CN104933482A - Power equipment overhaul optimization method based on fuzzy service life reduction - Google Patents

Abstract

The invention provides a power equipment overhaul optimization method based on fuzzy service life reduction. The method comprises the following steps: according to uncertainty on an enhancement effect of an equipment fault rate by an overhaul activity, carrying out fuzzy fitting on the fault rate in the historical data of equipment, proposing a fuzzy service life reduction fault rate prediction model, and comprehensively considering reliability and economy to establish an elastic state overhaul decision optimization model; and adopting the fuzzy service life reduction model to calculate a fault rate distribution function of the overhauled equipment, and applying the elastic state overhaul decision optimization model to carry out the solving optimization of power equipment overhaul time, wherein a fault rate limiting value serves as an constraint condition of an extremum of the fault rate distribution function of the overhauled equipment to cause the whole life cycle of the equipment to be economic. The method fully considers the fuzziness and the randomness of the overhaul activity on the failure probability and the service life of single power transformation equipment, is favorable for a power grid enterprise to reasonably organize an overhaul plane and reliably prolongs the service life of the equipment.

Description

Based on the electric power apparatus examination optimization method of fuzzy enlistment age rollback

Technical field

The present invention relates to power equipment maintenance technology field, particularly a kind of electric power apparatus examination optimization method based on fuzzy enlistment age rollback.

Background technology

Power equipment is the important substance guarantee maintaining and improve power supply enterprise's productive capacity, the normal operation of electric system was often destroyed once lose efficacy, bring huge economic loss, the repair and maintenance work of reasonable arrangement equipment is to guaranteeing the equipment general level of the health, safeguarding power network safety operation and ensureing that national economy has vital role.

Overall life cycle cost (Life Circle Cost, LCC) management philosophy and method become the realistic choice that International Power develops just gradually, and the operation expense of grid equipment and failure cost occupy larger specific gravity in overall life cycle cost, how on the basis of coordinating economy and reliability relation, to arrange the O&M service work of equipment to be one of important step advancing assets life-cycle management, therefore the turnaround plan of power equipment is optimized very necessary.

Be optimized method to the turnaround plan of power equipment to mainly contain: by Cost Estimation, suppose that the maintenance after each fault makes equipment reparation as newly, construct the cost model under prophylactic repair and repair based on condition of component; The Strategies of Maintenance of certain time of running is discussed, compares that transformer is not repaiied, overhaul, light maintenance and replacing four kinds of modes are optimized the impact of Life Cycle Cost; Optimum Strategies of Maintenance under two kinds of prophylactic repair patterns; Decision optimization is carried out on the basis of prophylactic repair strategy and repair based on condition of component strategy, namely carries out repair based on condition of component etc. when the constraint condition of setting exceedes a certain threshold value.Following several problem is there is: reckoning without maintenance affects situation to reliability in these methods, the model set up is perfect not, from the angle of whole life cycle, Strategies of Maintenance is not optimized, reckon without the requirement of equipment dependability aspect, be difficult to obtain real optimum Strategies of Maintenance.Therefore, existing method does not address this problem well.

Summary of the invention

The object of the present invention is to provide a kind of electric power apparatus examination optimization method based on fuzzy enlistment age rollback, to solve the problem being difficult to obtain real optimum Strategies of Maintenance existing in the existing method be optimized the turnaround plan of power equipment.

For achieving the above object, the invention provides a kind of electric power apparatus examination optimization method based on fuzzy enlistment age rollback, comprise the following steps:

S1: the fuzzy matching carrying out electrical equipment fault rate according to electrical equipment fault rate historical data, obtaining fitting result is:

The Random-fuzzy distribution function of equipment failure rate Y (t) is:

$\hat{Y}\left(t\right)=(\widehat{\mathrm{\λ}}\left(t\right),{\hat{c}}_1\left(t\right),{\hat{c}}_2\left(t\right))$

Wherein, for the central value of failure rate Triangular Fuzzy Number, for right avertence difference, for left avertence difference;

S2: the fuzzy enlistment age rollback failure rate forecast model setting up power equipment in conjunction with described fitting result, obtains the equivalent enlistment age of overhauling rear power equipment according to repair time sequence and central value the λ ' (t of the bathtub curve Triangular Fuzzy Number of the rear power equipment of kth time maintenance _k), right avertence difference c' ₁(t _k) and left avertence difference c' ₂(t _k),

Wherein, for according to t' _kcalculate rollback point failure rate fuzzy number expectation value;

S3: carry out cost of overhaul estimation and failure cost estimation, and build elastic stage maintenance decision Optimized model accordingly, the constraint condition that failure rate limit value is worth as the equipment failure rate distribution function after maintenance most by this model, model is as follows:

$\begin{array}{c}\begin{array}{cc}\min & f\left(\stackrel{\→}{T}\right)\end{array},={{\hat{C}}_M}^{\′}+{{\hat{C}}_F}^{\′}\\ =\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{\hat{C}}_M{\left(\frac{1}{1+r_d}\right)}^{t_k}+\underset{t=1}{\overset{T_A}{\mathrm{\Σ}}}{\hat{C}}_F{\mathrm{\λ}}^{\′}\left(t\right){\left(\frac{1}{1+r_d}\right)}^t\end{array},$

s.t. λ _min≤λ'(t)≤λ _max

In formula: use decision vector represent the time of each maintenance; for major overhaul cost; for total failare cost; for the blur estimation value of the single cost of overhaul; for the blur estimation value of single failure cost; t _kfor the enlistment age of equipment when kth time is overhauled; N is maintenance number of times total in plant life cycle; T _afor service life of equipment; r _dfor considering the discount rate after the factors such as inflation rate, interest rate, the exchange rate; λ ' (t) is the failure rate distribution function of equipment after maintenance; λ _minfor failure rate lower limit; λ _maxfor the failure rate upper limit.

S4: the failure rate distribution function calculating the rear equipment of maintenance according to the fuzzy enlistment age rollback failure rate forecast model of described power equipment, then use the elastic stage maintenance decision Optimized model of step S3 to carry out the solving-optimizing of electric power apparatus examination time.

Preferably, in described step S1, the process of fuzzy matching is specially: the electrical equipment fault rate adopting fuzzy fitting function to represent banded in historical data, is expressed as the Random-fuzzy distribution function of equipment failure rate Y (t):

$\hat{Y}\left(t\right)=(\widehat{\mathrm{\λ}}\left(t\right),{\hat{c}}_1\left(t\right),{\hat{c}}_2\left(t\right))$

Thus obtain dividing value curve on the right of failure rate and failure rate left side dividing value curve ${\widehat{\mathrm{\λ}}}_2\left(t\right)=\widehat{\mathrm{\λ}}\left(t\right)-{\hat{c}}_2\left(t\right).$

Preferably, described fuzzy enlistment age rollback failure rate forecast model is specially:

By fuzzy evaluation correction equivalence enlistment age, for the time of each maintenance : first, if the enlistment age rollback of power equipment is to t' after kth time maintenance _kmoment, wherein, ${t^{\′}}_k=\left\{\begin{array}{cc}(1-\mathrm{\α})T_1& k=1\\ t_{\mathrm{eq},k-1}+(1-\mathrm{\α})(T_k-T_{k-1})& k=2,...,n\end{array}\right.,$ α is service age reduction factor;

Secondly, according to t' _kcalculating rollback point failure rate fuzzy number expectation value is: $E\left(\right[\hat{Y}\left({t^{\′}}_k\right)\left]\right)=\frac{1}{4}[{\widehat{\mathrm{\λ}}}_1\left({t^{\′}}_k\right)+2\widehat{\mathrm{\λ}}\left({t^{\′}}_k\right)+{\widehat{\mathrm{\λ}}}_2\left({t^{\′}}_k\right)],$ Wherein, for failure rate median profile, for dividing value curve on the right of failure rate, for failure rate left side dividing value curve;

Finally, according to expectation value at bathtub curve on search corresponding working time and be and by t _{eq, k}as the equivalent enlistment age of power equipment after kth time maintenance; After obtaining kth time maintenance, the central value of electrical equipment fault rate curve Triangular Fuzzy Number is simultaneously right avertence difference is ${c^{\′}}_1\left(t_k\right)={\hat{c}}_1\left(t_{\mathrm{eq},k}\right),$ Left avertence difference is ${c^{\′}}_2\left(t_k\right)={\hat{c}}_2\left(t_{\mathrm{eq},k}\right).$

Preferably, described cost of overhaul estimation is specially: according to statistics, represent the blur estimation value of the single cost of overhaul with Triangular Fuzzy Number: wherein, C _mLfor the lower limit of single cost of overhaul statistic, C _mRfor the upper limit of single cost of overhaul statistic, C _mfor the value that possibility in single cost of overhaul statistic is maximum;

And the expectation value obtaining the cost of overhaul is:

Described failure cost estimation is specially: establish power equipment single failure cost C _ftaken by corrective maintenance costs and breakdown loss and form: wherein, C _{fM, k}for the k item expense in single failure maintenance, P _lossfor loss of outage load, T is single power failure duration, and p is poor for purchasing sale of electricity electricity price;

Again according to statistics, obtain the blur estimation value of single failure cost: wherein, C _fLfor the lower limit of single failure cost statistics numerical value, C _fRfor the upper limit of single failure cost statistics numerical value, C _ffor the value that possibility in single failure cost statistics numerical value is maximum;

And the expectation value obtaining single failure cost is:

Preferably, in described step S3, after maintenance, failure rate distribution function λ ' (t) obtains in the following manner:

If corresponding repair time sequence is T ₁, T ₂..., T _n, after maintenance, failure rate distribution function λ ' (t) is expressed as:

${\mathrm{\&lambda;}}^{\&prime;}\left(t\right)=\left\{\begin{array}{cc}\widehat{\mathrm{\&lambda;}}\left(t\right)& 0\&le;t\&le;T_1\\ \widehat{\mathrm{\&lambda;}}(t+t_{\mathrm{eq},k-1}-T_{k-1})& T_{k-1}<t\&le;T_k(k=2,...,n)\\ \widehat{\mathrm{\&lambda;}}(t+t_{\mathrm{eq},n}-T_n)& T_n<t\&le;T_A\end{array}\right..$

Preferably, when described step S3 performs solving-optimizing, be specially: after repair based on condition of component each time, the change of bonding apparatus bathtub curve, the failure rate upper limit and failure rate lower limit, the next one being overhauled the time is located in the limited range of permission, and the enlistment age of equipment is located in the limited range of permission, solve by limited recirculating the optimum solution that operation then obtains the electric power apparatus examination time.

Preferably, described step S4 solution procedure is as follows:

After kth time maintenance, when failure rate drops to equivalent enlistment age t _{eq, k}during corresponding failure rate, retrain by failure rate limit value, next overhauls time T _k+1in limited range:

$\max \{{\widehat{\mathrm{\&lambda;}}}^{-1}\left({\mathrm{\&lambda;}}_{\min }\right)-t_{\mathrm{eq},k},0\}+T_k<T_{k+1}\&le;\min \{{\widehat{\mathrm{\&lambda;}}}^{-1}\left({\mathrm{\&lambda;}}_{\max }\right)-t_{\mathrm{eq},k}+T_k,T_A\}$

Service life of equipment T _alimited, from first maintenance moment, enumerate successively under the time-constrain in maintenance time and obtain the next possibility repair time; Obtained the sequence of multiple feasible repair time by embedded loops operation, largest loop tuple is set to T _asecondary;

Again to the time series of each maintenance carry out calculating rear failure rate distribution function λ ' (t) of maintenance, try to achieve functional value according to elastic stage maintenance decision Optimized model

Solve operation by circulation, in all feasible solutions, try to achieve the optimal value of elastic stage maintenance decision Optimized model.

Because the service work of equipment can improve equipment performance, the present invention promotes the uncertainty of effect to electrical equipment fault rate according to maintenance activity, fuzzy matching is carried out to failure rate in device history data, fuzzy enlistment age rollback failure rate forecast model is proposed, for quantification service work to the repairing effect of equipment performance.On the basis of analytical equipment overall life cycle cost, consider reliability and economy, propose the elastic stage maintenance decision Optimized model based on fuzzy enlistment age rollback.By the failure rate distribution function adopting fuzzy enlistment age rollback model to calculate the rear equipment of maintenance, and elastic stage maintenance decision Optimized model is used to carry out the solving-optimizing of electric power apparatus examination type and time.Wherein, using the constraint condition that failure rate limit value is worth as the rear equipment failure rate distribution function of maintenance most, make the overall life cycle cost of equipment more economical.The method has taken into full account that maintenance is to single converting equipment failure probability and the ambiguity in serviceable life and randomness, on the basis of analytical equipment overall life cycle cost, consider reliability and economy, repair based on condition of component optimization method based on fuzzy enlistment age rollback is proposed, the model proposed is conducive to electric power enterprise reasonable arrangement turnaround plan, reliable extension device serviceable life.

Accompanying drawing explanation

Fig. 1 is the electric power apparatus examination optimization method process flow diagram based on fuzzy enlistment age rollback provided by the invention;

Fig. 2 is that the preferred embodiment of the present invention is according to the failure rate distribution curve after the fuzzy matching of transformer fault rate historical data;

The failure rate distribution curve that Fig. 3 obtains by the preferred embodiment of the present invention under optimum solution.

Embodiment

For better the present invention being described, hereby with a preferred embodiment, and accompanying drawing is coordinated to elaborate to the present invention, specific as follows:

As shown in Figure 1, the electric power apparatus examination optimization method based on fuzzy enlistment age rollback that the present embodiment provides, comprises the following steps:

S1: the fuzzy matching carrying out electrical equipment fault rate according to electrical equipment fault rate historical data, obtains fitting result;

S2: the fuzzy enlistment age rollback model setting up power equipment in conjunction with described fitting result, can obtain the equivalent enlistment age of overhauling rear equipment according to repair time sequence, and kth time overhauls central value and the deviate change of the bathtub curve Triangular Fuzzy Number of rear power equipment;

S3: carry out cost of overhaul estimation and failure cost estimation, and build elastic stage maintenance decision Optimized model accordingly;

S4: the failure rate distribution function calculating the rear equipment of maintenance according to the fuzzy enlistment age rollback failure rate forecast model of described power equipment, then use the elastic stage maintenance decision Optimized model of step S3 to carry out the solving-optimizing of electric power apparatus examination time.

Particularly, the present embodiment is described in detail for Repair of Transformer:

To 110kV, 50MVA double winding oil-filled transformer, assuming that operation life is 30 years, the Repair of Transformer optimization method applied based on fuzzy enlistment age rollback determines optimum Strategies of Maintenance, as follows:

S1: carry out fuzzy matching according to transformer fault rate historical data.Fuzzy matching is specially: adopt the equipment failure rate that fuzzy fitting function represents banded in historical data, the Random-fuzzy distribution function of equipment failure rate Y (t) is expressed as:

$\hat{Y}\left(t\right)=(\widehat{\mathrm{\&lambda;}}\left(t\right),{\hat{c}}_1\left(t\right),{\hat{c}}_2\left(t\right))$

Wherein, for the central value of failure rate Triangular Fuzzy Number, for right avertence difference, for left avertence difference.Failure rate Fuzzy Distribution curve after fuzzy matching in the present embodiment as shown in Figure 2, obtains fitting result failure rate central value curve the right dividing value curve left side dividing value curve

S2: the fuzzy enlistment age rollback failure rate forecast model setting up power equipment in conjunction with above-mentioned fitting result.Fuzzy enlistment age rollback failure rate forecast model is as follows:

For the time series of maintenance : first, after kth time maintenance, the enlistment age rollback of power equipment is to t' _kmoment.For first time maintenance, Backoff time point t' ₁=(1-α) T ₁, α is service age reduction factor.To k=2,3 ..., n, t' _k=t _{eq, k-1}+ (1-α) (T _k-T _k-1) relevant to the front activity of maintenance several times.

Secondly, according to t' _kcalculate rollback point failure rate fuzzy number expectation value: $E\left(\right[\hat{Y}\left({t^{\&prime;}}_k\right)\left]\right)=\frac{1}{4}[{\widehat{\mathrm{\&lambda;}}}_1\left({t^{\&prime;}}_k\right)+2\widehat{\mathrm{\&lambda;}}\left({t^{\&prime;}}_k\right)+{\widehat{\mathrm{\&lambda;}}}_2\left({t^{\&prime;}}_k\right)],$ Wherein, for failure rate median profile, for dividing value curve on the right of failure rate, for failure rate left side dividing value curve.

Finally, according to expectation value at bathtub curve on search corresponding working time be the equivalent enlistment age t of the rear power equipment of kth time maintenance _{eq, k}.And the central value of electrical equipment fault rate curve Triangular Fuzzy Number is after obtaining kth time maintenance right avertence difference left avertence difference

S3: carry out cost of overhaul estimation and failure cost estimation.

Cost of overhaul estimation is specially: according to statistics, represent the blur estimation value of the single cost of overhaul with Triangular Fuzzy Number: wherein, C _mLequal the lower limit of single cost of overhaul statistic, C _mRequal the upper limit of single cost of overhaul statistic, C _mfor the value that possibility in single cost of overhaul statistic is maximum.

And the expectation value calculating the cost of overhaul is:

And failure cost estimation is specially: establish converting equipment single failure cost C _ftaken by corrective maintenance costs and breakdown loss and form, then have: $C_F=\underset{k}{\mathrm{\&Sigma;}}{C}_{\mathrm{FM},k}+P_{\mathrm{loss}}\&times;T\&times;p,$

In formula: C _{fM, k}for the k item expense in single failure maintenance, P _lossfor loss of outage load, T is single power failure duration, and p is poor for purchasing sale of electricity electricity price.

Again according to statistics, obtain the blur estimation value of single failure cost: wherein, C _fLequal the lower limit of single failure cost statistics numerical value, C _fRequal the upper limit of single failure cost statistics numerical value, C _ffor the value that possibility in single failure cost statistics numerical value is maximum.

And the expectation value obtaining single failure cost is:

In the present embodiment, obtain single repair based on condition of component cost estimation value according to statistics for [8.1,8,9.9] ten thousand yuan, single failure cost estimation value for [144,160,176] ten thousand yuan.

Build elastic stage maintenance decision Optimized model, the constraint condition that failure rate is worth as the equipment failure rate distribution function after maintenance most by this model according to cost of overhaul estimation and failure cost estimation, model is as follows:

$\begin{array}{c}\begin{array}{cc}\min & f\left(\stackrel{\&RightArrow;}{T}\right)\end{array},={{\hat{C}}_M}^{\&prime;}+{{\hat{C}}_F}^{\&prime;}\\ =\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{\hat{C}}_M{\left(\frac{1}{1+r_d}\right)}^{t_k}+\underset{t=1}{\overset{T_A}{\mathrm{\&Sigma;}}}{\hat{C}}_F{\mathrm{\&lambda;}}^{\&prime;}\left(t\right){\left(\frac{1}{1+r_d}\right)}^t\end{array},$

s.t. λ _min≤λ'(t)≤λ _max

In formula: use decision vector represent the time of each maintenance; for major overhaul cost; for total failare cost; for the blur estimation value of the single cost of overhaul; for the blur estimation value of single failure cost; t _kfor equipment enlistment age when kth time is overhauled; N is maintenance number of times total in plant life cycle; T _afor service life of equipment; r _dfor considering the discount rate after the factors such as inflation rate, interest rate, the exchange rate; λ ' (t) is equipment failure rate distribution function after maintenance; λ _minfor failure rate lower limit; λ _maxfor the failure rate upper limit.

When performing solving-optimizing by above-mentioned Optimized model, be specially: after repair based on condition of component each time, in conjunction with change and the failure rate bound of bathtub curve, the next one being overhauled the time is located in the limited range of permission, and the active time of equipment is in the limited range allowed, solve by limited recirculating the optimum solution that operation can obtain Repair of Transformer type and time.

S4: the failure rate distribution function calculating the rear equipment of maintenance according to the fuzzy enlistment age rollback failure rate forecast model of described power equipment:

After kth time maintenance, when failure rate drops to equivalent enlistment age t _{eq, k}during corresponding failure rate, retrain by failure rate limit value, next overhauls time T _k+1in limited range:

$\max \{{\widehat{\mathrm{\&lambda;}}}^{-1}\left({\mathrm{\&lambda;}}_{\min }\right)-t_{\mathrm{eq},k},0\}+T_k<T_{k+1}\&le;\min \{{\widehat{\mathrm{\&lambda;}}}^{-1}\left({\mathrm{\&lambda;}}_{\max }\right)-t_{\mathrm{eq},k}+T_k,T_A\}$

Service life of equipment T _alimited, from first maintenance moment, enumerate successively under the time-constrain in maintenance time and obtain the next possibility repair time; Obtained the sequence of multiple feasible repair time by cycling, largest loop tuple is set to T _asecondary; Again to the time series of each maintenance carry out calculating rear failure rate distribution function λ ' (t) of maintenance.

The elastic stage maintenance decision Optimized model of step S3 is used to try to achieve functional value again solve operation by circulation, in all feasible solutions, try to achieve the optimal value of elastic stage maintenance decision Optimized model.

In the present embodiment, if repair based on condition of component service age reduction factor α=0.4.Adopt fuzzy enlistment age rollback failure rate forecast model to calculate the failure rate distribution function of the rear equipment of maintenance, use elastic stage maintenance model to carry out decision optimization, the optimum solution obtained is namely carried out repair based on condition of component in the 12nd, 20,26 year respectively, Fig. 3 gives the distribution curve of the failure rate under corresponding Strategies of Maintenance.Corresponding optimum maintenance and fault total cost wan Yuan, maintenance with the expectation value of fault total cost is: 70.694 ten thousand yuan.

The inventive method considers that maintenance activity is to the uncertainty of the reparation effectiveness of the power equipments such as transformer, proposes fuzzy enlistment age backing method, and carries out forecast analysis in conjunction with fuzzy theory to the failure rate of equipment.Based on the prediction to equipment dependability variation tendency, propose flexible state maintenance method, make the time between overhauls(TBO) more flexible, the electric power apparatus examination decision optimization model of foundation also improves economy while raising reliability.

The above; be only the specific embodiment of the present invention, but protection scope of the present invention is not limited thereto, any those skilled in the art is in the technical scope that the present invention discloses; the distortion do the present invention or replacement, all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of described claim.

Claims (7)

1., based on an electric power apparatus examination optimization method for fuzzy enlistment age rollback, it is characterized in that, comprise the following steps:

S1: the fuzzy matching carrying out electrical equipment fault rate according to electrical equipment fault rate historical data, obtaining fitting result is:

The Random-fuzzy distribution function of equipment failure rate Y (t) is:

$\hat{Y}\left(t\right)=(\widehat{\mathrm{\&lambda;}}\left(t\right),{\hat{c}}_1\left(t\right),{\hat{c}}_2\left(t\right))$

Wherein, for the central value of failure rate Triangular Fuzzy Number, for right avertence difference, for left avertence difference;

S2: the fuzzy enlistment age rollback failure rate forecast model setting up power equipment in conjunction with described fitting result, obtains the equivalent enlistment age of overhauling rear power equipment according to repair time sequence and central value the λ ' (t of the bathtub curve Triangular Fuzzy Number of the rear power equipment of kth time maintenance _k), right avertence difference c' ₁(t _k) and left avertence value c' ₂(t _k),

Wherein, for according to t' _kcalculate rollback point failure rate fuzzy number expectation value;

S3: carry out cost of overhaul estimation and failure cost estimation, and build elastic stage maintenance decision Optimized model accordingly, the constraint condition that failure rate limit value is worth as the equipment failure rate distribution function after maintenance most by this model, model is as follows:

$\begin{array}{cc}\min & f\left(\stackrel{\&RightArrow;}{T}\right)={{\hat{C}}_M}^{\&prime;}+{{\hat{C}}_F}^{\&prime;}\\ & =\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{\hat{C}}_M{\left(\frac{1}{1+r_d}\right)}^{t_k}+\underset{t=1}{\overset{T_A}{\mathrm{\&Sigma;}}}{\hat{C}}_F{\mathrm{\&lambda;}}^{\&prime;}\left(t\right){\left(\frac{1}{1+r_d}\right)}^t\end{array},$

s.t. λ _min≤λ′(t)≤λ _max

Wherein, decision vector is used represent the time of each maintenance; for major overhaul cost; for total failare cost; for the blur estimation value of the single cost of overhaul; for the blur estimation value of single failure cost; t _kfor the enlistment age of equipment when kth time is overhauled; N is maintenance number of times total in plant life cycle; T _afor service life of equipment; r _dfor considering the discount rate after the factors such as inflation rate, interest rate, the exchange rate; λ ' (t) is the failure rate distribution function of equipment after maintenance; λ _minfor failure rate lower limit; λ _maxfor the failure rate upper limit.

S4: the failure rate distribution function calculating the rear equipment of maintenance according to the fuzzy enlistment age rollback failure rate forecast model of described power equipment, then use the elastic stage maintenance decision Optimized model of step S3 to carry out the solving-optimizing of electric power apparatus examination time.

2. the electric power apparatus examination optimization method based on fuzzy enlistment age rollback according to claim 1, it is characterized in that, in described step S1, the process of fuzzy matching is specially: the electrical equipment fault rate adopting fuzzy fitting function to represent banded in historical data, is expressed as the Random-fuzzy distribution function of equipment failure rate Y (t):

$\hat{Y}\left(t\right)=(\widehat{\mathrm{\&lambda;}}\left(t\right),{\hat{c}}_1\left(t\right),{\hat{c}}_2\left(t\right))$

Thus obtain dividing value curve on the right of failure rate and failure rate left side dividing value curve ${\widehat{\mathrm{\&lambda;}}}_2\left(t\right)={\widehat{\mathrm{\&lambda;}}}_{\left(t\right)}-{\hat{c}}_2\left(t\right).$

3. the electric power apparatus examination optimization method based on fuzzy enlistment age rollback according to claim 1, is characterized in that, described fuzzy enlistment age rollback failure rate forecast model is specially:

By fuzzy evaluation correction equivalence enlistment age, for the time of each maintenance first, if the enlistment age rollback of power equipment is to t' after kth time maintenance _kmoment, wherein, ${t^{\&prime;}}_k=\left\{\begin{array}{cc}(1-\mathrm{\&alpha;})T_1& k=1\\ t_{\mathrm{eq},k-1}+(1-\mathrm{\&alpha;})(T_k-T_{k-1})& k=2,...,n\end{array}\right.,$ α is service age reduction factor;

Secondly, according to t' _kcalculating rollback point failure rate fuzzy number expectation value is: $E\left(\right[\hat{Y}\left({t^{\&prime;}}_k\right)\left]\right)=\frac{1}{4}[{\widehat{\mathrm{\&lambda;}}}_1\left({t^{\&prime;}}_k\right)+2\widehat{\mathrm{\&lambda;}}\left({t^{\&prime;}}_k\right)+{\widehat{\mathrm{\&lambda;}}}_2\left({t^{\&prime;}}_k\right)],$ Wherein, for failure rate median profile, for dividing value curve on the right of failure rate, for failure rate left side dividing value curve;

Finally, according to expectation value at bathtub curve on search corresponding working time and be and by t _{eq, k}as the equivalent enlistment age of power equipment after kth time maintenance; After obtaining kth time maintenance, the central value of electrical equipment fault rate curve Triangular Fuzzy Number is simultaneously right avertence difference is ${c^{\&prime;}}_1\left(t_k\right)={\hat{c}}_1\left(t_{\mathrm{eq},k}\right),$ Left avertence difference is

4. the electric power apparatus examination optimization method based on fuzzy enlistment age rollback according to claim 1, is characterized in that,

Described cost of overhaul estimation is specially: according to statistics, represent the blur estimation value of the single cost of overhaul with Triangular Fuzzy Number: wherein, C _mLfor the lower limit of single cost of overhaul statistic, C _mRfor the upper limit of single cost of overhaul statistic, C _mfor the value that possibility in single cost of overhaul statistic is maximum;

And the expectation value obtaining the cost of overhaul is:

Described failure cost estimation is specially: establish power equipment single failure cost C _ftaken by corrective maintenance costs and breakdown loss and form: wherein, C _{fM, k}for the k item expense in single failure maintenance, P _lossfor loss of outage load, T is single power failure duration, and p is poor for purchasing sale of electricity electricity price;

Again according to statistics, obtain the blur estimation value of single failure cost: wherein, C _fLfor the lower limit of single failure cost statistics numerical value, C _fRfor the upper limit of single failure cost statistics numerical value, C _ffor the value that possibility in single failure cost statistics numerical value is maximum;

And the expectation value obtaining single failure cost is:

5. the electric power apparatus examination optimization method based on fuzzy enlistment age rollback according to claim 1 or 3, is characterized in that, in described step S3, after maintenance, failure rate distribution function λ ' (t) obtains in the following manner:

If corresponding repair time sequence is T ₁, T ₂..., T _n, after maintenance, failure rate distribution function λ ' (t) is expressed as:

${\mathrm{\&lambda;}}^{\&prime;}\left(t\right)=\left\{\begin{array}{cc}\widehat{\mathrm{\&lambda;}}\left(t\right)& 0\&le;t\&le;T_1\\ \widehat{\mathrm{\&lambda;}}(t+t_{\mathrm{eq},k-1}-T_{k-1})& T_{k-1}<t\&le;T_k(k=2,...,n)\\ \widehat{\mathrm{\&lambda;}}(t+t_{\mathrm{eq},n}-T_n)& T_n<t\&le;T_A\end{array}\right..$

6. the electric power apparatus examination optimization method based on fuzzy enlistment age rollback according to claim 1, it is characterized in that, when described step S3 performs solving-optimizing, be specially: after repair based on condition of component each time, the change of bonding apparatus bathtub curve, the failure rate upper limit and failure rate lower limit, the next one being overhauled the time is located in the limited range of permission, and the enlistment age of equipment is located in the limited range of permission, solve by limited recirculating the optimum solution that operation then obtains the electric power apparatus examination time.

7. the electric power apparatus examination optimization method based on fuzzy enlistment age rollback according to claim 1, is characterized in that, described step S4 solution procedure is as follows:

After kth time maintenance, when failure rate drops to equivalent enlistment age t _{eq, k}during corresponding failure rate, retrain by failure rate limit value, next overhauls time T _k+1in limited range:

$\max \{{\widehat{\mathrm{\&lambda;}}}^{-1}\left({\mathrm{\&lambda;}}_{\min }\right)-t_{\mathrm{eq},k},0\}+T_k<T_{k+1}\&le;\min \{{\widehat{\mathrm{\&lambda;}}}^{-1}\left({\mathrm{\&lambda;}}_{\max }\right)-t_{\mathrm{eq},k}+T_k,T_A\}$

Service life of equipment T _alimited, from first maintenance moment, enumerate successively under the time-constrain in maintenance time and obtain the next possibility repair time; Obtained the sequence of multiple feasible repair time by embedded loops operation, largest loop tuple is set to T _asecondary;

Again to the time series of each maintenance carry out calculating rear failure rate distribution function λ ' (t) of maintenance, try to achieve functional value according to elastic stage maintenance decision Optimized model

Solve operation by circulation, in all feasible solutions, try to achieve the optimal value of elastic stage maintenance decision Optimized model.