CN105976064A - In-service structure optimal maintenance design method based on convex model time-variation reliability - Google Patents

Abstract

The invention discloses an in-service structure optimal maintenance design method based on convex model time-variation reliability. The method comprehensively considers the influence of uncertainty under the time effect to the in-service structural mechanic behavior. At first, time-variation uncertainty parameters are characterized by defining the convex model process, and the explicit expression of the limit state function characteristic quantities is deduced; based on the spanning theory of vibration mechanics and the structure non-probabilistic reliability model, the time-variation reliability index of the in-service structure based on the convex model is defined; furthermore, by taking the relationship between the maintenance cost and the service life of the structure into account, an in-service structure reliability design model is built based on the optimal maintenance decision; and by taking the reliability as the optimization target and maintenance time as the design variable, and repeating iterations through an intelligent optimization algorithm, the optimal maintenance and reinforcement design scheme for the drafted service period structure can be finally obtained.

Description

A kind of existing structure optimum Maintenance Design method based on convex model time-varying reliability

Technical field

The present invention relates to safety evaluation and the maintenance technology field of existing structure, particularly to considering convex model time-varying not Analysis of structural reliability under definitiveness designs with optimizing, and the through engineering approaches reliably controlling theory for planning large scale structure further should With and towards existing structure optimum maintaining scheme formulation provide referential theoretical foundation.

Background technology

Existing structure, also referred to as service structure or existing structure, be necessarily accompanied with knot during it is built and uses The problems such as structure is aging, hydraulic performance decline, reliability decay in time is also irreversible.Reasonably maintenance service, can be significantly The safety of lift structure, has an extension of enlistment.But, maintenance itself needs to pay certain economic cost, if maintenance selects not When, not only potential safety hazard can not be solved, it is also possible to bring huge lost revenue.Therefore, seek optimal maintenance and reinforcement scheme, Can be with compromise between security and the requirement of economy, engineering significance is self-evident.

But, the Service Environment of engineering structure is relative complex, and dynamic load undulatory property is strong；Additionally, manufacturing processing technic and The performance dispersion that material anisotropism is caused is the most inevitable.Above-mentioned uncertain effect can be accumulated the most climing over time Prolong, the degeneration of material constitutive and the alternation of dynamic load, largely effect in mechanical behavior and the lifetime of existing structure Security performance.The formulation of existing Maintenance Design scheme often cannot effectively be counted and above-mentioned time-varying Hurst index problem, causes setting Meter scheme coarse the most feasible.Summary situation, carries out time-varying Hurst index analysis and optimum dimension for existing structure Protect the research of method for designing in recent years by academia and the extensive concern of engineering circles and great attention.

Currently, under the maintenance scheme for existing structure is typically some particular moment of comprehensive consideration, structural behaviour promotes Expection is formulated with the rapport between maintenance cost, and maintenance effects is combined by meter not yet in effect and time-varying Hurst index effect Group photo rings.Therefore, existing maintenance and reinforcement means were typically redundancy, to sacrifice economic benefit and time cost as cost, Exchanging effective lifting of structure military service performance for, this constrains the original intention of refinement maintenance design to a certain extent.

The optimum that the present invention is directed to existing structure safeguards that Scheme of Strengthening design is mainly carried out in the following way: limits and safeguards Cost, i.e. repairs number of times, by the rationally selection (using the time as optimizing design variable) of repair time, it is achieved existing structure takes The maximization (security performance is as object function) of convex model time-dependent ability in the labour phase, and then objectively extend maintenance next time Time interval, it is ensured that existing structure function can the minimizing of continuity and resource loss.

Summary of the invention

The technical problem to be solved in the present invention is: overcome the deficiencies in the prior art, it is provided that a kind of peace for existing structure Full property evaluation with most preferably safeguard repair capsule method, take into full account the time-varying Hurst index effect generally existed in Practical Project problem Should, measure as passing judgment on the quantitative criteria that whether safe existing structure is using the non-probability time-varying reliability proposed, also serve as simultaneously The Optimization goal of Maintenance Design, to set the design variable that is chosen for most preferably safeguarding the moment under maintenance times, obtained optimization Design result more conforms to truth, and engineering adaptability is higher.

The technical solution used in the present invention is: a kind of existing structure optimum Maintenance Design based on convex model time-varying reliability Method, implementation step is as follows:

The first step: consider the time-varying Hurst index parameter being present in existing structure, define convex model process { X (t) ∈ X^I T (), t ∈ T} is characterized.Wherein, T is complete lifecycle.For any time t_i, (i=1,2 ...), X (t_i) will convert For discrete convex model variable, limited multiple convex model variablees are combined and are constituted a super ellipsoids territory.During in order to preferably describe Become the feature of uncertain parameters, define the mean value function X of convex model process further^c(t), function of radius X^r(t) and variance Function D_XT the expression formula of () is as follows:

$X^c\left(t\right)=\frac{\stackrel{\‾}{X\left(t\right)}+\underset{\‾}{X\left(t\right)}}{2},X^r\left(t\right)=\frac{\stackrel{\‾}{X\left(t\right)}+\underset{\‾}{X\left(t\right)}}{2},D_X\left(t\right)={\left(X^r\right(t\left)\right)}^2={\left(\frac{\stackrel{\‾}{X\left(t\right)}+\underset{\‾}{X\left(t\right)}}{2}\right)}^2$

Additionally, any t the most in the same time₁And t₂Correlation Coefficient Function ρ_X(t₁,t₂) and two various process X (t) and Y T () is respectively at moment t₁And t₂Under cross-correlation coefficient function ρ_XY(t₁,t₂) it is represented by:

${\mathrm{\ρ}}_X(t_1,t_2)=\frac{{\mathrm{Cov}}_X(t_1,t_2)}{\sqrt{D_X\left(t_1\right)}\·\sqrt{D_X\left(t_2\right)}},{\mathrm{\ρ}}_{XY}(t_1,t_2)=\frac{{\mathrm{Cov}}_{XY}(t_1,t_2)}{\sqrt{D_X\left(t_1\right)}\·\sqrt{D_Y\left(t_2\right)}}$

Wherein, Cov_X(t₁,t₂) it is that convex model process X (t) is at moment t₁And t₂Auto-covariance function, Cov_XY(t₁,t₂) For convex model process X (t) with Y (t) at moment t₁And t₂Under cross covariance function.

Second step: utilize the convex model process that the first step proposes, builds existing structure line based on n dimension time-varying Hurst index Property power function:

$g(t,X(t),d)=g(t,a(t),X(t\left)\right)=a_0\left(t\right)+a\left(t\right)X\left(t\right)=a_0\left(t\right)+\underset{i=1}{\overset{n}{\Σ}}{a}_i\left(t\right)X_i\left(t\right)$

Wherein, X (t)=(X₁(t),X₂(t),...,X_n(t))^TRepresent the convex model process vector considering cross correlation, a (t)=(a₀(t),a₁(t),a₂(t),...,a_n(t)) represent time-varying coefficient vector, d represents design vector.Based on intervl mathematics Algorithm, derives the mean value function g of power function feature^c(t, a (t), X (t)) and function of radius g^r(t,a(t),X(t)) As follows:

$g^c(t,a(t),X(t\left)\right)=g^c\left(t\right)=a_0\left(t\right)+\underset{i=1}{\overset{n}{\Σ}}\left(a_i\right(t)\·X_i^c(t\left)\right)$

With

$\begin{array}{c}{g}^r(t,a(t),X\left(t\right))\\ =g^r\left(t\right)=\sqrt{\underset{i=1}{\overset{n}{\Σ}}{\left(a_i\right(t)\·X_i^r(t\left)\right)}^2+\underset{i=1}{\overset{n}{\Σ}}\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}{\mathrm{\ρ}}_{X_i{X}_j}(t,t)\·a_i\left(t\right)\·a_j\left(t\right)\·X_i^r\left(t\right)\·X_j^r\left(t\right)}\end{array}$

Wherein,WithThe most convex The mean vector of model process X (t) and radius vectors,Represent process X_i(t) and X_jT () is at the cross correlation of moment t Number, i and j is counting index.Additionally, variance function D_g(t) and correlation Coefficient Function ρ_g(t₁,t₂) mathematic(al) representation divide It is not:

D_g(t)=g^r(t)²,

Wherein, Cov_g(t₁,t₂) represent power function g (t, X (t), covariance function d).

3rd step: based on passing through theory first and combining the power function that second step builds, by the time discretization period, It is defined as follows and passes through event E_iThe possibility degree index occurred:

PI{E_k}=Pos{g (k Δ t, X (k Δ t), d) ＞ 0 ∩ g ((k+1) Δ t, X ((k+1) Δ t), d) ＜ 0}

Wherein, PI{ } represent the possibility degree that event occurs, ((k Δ t) d) represents that existing structure is when k Δ t to g for k Δ t, X Carving safety (power function is more than zero), (((k+1) Δ t) d) represents that existing structure loses in (k+1) Δ t to g for (k+1) Δ t, X Effect (power function be less than zero), what symbol " ∩ " represented event ships calculation, and i is counting index, Δ t express time increment.Above formula In, event E_kBeing expressed as existing structure to there occurs within the time period [k Δ t, (k+1) Δ t] and once pass through, it is micro-that Δ t is usually one In a small amount, its value is set as the 1/1000 of life cycle management T.

4th step: travel through and pass through possibility degree PI{E in all time periods_k, the convex model time-varying calculating existing structure can By degree parameter:

$R_s\left(T\right)=1-Pos\left(0\right)+\underset{k=1}{\overset{k\mathrm{\Δ}t=T}{\Σ}}\left(PI\right\{E_i\left\}\right)$

Wherein, R_s(T) representing the time-dependent ability in whole life cycle T, Pos (0) represents that structure at initial time is There is the possibility degree lost efficacy, solve above formula and can realize effective assessment of existing structure power safety situation.

5th step: with the time-dependent ability R of the 4th step definition_s(T) as optimization aim, to safeguard that the moment t reinforced makees For design variable, build the time-varying reliability mathematical optimization models safeguarded towards existing structure optimum, and with ant colony intelligence algorithm Realize complete Optimized Iterative process.Here, the time-varying reliability Optimized model safeguarded towards existing structure optimum is described as:

find:t^*

max R_s(T,t^*)

t^*={ t₁,t₂,...,t_N|N≤N_Allowable}

Wherein, t^*The discrete time collection reinforced, t is safeguarded for optimum_NFor the last moment safeguarded, R_s(T,t^*) represent Time-dependent ability after safeguarding for existing structure experience optimum, L_lD () is the l definitiveness constraint equation,Corresponding l Definitiveness retrains condition allowable, N≤N_SetThe n times represented are safeguarded should be not more than setting value N_Set。

6th step: in iterative process, if current design is compared to a upper feasible solution, the change hundred relatively of object function When proportion by subtraction is more than preset value ξ, the ant colony of design variable resets and updates, and the value being complete iterations is increased by one, and returns Second step, otherwise, carries out the 7th step.Here, the preset value ξ of tolerance percentage ratio is set as 1%.

7th step: if global optimum's design is fairly close with the target function value of the overall situation Suboptimal Design scheme, When before and after i.e., the tolerance percentage ratio of twice feasible solution is less than preset value ξ, terminate calculating, in the global optimum's design that will obtain Variable parameter safeguard Scheme of Strengthening as final existing structure optimum.

Present invention advantage compared with prior art is: the invention provides under consideration time-varying Hurst index effect in-service The new approaches of structural safety assessment and optimum optimal decision, make up and perfect traditional the deterministic design is theoretical and static probability The limitation of reliability theory method.Constructed based on convex model time-varying reliability optimum maintenance optimization designs a model, and one Aspect compensate for the design risk that the deterministic design is brought, on the other hand relatively static reliability method, based on passing through reason first The time-dependent ability computational methods of opinion, more reasonably meter and the temporal correlation of dynamic response, it is ensured that structure is in the life-cycle The accurate tolerance of security postures in cycle, the minute design for maintenance scheme provides effective constraints.

Accompanying drawing explanation

Fig. 1 is to the present invention is directed to existing structure optimum Maintenance Design flow chart based on convex model time-varying reliability；

Fig. 2 is that the convex model process auto-covariance function that the present invention proposes calculates schematic diagram, and wherein, Fig. 2 (a) is feasible zone In the situation of first and third quadrant, Fig. 2 (b) is feasible zone second, four-quadrant situation；

Fig. 3 is to pass through crevice failure computational methods schematic diagram, wherein, Fig. 3 (a) in the tiny time section that the present invention proposes For power function feasible zone in tiny time section, Fig. 3 (b) is to pass through the geometry territory that event occurs after standardization；

Fig. 4 is that the existing structure time-varying reliability under the conditions of the consideration single that the present invention proposes is safeguarded optimizes schematic diagram, its In, Fig. 4 (a) is that the geometry of single optimum Maintenance Design model characterizes, and Fig. 4 (b) is time-dependent ability iteration course schematic diagram；

Fig. 5 is the model schematic of in-service composite laminated structures in the embodiment of the present invention；

Fig. 6 is the optimum Maintenance Design result schematic diagram of θ=15 ° operating mode in the embodiment of the present invention, and wherein, Fig. 6 (a) is The excellent interference situation safeguarding after load interval process and intensity interval process, Fig. 6 (b) be maintenance opportunity optimal choice (time: 16.1；Reliability: 0.9646)；

Fig. 7 is the optimum Maintenance Design result schematic diagram of θ=45 ° operating mode in the embodiment of the present invention, and wherein, Fig. 7 (a) is The excellent interference situation safeguarding after load interval process and intensity interval process, Fig. 7 (b) be maintenance opportunity optimal choice (time: 18.0；Reliability: 1).

Detailed description of the invention

Below in conjunction with the accompanying drawings and detailed description of the invention further illustrates the present invention.

As it is shown in figure 1, the present invention proposes a kind of existing structure optimum Maintenance Design based on convex model time-varying reliability Method, comprises the following steps:

(1) consider the time-varying Hurst index parameter being present in existing structure, define convex model process { X (t) ∈ X^I(t), T ∈ T} is characterized.Wherein, T is complete lifecycle.For any time t_i, (i=1,2 ...), X (t_i) translate into from The convex model variable dissipated, limited multiple convex model variablees are combined and are constituted a super ellipsoids territory.In order to preferably describe time-varying not The feature of deterministic parameter, defines the mean value function X of convex model process further^c(t), function of radius X^r(t) and variance function D_XT the expression formula of () is as follows:

$X^c\left(t\right)=\frac{\stackrel{\‾}{X\left(t\right)}+\underset{\‾}{X\left(t\right)}}{2},X^r\left(t\right)=\frac{\stackrel{\‾}{X\left(t\right)}-\underset{\‾}{X\left(t\right)}}{2},D_X\left(t\right)={\left(X^r\right(t\left)\right)}^2={\left(\frac{\stackrel{\‾}{X\left(t\right)}-\underset{\‾}{X\left(t\right)}}{2}\right)}^2$

Additionally, any t the most in the same time₁And t₂Correlation Coefficient Function ρ_X(t₁,t₂) and two various process X (t) and Y T () is respectively at moment t₁And t₂Under cross-correlation coefficient function ρ_XY(t₁,t₂) it is represented by:

${\mathrm{\ρ}}_X(t_1,t_2)=\frac{{\mathrm{Cov}}_X(t_1,t_2)}{\sqrt{D_X\left(t_1\right)}\·\sqrt{D_X\left(t_2\right)}},{\mathrm{\ρ}}_{XY}(t_1,t_2)=\frac{{\mathrm{Cov}}_{XY}(t_1,t_2)}{\sqrt{D_X\left(t_1\right)}\·\sqrt{D_Y\left(t_2\right)}}$

Wherein, Cov_X(t₁,t₂) it is that convex model process X (t) is at moment t₁And t₂Auto-covariance function, Cov_XY(t₁,t₂) For convex model process X (t) with Y (t) at moment t₁And t₂Under cross covariance function.As in figure 2 it is shown, Cov_X(t₁,t₂) can by under Formula explicit solution:

${\mathrm{Cov}}_X(t_1,t_2)=(r_m^2-1)\·X^r\left(t_1\right)\·X^r\left(t_2\right),0\≤r_m\≤\sqrt{2}$

Wherein, r_mRepresent Fig. 2 convexity model variable X (t₁) and X (t₂) deflection elliptic domain half axial length that formed after standardization. Similarly, Cov_XY(t₁,t₂) it is represented by:

${\mathrm{Cov}}_{XY}(t_1,t_2)=(r_{m^{*}}^2-1)\·X^r\left(t_1\right)\·Y^r\left(t_2\right),0\≤r_{m^{*}}\≤\sqrt{2}$

Wherein,Represent convex model variable X (t₁) and Y (t₂) deflection elliptic domain half axial length that formed after standardization.

(2) utilize the convex model process that the first step proposes, build existing structure linearisation based on n dimension time-varying Hurst index Power function:

$g(t,X(t),d)=g(t,a(t),X(t\left)\right)=a_0\left(t\right)+a\left(t\right)X\left(t\right)=a_0\left(t\right)+\underset{i=1}{\overset{n}{\Σ}}{a}_i\left(t\right)X_i\left(t\right)$

Wherein, X (t)=(X₁(t),X₂(t),...,X_n(t))^TRepresent the convex model process vector considering cross correlation, a (t)=(a₀(t),a₁(t),a₂(t),...,a_n(t)) represent time-varying coefficient vector, d represents design vector.Based on intervl mathematics Algorithm, derives the mean value function g of power function feature^c(t, a (t), X (t)) and function of radius g^r(t,a(t),X(t)) As follows:

$g^c(t,a(t),X(t\left)\right)=g^c\left(t\right)=a_0\left(t\right)+\underset{i=1}{\overset{n}{\Σ}}\left(a_i\right(t)\·X_i^c(t\left)\right)$

With

$\begin{array}{c}{g}^r(t,a(t),X\left(t\right))\\ =g^r\left(t\right)=\sqrt{\underset{i=1}{\overset{n}{\Σ}}{\left(a_i\right(t)\·X_i^r(t\left)\right)}^2+\underset{i=1}{\overset{n}{\Σ}}\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}{\mathrm{\ρ}}_{X_i{X}_j}(t,t)\·a_i\left(t\right)\·a_j\left(t\right)\·X_i^r\left(t\right)\·X_j^r\left(t\right)}\end{array}$

Wherein,WithThe most convex The mean vector of model process X (t) and radius vectors,Represent process X_i(t) and X_jT () is at the cross correlation of moment t Number, i and j is counting index.Additionally, variance function D_g(t) and correlation Coefficient Function ρ_g(t₁,t₂) mathematic(al) representation divide It is not:

D_g(t)=g^r(t)²,

Wherein, Cov_g(t₁,t₂) (concrete mathematic(al) representation is such as t, X (t), covariance function d) to represent power function g Under:

$\begin{array}{c}{\mathrm{Cov}}_g(t_1,t_2)=\underset{i=1}{\overset{n}{\Σ}}{\mathrm{\ρ}}_{X_i}(t_1,t_2)\·a_i\left(t_1\right)\·a_i\left(t_2\right)\·X_i^r\left(t_1\right)\·X_i^r\left(t_2\right)\\ +\underset{i=1}{\overset{n}{\Σ}}\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}{\mathrm{\ρ}}_{X_i{X}_j}(t_1,t_2)\·a_i\left(t_1\right)\·a_j\left(t_2\right)\·X_i^r\left(t_1\right)\·X_j^r\left(t_2\right)\end{array}$

Wherein,It it is convex model variable X_i(t₁) and X_i(t₂) autocorrelation coefficient,Represent convex model Variable X_i(t₁) and X_j(t₂) cross-correlation coefficient.

(3) based on passing through theory first and combining the power function that second step builds, by time discretization period, definition Pass through event E as follows_iThe possibility degree index occurred:

PI{E_k}=Pos{g (k Δ t, X (k Δ t), d) ＞ 0 ∩ g ((k+1) Δ t, X ((k+1) Δ t), d) ＜ 0}

Wherein, PI{ } represent the possibility degree that event occurs, ((k Δ t) d) represents that existing structure is when k Δ t to g for k Δ t, X Carving safety (power function is more than zero), (((k+1) Δ t) d) represents that existing structure loses in (k+1) Δ t to g for (k+1) Δ t, X Effect (power function be less than zero), what symbol " ∩ " represented event ships calculation, and i is counting index, Δ t express time increment.Above formula In, event E_kBeing expressed as existing structure to there occurs within the time period [k Δ t, (k+1) Δ t] and once pass through, it is micro-that Δ t is usually one In a small amount, its value is set as the 1/1000 of life cycle management T.Here, area ratio thought (as shown in Figure 3), PI{E are introduced_kCan Be defined as passing through geometrical condition and the interference area of power function feasible zone with during total feasible zone (deflection elliptic domain) area Ratio, it may be assumed that

In above formula, geometrical boundary condition is:With Calculating Being typically a piecewise function, need to combine geometrical boundary and feasible zone intersects condition stub discussion.

(4) travel through and pass through possibility degree PI{E in all time periods_k, calculate the convex model time-dependent ability of existing structure Parameter:

$R_s\left(T\right)=1-Pos\left(0\right)+\underset{k=1}{\overset{k\mathrm{\Δ}t=T}{\Σ}}\left(PI\right\{E_i\left\}\right)$

Wherein, R_s(T) representing the time-dependent ability in whole life cycle T, Pos (0) represents that structure at initial time is There is the possibility degree lost efficacy, solve above formula and can realize effective assessment of existing structure power safety situation.

(5) with the time-dependent ability R of the 4th step definition_s(T) as optimization aim, to safeguard that the moment t reinforced is as setting Meter variable, builds the time-varying reliability mathematical optimization models safeguarded towards existing structure optimum, and realizes with ant colony intelligence algorithm Complete Optimized Iterative process.Here, the time-varying reliability Optimized model safeguarded towards existing structure optimum is described as:

find:t^*

max R_s(T,t^*)

t^*={ t₁,t₂,...,t_N|N≤N_Allowable}

Wherein, t^*The discrete time collection reinforced, t is safeguarded for optimum_NFor the last moment safeguarded, R_s(T,t^*) represent Time-dependent ability after safeguarding for existing structure experience optimum, L_lD () is the l definitiveness constraint equation,Corresponding l Definitiveness retrains condition allowable, N≤N_SetThe n times represented are safeguarded should be not more than setting value N_Set.Fig. 4 gives setting single The schematic diagram that under the conditions of maintenance, existing structure time-varying reliability optimizes.

The iteration of Optimized model utilizes ant group algorithm to realize above, and its core formula is expressed as:

${\mathrm{\τ}}_{uv}(T_0+N)={\mathrm{\Ψ}}_N\·{\mathrm{\τ}}_{uv}\left(T_0\right)+\underset{w=1}{\overset{W}{\Σ}}{\mathrm{\Δ\τ}}_{uv}^w(T_0,T_0+N)$

Wherein, τ_uv(T₀+ N) and τ_uv(T₀) represent moment T respectively₀+ N and T₀From design point u to v, information is carried out between lower ant colony Exchange and the pheromone transmitted, W is population total,Reflection is ant colony individuality w letter from design point u to v Breath element loss, Ψ_NFor weight coefficient.

(6) in iterative process, if current design is compared to a upper feasible solution, the Relative percent change of object function During more than preset value ξ, the ant colony of design variable resets and updates, and the value being complete iterations is increased by one, and returns second Step, otherwise, carries out the 7th step.Here, the preset value ξ of tolerance percentage ratio is set as 1%.

(7) if global optimum's design with the overall situation Suboptimal Design scheme target function value fairly close, i.e. before When the tolerance percentage ratio of rear twice feasible solution is less than preset value ξ, terminate calculating, the change in the global optimum's design that will obtain Amount parameter safeguards Scheme of Strengthening as final existing structure optimum.

Embodiment:

In order to understand the feature of this invention and the suitability actual to engineering thereof more fully, the present invention is directed to such as Fig. 5 institute Show that in-service 24 layer laminated composite plate structures carries out single and safeguard the optimal conceptual design reinforced.It uses symmetric layups side Case [θ/θ/θ/θ/θ/θ/-θ/-θ/-θ/-θ/-θ/-θ]_Symmetrical.This structure is by acting on the concentrfated load of geometric center, and uses Arbitrary loading uses restraint.Length l of plate and width b are 100mm, and every laminate thickness is t=0.147mm.Plies of material has Having transverse isotropy, its density is ρ=1.38 × 10³kg/m³.This laminate engineering strength parameter information is as shown in table 1, table 2 List the non-probability force model uncertainty feature of laminate modulus.

Table 1

Table 2

θ=15 ° and two kinds, θ=45 ° layering type are discussed respectively, and corresponding load working condition is respectively as follows:

Assuming that the average process of structural strength properties rises according to a certain percentage after Wei Huing, radius process is with under same ratio Fall, corresponding proportionality coefficient be defined as building at the beginning of the nominal value of structure allowable load, i.e. intensity, and currently safeguard moment structure The ratio of residual intensity nominal value.Then, the optimum Maintenance Design method that the present invention proposes is utilized, it is considered to life cycle management is T= 20 years, carry out single and reinforce the formulation result of strategy as shown in Figure 6, Figure 7.It can be seen that through single under (1) above two operating mode Laminated plate structure security performance after suboptimum is safeguarded is substantially improved, and time-dependent ability index is carried by 0.5291 and 0.8456 respectively Rise to 0.9646 and 1；Particularly for this operating mode of θ=15 °, the military service phase of structure is effectively extended, and is greatly improved it The bearing capacity of in-service period.(2) during as seen in Figure 6, safeguarding the selection military service follow-up for structure on opportunity Safety effects is huge, if opportunity is improper, not only paid the cost of Financial cost, more cannot real effective lift structure Reliability, thus face the awkward circumstances of " lose-lose ".(3) as it is shown in fig. 7, work as R_s(T)=1, i.e. abampere in the structure military service phase Full-time corresponding maintenance time is chosen not unique, and from reality application angle, we can delay maintenance.On the one hand, Ke Yiyou The active time of effect extending structure, expands the time interval safeguarded next time；On the other hand, we are considering the warps such as artificial and material During the consume of Ji property, additionally it should be noted that subsidiary time cost, the most late execution of cost payout of equal extent, due to time cumulation Added losses impact is the least.

In sum, the present invention proposes a kind of existing structure optimum Maintenance Design side based on convex model time-varying reliability Method.The method utilizes convex model process to describe uncertain parameters, refers to using time-varying reliability as the quantization of safety of structure Mark；Consider the contact between the lifting of structural maintenance Cost And Performance, be target to the maximum with reliability, with limited by setting up Secondary maintenance time is the Optimized model of design variable, combined with intelligent optimizing algorithm, can make meter and time-varying Hurst index effect The optimal maintenance program of existing structure answered, can be that in engineering, rationally repairing of large scale structure provides the theories integration of necessity.

Below it is only the concrete steps of the present invention, protection scope of the present invention is not constituted any limitation；Its expansible should For replacing containing multi-source probabilistic existing structure optimum Maintenance Design field, all employing equivalents or equivalence and formed Technical scheme, within the scope of all falling within rights protection of the present invention.

Non-elaborated part of the present invention belongs to the known technology of those skilled in the art.

Claims (6)

1. an existing structure optimum Maintenance Design method based on convex model time-varying reliability, it is characterised in that realize step such as Under:

The first step: consider the time-varying Hurst index parameter being present in existing structure, define convex model process { X (t) ∈ X^I(t),t ∈ T} is characterized, and wherein, T is complete lifecycle, for any time t_i, (i=1,2 ...), X (t_i) translate into from The convex model variable dissipated, limited multiple convex model variablees are combined and are constituted a super ellipsoids territory, in order to preferably describe time-varying not The feature of deterministic parameter, defines the mean value function X of convex model process further^c(t), function of radius X^r(t), variance function D_X (t), the most in the same time t₁And t₂Correlation Coefficient Function ρ_X(t₁,t₂) and two various process X (t) and Y (t) exist respectively Moment t₁And t₂Under cross-correlation coefficient function ρ_XY(t₁,t₂)；

Second step: utilize the convex model process that the first step proposes, builds existing structure linearisation based on n dimension time-varying Hurst index Power function:

$g(t,X(t),d)=g(t,a(t),X(t\left)\right)=a_0\left(t\right)+a\left(t\right)X\left(t\right)=a_0\left(t\right)+\underset{i=1}{\overset{n}{\Σ}}{a}_i\left(t\right)X_i\left(t\right)$

Wherein, X (t)=(X₁(t),X₂(t),...,X_n(t))^TThe convex model process vector of expression consideration cross correlation, a (t)= (a₀(t),a₁(t),a₂(t),...,a_n(t)) represent time-varying coefficient vector, d represents design vector.Based on intervl mathematics operation method Then, the mean value function g of power function feature is derived^c(t, a (t), X (t)), function of radius g^r(t, a (t), X (t)), variance letter Number D_g(t) and correlation Coefficient Function ρ_g(t₁,t₂) mathematic(al) representation；

3rd step: based on passing through theory first and combining the power function that second step builds, by time discretization period, definition Pass through event E as follows_kThe possibility degree index occurred:

PI{E_k}=Pos{g (k Δ t, X (k Δ t), d) ＞ 0 ∩ g ((k+1) Δ t, X ((k+1) Δ t), d) ＜ 0}

Wherein, PI{ } represent the possibility degree that event occurs, ((k Δ t) d) represents that existing structure is pacified in k Δ t to g for k Δ t, X Entirely, now power function is more than zero, and (((k+1) Δ t) d) represents that existing structure loses in (k+1) Δ t to g for (k+1) Δ t, X Effect, now power function be less than zero, symbol " ∩ " represent event ship calculation, k is counting index, Δ t express time increment；

4th step: travel through and pass through possibility degree PI{E in all time periods_k, calculate the convex model time-dependent ability meter of existing structure Calculation index:

$R_s\left(T\right)=1-Pos\left(0\right)+\underset{k=1}{\overset{k\mathrm{\Δ}t=T}{\Σ}}\left(PI\right\{E_k\left\}\right)$

Wherein, R_s(T) representing the time-dependent ability in whole life cycle T, Pos (0) represents that structure is i.e. lost at initial time The possibility degree of effect, solves above formula and can realize effective assessment of existing structure power safety situation；

5th step: with the time-dependent ability R of the 4th step definition_s(T) as optimization aim, to safeguard that the moment t reinforced is as design Variable, builds the time-varying reliability mathematical optimization models safeguarded towards existing structure optimum, and has realized with ant colony intelligence algorithm Whole Optimized Iterative process；

6th step: in iterative process, if current design is compared to a upper feasible solution, the Relative percent change of object function During more than preset value ξ, the ant colony of design variable resets and updates, and the value being complete iterations is increased by one, and returns second Step, otherwise, carries out the 7th step；

7th step: if global optimum's design with the overall situation Suboptimal Design scheme target function value fairly close, i.e. before When the tolerance percentage ratio of rear twice feasible solution is less than preset value ξ, terminate calculating, the change in the global optimum's design that will obtain Amount parameter safeguards Scheme of Strengthening as final existing structure optimum.

A kind of existing structure optimum Maintenance Design method based on convex model time-varying reliability the most according to claim 1, It is characterized in that: the mean value function X of described first step convexity model process^c(t), function of radius X^r(t) and variance function D_X T the expression formula of () is as follows:

$X^c\left(t\right)=\frac{\stackrel{\‾}{X\left(t\right)}+\underset{\‾}{X\left(t\right)}}{2},X^r\left(t\right)=\frac{\stackrel{\‾}{X\left(t\right)}-\underset{\‾}{X\left(t\right)}}{2},D_X\left(t\right)={\left(X^r\right(t\left)\right)}^2={\left(\frac{\stackrel{\‾}{X\left(t\right)}-\underset{\‾}{X\left(t\right)}}{2}\right)}^2$

Additionally, correlation Coefficient Function ρ_X(t₁,t₂) and cross-correlation coefficient function ρ_XY(t₁,t₂) it is represented by:

${\mathrm{\ρ}}_X\left(t_1,t_2\right)=\frac{{\mathrm{Cov}}_X\left(t_1,t_2\right)}{\sqrt{D_X\left(t_1\right)}\·\sqrt{D_X\left(t_2\right)}},{\mathrm{\ρ}}_{XY}\left(t_1,t_2\right)=\frac{{\mathrm{Cov}}_{XY}\left(t_1,t_2\right)}{\sqrt{D_X\left(t_1\right)}\·\sqrt{D_Y\left(t_2\right)}}$

Wherein, Cov_X(t₁,t₂) it is that convex model process X (t) is at moment t₁And t₂Auto-covariance function, Cov_XY(t₁,t₂) it is convex Model process X (t) and Y (t) are at moment t₁And t₂Under cross covariance function.

A kind of existing structure optimum Maintenance Design method based on convex model time-varying reliability the most according to claim 1, It is characterized in that: the mean value function g of power function feature in described second step^c(t, a (t), X (t)) and function of radius g^r(t,a (t), X (t)) it is expressed as:

$g^c(t,a(t),X(t\left)\right)=g^c\left(t\right)=a_0\left(t\right)+\underset{i=1}{\overset{n}{\Σ}}\left(a_i\right(t)\·X_i^c(t\left)\right)$

With

$\begin{array}{c}{g}^r(t,a(t),X(t\left)\right)\\ =g^r\left(t\right)=\sqrt{\underset{i=1}{\overset{n}{\Σ}}{\left(a_i\right(t)\·X_i^r(t\left)\right)}^2+\underset{i=1}{\overset{n}{\Σ}}\underset{j\≠i}{\overset{n}{\underset{j=1}{\mathrm{\Σ}}}}{\mathrm{\ρ}}_{X_i{X}_j}(t,t)\·a_i\left(t\right)\·a_j\left(t\right)\·X_i^r\left(t\right)\·X_j^r\left(t\right)}\end{array}$

Wherein,WithIt is respectively convex model The mean vector of process X (t) and radius vectors,Represent process X_i(t) and X_jT () is at the cross-correlation coefficient of moment t, i It is counting index with j, additionally, variance function D_g(t) and correlation Coefficient Function ρ_g(t₁,t₂) mathematic(al) representation be respectively as follows:

$D_g\left(t\right)=g^r{\left(t\right)}^2,{\mathrm{\ρ}}_g(t_1,t_2)=\frac{{\mathrm{Cov}}_g(t_1,t_2)}{\sqrt{D_g\left(t_1\right)}\·\sqrt{D_g\left(t_2\right)}}$

Wherein, D_gT () represents power function g (t, X (t), covariance function d).

A kind of existing structure optimum Maintenance Design method based on convex model time-varying reliability the most according to claim 1, It is characterized in that: event E in described 3rd step_kIt is expressed as existing structure and there occurs one within the time period [k Δ t, (k+1) Δ t] Secondary passing through, Δ t is usually a small quantity, and its value is set as the 1/1000 of life cycle management T.

A kind of existing structure optimum Maintenance Design method based on convex model time-varying reliability the most according to claim 1, It is characterized in that: the time-varying reliability Optimized model safeguarded towards existing structure optimum in described 5th step is described as:

find:t^*

max R_s(T,t^*)

t^*={ t₁,t₂,...,t_N|N≤N_Allowable}

Wherein, t^*The discrete time collection reinforced, t is safeguarded for optimum_NFor the last moment safeguarded, R_s(T,t^*) be expressed as in-service Time-dependent ability after structure experience optimum maintenance, L_lD () is the l definitiveness constraint equation,Corresponding the l definitiveness Retrain condition allowable, N≤N_SetThe n times represented are safeguarded should be not more than setting value N_Set。

A kind of existing structure optimum Maintenance Design method based on convex model time-varying reliability the most according to claim 1, It is characterized in that: in described 6th step, the preset value ξ of tolerance percentage ratio is set as 1%.