CN105718728B - A kind of method calculated automatically for road roller number of rolling - Google Patents
A kind of method calculated automatically for road roller number of rolling Download PDFInfo
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- CN105718728B CN105718728B CN201610036705.8A CN201610036705A CN105718728B CN 105718728 B CN105718728 B CN 105718728B CN 201610036705 A CN201610036705 A CN 201610036705A CN 105718728 B CN105718728 B CN 105718728B
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- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16Z—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS, NOT OTHERWISE PROVIDED FOR
- G16Z99/00—Subject matter not provided for in other main groups of this subclass
Abstract
A kind of method calculated automatically for road roller number of rolling provided by the invention, is related to road roller and rolls field, wherein, the described method includes roll the plane coordinates information of track according to road roller, trajectory segment rolled to described, obtain each single hop and roll track；Track fitting straight line is rolled to each single hop, the periodicity changed according to the straight line parameter after fitting, determines the separation of number of rolling, obtain separate unit road roller single pass and roll wheelmark information；Each road roller separate unit road roller single pass of each time is rolled into wheelmark information superposition, determines number of rolling information.The above method is used for realization one or more road roller to when work surface rolls, according to the different type of road roller, the number of rolling of all kinds road roller for calculating current work face automatic in real time and number of rolling distribution situation, on-site personnel is sent out immediately and leak pressure, under-voltage region again, to ensure construction quality.
Description
Technical field
The present invention relates to road roller to roll field, more particularly to a kind of side calculated automatically for road roller number of rolling
Method.
Background technology
In the current computational methods to road roller compacting counting, although there is the calculating of preliminary compacting counting, meter
Calculation method is more extensive, and precision controlling is relatively low, and on-site personnel can not accurately learn the number of rolling of each specific location.By
A kind of it is used for stone roller of one or more road roller to roadbed, road surface, dam when filling thing and carrying out joint compacting operation in no
Pass automatic calculating method is pressed, on-site personnel cannot find that Lou pressure, under-voltage region, construction quality are difficult to ensure in time.
The content of the invention
The defects of for the prior art, the present invention, which proposes, to be solved one kind of above-mentioned technical problem and is rolled time for road roller
The method that number calculates automatically.
In a first aspect, the present invention provides a kind of method calculated automatically for road roller number of rolling, including：
The plane coordinates information of track is rolled according to road roller, trajectory segment is rolled to described, each single hop is obtained and rolls rail
Mark；
Track fitting straight line is rolled to each single hop, the periodicity changed according to the straight line parameter after fitting, determines to grind
The separation of pass is pressed, separate unit road roller single pass is obtained and rolls wheelmark information；
Each road roller separate unit road roller single pass of each time is rolled into wheelmark information superposition, determines number of rolling information.
Preferably, to it is described roll trajectory segment before, the method further includes, and the earth of road roller rolling wheel is sat
Mark is converted into plane coordinates.
Preferably, it is described to it is described roll trajectory segment before, the method further includes：Roll track to described and locate in advance
Reason, removes and rolls data point static in track and the big data point of error.
Preferably, the cyclically-varying that the straight line parameter according to after fitting changes, determines the separation of number of rolling,
Specifically include：
When road roller is rolled to opposite side successively in operating area from side, according to the straight line after fitting in X-axis or Y-axis
The periodicity of the change of intercept extreme value, determines the separation of number of rolling；
Or
When road roller is rolled inwardly successively in operating area by outside, cut according to the straight line after fitting in X-axis or Y-axis
Away from change periodicity, determine the separation of number of rolling.
Preferably, the cyclically-varying that the straight line parameter according to after fitting changes, determines the separation of number of rolling
Further include：
Determine that first segment rolls the distance that the point on the straight line of track fitting rolls the straight line of track fitting to second segment, if
The distance is less than preset value, then the second segment rolls separation of the straight line not as definite number of rolling of track fitting.
Second aspect, the present invention provide a kind of device calculated automatically for road roller number of rolling, including：
Segmenting unit, for rolling the plane coordinates information of track according to road roller, rolls trajectory segment to described, obtains
Each single hop rolls track；
Fitting boundary unit, for rolling track fitting straight line to each single hop, becomes according to the straight line parameter after fitting
The periodicity of change, determines the separation of number of rolling, obtains separate unit road roller single pass and rolls wheelmark information；
Determination unit, for the separate unit road roller single pass of each time of each road roller to be rolled wheelmark information superposition, determines to roll
Pass information.
Preferably, described device further includes, conversion unit, for the geodetic coordinates of road roller rolling wheel to be converted into plane
Coordinate.
Preferably, described device further includes：Pretreatment unit, for rolling track pretreatment to described, removal rolls rail
Static data point and the big data point of error in mark.
Preferably, the fitting boundary unit, is specifically used for,
When road roller is rolled to opposite side successively in operating area from side, according to the straight line after fitting in X-axis or Y-axis
The periodicity of the change of intercept extreme value, determines the separation of number of rolling；
Or
When road roller is rolled inwardly successively in operating area by outside, cut according to the straight line after fitting in X-axis or Y-axis
Away from change periodicity, determine the separation of number of rolling.
Preferably, the fitting boundary unit is additionally operable to：
Determine that first segment rolls the distance that the point on the straight line of track fitting rolls the straight line of track fitting to second segment, if
The distance is less than preset value, then the second segment rolls separation of the straight line not as definite number of rolling of track fitting.
As shown from the above technical solution, the present invention provides a kind of method calculated automatically for road roller number of rolling, uses
It is automatic in real time to calculate according to the different type of road roller in realizing one or more road roller to when work surface rolls
The number of rolling of all kinds road roller in current work face and number of rolling distribution situation, on-site personnel is sent out immediately
Pressure, under-voltage region are leaked again, to ensure construction quality.
Brief description of the drawings
Fig. 1 is the flow for being used for the method that road roller number of rolling the calculates automatically signal that one embodiment of the invention provides
Figure；
Fig. 2 is the flow for being used for the method that road roller number of rolling the calculates automatically signal that another embodiment of the present invention provides
Figure；
Fig. 3 is the structural representation for being used for the device that road roller number of rolling calculates automatically that one embodiment of the invention provides
Figure.
Embodiment
With reference to the accompanying drawings and examples, the embodiment of the present invention is described in further detail.Implement below
Example is used to illustrate the present invention, but is not limited to the scope of the present invention.
Fig. 1 shows that the flow for being used for the method that road roller number of rolling calculates automatically that one embodiment of the invention provides is shown
It is intended to, as shown in Figure 1, the number of rolling computational methods of the present embodiment are as described below.
101st, the plane coordinates information of track is rolled according to road roller, trajectory segment is rolled to described, each single hop is obtained and grinds
Press track.
It is understood that according to the rolling wheel width calculation road roller of the driving trace data of road roller and road roller
Roll region.
102nd, track fitting straight line is rolled to each single hop, the periodicity changed according to the straight line parameter after fitting, really
Determine the separation of number of rolling, obtain separate unit road roller single pass and roll wheelmark information.
It is understood that rolling point time numbering of track according to each road roller, track base is rolled after at each point
On plinth, the rolling wheel width information of corresponding road roller is added, according to the flat resolution of actual needs, by operating area grid
Change, generate separate unit point time respectively and roll wheelmark figure；In separate unit point in wheelmark figure is rolled, it is no more than 2 times with rolling layer for mark
The influence of the lap of the adjacent middle wheelmark round-trip twice of quasi- removal, forms platform point time and rolls mark state diagram；
103rd, the separate unit road roller single pass of each time of each road roller is rolled into wheelmark information superposition, determines number of rolling information.
It is understood that the corresponding separate unit of same kind road roller point is generated such all over state diagram superposition is rolled
The collaboration of type road roller point time rolls state diagram；By the collaboration of each time point all over state diagram superposition is rolled, this work surface is generated
Cooperate with number of rolling figure；
On the basis of number of rolling figure is cooperateed with, the grid number of different number of rolling is counted, calculates different number of rolling
The ratio that grid is put in grid is always rolled, forms collaboration and rolls statistical report form.Rolled according to number of rolling information and requirement
Whether pass information, determine in leakage pressure, under-voltage region in this working face, and is indicated.
The above method passes through the real-time collaborative number of rolling figure of this work surface during exhibition real-time to on-site personnel, scene pressure
Road machine machine hand can be sent out in real time leaks pressure, under-voltage region, timely ftercompction again.Field operation commanding can in real time grasp and effectively refer to
Wave the overall process of rolling operation.
In a preferred embodiment of the invention, to it is described roll trajectory segment before, the method further includes,
The geodetic coordinates of road roller rolling wheel is converted into plane coordinates.
It is understood that before calculating number of rolling, all road roller position datas are changed by geodetic coordinates (B, L, H)
For plane coordinates (N, E, U), it is not required to change if position data is plane coordinates.
In a preferred embodiment of the invention, it is described to it is described roll trajectory segment before, the method is also wrapped
Include：Track pretreatment is rolled to described, removes and rolls data point static in track and the big data point of error.So that calculate knot
Fruit is more accurate.
In a preferred embodiment of the invention, the periodicity that the straight line parameter according to after fitting changes becomes
Change, determine the separation of number of rolling, specifically include：
When road roller is rolled to opposite side successively in operating area from side, according to the straight line after fitting in X-axis or Y-axis
The periodicity of the change of intercept extreme value, determines the separation of number of rolling；
Or
When road roller is rolled inwardly successively in operating area by outside, cut according to the straight line after fitting in X-axis or Y-axis
Away from change periodicity, determine the separation of number of rolling.
It is understood that extract the X-axis intercept of the fitting a straight line of each track after each road roller segmentation, Y intercept
Data, according to X-axis intercept, the flex point (when being rolled successively toward opposite side from the side of operating area) of Y intercept change or according to X
Y-intercept, Y intercept period of change (when being rolled successively toward inner side on the outside of from the operating area) segmentation of starting point as number of rolling
Point, each section of corresponding number of rolling volume for rolling track and being belonged to is marked according to each time of calculating number of rolling waypoint respectively
Number；
In a preferred embodiment of the invention, the periodicity that the straight line parameter according to after fitting changes becomes
Change, determine that the separation of number of rolling further includes：
Determine that first segment rolls the distance that the point on the straight line of track fitting rolls the straight line of track fitting to second segment, if
The distance is less than preset value, then the second segment rolls separation of the straight line not as definite number of rolling of track fitting.
It is understood that preset value described in the present embodiment is the half of rolling wheel width, but the present invention is not limited to
This numerical value, preset value can specifically be limited according to actual conditions.According to the fitting a straight line of adjacent two sections of tracks after segmentation
Slope, X-axis intercept, Y intercept calculate two fitting a straight lines and the distance in X-axis, the near intersections of Y-axis, with putting down for the distance
Compared with average and half of rolling wheel width of current road roller or so, judge whether adjacent two sections of tracks belong to road roller one
It is round-trip in rolling operation, belong at the orbit segment of " returning " and be segmented not as the follow-up number of rolling；
In addition, the specific method that rolling wheel mark is calculated in number of rolling computational methods provided by the invention is as described below：
What deserves to be explained is using first point of every section of track data as starting point, using the last point of every section of track data as
The terminal of this section of track, to correspond to the width of road roller rolling wheel as the width of wheelmark.
The center line for originating wheelmark is used as using the line of first point and second point；With the company of last point and point second from the bottom
Line is as the center line for terminating wheelmark.With with originate wheelmark central axis, and using first point of line segment as midpoint as
The start line of beginning wheelmark；With the central axis with terminating wheelmark, and the line segment using last point as midpoint is used as termination wheelmark
Terminated line.
In addition at and last point, since second point, this section (first is used as using the line of this point and former point at first point
Point to second point be first segment, and so on) center line of wheelmark, using the line of this point and subsequent point as hypomere wheelmark in
Heart line.With respectively pass through the preceding paragraph wheelmark start line two-end-point, and with two straight lines of the centerline parallel of this section of wheelmark
As the left bounding lines of this section of wheelmark, (put down at angle with the angular bisector of the center line of this section of wheelmark and the center line of hypomere wheelmark
Separated time has two orthogonal straight lines.The intersection point of two angular bisector and the left bounding lines of this section of wheelmark is first calculated, and is divided
The sum of corresponding two intersection points and this point distance are not asked, it is corresponding in the case of then two intersection points of selection are shorter with the sum of this point distance
That angle horizontal line) terminated line as this section of wheelmark.The terminated line of this section of wheelmark while the start line as hypomere wheelmark.
To ready-portioned grid judges in work surface, in this section of wheelmark start line, terminated line and left bounding lines
The number of rolling of grid within the scope of surrounding adds 1.The rest may be inferred, completes all calculating for rolling wheelmark.
The above method can realize that more different type road roller work compound compacting countings calculate automatically in same work surface,
The number of rolling of different type road roller calculates respectively, and calculated automatically provided by the present invention for road roller number of rolling
Number of rolling image resolution ratio in method can be self-defined on demand, the compacting counting in accurate expression arbitrary size region.
Fig. 2 shows the flow for being used for the method that road roller number of rolling calculates automatically that another embodiment of the present invention provides
Schematic diagram, as shown in Fig. 2, the number of rolling computational methods of the present embodiment are as described below.
The position data of each road roller from database extraction current work face；
Geodetic coordinates (B, L, H) is converted into plane coordinates (N, E, U)；
Initial filter is carried out to plane coordinates, removes redundant data, smooth jumping point；
The flex point of driving trace is found out in road roller driving trace data after the filtering；
The track of rolling of each road roller is segmented according to switch-back point；
Linear fit is carried out to every section of track of each road roller；
Two fittings are calculated according to the slope of the fitting a straight line of adjacent two sections of tracks after segmentation, X-axis intercept, Y intercept
Straight line and the distance in X-axis, the near intersections of Y-axis, with the average value and the one of the rolling wheel width of current road roller of the distance
Half left and right compare, and it is round-trip in a rolling operation to judge whether adjacent two sections of tracks belong to road roller, belongs to the rail of " returning "
It is segmented at mark section not as the follow-up number of rolling；
X-axis intercept, the Y intercept data of the fitting a straight line of each track after each road roller segmentation are extracted, are cut according to X-axis
Flex point (when being rolled successively toward opposite side from the side of operating area) away from the change of, Y intercept or according to X-axis intercept, Y intercept
Period of change (when being rolled successively toward inner side on the outside of from the operating area) waypoint of starting point as number of rolling, according to each of calculating
Each section of corresponding number of rolling numbering for rolling track and being belonged to is marked respectively all over a number of rolling waypoint；
According to each road roller roll track point all over numbering, each point all over after roll track on the basis of, add correspond to
The rolling wheel width information of road roller, according to the flat resolution of actual needs, by operating area gridding, generates separate unit respectively
Point all over rolling wheelmark figure；
In separate unit point in wheelmark figure is rolled, it is no more than 2 times with rolling layer and removes the more of wheelmark lap for standard
Remaining part point, forms platform point time and rolls mark state diagram；
The corresponding separate unit of same kind road roller point divides all over state diagram superposition, the collaboration of generation the type road roller is rolled
All over rolling state diagram；
The collaboration of each time point generates the collaboration number of rolling figure of this work surface all over state diagram superposition is rolled；
On the basis of number of rolling figure is cooperateed with, the grid number of different number of rolling is counted, calculates different number of rolling
The ratio that grid is put in grid is always rolled, forms collaboration and rolls statistical report form.
Pass through the real-time collaborative number of rolling figure of this work surface during exhibition real-time to on-site personnel, live road roller machine hand
It can in real time send out and leak pressure, under-voltage region, timely ftercompction again.Field operation commanding, which can in real time grasp and effectively command, rolls work
The overall process of industry.
Above method offer one kind is filled thing to roadbed, road surface, dam etc. for one or more road roller and is combined
Number of rolling automatic calculating method during compacting operation.
Fig. 3 shows that the structure for being used for the device that road roller number of rolling calculates automatically that one embodiment of the invention provides is shown
It is intended to, as shown in figure 3, the number of rolling computing device of the present embodiment includes：
Segmenting unit 31, for rolling the plane coordinates information of track according to road roller, rolls trajectory segment to described, obtains
Track is rolled to each single hop；
Fitting boundary unit 32, for rolling track fitting straight line to each single hop, according to the change of the straight line after fitting
The periodicity of change, determines the separation of number of rolling, obtains separate unit road roller single pass and rolls wheelmark information；
Determination unit 33, for the separate unit road roller single pass of each time of each road roller to be rolled wheelmark information superposition, determines to grind
Press pass information.
In another preferred embodiment of the present invention, it is unshowned that described device further includes Fig. 3, conversion unit 34,
For the geodetic coordinates of road roller rolling wheel to be converted into plane coordinates.
In another preferred embodiment of the present invention, it is unshowned that described device further includes Fig. 3：Pretreatment unit
35, for rolling track pretreatment to described, remove and roll data point static in track and the big data point of error.
In another preferred embodiment of the present invention, the fitting boundary unit 32, is specifically used for,
When road roller is rolled to opposite side successively in operating area from side, according to the straight line after fitting in X-axis or Y-axis
The periodicity of the change of intercept extreme value, determines the separation of number of rolling；
Or
When road roller is rolled inwardly successively in operating area by outside, cut according to the straight line after fitting in X-axis or Y-axis
Away from change periodicity, determine the separation of number of rolling.
In another preferred embodiment of the present invention, the fitting boundary unit 32 is additionally operable to：
Determine that first segment rolls the distance that the point on the straight line of track fitting rolls the straight line of track fitting to second segment, if
The distance is less than preset value, then the second segment rolls separation of the straight line not as definite number of rolling of track fitting.
It will be appreciated that above device and the above method are one-to-one relations, the implementation detail in the above method
Suitable for above device, therefore, the present embodiment is no longer described in detail the specific implementation details of above device.
A kind of one or more road roller of above-mentioned offer fills thing to roadbed, road surface, dam etc. and carries out joint compacting operation
When number of rolling automatic computing equipment, one or more road roller is realized to when work surface rolls, according to road roller
Different type, the number of rolling and number of rolling distribution situation of all kinds road roller for calculating current work face automatic in real time
, on-site personnel is sent out immediately and leak pressure, under-voltage region again, to ensure construction quality.
It will be understood by those skilled in the art that the module in the equipment in embodiment can adaptively be changed
And they are provided in the different one or more equipment of the embodiment.Can the module in embodiment or unit or
Component is combined into a module or unit or component, and can be divided into multiple submodule or subelement or subgroup in addition
Part.Except at least some in such feature and/or process or unit are mutually exclusive parts, any combinations can be used
To all features disclosed in this specification (including adjoint claim, summary and attached drawing) and such disclosed any side
All processes or unit of method or equipment are combined.Unless expressly stated otherwise, this specification (including adjoint right will
Ask, make a summary and attached drawing) disclosed in each feature can be replaced by the alternative features for providing identical, equivalent or similar purpose.
In addition, it will be appreciated by those of skill in the art that although some embodiments described herein include other embodiments
In included some features rather than further feature, but the combination of the feature of different embodiments means in of the invention
Within the scope of and form different embodiments.For example, in the following claims, embodiment claimed is appointed
One of meaning mode can use in any combination.
The all parts embodiment of the present invention can be with hardware realization, or to be run on one or more processor
Software module realize, or realized with combinations thereof.It should be noted that above-described embodiment the present invention will be described and
Do not limit the invention, and those skilled in the art can set without departing from the scope of the appended claims
Count out alternative embodiment.In the claims, any reference symbol between bracket should not be configured to claim
Limitation.Word "comprising" does not exclude the presence of element or step not listed in the claims.Word before element
"a" or "an" does not exclude the presence of multiple such elements.The present invention can be by means of including the hardware of some different elements
And realized by means of properly programmed computer.In if the unit claim of equipment for drying is listed, in these devices
Several can be embodied by same hardware branch.The use of word first, second, and third does not indicate that
Any order.These words can be construed to title.
Finally it should be noted that：One of ordinary skill in the art will appreciate that：Various embodiments above is only illustrating this hair
Bright technical solution, rather than its limitations；Although the present invention is described in detail with reference to foregoing embodiments, this area
Those of ordinary skill should be understood：It can still modify the technical solution described in foregoing embodiments, or
Equivalent substitution is carried out to which part or all technical characteristic；And these modifications or replacement, do not make appropriate technical solution
Essence depart from the scope of the claims in the present invention.
Claims (10)
- A kind of 1. method calculated automatically for road roller number of rolling, it is characterised in that including：The plane coordinates information of track is rolled according to road roller, trajectory segment is rolled to described, each single hop is obtained and rolls track；Track fitting straight line is rolled to each single hop, the periodicity changed according to the straight line parameter after fitting determines to roll time Several separations, obtains separate unit road roller single pass and rolls wheelmark information；Each road roller separate unit road roller single pass of each time is rolled into wheelmark information superposition, determines number of rolling information.
- 2. according to the method described in claim 1, it is characterized in that, to it is described roll trajectory segment before, the method is also Including the geodetic coordinates of road roller rolling wheel is converted into plane coordinates.
- 3. according to the method described in claim 1, it is characterized in that, it is described to it is described roll trajectory segment before, the method Further include：Track pretreatment is rolled to described, removes and rolls data point static in track and the big data point of error.
- 4. the according to the method described in claim 1, it is characterized in that, periodicity that the straight line parameter according to after fitting changes Change, determines the separation of number of rolling, specifically includes：When road roller is rolled to opposite side successively in operating area from side, according to the straight line after fitting in X-axis or Y intercept The periodicity of the change of extreme value, determines the separation of number of rolling；OrWhen road roller is rolled inwardly successively in operating area by outside, according to the straight line after fitting in X-axis or Y intercept The periodicity of change, determines the separation of number of rolling.
- 5. the according to the method described in claim 4, it is characterized in that, periodicity that the straight line parameter according to after fitting changes Change, determines that the separation of number of rolling further includes：Determine that first segment rolls the distance that the point on the straight line of track fitting rolls the straight line of track fitting to second segment, if described Distance is less than preset value, then the second segment rolls separation of the straight line not as definite number of rolling of track fitting.
- A kind of 6. device calculated automatically for road roller number of rolling, it is characterised in that including：Segmenting unit, for rolling the plane coordinates information of track according to road roller, rolls trajectory segment to described, obtains each list Section rolls track；Fitting boundary unit, for rolling track fitting straight line to each single hop, according to the week of straight line parameter change after fitting Phase property, determines the separation of number of rolling, obtains separate unit road roller single pass and rolls wheelmark information；Determination unit, for the separate unit road roller single pass of each time of each road roller to be rolled wheelmark information superposition, determines number of rolling Information.
- 7. device according to claim 6, it is characterised in that described device further includes, conversion unit, for by road roller The geodetic coordinates of rolling wheel is converted into plane coordinates.
- 8. device according to claim 6, it is characterised in that described device further includes：Pretreatment unit, for described Track pretreatment is rolled, removes and rolls data point static in track and the big data point of error.
- 9. device according to claim 6, it is characterised in that the fitting boundary unit, is specifically used for,When road roller is rolled to opposite side successively in operating area from side, according to the straight line after fitting in X-axis or Y intercept The periodicity of the change of extreme value, determines the separation of number of rolling；OrWhen road roller is rolled inwardly successively in operating area by outside, according to the straight line after fitting in X-axis or Y intercept The periodicity of change, determines the separation of number of rolling.
- 10. device according to claim 9, it is characterised in that the fitting boundary unit is additionally operable to：Determine that first segment rolls the distance that the point on the straight line of track fitting rolls the straight line of track fitting to second segment, if described Distance is less than preset value, then the second segment rolls separation of the straight line not as definite number of rolling of track fitting.
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| CN106320391B (en) * | 2016-08-16 | 2018-08-21 | 中国电建集团成都勘测设计研究院有限公司 | The Experimental Determination Method of rolling earth-rock dam rolling layer |
| CN106758698B (en) * | 2016-12-08 | 2019-03-29 | 广州中海达定位技术有限公司 | Road roller control method and device |
| CN107169041A (en) * | 2017-04-24 | 2017-09-15 | 江苏中路信息科技有限公司 | Subgrade and pavement compacting counting monitoring device and method based on grid graph |
| CN109857097B (en) * | 2018-12-07 | 2022-04-12 | 北京中交睿达科技有限公司 | Method and system for monitoring road surface rolling process |
| CN110646813A (en) * | 2019-09-30 | 2020-01-03 | 长安大学 | Method and device for monitoring rolling pass of road roller and judging whether rolling is qualified |
| CN113481780B (en) * | 2021-06-04 | 2022-02-15 | 西南交通大学 | Roadbed overlapping rolling range calculation method, device and equipment and readable storage medium |
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