CN103761442B - Forecasting method and device for flow parameters of micro areas - Google Patents
Forecasting method and device for flow parameters of micro areas Download PDFInfo
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Abstract
The invention discloses a forecasting method and device for flow parameters of micro areas. Firstly, the time series of fixed parameters A and the time series of flow parameters B of a macro area are collected; secondly, according to the relation between the macro area and each micro area, the time series of fixed parameters A of each micro area is obtained; thirdly, by means of a state equation of extended Kalman filtering, the relation between the time series of the fixed parameters and the time series of the flow parameters B is obtained; fourthly, by means of the obtained relation between the fixed parameters A and the flow parameters B, a forecasting value of the time series of the flow parameters B of each micro area is obtained; finally, according to the obtained time series of the fixed parameters A of each micro area and the forecasting value of the time series of the flow parameters B of each micro area, resource optimization is conducted on each micro area. The forecasting method and device change the black-box situation of the micro areas, the states of the flow parameters in the micro areas are forecasted, resources are utilized according to forecasting results, and therefore the resources are optimized; meanwhile, the extended Kalman filtering algorithm is used, the obtained results are accurate, the error rate is low, and very good application value is obtained.
Description
Technical field
The present invention relates to data mining technology field, the Forecasting Methodology and dress of more particularly to a kind of film micro area flow parameter
Put.
Background technology
Prior art cannot in time obtain film micro area（Such as one section management on small scale unit）Flow parameter（Change is frequently
Data）Situation, it is impossible to understand the state of film micro area flow parameter in real time, film micro area is constantly in " black box " state, affect
The planning of the various schemes of film micro area, enforcement.
The content of the invention
Based on above-mentioned situation, the present invention proposes a kind of Forecasting Methodology of film micro area flow parameter, obtains film micro area flowing
The state of parameter, with reference to resource is actually utilized, with good using value.
To achieve these goals, the technical scheme is that：
A kind of Forecasting Methodology of film micro area flow parameter, comprises the following steps：
Collect the time series and the time series of flow parameter B of the fixed parameter A in grand region；
According to grand region and each film micro area relation, the time series of the fixed parameter A in collected grand region is carried out point
Class, collect, obtain the time series of the fixed parameter A of each film micro area；
Time series and the time series of flow parameter B based on the fixed parameter A in collected grand region, using extension
The state equation of Kalman filtering, the relation being fixed between the time series of the time series of parameter A and flow parameter B；
Based on the time series of the fixed parameter A of resulting each film micro area, the time of tried to achieve fixed parameter A is utilized
Relation between the time series of sequence and flow parameter B, obtains the time series forecasting value of the flow parameter B of each film micro area；
According to the time series and the time series forecasting value of flow parameter B of the fixed parameter A of each film micro area for being obtained
Resource optimization is carried out to each film micro area.
For prior art problem, the invention allows for a kind of prediction meanss of film micro area flow parameter, improve existing
The present situation of film micro area " black box ", is adapted to application.
Specific implementation is：A kind of prediction meanss of film micro area flow parameter, including：
Collection module, for collecting the time series and the time series of flow parameter B of the fixed parameter A in grand region；
Classifying Sum module, for according to grand region and each film micro area relation, the fixed parameter A to collected grand region
Time series classified, collected, obtain the time series of the fixed parameter A of each film micro area；
Processing module, the time series and the time sequence of flow parameter B based on the fixed parameter A in collected grand region
Row, using the state equation of EKF, are fixed the time series of parameter A and the time series of flow parameter B
Between relation；
Prediction module, based on the time series of the fixed parameter A of resulting each film micro area, utilizes tried to achieve fixed ginseng
Relation between the time series and the time series of flow parameter B of amount A, obtains the time sequence of the flow parameter B of each film micro area
Row predicted value；
Optimization module, for according to the time series of the fixed parameter A of each film micro area for being obtained and flow parameter B when
Between sequence prediction value resource optimization is carried out to each film micro area.
Compared with prior art, beneficial effects of the present invention are：The Forecasting Methodology and dress of film micro area flow parameter of the present invention
Put, first collect the time series and the time series of flow parameter B of the fixed parameter A in grand region；Then according to grand region with it is each
Film micro area relation, is classified, is collected to the time series of the fixed parameter A in collected grand region, obtains each film micro area
The time series of fixed parameter A；Again based on collected grand region fixed parameter A time series and flow parameter B when
Between sequence, using the state equation of EKF, be fixed the time series of parameter A and the time of flow parameter B
Relation between sequence；The time series of the fixed parameter A of resulting each film micro area is based on again, utilizes tried to achieve fixed ginseng
Relation between the time series and the time series of flow parameter B of amount A, obtains the time sequence of the flow parameter B of each film micro area
Row predicted value；The time series of time series and flow parameter B finally according to the fixed parameter A of each film micro area for being obtained is pre-
Measured value carries out resource optimization to each film micro area.After technology using the present invention, the present situation of film micro area " black box " is changed, predicted
The state of film micro area flow parameter, according to predicting the outcome resource is utilized, and is optimized resource, while being calculated using spreading kalman
Method, obtains result accurately, and error rate is low, with good using value.
Description of the drawings
Fig. 1 is the schematic flow sheet of the Forecasting Methodology of film micro area flow parameter in one embodiment；
Fig. 2 is the structural representation of the prediction meanss of film micro area flow parameter in one embodiment.
Specific embodiment
To make the objects, technical solutions and advantages of the present invention become more apparent, below in conjunction with drawings and Examples, to this
Invention is described in further detail.It should be appreciated that specific embodiment described herein is only to explain the present invention,
Protection scope of the present invention is not limited.
The Forecasting Methodology of film micro area flow parameter in one embodiment, as shown in figure 1, comprising the following steps：
Step S101：Collect grand region（The conventional administrative region in such as one province or city）Fixed parameter A（Change is little
Data）Time series and flow parameter B（Change frequently data）Time series；
Step S102：According to grand region and each film micro area（Such as one section management on small scale unit）Relation, to collected
The time series of the fixed parameter A in grand region is classified, is collected, and obtains the time series of the fixed parameter A of each film micro area；
Step S103：Time series and the time sequence of flow parameter B based on the fixed parameter A in collected grand region
Row, using the state equation of EKF, are fixed the time series of parameter A and the time series of flow parameter B
Between relation；
Step S104：Based on the time series of the fixed parameter A of resulting each film micro area, tried to achieve fixed ginseng is utilized
Relation between the time series and the time series of flow parameter B of amount A, obtains the time sequence of the flow parameter B of each film micro area
Row predicted value；
Step S105：According to the time series and the time sequence of flow parameter B of the fixed parameter A of each film micro area for being obtained
Row predicted value carries out resource optimization to each film micro area.
It is evidenced from the above discussion that, this method changes the present situation of film micro area " black box ", with reference to resource is actually utilized, has
Good using value.
As one embodiment, after the time series forecasting value of the flow parameter B for obtaining each film micro area, also wrap
Include：According to the relation between the time series of the flow parameter B of the time series and grand region of the flow parameter B of each film micro area,
Correct the time series forecasting value of the flow parameter B of each film micro area.
As one embodiment, after the time series forecasting value of the flow parameter B for obtaining each film micro area, also wrap
Include：The time series actual value of the flow parameter B of arbitrary film micro area w in each film micro area is collected, the flowing with the film micro area w is joined
The time series forecasting value of amount B carries out error analysis, according to the result of error analysis, corrects the flow parameter of each film micro area
The time series forecasting value of B.
Used as one embodiment, the time series forecasting value of the flow parameter B of each film micro area is calculated by following steps
Obtain：
The time series of the fixed parameter A of each film micro area is AiIf the time series of the flow parameter B of each film micro area is Bi,
i=1,2,...,N；
The computing formula of prediction matrix T (x) is：T(x)=[A1,A2,...,AN], state variableComputing formula be：
State variableMeet with its corresponding covariance matrix P：Pk+1|k=Pk|k+Qk, wherein QkFor kth
The excitation covariance matrix of secondary iterative process,Prior state for the step of kth+1 under state status before the known step of kth+1 is estimated
Meter,For the posteriority state estimation of kth step；
Calculate kalman gain：Wherein P is covariance matrix；J is Jacobian matrix, its meter
Calculating formula is：Wherein T (x) is prediction matrix；S is remaining covariance matrix, and its computing formula is：Wherein RkFor the spectator noise covariance matrix of kth time iteration；
Update state variableIt is with its corresponding covariance matrix P：
Pk+1|k+1=(I-Kk+1Jk+1)Pk+1|k, wherein K is kalman gain；For remnants
Variable, its computing formula is：Wherein mkFor the observation variable of kth time iteration, T (x) is prediction square
Battle array；I is unit matrix, and J is Jacobian matrix；For the posteriority state estimation of the step of kth+1,For the known step of kth+1
In the past the prior state of the step of kth+1 was estimated under state status.
It is not excluded for also other methods.
The prediction meanss of film micro area flow parameter in one embodiment, as shown in Fig. 2 including：
Collection module, for collecting the time series and the time series of flow parameter B of the fixed parameter A in grand region；
Classifying Sum module, for according to grand region and each film micro area relation, the fixed parameter A to collected grand region
Time series classified, collected, obtain the time series of the fixed parameter A of each film micro area；
Processing module, the time series and the time sequence of flow parameter B based on the fixed parameter A in collected grand region
Row, using the state equation of EKF, are fixed the time series of parameter A and the time series of flow parameter B
Between relation；
Prediction module, based on the time series of the fixed parameter A of resulting each film micro area, utilizes tried to achieve fixed ginseng
Relation between the time series and the time series of flow parameter B of amount A, obtains the time sequence of the flow parameter B of each film micro area
Row predicted value；
Optimization module, for according to the time series of the fixed parameter A of each film micro area for being obtained and flow parameter B when
Between sequence prediction value resource optimization is carried out to each film micro area.
As shown in Fig. 2 a preferred embodiment of each module annexation of this device is：Collection module, Classifying Sum
Module, processing module, prediction module and optimization module are linked in sequence successively.
First collection module collects the time series and the time series of flow parameter B of the fixed parameter A in grand region；Then
Classifying Sum module is entered according to grand region and each film micro area relation to the time series of the fixed parameter A in collected grand region
Row is classified, is collected, and obtains the time series of the fixed parameter A of each film micro area；Again collected grand region is based on by processing module
Fixed parameter A time series and the time series of flow parameter B, using the state equation of EKF, obtain
Relation between the time series and the time series of flow parameter B of fixed parameter A；By prediction module based on resulting each micro-
The time series of the fixed parameter A in region, utilizes the time series and the time sequence of flow parameter B of tried to achieve fixed parameter A
Relation between row, obtains the time series forecasting value of the flow parameter B of each film micro area；Last optimization module is according to being obtained
It is excellent that the time series of fixed parameter A and the time series forecasting value of flow parameter B of each film micro area carries out resource to each film micro area
Change.This device obtains the state of film micro area flow parameter, and according to the result for obtaining resource is used, and is optimized resource, is adapted to
Practical application.
As one embodiment, also including correcting module a, for the flow parameter B for obtaining each film micro area when
Between after sequence prediction value, according to the time series of the time series of the flow parameter B of each film micro area and the flow parameter B in grand region
Between relation, correct the time series forecasting value of the flow parameter B of each film micro area.
As one embodiment, also including correcting module b, for the flow parameter B for obtaining each film micro area when
Between after sequence prediction value, collect the time series actual value of the flow parameter B of arbitrary film micro area w in each film micro area, it is micro- with described
The time series forecasting value of the flow parameter B of region w carries out error analysis, according to the result of error analysis, corrects described each micro-
The time series forecasting value of the flow parameter B in region.
Used as one embodiment, the time series forecasting value of the flow parameter B of each film micro area is calculated by following steps
Obtain：
The time series of the fixed parameter A of each film micro area is AiIf the time series of the flow parameter B of each film micro area is Bi,
i=1,2,...,N；
The computing formula of prediction matrix T (x) is：T(x)=[A1,A2,...,AN], state variableComputing formula be：
State variableMeet with its corresponding covariance matrix P：Pk+1|k=Pk|k+Qk, wherein QkFor kth
The excitation covariance matrix of secondary iterative process,Prior state for the step of kth+1 under state status before the known step of kth+1 is estimated
Meter,For the posteriority state estimation of kth step；
Calculate kalman gain：Wherein P is covariance matrix；J is Jacobian matrix, its meter
Calculating formula is：Wherein T (x) is prediction matrix；S is remaining covariance matrix, and its computing formula is：Wherein RkFor the spectator noise covariance matrix of kth time iteration；
Update state variableIt is with its corresponding covariance matrix P：
Pk+1|k+1=(I-Kk+1Jk+1)Pk+1|k, wherein K is kalman gain；For remnants
Variable, its computing formula is：Wherein mkFor the observation variable of kth time iteration, T (x) is prediction square
Battle array；I is unit matrix, and J is Jacobian matrix；For the posteriority state estimation of the step of kth+1,For the known step of kth+1
In the past the prior state of the step of kth+1 was estimated under state status.
It is not excluded for also other methods.
Embodiment described above only expresses the several embodiments of the present invention, and its description is more concrete and detailed, but and
Therefore the restriction to the scope of the claims of the present invention can not be interpreted as.It should be pointed out that for one of ordinary skill in the art
For, without departing from the inventive concept of the premise, some deformations and improvement can also be made, these belong to the guarantor of the present invention
Shield scope.Therefore, the protection domain of patent of the present invention should be defined by claims.
Claims (8)
1. a kind of Forecasting Methodology of film micro area flow parameter, it is characterised in that comprise the following steps：
Collect the time series and the time series of flow parameter B of the fixed parameter A in grand region；
According to grand region and each film micro area relation, the time series of the fixed parameter A in collected grand region is classified, converged
Always, the time series of the fixed parameter A of each film micro area is obtained；
Time series and the time series of flow parameter B based on the fixed parameter A in collected grand region, using extension karr
The state equation of graceful filtering, obtains the time of the flow parameter B of the time series and each film micro area of the fixed parameter A of each film micro area
Relation between sequence；
Based on the time series of the fixed parameter A of resulting each film micro area, the fixed parameter A of each film micro area tried to achieve is utilized
Time series and each film micro area flow parameter B time series between relation, obtain the flow parameter B's of each film micro area
Time series forecasting value；
According to the time series of the flow parameter B of the time series and each film micro area of the fixed parameter A of each film micro area for being obtained
Predicted value carries out resource optimization to each film micro area；
After the time series forecasting value of the flow parameter B for obtaining each film micro area, also include：According to the flowing of each film micro area
Relation between the time series of the flow parameter B in the time series of parameter B and grand region, corrects the flowing of each film micro area
The time series forecasting value of parameter B.
2. the Forecasting Methodology of film micro area flow parameter according to claim 1, it is characterised in that the stream of each film micro area
The time series forecasting value of dynamic parameter B is calculated by following steps：
The time series of the fixed parameter A of each film micro area is AiIf the time series of the flow parameter B of each film micro area is Bi, i=
1,2,...,N；
The computing formula of prediction matrix T (x) is：T (x)=[A1,A2,...,AN], state variableComputing formula be：
State variableMeet with its corresponding covariance matrix P：Pk+1|k=Pk|k+Qk, wherein QkFor kth time repeatedly
For the excitation covariance matrix of process,Prior state for the step of kth+1 under state status before the known step of kth+1 estimates,For the posteriority state estimation of kth step；
Calculate kalman gain：P is covariance matrix；J is Jacobian matrix, and its computing formula is：Wherein T (x) is prediction matrix；S is remaining covariance matrix, and its computing formula is：Wherein RkFor the spectator noise covariance matrix of kth time iteration；
Update state variableIt is with its corresponding covariance matrix P：
Pk+1|k+1=(I-Kk+1Jk+1)Pk+1|k, wherein K is kalman gain；For remaining variable,
Its computing formula is：mkFor the observation variable of kth time iteration, T (x) is prediction matrix；I is unit
Matrix, J is Jacobian matrix；For the posteriority state estimation of the step of kth+1,For state status before the known step of kth+1
The prior state of the lower step of kth+1 is estimated.
3. a kind of Forecasting Methodology of film micro area flow parameter, it is characterised in that comprise the following steps：
Collect the time series and the time series of flow parameter B of the fixed parameter A in grand region；
According to grand region and each film micro area relation, the time series of the fixed parameter A in collected grand region is classified, converged
Always, the time series of the fixed parameter A of each film micro area is obtained；
Time series and the time series of flow parameter B based on the fixed parameter A in collected grand region, using extension karr
The state equation of graceful filtering, obtains the time of the flow parameter B of the time series and each film micro area of the fixed parameter A of each film micro area
Relation between sequence；
Based on the time series of the fixed parameter A of resulting each film micro area, the fixed parameter A of each film micro area tried to achieve is utilized
Time series and each film micro area flow parameter B time series between relation, obtain the flow parameter B's of each film micro area
Time series forecasting value；
According to the time series of the flow parameter B of the time series and each film micro area of the fixed parameter A of each film micro area for being obtained
Predicted value carries out resource optimization to each film micro area；
After the time series forecasting value of the flow parameter B for obtaining each film micro area, also include：Collect arbitrary in each film micro area
The time series actual value of the flow parameter B of film micro area w, enters with the time series forecasting value of the flow parameter B of the film micro area w
Row error analysis, according to the result of error analysis, corrects the time series forecasting value of the flow parameter B of each film micro area.
4. the Forecasting Methodology of film micro area flow parameter according to claim 3, it is characterised in that the stream of each film micro area
The time series forecasting value of dynamic parameter B is calculated by following steps：
The time series of the fixed parameter A of each film micro area is AiIf the time series of the flow parameter B of each film micro area is Bi, i=
1,2,...,N；
The computing formula of prediction matrix T (x) is：T (x)=[A1,A2,...,AN], state variableComputing formula be：
State variableMeet with its corresponding covariance matrix P：Pk+1|k=Pk|k+Qk, wherein QkFor kth time repeatedly
For the excitation covariance matrix of process,Prior state for the step of kth+1 under state status before the known step of kth+1 estimates,For the posteriority state estimation of kth step；
Calculate kalman gain：P is covariance matrix；J is Jacobian matrix, and its computing formula is：Wherein T (x) is prediction matrix；S is remaining covariance matrix, and its computing formula is：Wherein RkFor the spectator noise covariance matrix of kth time iteration；
Update state variableIt is with its corresponding covariance matrix P：
Pk+1|k+1=(I-Kk+1Jk+1)Pk+1|k, wherein K is kalman gain；For remaining variable,
Its computing formula is：mkFor the observation variable of kth time iteration, T (x) is prediction matrix；I is unit
Matrix, J is Jacobian matrix；For the posteriority state estimation of the step of kth+1,For state status before the known step of kth+1
The prior state of the lower step of kth+1 is estimated.
5. a kind of prediction meanss of film micro area flow parameter, it is characterised in that include：
Collection module, for collecting the time series and the time series of flow parameter B of the fixed parameter A in grand region；
Classifying Sum module, for according to grand region and each film micro area relation, to the fixed parameter A in collected grand region when
Between sequence classified, collected, obtain the time series of the fixed parameter A of each film micro area；
Processing module, the time series and the time series of flow parameter B based on the fixed parameter A in collected grand region, profit
With the state equation of EKF, time series and the flowing of each film micro area of the fixed parameter A of each film micro area are obtained
Relation between the time series of parameter B；
Prediction module, based on the time series of the fixed parameter A of resulting each film micro area, utilizes each film micro area for being tried to achieve
Relation between the time series of the time series of fixed parameter A and the flow parameter B of each film micro area, obtains the stream of each film micro area
The time series forecasting value of dynamic parameter B；
Optimization module, for being joined according to the flowing of the time series of the fixed parameter A of each film micro area for being obtained and each film micro area
The time series forecasting value of amount B carries out resource optimization to each film micro area；
Also include correcting module a, for after the time series forecasting value of the flow parameter B for obtaining each film micro area, according to
Relation between the time series of the time series of the flow parameter B of each film micro area and the flow parameter B in grand region, amendment is described
The time series forecasting value of the flow parameter B of each film micro area.
6. prediction meanss of film micro area flow parameter according to claim 5, it is characterised in that the stream of each film micro area
The time series forecasting value of dynamic parameter B is calculated by following steps：
The time series of the fixed parameter A of each film micro area is AiIf the time series of the flow parameter B of each film micro area is Bi, i=
1,2,...,N；
The computing formula of prediction matrix T (x) is：T (x)=[A1,A2,...,AN], state variableComputing formula be：
State variableMeet with its corresponding covariance matrix P：Pk+1|k=Pk|k+Qk, wherein QkFor kth time repeatedly
For the excitation covariance matrix of process,Prior state for the step of kth+1 under state status before the known step of kth+1 estimates,For the posteriority state estimation of kth step；
Calculate kalman gain：P is covariance matrix；J is Jacobian matrix, and its computing formula is：Wherein T (x) is prediction matrix；S is remaining covariance matrix, and its computing formula is：Wherein RkFor the spectator noise covariance matrix of kth time iteration；
Update state variableIt is with its corresponding covariance matrix P：
Wherein K is kalman gain；For remaining change
Measure, its computing formula is：mkFor the observation variable of kth time iteration, T (x) is prediction matrix；I is
Unit matrix, J is Jacobian matrix；For the posteriority state estimation of the step of kth+1,For state before the known step of kth+1
In the case of the step of kth+1 prior state estimate.
7. a kind of prediction meanss of film micro area flow parameter, it is characterised in that include：
Collection module, for collecting the time series and the time series of flow parameter B of the fixed parameter A in grand region；
Classifying Sum module, for according to grand region and each film micro area relation, to the fixed parameter A in collected grand region when
Between sequence classified, collected, obtain the time series of the fixed parameter A of each film micro area；
Processing module, the time series and the time series of flow parameter B based on the fixed parameter A in collected grand region, profit
With the state equation of EKF, time series and the flowing of each film micro area of the fixed parameter A of each film micro area are obtained
Relation between the time series of parameter B；
Prediction module, based on the time series of the fixed parameter A of resulting each film micro area, utilizes each film micro area for being tried to achieve
Relation between the time series of the time series of fixed parameter A and the flow parameter B of each film micro area, obtains the stream of each film micro area
The time series forecasting value of dynamic parameter B；
Optimization module, for being joined according to the flowing of the time series of the fixed parameter A of each film micro area for being obtained and each film micro area
The time series forecasting value of amount B carries out resource optimization to each film micro area；
Also include correcting module b, for after the time series forecasting value of the flow parameter B for obtaining each film micro area, collecting
The time series actual value of the flow parameter B of arbitrary film micro area w in each film micro area, with the flow parameter B of the film micro area w when
Between sequence prediction value carry out error analysis, according to the result of error analysis, correct the time of the flow parameter B of each film micro area
Sequence prediction value.
8. prediction meanss of film micro area flow parameter according to claim 7, it is characterised in that the stream of each film micro area
The time series forecasting value of dynamic parameter B is calculated by following steps：
The time series of the fixed parameter A of each film micro area is AiIf the time series of the flow parameter B of each film micro area is Bi, i=
1,2,...,N；
The computing formula of prediction matrix T (x) is：T (x)=[A1,A2,...,AN], state variableComputing formula be：
State variableMeet with its corresponding covariance matrix P：Pk+1|k=Pk|k+Qk, wherein QkFor kth time repeatedly
For the excitation covariance matrix of process,Prior state for the step of kth+1 under state status before the known step of kth+1 estimates,For the posteriority state estimation of kth step；
Calculate kalman gain：P is covariance matrix；J is Jacobian matrix, and its computing formula is：Wherein T (x) is prediction matrix；S is remaining covariance matrix, and its computing formula is：Wherein RkFor the spectator noise covariance matrix of kth time iteration；
Update state variableIt is with its corresponding covariance matrix P：
Pk+1|k+1=(I-Kk+1Jk+1)Pk+1|k, wherein K is kalman gain；For remaining variable,
Its computing formula is：mkFor the observation variable of kth time iteration, T (x) is prediction matrix；I is unit
Matrix, J is Jacobian matrix；For the posteriority state estimation of the step of kth+1,For state status before the known step of kth+1
The prior state of the lower step of kth+1 is estimated.
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| A micro regional market share real-time prediction based on extended Kalman;Cuifeng Du et al.;《2013 internationalconference on Mechatronics and Semiconductor Materials(ICMSCM 2013)》;20130928;第475-478页 * |
| The Global Characteristic Cluster to the Base Station Classification;Shibao Jiang et al.;《2013 internationalconference on Mechatronics and Semiconductor Materials(ICMSCM 2013)》;20130928;第1088-1091页 * |
| Traffic forecast based on empirical mode decomposition and RBF neural network;Shibao Jiang et al.;《2013 internationalconference on Mechatronics and Semiconductor Materials(ICMSCM 2013)》;20130928;第1270-1273页 * |
| 网络流量预测方法;董梦丽等;《计算机工程》;20110831;第37卷(第16期);第98-102页 * |
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