CN101577408A - Comprehensive analysis method of reliability of transmission line tower structure - Google Patents

Abstract

The invention provides a comprehensive analysis method of reliability of a transmission line tower structure. The comprehensive analysis method comprises the following steps of: using a first-order second-moment method to calculate the theoretical reliability of components of the transmission line tower structure, adopting a narrow limit method to calculate the theoretical reliability of the transmission line tower structural system and calculating the reliability index of the tower structural system of actual lines, thus being capable of carrying out comparison and analysis to the theoretical value and the actual value, being capable of being used for carrying out evaluation and analysis to the setting level of reliability of the transmission line tower structure, and the like.

Description

A kind of comprehensive analysis method of reliability of transmission line tower structure

Technical field

The invention belongs to the transmission line structure field, be specifically related to a kind of comprehensive analysis method of 500kV reliability of transmission line tower structure.

Background technology

The method for designing of China's transmission line tower structure is broadly divided into three periods, and the Allowable Stress Design method (single method of safety coefficients) of the former Soviet Union is continued to use in the transmission line design always before 1994; After 1994, the lines wind load has been considered the adjustment factor beta _C" 110～500kV aerial power transmission line designing technique rules " DL/T 5092-1999 of promulgation in 1999 changes into and adopts the limit state design method of probability for the basis, adopts the design expression formula of partial safety factor.Because the replacement of method for designing and design standard makes the level of reliability of China 500kV circuit not have clear and definite index.

Summary of the invention

Adopt FOSM that the level of reliability of China 500kV transmission line tower structure member is calibrated, adopt narrow bound method to calculate the level of reliability of the 500kV transmission line tower structure system of China's different times design, and the situation that the accident of falling the tower appears in the existing 500kV working line of China investigated, contrast " building structure RELIABILITY DESIGN unified standard " GB 50068-2001 and made rational evaluation.

Technical scheme of the present invention is to use following method () and method (two) to carry out the theoretical value that Theoretical Calculation draws reliability of transmission line tower structure, using method (three) draws the actual value of reliability of transmission line tower structure, thereby can compare analysis to theoretical value and actual value:

Method (one): adopt the reliability of FOSM computing electric power line tower structure member, its step is as follows:

(10) the structure function function of member is:

g(R，S _G，S _Q)＝R-S _G-S _Q；

(11) regularity of distribution of each stochastic variable and statistical parameter are as follows:

K _R=1.14, V _R=0.12, R is a structure reactance, obeys logarithm normal distribution;

K _G=1.06, V _G=0.07, S _GBe dead load action effect, Normal Distribution;

K _Q=1.00, V _Q=0.193, S _QBe the wind action effect, obey extreme value I type and distribute;

In the formula: K _R=μ _R/ R _K, $K_{S_G}={\mathrm{\μ}}_{S_G}/S_{\mathrm{GK}},$ $K_Q={\mathrm{\μ}}_{S_Q}/S_{\mathrm{QK}};$

V _R＝σ _R/μ _R， $V_G={\mathrm{\σ}}_{S_G}/{\mathrm{\μ}}_{S_G},$ $V_Q={\mathrm{\σ}}_{S_G}/{\mathrm{\μ}}_{S_G};$

μ _R,

Be respectively R, S _G, S _QAverage;

σ _R,

Be respectively R, S _G, S _QMean square deviation;

(12) supposition design checking computations point initial value:

The data point of worst each stochastic variable of structure is checked a little as structural design, and described structural design checking computations point is certain point in the structure function function, and initial value of supposition carries out continuous iterative computation to obtain below, and the initial value point of described supposition is: (S _QK=1, S _GK=0.25, R _K=1.8479),

Suppose: when ρ=4, S _QK=1,

Then, S _GK=0.25, R _K=K (γ _GS _GK+ γ _QS _QK)=1.8479,

μ _QK＝1，μ _GK＝0.265，μ _R＝2.1066，

σ _QK＝0.193，σ _GK＝0.01855，σ _R＝0.252792；

(13) the abnormal variable is carried out the equivalent normalize and obtains its equivalent average and variance:

The abnormal basic random variables is carried out the equivalent normalize handle, be converted into equivalent normal random variable,, and obey the wind action effect S that extreme value I type distributes as the structure reactance R of obeys logarithm normal distribution _Q, switch condition is that each basic random variables after guaranteeing to change equates before design checks a tail area of punishment cloth density function and changes;

(14) ask the direction cosines of limiting condition face each coordinate in the standard normal coordinate system, computing formula is as follows:

$\cos {\mathrm{\θ}}_{X_i}=\frac{-\frac{\∂g}{\∂X_i}{|}_{P^{*}}{\mathrm{\σ}}_{X_i}}{{\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left(\frac{\∂g}{\∂X_i}\right){|}_{P^{*}}{{\mathrm{\σ}}_{X_i})}^2\right]}^{1/2}}$

cosθ _R＝-0.8053， ${\cos \mathrm{\θ}}_{S_G}=0.0593,$ ${\cos \mathrm{\θ}}_{S_Q}=0.5900;$

(15) try to achieve reliability index β by limit state equation _i:

$\mathrm{\β}=\frac{{\mathrm{\μ}}_g}{{\mathrm{\σ}}_g}=\frac{g(x_1^{*},...,x_n^{*})+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{\∂g}{\∂X_i}{|}_{P^{*}}({\mathrm{\μ}}_{X_i}-x_i^{*})}{{\left[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left(\frac{\∂g}{\∂X_i}\right){|}_{P^{*}}{{\mathrm{\σ}}_{X_i})}^2\right]}^{1/2}}=2.747;$

(16) utilize the β that has tried to achieve _iReach the checking computations point that direction cosines are looked for novelty:

Computing formula: $x_i^{*}={\mathrm{\μ}}_{X_i}+{\mathrm{\σ}}_{X_i}\mathrm{\β}\cos {\mathrm{\θ}}_{X_i}$

R ^*＝1.5344，S _G ^*＝0.2680，S _Q ^*＝1.2663；

(17) if | β _I-1-β _i|≤0.01 draws final β;

(18) if | B _I-1-β _i| 〉=0.01 value of utilizing this checking computations point coordinates to replace last time, proceeded for (3) step, up to drawing final β;

Method (two): adopt narrow bound method computing electric power line tower structure The System Reliability, its step is as follows:

(1) computing formula:

Use E _i(i=1 ..., n) incident of i failure mode appears in expression structural system, by narrow bound method, and series connection system failure probability P _FsCompass can be expressed as:

$P\left(E_1\right)+\max \left[\underset{i=2}{\overset{n}{\mathrm{\&Sigma;}}}\right\{P\left(E_i\right)-\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}P(E_i\&cap;E_j)\},0]\&le;P_{\mathrm{fs}}\&le;\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}P\left(E_i\right)-\underset{i=2}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j<i}{\max }P(E_i\&cap;E_j)---\left(1\right)$

P (E in the formula _i) expression E _iThe failure probability of incident, and have:

$\max (\widetilde{P_{f_1}},\widetilde{P_{f_2}})\&le;P(E_i\&cap;E_j)\&le;\widetilde{P_{f_1}}+\widetilde{P_{f_2}}---\left(2\right)$

$\widetilde{P_{f_1}}=\mathrm{\&Phi;}(-{\mathrm{\&beta;}}_i)\mathrm{\&Phi;}(-{{\mathrm{\&beta;}}^{\&prime;}}_i),$ $\widetilde{P_{f_2}}=\mathrm{\&Phi;}(-{\mathrm{\&beta;}}_j)\mathrm{\&Phi;}(-{{\mathrm{\&beta;}}^{\&prime;}}_j)---\left(3\right)$

${{\mathrm{\&beta;}}^{\&prime;}}_i=\frac{{\mathrm{\&beta;}}_j-{\mathrm{\&rho;}}_{\mathrm{ij}}{\mathrm{\&beta;}}_i}{\sqrt{1-{\mathrm{\&rho;}}_{\mathrm{ij}}^2}},$ ${{\mathrm{\&beta;}}^{\&prime;}}_j=\frac{{\mathrm{\&beta;}}_i-{\mathrm{\&rho;}}_{\mathrm{ij}}{\mathrm{\&beta;}}_j}{\sqrt{1-{\mathrm{\&rho;}}_{\mathrm{ij}}^2}}---\left(4\right)$

ρ _IjBe different failure mode E _i, E _jBetween coefficient correlation, if g _i, g _jBe independent basic random variables X _i(i=1 ..., linear function n), that is:

$g_i=\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ik}}{X}_k,$ $g_j=\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_{\mathrm{jk}}{X}_k,$

To tower structure:

${\mathrm{\&rho;}}_{\mathrm{ij}}=\frac{{\left({\mathrm{\&sigma;}}_{S_G}\right)}^2+{\left({\mathrm{\&sigma;}}_{S_Q}\right)}^2}{{\left({\mathrm{\&sigma;}}_R\right)}^2+{\left({\mathrm{\&sigma;}}_{S_G}\right)}^2+{\left({\mathrm{\&sigma;}}_{S_Q}\right)}^2}---\left(5\right)$

Method (three): the tower structure The System Reliability index of calculating actual track:

(1) investigation statistics 500kV transmission line over the years falls the situation of tower;

(2) year failure frequency P _fCalculating:

P _f＝N _f/N

The total radix of N=∑ iron tower * operation year number (base year),

N _fFor falling the sum of tower,

Relative error: $\mathrm{\&epsiv;}=\frac{|\stackrel{\&OverBar;}{P_f}-{P^{\&prime;}}_f|}{\stackrel{\&OverBar;}{P_f}}\&le;2\sqrt{\frac{1-\stackrel{\&OverBar;}{P_f}}{N\stackrel{\&OverBar;}{P_f}}};$

(3) year failure probability scope P ' _fReckoning:

P′ _f＝(1±ε)P _f

(3) failure probability in the T design reference period:

P _f＝1-(1-P′ _f) ^T

(4) Shi Ji system failure probability:

P _fLook into gaussian distribution table and can get actual system failure probability.

The advantage of the inventive method is: carried out the reliability calibration operation of 500kV circuit from theoretical and the actual track situation of falling the tower two aspects, this reliability analysis for other electric pressure and even UHV transmission line has the certain experiences reference value.

Description of drawings

Fig. 1 is the FOSM computing method structural elements RELIABILITY INDEX flow chart of method of the present invention ().

Embodiment

The present invention is further described below in conjunction with drawings and Examples.

The reliability of research China 500kV transmission line tower structure member, to China in history the level of reliability of the 500kV transmission line of different phase design made rational evaluation.Extensively investigation China has the accident of falling the tower that the 500kV transmission line occurs now, adopts the method for probability theory, verifies the difference of actual reliability and theoretical level of reliability.

1, the 500kV transmission line tower structure member RELIABILITY INDEX of FOSM calculating:

Using method (one): adopt the reliability of FOSM computing electric power line tower structure member, its step is as follows:

1. the structure function function of member is:

g(R，S _G，S _Q)＝R-S _G-S _Q；

2. the regularity of distribution of each stochastic variable and statistical parameter are as follows:

K _R=1.14, V _R=0.12, R is a structure reactance, obeys logarithm normal distribution;

K _G=1.06, V _G=0.07, S _GBe dead load action effect, Normal Distribution;

K _Q=1.00, V _Q=0.193, S _QBe the wind action effect, obey extreme value I type and distribute;

In the formula: K _R=μ _R/ R _K, $K_{S_G}={\mathrm{\&mu;}}_{S_G}/S_{\mathrm{GK}},$ $K_Q={\mathrm{\&mu;}}_{S_Q}/S_{\mathrm{QK}}$

V _R＝σ _R/μ _R， $V_G={\mathrm{\&sigma;}}_{S_G}/{\mathrm{\&mu;}}_{S_G},$ $V_Q={\mathrm{\&sigma;}}_{S_G}/{\mathrm{\&mu;}}_{S_G}$

μ _R, Be respectively R, S _G, S _QAverage;

σ _R, Be respectively R, S _G, S _QMean square deviation;

3. the supposition design checks the some initial value:

The data point of worst each stochastic variable of structure is checked a little as structural design, and described structural design checking computations point is certain point in the structure function function, and initial value of supposition carries out continuous iterative computation to obtain below, and the initial value point of described supposition is: (S _QK=1, S _GK=0.25, R _K=1.8479),

Suppose: when ρ=4, S _QK=1,

Then, S _GK=0.25, R _K=K (γ _GS _GK+ γ _QS _QK)=1.8479,

μ _QK＝1，μ _GK＝0.265，μ _R＝2.1066，

σ _QK＝0.193，σ _GK＝0.01855，σ _R＝0.252792；

4. to the equivalent normalize of abnormal variable and obtain its equivalent average and variance:

The abnormal basic random variables is carried out the equivalent normalize handle, be converted into equivalent normal random variable,, and obey the wind action effect S that extreme value I type distributes as the structure reactance R of obeys logarithm normal distribution _Q, switch condition is that each basic random variables after guaranteeing to change equates before design checks a tail area of punishment cloth density function and changes;

5. ask the direction cosines of limiting condition face each coordinate in the standard normal coordinate system, computing formula is as follows:

$\cos {\mathrm{\&theta;}}_{X_i}=\frac{-\frac{\&PartialD;g}{\&PartialD;X_i}{|}_{P^{*}}{\mathrm{\&sigma;}}_{X_i}}{{\left[\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\frac{\&PartialD;g}{\&PartialD;X_i}\right){|}_{P^{*}}{{\mathrm{\&sigma;}}_{X_i})}^2\right]}^{1/2}}$

cosθ _R＝-0.8053， ${\cos \mathrm{\&theta;}}_{S_G}=0.0593,$ ${\cos \mathrm{\&theta;}}_{S_Q}=0.5900$

6. try to achieve reliability index β by limit state equation _i:

$\mathrm{\&beta;}=\frac{{\mathrm{\&mu;}}_g}{{\mathrm{\&sigma;}}_g}=\frac{g(x_1^{*},...,x_n^{*})+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{\&PartialD;g}{\&PartialD;X_i}{|}_{P^{*}}({\mathrm{\&mu;}}_{X_i}-x_i^{*})}{{\left[\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\frac{\&PartialD;g}{\&PartialD;X_i}\right){|}_{P^{*}}{{\mathrm{\&sigma;}}_{X_i})}^2\right]}^{1/2}}=2.747$

7. utilize the β that has tried to achieve _iReach the checking computations point that direction cosines are looked for novelty:

Computing formula: $x_i^{*}={\mathrm{\&mu;}}_{X_i}+{\mathrm{\&sigma;}}_{X_i}\mathrm{\&beta;}\cos {\mathrm{\&theta;}}_{X_i}$

R ^*＝1.5344，S _G ^*＝0.2680，S _Q ^*＝1.2663；

8. if | β _I-1-β _i|≤0.01 draws final β;

9. if | β _I-1-β _i| 〉=0.01 value of utilizing this checking computations point coordinates to replace last time, proceeded for (3) step, up to drawing final β;

Fig. 1 is a FOSM computing method structural elements RELIABILITY INDEX flow chart of the present invention, according to FOSM shown in Figure 1, the RELIABILITY INDEX of 500kV transmission line tower structure member under the strong wind operating mode that calculates China's different times design sees the following form: ρ is the ratio of wind load effect and horizontal load action effect in the table; V is the ratio that lines wind load effect accounts for total wind load effect.

Table 1 500kV transmission line tower structure member RELIABILITY INDEX

2, the 500kV transmission line tower structure The System Reliability index of narrow bound method calculating:

Using method (two): adopt narrow bound method computing electric power line tower structure The System Reliability, its step is as follows:

(1) computing formula:

Use E _i(i=1 ..., n) incident of i failure mode appears in expression structural system, by narrow bound method, and series connection system failure probability P _FsCompass can be expressed as:

$P\left(E_1\right)+\max \left[\underset{i=2}{\overset{n}{\mathrm{\&Sigma;}}}\right\{P\left(E_i\right)-\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}P(E_i\&cap;E_j)\},0]\&le;P_{\mathrm{fs}}\&le;\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}P\left(E_i\right)-\underset{i=2}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j<i}{\max }P(E_i\&cap;E_j)---\left(1\right)$

P (E in the formula _i) expression E _iThe failure probability of incident, and have:

$\max (\widetilde{P_{f_1}},\widetilde{P_{f_2}})\&le;P(E_i\&cap;E_j)\&le;\widetilde{P_{f_1}}+\widetilde{P_{f_2}}---\left(2\right)$

$\widetilde{P_{f_1}}=\mathrm{\&Phi;}(-{\mathrm{\&beta;}}_i)\mathrm{\&Phi;}(-{{\mathrm{\&beta;}}^{\&prime;}}_i),$ $\widetilde{P_{f_2}}=\mathrm{\&Phi;}(-{\mathrm{\&beta;}}_j)\mathrm{\&Phi;}(-{{\mathrm{\&beta;}}^{\&prime;}}_j)---\left(3\right)$

${{\mathrm{\&beta;}}^{\&prime;}}_i=\frac{{\mathrm{\&beta;}}_j-{\mathrm{\&rho;}}_{\mathrm{ij}}{\mathrm{\&beta;}}_i}{\sqrt{1-{\mathrm{\&rho;}}_{\mathrm{ij}}^2}},$ ${{\mathrm{\&beta;}}^{\&prime;}}_j=\frac{{\mathrm{\&beta;}}_i-{\mathrm{\&rho;}}_{\mathrm{ij}}{\mathrm{\&beta;}}_j}{\sqrt{1-{\mathrm{\&rho;}}_{\mathrm{ij}}^2}}---\left(4\right)$

ρ _IjBe different failure mode E _i, E _jBetween coefficient correlation.If g _i, g _jBe independent basic random variables X _i(i=1 ..., linear function n), promptly

$g_i=\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ik}}{X}_k,$ $g_j=\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_{\mathrm{jk}}{X}_k$

To tower structure:

${\mathrm{\&rho;}}_{\mathrm{ij}}=\frac{{\left({\mathrm{\&sigma;}}_{S_G}\right)}^2+{\left({\mathrm{\&sigma;}}_{S_Q}\right)}^2}{{\left({\mathrm{\&sigma;}}_R\right)}^2+{\left({\mathrm{\&sigma;}}_{S_G}\right)}^2+{\left({\mathrm{\&sigma;}}_{S_Q}\right)}^2}---\left(5\right)$

(2) sample calculation

Tower structure variable load effect and permanent load effect ratio ρ=4～8 when ρ=4, calculate ρ by formula (5) _{Ij (4)}=0.376; When ρ=8, ρ _{Ij (8)}=0.425.Getting all is worth: ρ _Ij=0.40.

Adjust factor beta when not considering wind load _C, when calculating by single method of safety coefficients, the RELIABILITY INDEX β of 500kV tower structure member is about 2.3～2.4, average 2.35, and then the probability of each failure mode appearance of shaft tower is:

P(E _i)＝P _fi＝Φ(-β)＝Φ(-2.35)＝9.387×10 ^-3

Calculate by formula (4): β ' _i=β ' _j=1.538

Calculate by formula (3): $\widetilde{P_{f_1}}=\widetilde{P_{f_2}}=5.82\&times;{10}^{-4}$

Get by formula (2): 3.74 * 10 ^-4≤ P (E _i∩ E _j)≤7.48 * 10 ^-4

If get 3 tower structure system failure modes, i.e. n=3, by formula (1):

2.47×10 ^-2≤P _fs≤2.70×10 ^-2

Look into the normal distyribution function table and get system RELIABILITY INDEX: β _s=1.93～1.97

Electric power line pole tower belongs to space truss structure, and its reliability analysis model can adopt series connection, and the failure mode of getting the 500kV electric power line pole tower is 3～5, system failure probability P _FsCompass is expressed as:

$P\left(E_1\right)+\max \left[\underset{i=2}{\overset{n}{\mathrm{\&Sigma;}}}\right\{P\left(E_i\right)-\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}P(E_i\&cap;E_j)\},0]\&le;P_{f_i}\&le;\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}P\left(E_i\right)-\underset{j=2}{\overset{i-1}{\mathrm{\&Sigma;}}}\underset{j<i}{\max }P(E_i\&cap;E_j)$

Calculate the tower structure The System Reliability by narrow bound method and the results are shown in Table 2:

Table 2 500kV transmission line tower structure system failure probability and RELIABILITY INDEX scope

3, the existing 500kV circuit situation of falling tower investigation related data of China and practical systems RELIABILITY INDEX are calculated:

Using method (three): the tower structure The System Reliability index of actual track is calculated:

(1) investigation statistics 500kV transmission line over the years falls the situation of tower;

(2) year failure frequency P _fCalculating:

P _f＝N _f/N

The total radix of N=∑ iron tower * operation year number (base year),

N _fFor falling the sum of tower,

Relative error: $\mathrm{\&epsiv;}=\frac{|\stackrel{\&OverBar;}{P_f}-{P^{\&prime;}}_f|}{\stackrel{\&OverBar;}{P_f}}\&le;2\sqrt{\frac{1-\stackrel{\&OverBar;}{P_f}}{N\stackrel{\&OverBar;}{P_f}}};$

(3) year failure probability scope P ' _fReckoning:

P′ _f＝(1±ε)P _f

(3) failure probability in the T design reference period:

P _f＝1-(1-P′ _f) ^T

(4) Shi Ji system failure probability:

P _fLook into gaussian distribution table and can get actual system failure probability.

The table 3 actual motion 500kV electric power line pole tower situation of collapsing is added up

The project time	Total line length (km)	The total radix of tower	The accumulative total number of times of falling the tower	The accumulative total number of falling the column foot
					1985	1656	4140	0	0
1986	2764	6910	0	0
					1987	4380	10950	0	0
1988	5738	14345	1	4
					1989	7086	17715	2	8
1990	7122	17805	2	8
					1991	7523	18808	2	8
1992	8127	20318	3	12
					1993	10023	25058	4	19
1994	12037	30093	7	26
					1995	14051	35128	8	27
1996	16065	40163	8	27
					1997	18079	45198	8	27
1998	20093	50233	9	31
					1999	22927	57318	14	51
2000	26837	67093	16	62
					2001	33389	83473	17	65
2002	36745	91863	18	69
					2003	43616	109040	18	69
2004	54705	136763	18	69
					2005	62344	155860	22	99
2006	76460	191150	23	101

Move total base year number:

N=4140 * 22+ (6910-4140) * 21+ ... + (191150-155860) * 1=1203770 (base year)

Year failure frequency: P _f=N _f/ N=101/1203770=8.39 * 10 ^-5

Relative error:

$\mathrm{\&epsiv;}=\frac{|\stackrel{\&OverBar;}{P_f}-{P^{\&prime;}}_f|}{\stackrel{\&OverBar;}{P_f}}\&le;2\sqrt{\frac{1-\stackrel{\&OverBar;}{P_f}}{N\stackrel{\&OverBar;}{P_f}}}=2\sqrt{\frac{1-8.39\&times;{10}^{-5}}{1203770\&times;8.39\&times;{10}^{-5}}}=0.20$

Year failure probability: P ' _f=(1 ± ε) P _f=(6.712～10.068) * 10 ^-5

Getting design reference period T is failure probability in 50 years: P _f=1-(1-P ' _f) ^T=(3.35～5.02) * 10 ^-3

Think overhead line structures inefficacy Normal Distribution, can get 500kV overhead line structures structural reliability statistical indicator and be: 2.57～2.72.

4. evaluation result:

(1) the tower structure reliability calculates: constantly perfect along with the improvement of method for designing and design specification, China 500kV overhead line structures structural reliability is progressively improving.

(2) the 500kV transmission line tower structure member reliability that designs by the existing tower structure design specification of China satisfies the standard of the secondary ductile reinforced member of " building structure RELIABILITY DESIGN unified standard " regulation.

(3) the 500kV transmission line tower structure system failure probability of Theoretical Calculation is greater than the considered repealed probability of tower structure statistics, and this explanation design condition with respect to planning when the actual use of shaft tower also has certain margin of safety.

The present invention has been described according to preferred embodiment.Obviously, reading and understanding above-mentioned detailed description postscript and can make multiple correction and replacement.What this invention is intended to is that the application is built into all these corrections and the replacement that has comprised within the scope that falls into the appended claims or its equivalent.

Claims (1)

1, a kind of comprehensive analysis method of reliability of transmission line tower structure, it is characterized in that using following method () and method (two) to carry out the theoretical value that Theoretical Calculation draws reliability of transmission line tower structure, using method (three) draws the actual value of reliability of transmission line tower structure, thereby can compare analysis to theoretical value and actual value:

Method (one): adopt the reliability of FOSM computing electric power line tower structure member, its step is as follows:

(1) the structure function function of member is:

g(R，S _G，S _Q)＝R-S _G-S _Q；

(2) regularity of distribution of each stochastic variable and statistical parameter are as follows:

K _R=1.14, V _R=0.12, R is a structure reactance, obeys logarithm normal distribution;

K _G=1.06, V _G=0.07, S _GBe dead load action effect, Normal Distribution;

K _Q=1.00, V _Q=0.193, S _QBe the wind action effect, obey extreme value I type and distribute;

In the formula: K _R=μ _R/ R _K, $K_{S_G}={\mathrm{\&mu;}}_{S_G}/S_{\mathrm{GK}},$ $K_Q={\mathrm{\&mu;}}_{S_Q}/S_{\mathrm{QK}};$

V _R＝σ _R/μ _R， $V_G={\mathrm{\&sigma;}}_{S_G}/{\mathrm{\&mu;}}_{S_G},$ $V_Q={\mathrm{\&sigma;}}_{S_G}/{\mathrm{\&mu;}}_{S_G};$

μ _R,

Be respectively R, S _G, S _QAverage;

σ _R,

Be respectively R, S _G, S _QMean square deviation;

(3) supposition design checking computations point initial value:

The data point of worst each stochastic variable of structure is checked a little as structural design, and described structural design checking computations point is certain point in the structure function function, and initial value of supposition carries out continuous iterative computation to obtain below, and the initial value point of described supposition is: (S _QK=1, S _GK=0.25, R _K=1.8479),

Suppose: when ρ=4, S _QK=1,

Then, S _GK=0.25, R _K=K (γ _GS _GK+ γ _QS _QK)=1.8479,

μ _QK＝1，μ _GK＝0.265，μ _R＝2.1066，

σ _QK＝0.193，σ _GK＝0.01855，σ _R＝0.252792；

(4) the abnormal variable is carried out the equivalent normalize and obtains its equivalent average and variance:

The abnormal basic random variables is carried out the equivalent normalize handle, be converted into equivalent normal random variable,, and obey the wind action effect S that extreme value I type distributes as the structure reactance R of obeys logarithm normal distribution _Q, switch condition is that each basic random variables after guaranteeing to change equates before design checks a tail area of punishment cloth density function and changes;

(5) ask the direction cosines of limiting condition face each coordinate in the standard normal coordinate system, computing formula is as follows:

$\cos {\mathrm{\&theta;}}_{X_i}=\frac{-\frac{\&PartialD;g}{\&PartialD;X_i}{|}_{P^{*}}{\mathrm{\&sigma;}}_{X_i}}{{\left[\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\frac{\&PartialD;g}{\&PartialD;X_i}\right){|}_{P^{*}}{{\mathrm{\&sigma;}}_{X_i})}^2\right]}^{1/2}}$

cosθ _R＝-0.8053， $\cos {\mathrm{\&theta;}}_{S_G}=0.0593,$ ${\cos \mathrm{\&theta;}}_{S_Q}=0.5900;$

(6) try to achieve reliability index β by limit state equation _i:

$\mathrm{\&beta;}=\frac{{\mathrm{\&mu;}}_g}{{\mathrm{\&sigma;}}_g}=\frac{g(x_1^{*},...,x_n^{*})+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{\&PartialD;g}{\&PartialD;X_i}{|}_{P^{*}}({\mathrm{\&mu;}}_{X_i}-x_i^{*})}{{\left[\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\frac{\&PartialD;g}{\&PartialD;X_i}\right){|}_{P^{*}}{{\mathrm{\&sigma;}}_{X_i})}^2\right]}^{1/2}}=2.747;$

(7) utilize the β that has tried to achieve _iReach the checking computations point that direction cosines are looked for novelty:

Computing formula: $x_i^{*}={\mathrm{\&mu;}}_{X_i}+{\mathrm{\&sigma;}}_{X_i}\mathrm{\&beta;}\cos {\mathrm{\&theta;}}_{X_i}$

R ^*＝1.5344，S _G ^*＝0.2680，S _Q ^*＝1.2663；

(8) if | β _I-1-β _i|≤0.01 draws final β;

(9) if | β _I-1-β _i| 〉=0.01 value of utilizing this checking computations point coordinates to replace last time, proceeded for (3) step, up to drawing final β;

Method (two): adopt narrow bound method computing electric power line tower structure The System Reliability, its step is as follows:

(1) computing formula:

Use E _i(i=1 ..., n) incident of i failure mode appears in expression structural system, by narrow bound method, and series connection system failure probability P _FsCompass can be expressed as:

$P\left(E_1\right)+\max \left[\underset{i=2}{\overset{n}{\mathrm{\&Sigma;}}}\right\{P\left(E_i\right)-\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}P(E_i\&cap;E_j)\},0]\&le;P_{\mathrm{fs}}\&le;\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}P\left(E_i\right)-\underset{i=2}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j<i}{\max }P(E_i\&cap;E_j)---\left(1\right)$

P (E in the formula _i) expression E _iThe failure probability of incident, and have:

$\max (\widetilde{P_{f_1}},\widetilde{P_{f_2}})\&le;P(E_i\&cap;E_j)\&le;\widetilde{P_{f_1}}+\widetilde{P_{f_2}}---\left(2\right)$

$\widetilde{P_{f_1}}=\mathrm{\&Phi;}(-{\mathrm{\&beta;}}_i)\mathrm{\&Phi;}(-{{\mathrm{\&beta;}}^{\&prime;}}_i),$ $\widetilde{P_{f_2}}=\mathrm{\&Phi;}(-{\mathrm{\&beta;}}_j)\mathrm{\&Phi;}(-{{\mathrm{\&beta;}}^{\&prime;}}_j)---\left(3\right)$

${{\mathrm{\&beta;}}^{\&prime;}}_i=\frac{{\mathrm{\&beta;}}_j-{\mathrm{\&rho;}}_{\mathrm{ij}}{\mathrm{\&beta;}}_i}{\sqrt{1-{\mathrm{\&rho;}}_{\mathrm{ij}}^2}},$ ${{\mathrm{\&beta;}}^{\&prime;}}_j=\frac{{\mathrm{\&beta;}}_i-{\mathrm{\&rho;}}_{\mathrm{ij}}{\mathrm{\&beta;}}_j}{\sqrt{1-{\mathrm{\&rho;}}_{\mathrm{ij}}^2}}---\left(4\right)$

ρ _IjBe different failure mode E _i, E _jBetween coefficient correlation, if g _i, g _jBe independent basic random variables X _i(i=1 ..., linear function n), that is:

$g_i=\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ik}}{X}_k,$ $g_j=\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_{\mathrm{jk}}{X}_k,$

To tower structure:

${\mathrm{\&rho;}}_{\mathrm{ij}}=\frac{{\left({\mathrm{\&sigma;}}_{S_G}\right)}^2+{\left({\mathrm{\&sigma;}}_{S_Q}\right)}^2}{{\left({\mathrm{\&sigma;}}_R\right)}^2+{\left({\mathrm{\&sigma;}}_{S_G}\right)}^2+{\left({\mathrm{\&sigma;}}_{S_Q}\right)}^2}---\left(5\right)$

Method (three): the tower structure The System Reliability index of calculating actual track:

(1) investigation statistics 500kV transmission line over the years falls the situation of tower;

(2) year failure frequency P _fCalculating:

P _f＝N _f/N

The total radix of N=∑ iron tower * operation year number (base year),

N _fFor falling the sum of tower,

Relative error: $\mathrm{\&epsiv;}=\frac{|\stackrel{\&OverBar;}{P_f}-{P^{\&prime;}}_f|}{\stackrel{\&OverBar;}{P_f}}\&le;2\sqrt{\frac{1-\stackrel{\&OverBar;}{P_f}}{N\stackrel{\&OverBar;}{P_f}}};$

(3) year failure probability scope P ' _fReckoning:

P′ _f＝(1±ε)P _f

(3) failure probability in the T design reference period:

P _f＝1-(1-P′ _f) ^T

(4) Shi Ji system failure probability:

P _fLook into gaussian distribution table and can get actual system failure probability.