CN105975735B - A kind of modeling method for power equipment health state evaluation - Google Patents
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Abstract
The invention discloses a kind of modeling methods for power equipment health state evaluation, it is related to technical field of electric power, it can be realized the operation health status characteristic to power equipment to model, consequently facilitating carrying out it operation such as reasonable employment and maintenance, failure predication and distribution management.The modeling method for being used for power equipment health state evaluation includes: the state figureofmerit for obtaining the operating status for reflecting the power equipment；Using analytic hierarchy process (AHP), judgment matrix is established；Based on the judgment matrix, the weight of each state figureofmerit is obtained；Establish the fuzzy evaluation collection for being suitable for the power equipment；Nondimensionalization processing is carried out to each state figureofmerit；Nondimensionalization treated each state figureofmerit is obtained to the subjection degree of the fuzzy evaluation collection, that establishes the power equipment is subordinate to ordered series of numbers；Using grey correlation theory, it is subordinate to ordered series of numbers described in processing, obtains the model suitable for the power equipment health state evaluation.
Description
Technical field
The present invention relates to technical field of electric power more particularly to a kind of modeling sides for power equipment health state evaluation
Method.
Background technique
With the rapid development of economy, the power supply situation growing tension in China, throughout the country only because of network system
The main reason for economic loss caused by failure is as high as trillion, analyzes its can not be located in time to the failure of network system
Reason.
Because China's electric power enterprise executes always the unified periodic inspection system in the whole nation for a long time, substantive characteristics is simple
Based on the time cycle.This mode is clearly present that the actual state for not considering equipment, specific aim is strong in maintenance process, the palm
Hold negative effect of the fault observer that equipment state is inadequate, does not meet the existing power equipment service life, generation excess maintenance etc etc. no
Good problem, it is clear that whether troubleshooting system improves the reliability level for directly affecting power equipment, therefore by power equipment
Operation health status characteristic is modeled, its reasonable employment and maintenance, failure predication and distribution management etc. are operated, had
Particularly important meaning.
Summary of the invention
Technical problem to be solved by the present invention lies in provide a kind of modeling side for power equipment health state evaluation
Method can be realized the operation health status characteristic to power equipment and model, consequently facilitating carrying out reasonable employment and dimension to it
It repairs, the operation such as failure predication and distribution management.
In order to solve the above technical problems, the present invention adopts the following technical scheme:
This includes: for modeling method of power equipment health state evaluation
Obtain the state figureofmerit for reflecting the operating status of the power equipment；
Using analytic hierarchy process (AHP), judgment matrix is established；
Based on the judgment matrix, the weight of each state figureofmerit is obtained；
Establish the fuzzy evaluation collection for being suitable for the power equipment；
Nondimensionalization processing is carried out to each state figureofmerit；
According to each state figureofmerit to the subjection degree of the fuzzy evaluation collection, obtain the power equipment is subordinate to letter
Number；
Using grey correlation theory, weight, nondimensionalization processing result based on each state figureofmerit and it is subordinate to
Function obtains the model suitable for the power equipment health state evaluation.
Preferably, using analytic hierarchy process (AHP), establishing judgment matrix includes:
Based on the membership grouping between each state figureofmerit, orderly ladder hierarchical structure is established；
Based on the ladder hierarchical structure established, judgment matrix is established, the element of the judgment matrix is to belong to together
The comparison result of the figureofmerit of state two-by-two of one membership.
Preferably, it is based on the judgment matrix, the weight for obtaining each state figureofmerit includes:
Based on the judgment matrix established, by way of comparing two-by-two, determine in same membership and same level
The relative importance of each state figureofmerit；
According to the actual conditions of the power equipment, the weight of each state figureofmerit is obtained.
Preferably, based on the judgment matrix, after the weight for obtaining each state figureofmerit, further includes:
Using acquired weight, judge whether the judgment matrix meets consistency；
If not meeting, need to correct established judgment matrix and weight.
Preferably, it states and includes: to the weight progress nondimensionalization processing of each state figureofmerit
According to the degradation of each state figureofmerit, nondimensionalization processing is carried out to each state figureofmerit with score.
Preferably, nondimensionalization treated each state figureofmerit is obtained to the subjection degree of the fuzzy evaluation collection, is built
The ordered series of numbers that is subordinate to for founding the power equipment includes:
It establishes triangle and combines distribution membership function with trapezoidal；
Distribution membership function is combined with trapezoidal based on the triangle, obtains nondimensionalization treated each state figureofmerit
To the subjection degree of the fuzzy evaluation collection, so that establishes the power equipment is subordinate to ordered series of numbers.
Preferably, using grey correlation theory, it is subordinate to ordered series of numbers described in processing, obtains being suitable for the power equipment health shape
State assessment model include:
Establish the reference sequence that any evaluation is concentrated for the fuzzy evaluation；
Using grey correlation theory, the degree of association of ordered series of numbers Yu each reference sequence is subordinate to described in determination, obtains being suitable for described
The model of power equipment health state evaluation.
Preferably, determination is subordinate to ordered series of numbers and the degree of association of each reference sequence includes:
Obtain each reference sequence and the incidence coefficient for being subordinate to ordered series of numbers；
Based on the incidence coefficient, the degree of association of ordered series of numbers Yu each reference sequence is subordinate to described in determination.
Preferably, the fuzzy evaluation collection suitable for power equipment includes following evaluation:
Well, normally, suspicious, exception and danger.
Preferably, the reference sequence includes:
Kilter is [1,0,0,0,0], and normal condition is [0,1,0,0,0], and suspicious state is [0,0,1,0,0], different
Normal state is [0,0,0,1,0], and precarious position is [0,0,0,0,1].
In the inventive solutions, with the process of analytic hierarchy process (AHP) and step, including two ratio of such as construction therein
Compared with judgment matrix and the mathematical method of matrix operation, determine for some element of a upper level, in this level with its phase
Importance ranking --- the relative weight for closing element, calculates each layer element to the synthetic weight, etc. of aims of systems, all with routine
Analytic hierarchy process (AHP) is identical.
The present invention provides a kind of modeling method for power equipment health state evaluation, which uses first
The big task subdivision of power equipment health state evaluation is the small task for analyzing each state figureofmerit by analytic hierarchy process (AHP)；It
The weight for obtaining each state figureofmerit afterwards understands influence of each state figureofmerit to power equipment health state evaluation；Most
Afterwards, by grey correlation theory, clear overall merit is carried out to fuzzy overall evaluation, it is finally obtained for power equipment health
The model accuracy of status assessment is high, and staff is enabled to understand the health status of corresponding power equipment in time, thus
Convenient for carrying out the operation such as reasonable employment and maintenance, failure predication and distribution management to it.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, embodiment will be described below
Needed in attached drawing be briefly described, it should be apparent that, the accompanying drawings in the following description is only of the invention some
Embodiment for those of ordinary skill in the art without creative efforts, can also be attached according to these
Figure obtains other attached drawings.
Fig. 1 is the flow chart of the modeling method provided in an embodiment of the present invention for power equipment health state evaluation；
Fig. 2 is the state figureofmerit schematic diagram of cable run provided in an embodiment of the present invention；
Fig. 3 is the schematic diagram of membership function provided in an embodiment of the present invention.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are some of the embodiments of the present invention, instead of all the embodiments.Based on this hair
Embodiment in bright, every other implementation obtained by those of ordinary skill in the art without making creative efforts
Example, shall fall within the protection scope of the present invention.
The embodiment of the invention provides a kind of modeling methods for power equipment health state evaluation, as shown in Figure 1, should
Modeling method includes:
Step S101, the state figureofmerit of the operating status of reflection power equipment is obtained.
It realizes and the health status of power equipment is accurately and comprehensively assessed, needing to accurately hold can reflect that it runs shape
The quantity of state of state, and bonding state assessment operability, form comprising Test Information, operation information, inspection information shape
State duration set establishes evaluating status of electric power index system.Evaluation index system is divided into second level, and two-level index is state
Amount.As shown in Fig. 2, nine scales analytic hierarchy process can be used in the present invention and seek for the power cable in power equipment
Each quantity of state weight.
By taking cable run as an example, for cable run, the factor for influencing its operating status substantially may include cable sheet
Body, cable termination, cable intermediate joint, earthed system, cable passage and auxiliary equipment etc. six, wherein each single item all can be thin again
It is divided into multinomial state figureofmerit.For example, can be subdivided into line load, insulation resistance, cable for cable body and become
Shape, buried depth, fire protection flame retarding etc. totally five；For cable termination, filth, fire protection flame retarding, breakage and temperature can be subdivided into
Deng totally four；For cable intermediate joint, fire protection flame retarding, breakage, temperature, running environment etc. totally four can be subdivided into；
For earthed system, down conductor, ground resistance etc. totally two can be subdivided into；It, can for cable passage
It is subdivided into cable shaft, cable pipe trench environment etc. totally two；For auxiliary equipment, it is neat that firmness, mark can be subdivided into
Entirely, corrosion degree etc. totally three.
Based on the state figureofmerit found, analytic hierarchy process (AHP) is can be used in the embodiment of the present invention, to influence power equipment
Every state figureofmerit of health status is analyzed.
Step S102, using analytic hierarchy process (AHP), judgment matrix is established.
The basic principle of analytic hierarchy process (AHP) (The Analytic Hierarchy Process, abbreviation AHP) is decision
Person simplifies every complicated factor of object to be evaluated according to set standard and principle, and establishes and pass stepwise level knot
Structure.It passs stepwise hierarchical structure and complicated problem can be become simplified as, methodization, stratification.It is general to pass stepwise hierarchical structure
Including destination layer, rule layer and three layers of indicator layer, destination layer refers generally to for the scheduled target that studies a question, and rule layer indicates
Intermediate link needed for realizing the predeterminated target；Indicator layer is index, scheme used by order to realize predeterminated target etc..
In embodiments of the present invention, same layer is judged according to 1~9 grade of scale principle (as shown in table 1 below) of judgment matrix
Important relationship between secondary upper two element, obtains judgment matrix.Wherein matrix element indicates each first class index element XiRelative to Xj
The quantized value of importance, wherein i and j is integer.
Table 1 judgment matrix, 1~9 grade of scale principle
For cable run as shown in Figure 2, it can obtain following first class index judgment matrix A, need to illustrate
It is that V1, V2, V3, V4, V5, V6 in table 2 respectively represent cable itself, cable termination, cable intermediate joint, earthed system, electricity
Cable channel and auxiliary equipment:
2 cable run first class index judgment matrix of table
Step S103, it is based on judgment matrix, obtains the weight of each state figureofmerit.
AHP method is that complicated problem is decomposed into several compositing factors, these factors by interrelated degree and are subordinate to
Relationship is grouped the ladder hierarchical structure for being formed with sequence, forms a multi-level assay model, passes through the side compared two-by-two
Formula determines the relative importance of each factor in level, then according to the actual situation, to determine the weight coefficient of each factor.This method
Based on expert to the Subjective degree of indices importance, there is certain persuasion dynamics.Analytic hierarchy process (AHP) seeks weight
Method have geometric average method, arithmetic mean method, feature vector method, 4 kinds of least square method.
Based on judgment matrix, the weight of each state figureofmerit can be readily available.But the power that AHP method is calculated
Only having passed through consistency check again can just be used.
Specifically, calculating coincident indicator CI (Consistency Index) first, CI can be calculated by following formula:
Wherein λmaxIndicate that the maximum eigenvalue of judgment matrix, n represent the dimension of judgment matrix.
Secondly, calculating consistency ration:
Wherein, RI is Aver-age Random Consistency Index, and value can pass through 3 acquisitions of tabling look-up.When CR < 0.1, judgment matrix
Reliably；When CR >=0.1, matrix is unreliable, needs to re-establish matrix.
3 Aver-age Random Consistency Index of table
By calculating, CR=0.0047 < 0.1 of the judgment matrix in table 2, therefore the judgment matrix is examined by consistency
It tests.
The weight that AHP method is calculated, which has only passed through consistency check, can just be used, this has just ensured weight
Scientific and reasonability；Second, general objective is turned to orderly several levels and several elements, this is especially suitable for the body that has levels
The multiple index evaluation object of system；Third, operand involved in analytic hierarchy process (AHP) is little, and model is easily operated, convenient for simplicity
Operation solve challenge；4th, total evaluation index can be quantified by analytic hierarchy process (AHP), each lower layer of quantitative study
The problem of state figureofmerit is to the influence degree of the operating status of power equipment.
Similar, similarly, according to expert estimation, the two-level index judgment matrix of each first class index is established, using maximum special
Value indicative method can find out the weight of the corresponding quantity of state of all parts, as shown in table 4 below:
4 two-level index of table (quantity of state) weight
Step S103, the fuzzy evaluation collection for being suitable for power equipment is established.
For cable run, the embodiment of the present invention by the state demarcation of cable run be " good ", " normal ", " can
Doubt ", "abnormal", " danger " five kinds of states, i.e., determining fuzzy evaluation collection V={ good, normal, suspicious, exception, danger }, wherein
It is dangerous: 0~60；It is abnormal: 60~70；It is suspicious: 70~80；It is normal: 80~90；It is good: 90~100.Kilter refers to equipment
Stable, all quantity of states comply with standard or far from exceptional values.At this point, the probability of device fails is extremely low, it can be long-term
Operation.Normal condition refers to that state quantity of the equipment is normal or in which individual parameters show that reliability is slightly decreased, but reaches far away different
Constant value.At this point, should be overhauled according to the original maintenance plan arrangement of equipment；Suspicious state indicates that several quantity of states of equipment do not meet mark
Standard, but equipment operation is not influenced；Abnormality refers to that state quantity of the equipment is close to or up to the exceptional value in regulation, and display equipment will
Failure is wanted or has already appeared, but in a short time will not there is a situation where accidents.At this point, the period of overhaul of the equipments should be reduced；
Precarious position indicates that state quantity of the equipment danger exceeds exceptional value or jeopardy exception, and accident may occur at any time in operation for equipment.
It is overhauled at this point, equipment should have a power failure immediately.
Step S104, nondimensionalization processing is carried out to each state figureofmerit.
In multi objective system, since the unit of each index is different, dimension is different, the order of magnitude is different, is not easy to analyze, even
It will affect the result of evaluation.Therefore, it is unified standard, nondimensionalization processing is carried out to all evaluation indexes, with the amount of elimination
Guiding principle converts it into the differential other standard scores of dimensionless, incalculability, is then analyzed and evaluated again.
In multiple attribute synthetical evaluation, different evaluation index often has different dimension and dimensional unit, directly by it
Carry out synthesis be it is inappropriate, also without practical significance.So index value must be converted to nondimensional relative number.It is this
Remove the process of index dimension, the referred to as nondimensionalization (also referred to as unison quantization) of index, it is the premise of index comprehensive.Referring to more
It marks in practice of evaluation, often using the later numerical value of indices non-dimension as metrics evaluation value, at this point, nondimensionalization process just refers to
Mark actual value is converted into the process of metrics evaluation value (i.e. utility function value), nondimensionalization method namely refer to how to realize it is this
Conversion.Therefore, the nondimensionalization of index is an important content of overall merit, is had a major impact to comprehensive evaluation result.
There are many common nondimensionalization method name at present, as composite index law, range transformation method, senior middle school's difference converter technique,
Low middle poor converter technique, equalization method, Standardization Act, hydrometer method, efficiency coefficient method, exponential type efficiency coefficient method, logarithmic effect
Y-factor method Y, normal transformations method etc..
According to the degradation of state figureofmerit in the embodiment of the present invention, nondimensionalization is carried out to state figureofmerit with score
Processing, using hundred-mark system, score value assigns to 100 points from 0, using 60 points for as danger threshold, 100 points each to cable run for full marks
A unit status is given a mark.Each quantity of state index score is higher, shows that the operating status of the state figureofmerit is better.
Step S105, nondimensionalization treated each state figureofmerit is obtained to the subjection degree of fuzzy evaluation collection, is established
Power equipment is subordinate to ordered series of numbers.
The determination for being subordinate to ordered series of numbers is a highly important element in assessing.The ordered series of numbers that is subordinate to of power equipment has reacted each
Subjection degree of a quantity of state for each Comment gathers.Subjection degree is determined by membership function.The conjunction that membership function is chosen
Whether reason, it is directly related to the accuracy of final assessment result.
Triangle preferably as shown in Figure 3 of the embodiment of the present invention combines distribution membership function, the membership function meter with trapezoidal
It counts and comes relatively simple, and accuracy is not very greatly with compared to complicated membership function gap.
In fuzzy set, the value range of membership function codomain is [0,1], and membership function is as follows:
Membership function under kilter:
Membership function under normal condition:
Membership function under suspicious state:
Membership function under abnormality:
Membership function under precarious position:
Step S106, using grey correlation theory, it is subordinate to ordered series of numbers described in processing, obtains being suitable for power equipment health status
The model of assessment.
Grey correlation theory is one of important component of gray system theory, and be Grey System Analysis, modeling,
It predicts, the foundation stone of decision.Grey correlation analysis is that physical prototype is not known or lacked at all to operating mechanism and physical prototype
Gray relation serializing, medelling, and then establish Grey Relation Analysis Model, make gray relation quantization, sequence, clear, energy
Important technology analysis means are provided for the modeling of complication system.Grey correlation theory is introduced into fuzzy evaluation, mould is utilized
The fuzzy overall evaluation of paste object overcomes person in servitude to the degree of association of clear overall merit to determine the state grade of power equipment
Error caused by category degree principle.
If reference sequence is { X0, being compared ordered series of numbers is { Xi}={ Xi(1),Xi(2),…Xi(n) } reference sequence, is then defined
With by compared with ordered series of numbers it is as follows in the incidence coefficient of k point:
Wherein: Δi(k)=| X0(k)-Xi(k) |, MminFor two-stage lowest difference, MmaxFor two-stage maximum difference.
Then reference sequence with by compared with the degree of association r of ordered series of numbers it is as follows:
Five reference sequences used in the embodiment of the present invention have corresponded to the clear judge of five kinds of different conditions.Five kinds of states
Are as follows: kilter is [1,0,0,0,0], and normal condition is [0,1,0,0,0], and suspicious state is [0,0,1,0,0], abnormality
For [0,0,0,1,0], precarious position is [0,0,0,0,1].
Obviously, the above-mentioned ordered series of numbers that compared is to be subordinate to ordered series of numbers.
In a concrete application scene of the embodiment of the present invention, bright II924 is pacified with west of a city branch office, Nanning power supply bureau
The test of midium voltage cable route and inspection data are example, calculate its final various corresponding degree of membership of state.The track laying
Cable model be LSN 10/3.1-3X9.5m.This section of line load is the 70% of rated load；Insulation resistance test and initial value
Compare no marked difference；Cable profile has little damage at two；Fire protection flame retarding and buried depth all meet design requirement；Cable termination
There is filth on surface, slightly damaged, and alternate temperature difference is 7K, and connector temperature is 70 DEG C, and fire protection flame retarding measure is perfect；In cable indirectly
Fever without exception, running environment is excellent, and medial head is met the requirements without obvious breakage, fire protection flame retarding；Down conductor appearance is good
Good, ground resistance is 8.7 Ω；Cable shaft without ponding, cable pipe trench without ponding, without sinking, cable run protection zone running environment
Normally, fire protection flame retarding meets design requirement；Auxiliary equipment firmly installs, but has moderate corrosion, and mark mounting height is not up to wanted
It asks.
According to the practical health status of this section of cable run obtain each unit status measure it is point as follows:
Each unit status of table 5 measures point
Final Comprehensive Evaluation result are as follows: [0.9669,0.0369,0,0,0].It is clearly judged in conjunction with five kinds of states, and it is good
The degree of association of good state is 0.9669；The degree of association with normal condition is 0.0369；The degree of association with suspicious state is 0；With it is different
The degree of association of normal state is 0；The degree of association with precarious position is 0.Therefore, provable this section of cable run operates in normal shape
State.
In conclusion the embodiment of the invention provides a kind of modeling method for power equipment health state evaluation, it should
Modeling method uses analytic hierarchy process (AHP) first, is to analyze each quantity of state by the big task subdivision of power equipment health state evaluation
The small task of index；The weight for obtaining each state figureofmerit later understands each state figureofmerit to power equipment health shape
The influence of state assessment；Finally, clear overall merit is carried out to fuzzy overall evaluation by grey correlation theory, it is finally obtained
Model accuracy for power equipment health state evaluation is high, and staff is enabled to understand corresponding power equipment in time
Health status, consequently facilitating it is carried out reasonable employment and maintenance, failure predication and distribution management etc. operation.
Through the above description of the embodiments, it is apparent to those skilled in the art that the present invention can borrow
Help software that the mode of required common hardware is added to realize, naturally it is also possible to which the former is more preferably by hardware, but in many cases
Embodiment.Based on this understanding, the portion that technical solution of the present invention substantially in other words contributes to the prior art
Dividing can be embodied in the form of software products, which stores in a readable storage medium, such as count
The floppy disk of calculation machine, hard disk or CD etc., including some instructions are used so that computer equipment (it can be personal computer,
Server or the network equipment etc.) execute method described in each embodiment of the present invention.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
Those familiar with the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all contain
Lid is within protection scope of the present invention.Therefore, protection scope of the present invention should be based on the protection scope of the described claims.
Claims (2)
1. a kind of modeling method for power equipment health state evaluation characterized by comprising
Obtain the state figureofmerit for reflecting the operating status of the power equipment；
Using analytic hierarchy process (AHP), judgment matrix is established；
Based on the judgment matrix, the weight of each state figureofmerit is obtained；
Establish the fuzzy evaluation collection for being suitable for the power equipment；
Nondimensionalization processing is carried out to each state figureofmerit；
Nondimensionalization treated each state figureofmerit is obtained to the subjection degree of the fuzzy evaluation collection, the electric power is established and sets
Standby is subordinate to ordered series of numbers；
Using grey correlation theory, it is subordinate to ordered series of numbers described in processing, obtains the mould suitable for the power equipment health state evaluation
Type；
Using analytic hierarchy process (AHP), establishing judgment matrix includes:
Based on the membership grouping between each state figureofmerit, orderly ladder hierarchical structure is established；
Based on the ladder hierarchical structure established, judgment matrix is established, the element of the judgment matrix is to belong to same person in servitude
The comparison result of the figureofmerit of state two-by-two of category relationship；
Based on the judgment matrix, the weight for obtaining each state figureofmerit includes:
Based on the judgment matrix established, by way of comparing two-by-two, each shape in same membership and same level is determined
The relative importance of state figureofmerit；
According to the actual conditions of the power equipment, the weight of each state figureofmerit is obtained；
Based on the judgment matrix, after the weight for obtaining each state figureofmerit, further includes:
Using acquired weight, judge whether the judgment matrix meets consistency；
If not meeting, need to correct established judgment matrix and weight；
The weight to each state figureofmerit carries out nondimensionalization processing
According to the degradation of each state figureofmerit, nondimensionalization processing is carried out to each state figureofmerit with score；
Nondimensionalization treated each state figureofmerit is obtained to the subjection degree of the fuzzy evaluation collection, the electric power is established and sets
The standby ordered series of numbers that is subordinate to includes:
It establishes triangle and combines distribution membership function with trapezoidal；
Distribution membership function is combined with trapezoidal based on the triangle, obtains nondimensionalization treated each state figureofmerit to institute
The subjection degree of fuzzy evaluation collection is stated, so that establishes the power equipment is subordinate to ordered series of numbers；
Using grey correlation theory, it is subordinate to ordered series of numbers described in processing, obtains the mould suitable for the power equipment health state evaluation
Type includes:
Establish the reference sequence that any evaluation is concentrated for the fuzzy evaluation；
Using grey correlation theory, the degree of association of ordered series of numbers Yu each reference sequence is subordinate to described in determination, obtains being suitable for the electric power
The model of equipment health state evaluation；
Determination is subordinate to ordered series of numbers and the degree of association of each reference sequence includes:
Obtain each reference sequence and the incidence coefficient for being subordinate to ordered series of numbers；
Based on the incidence coefficient, the degree of association of ordered series of numbers Yu each reference sequence is subordinate to described in determination；
The fuzzy evaluation collection suitable for power equipment includes following evaluation:
Well, normally, suspicious, exception and danger.
2. modeling method according to claim 1, which is characterized in that the reference sequence includes:
Kilter is [1,0,0,0,0], and normal condition is [0,1,0,0,0], and suspicious state is [0,0,1,0,0], abnormal shape
State is [0,0,0,1,0], and precarious position is [0,0,0,0,1].
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