 unit information, different road parameters have different k values at sensor;

C _i---lay the needed comprehensive cost of sensor (real cost of sensor installation in the highway section) at the i place,, generally get identical C value, promptly get C for same section road _i=C;

X _i---0or 1,0 is illustrated in the i place and does not lay sensor, and 1 is illustrated in the i place lays sensor;

h _i(x)---lay the information density function of sensor at the i place, different road parameters has different h _i(x), for same section road, generally get identical h _i(x) value is promptly got h _i(x)=h (x);

Step 2: set up based on the maximum model of the information value of road network;

Come the consideration of regional transducer arrangements from both direction, the firstth, the crossing is is respectively imported and exported sensor and how to be arranged, and the secondth, how sensor is arranged between the highway section that the crossing is imported and exported; The layout of area sensor just is converted into both of these case like this, then they is combined, and forms the zone and is worth maximum model;

(1) crossing's transducer arrangements is analyzed

For through street and highway, generally will be in crossing import and export placement sensor, and then consider the laying situation in highway section between these two sensors; For the crossing of usual friendship, lay a sensor respectively in each exit, if ITS is higher to the accuracy requirement of crossing flow estimation, can consider to lay sensor respectively in the import and export of each crossing;

(2) each highway section transducer arrangements situation analysis in the zone

For the zone of being studied, suppose that the laying scheme of each crossing is fixed, consider transport information (speed, density, the flow) correlativity in each highway section, the higher highway section of correlativity is divided into one group, lay in one of every group selection and above highway section; For the highway section of determining to lay, the sensor that the crossing at two, highway section is laid is as first and last sensor, between sensor lay the maximum model solution of the information value that just can utilize the phase one.

5. the sensor network configuring method that regional traffic state as claimed in claim 4 obtains is characterized in that the Layout Problem of sensor is converted into the step of digraph problem; Proposed the cum rights matrix of sensor digraph, and the stage expense of sensor has been converted into the step of highway section expense; Road section information is worth the step that finding the solution of maximum model is converted into critical path problem; The shortest path of the dual graph by finding the solution the sensor digraph is tried to achieve the step of the arrangement of this highway section sensor;

Step 1: some parameters of model or function utilize experimental formula or historical data match to obtain, and the known conditions that obtains at last has: the unit information expense h of the i place placement sensor on the highway section of studying _i, information density function h _i(x), the integrated cost C of placement sensor _i, the parameter that needs to set is n, promptly studies the highway section and initially lays number of sensors, the laying that is converted into sensor like this is apart from d, if the research long L in highway section, then $d=\frac{L}{n-1}$ (sensor that L lays from the two ends, highway section is counted), the sensor distance of laying according to initial desire is determined n like this;

Step 2: according to the information density function of each sensor and utilize superpositing function $g_{12}\left(x\right)=h_1\left(x\right)\&CirclePlus;h_2\left(x\right)$ Calculate the overlapped information between any two sensors, obtain the information matrix I between following each sensor _Ij

Be constructed as follows digraph G (Fig. 2), wherein 1,2 ..., k, ..., n is respectively the numbering of placement sensor on the highway section, or represents the position of each sensor, and wherein any 2 all have an oriented circuit from the low grade to the high grade, the weights of each circuit are that value corresponding multiply by its corresponding unit information expense, i.e. information value between these 2 in the information matrix; Be w _Ij=k _IjI _Ij,

K wherein _IjGet average, promptly $k_{\mathrm{ij}}=\frac{k_i+k_j}{2};$

Finding the solution exactly of model looked for a paths from No. 1 sensor to the n sensor in this digraph, make the information value maximum on the path;

Step 3: consider the influence of each sensor comprehensive cost, whenever how will increase corresponding cost in the path through a sensor; Definition sensor i, the weight between the j is

$w_{\mathrm{ij}}=k_{\mathrm{ij}}{I}_{\mathrm{ij}}-\frac{1}{2}{C}_i-\frac{1}{2}{C}_j,$

Thereby can obtain the cum rights matrix of following digraph G:

Find the solution road section information and be worth maximum model with regard to being converted into the longest path problem of asking this digraph, each weights is asked its opposite number, get another digraph, define the dual graph that this digraph is former figure, note is made G ', so the cum rights matrix of this dual graph G ' is:

Ask shortest path like this,, find the solution with the floyed algorithm because negative value may appear in weights;

Step 4: by trying to achieve the shortest path of G ', find a longest path according to the path of G ' on former figure G, the highway section maximum information that obtain this moment is worth and is W=∑ w _Ij, w _IjBe each the cum rights value on the highway section, W the node of process be the disaggregation of model, promptly sensing station and the number that will lay of this highway section laid the maximum information that obtains the highway section like this and is worth.

6. the sensor network configuring method that obtains as claim 1,2,3,4 or 5 described regional traffic states is characterized in that considering the correlativity and the scale of investment of section traffic information, the step that whole road network is optimized;

Step 1: demarcate each parameter according to expressway, through street, trunk roads, branch road, unit information expense k is arranged _i, information density function parameter b _i, the comprehensive cost C of laying sensor _i

Step 2: analyze each crossing,, each crossing is laid in advance according to the arrangement principle of crossing;

Step 3: if zone bigger (as considering the sensor placement of entire city), be divided into some each zonules, each zone comprises that 20-30 highway section is (because of the increase along with distance, the correlativity of transport information can very fast attenuating), analyze the correlativity in each highway section, the highway section that each correlativity is strong is divided in groups;

Step 4: to each group, requirement must be provided with the highway section of sensor, then must lay; For the highway section that does not have particular requirement, guaranteeing at least in every group has a highway section to be laid, and chooses according to importance; Obtain needing in the road network to lay the highway section of sensor;

Step 5: if do not consider to drop into, get suitable laying, utilize the highway section of phase one to be worth maximum Model Calculation apart from d; In order to improve precision, every 1m lays, and result calculated is that the best under each highway section parameter is laid distance, counts thereby obtain best the laying, lays, and calculates and finishes; Drop into as if considering, do not consider to drop into calculating with above-mentioned earlier, obtain best the laying and count, always calculate and drop into,, then stop to calculate, otherwise enter step 6 as if dropping into less than estimating;

Step 6: Δ d is set, and constantly laying in the best in each highway section increases Δ d under the distance, recomputate, and drops into less than estimating up to total input, stops to calculate.

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