CN101382473B - EWMA control chart method for bridge structure safety alarm - Google Patents

Abstract

The invention discloses an EWMA control chart method for the safety early warning of bridge construction; the primary early warning limitation, the safety warning limitation and the corresponding tendency change limitation for the safety of the bridge construction are established by adopting the EWMA control chart according to all construction state information obtained by a monitoring system for the safety of the bridge construction, and the primary early warning limitation and the safety warning limitation are used as criterion to estimate the real-time monitoring information of the safety of the bridge construction and give an alarm; the beneficial technical effect of the method is that: the effective estimation of the safety of the construction is realized by extracting the feature information related to the safety of the construction from statistic analysis carried out to mass bridge monitoring data to dig the evolution rule of the construction performance, and the estimation process does not need a precise model and known motivation of the construction, thus having wide universality.

Description

The EWMA control chart method of bridge structure safe early warning

Technical field

The present invention relates to a kind of bridge structure safe early warning technology, relate in particular to a kind of EWMA control chart method of bridge structure safe early warning.

Background technology

Because the singularity that the complicacy of bridge structure itself and environment of living in and structural safety are estimated, the bigger limitation of existing structural safety evaluation method existence fails to obtain gratifying progress in practical application, be mainly reflected in following some:

(1) existing bridge structure safe evaluation theory based on model all derives from branch of mechanics, and its evaluation procedure depends critically upon the accurate Theory model of structure and the system incentive of determining; Yet the continuous variation in operational process of the serious disappearance of old bridge data and bridge structure parameter makes that the foundation of structure accurate model is very difficult, add the not intellectual of random environment excitation in the bridge structural health monitoring, make that safety evaluation runs into the obstacle that is difficult to go beyond based on structure of models.

(2) though obtained progressively attention based on the evaluation method of statistical study, its research and use the initial stage that still is in; The bridge enormous size, complex structure, vibration amplitude is very low, the common kinematic behavior index that adopts of statistical study is easily flooded by neighbourhood noise or is insensitive to local damage, and bridge structure safe evaluation and environmental characteristics (as temperature) are not connected effectively, its evaluation effect also can't engineering demands.

(3) though neural network has good performance when handling nonlinear problem,, can't between structural response and safe condition, set up effective causal relation owing to lack complete training sample.

(4) present safety evaluation adopts single method or single parameter to analyze mostly, and the uncertainty of environmental impact and test data imperfect makes monitored parameters fail the safety case of comprehensive reflect structure.

The existence of above problem, making does not also have a kind of gratifying bridge security overall evaluation system at present.

From above analysis as can be known, because the formation of bridge structure itself is very complicated, its performance is subjected to the influence of the various factors of structure environment of living in easily, makes also very the complexity and difficult of appraisal of structural safety.Although the evaluation method at bridge structure safe has much at present, because a variety of causes, these evaluation methods all have itself intrinsic defective, do not achieve satisfactory results as yet in practical application.

Along with deepening continuously of bridge structure Application of Monitoring System, system will collect a large amount of historical datas of the structural response under environmental excitation.In these huge mass datas, must imply the characteristic information of reflect structure safe condition, just, will run into great obstacle when utilizing traditional method that model is arranged to estimate because excitation is unknown.Therefore, according to these outstanding characteristics, how by statistical study to this mass data, therefrom extract the characteristic information of relevant structural safety, the development law of mining structure performance, the effective evaluation of implementation structure safety has more and more obtained people's attention.Because its evaluation procedure does not need the accurate model and the known excitation of structure, has versatility widely, and it provides fabulous opportunity for the mixing together of signal Processing subject and branch of mechanics.Therefore have important academic values and realistic meaning.

Control chart is a kind of graphical tools, in process of production, the sample data of randomly drawing is put in order, is write down and is marked on the control chart, drops on the inside and outside situation of control limit according to each observation data point and monitors product quality parameters situation over time.Control chart has been widely used in the every field of industry, so far as quality assurance, process monitoring, prediction and the control etc. of production run since founding.

The EWMA control chart is a kind of in the control chart commonly used, now has been widely used in fields such as process monitoring, prediction and quality control.Its outstanding feature is the historical information that can make full use of process, and the current near more historical information of adjusting the distance gives big more weight, and distance information far away is more then given more little weight.This characteristics are fit to describe the evolution rule of bridge structure response mobile load effect information and deteriorating effect information very much.

The EWMA control chart is defined as follows:

To a certain average is Z, and standard deviation is the statistic processes of σ

The controlled quentity controlled variable of single argument EWMA control chart is determined by following formula:

$Z_i=\mathrm{\λ}{\stackrel{\→}{X}}_i+(1-\mathrm{\λ})Z_{i-1}$

Wherein: i is a positive integer; λ is a smoothing parameter, and 0＜λ≤1;

It is the i group observations; Z ₀Be initial value.

Weight distribution characteristics according to EWMA control chart statistic can obtain its statistical nature: establishing each this capacity of taking a sample is n, and then the mathematical expectation E of statistic Z (Z) is:

$E\left(Z\right)=E\left(\stackrel{\→}{X}\right)=\stackrel{\‾}{Z}$

The variance D of statistic Z (Z) is:

$D\left(Z\right)=\frac{\mathrm{\λ}}{n(2-\mathrm{\λ})}[1-{(1-\mathrm{\λ})}^{2i}]D\left(\stackrel{\→}{X}\right)$

Standard deviation sigma _RFor:

${\mathrm{\σ}}_R=\sqrt{D\left(Z\right)}=\frac{\mathrm{\σ}}{\sqrt{n}}\sqrt{\left(\frac{\mathrm{\λ}}{2-\mathrm{\λ}}\right)[1-{(1-\mathrm{\λ})}^{2i}]}$

The control of EWMA control chart is limited to:

$\mathrm{UCL}=\stackrel{\‾}{Z}+k{\mathrm{\σ}}_R=\stackrel{\‾}{Z}+k\frac{\mathrm{\σ}}{\sqrt{n}}\sqrt{\left(\frac{\mathrm{\λ}}{2-\mathrm{\λ}}\right)[1-{(1-\mathrm{\λ})}^{2i}]}$

$\mathrm{LCL}=\stackrel{\‾}{Z}-k{\mathrm{\σ}}_R=\stackrel{\‾}{Z}-k\frac{\mathrm{\σ}}{\sqrt{n}}\sqrt{\left(\frac{\mathrm{\λ}}{2-\mathrm{\λ}}\right)[1-{(1-\mathrm{\λ})}^{2i}]}$

Wherein: k is a constant, is in the width of the control limit of slave mode in order to definition procedure.

When i was big, for simplicity, the control of EWMA control chart limit can adopt the limiting form of above-mentioned two formulas, that is:

$\mathrm{UCL}=\stackrel{\‾}{Z}+k\frac{\mathrm{\σ}}{\sqrt{n}}\sqrt{\frac{\mathrm{\λ}}{2-\mathrm{\λ}}}$

$\mathrm{LCL}=\stackrel{\‾}{Z}-k\frac{\mathrm{\σ}}{\sqrt{n}}\sqrt{\frac{\mathrm{\λ}}{2-\mathrm{\λ}}}$

Wherein: λ and k are the parameter of the controlled ARL of procurement process (Average Run Length: on average move chain length), and n is the size of sample subclass: the control of EWMA control chart at this moment is limited to a fixed interval scope.

Summary of the invention

The invention discloses a kind of EWMA control chart method of bridge structure safe early warning, it comprises: all configuration state information of obtaining at the bridge structure safe monitoring system, adopt the EWMA control chart to set up the elementary early warning limit and the security alarm limit of bridge structure safe, bridge structure is assessed and reported to the police as criterion.

Above-mentioned limits as criterion with elementary early warning limit and security alarm, bridge structure is assessed and reported to the police, comprise: the inner control limit [LCL of EWMA control chart, UCL] be elementary early warning limit, outer control limit [VCL, HCL] is the security alarm limit, limits [LCL when the value of the real-time monitoring information control chart statistic of bridge structure surpasses inner control, UCL] time, elementary early warning sent; When surmounting outer control limit [VCL, HCL], send security alarm as the value of real-time monitoring information control chart statistic.

On the basis as criterion with elementary early warning limit and security alarm limit, further combined with the alteration trend characteristic WRI index of monitoring information and secondary or three assessment results of RSI index, again bridge structure is assessed and reported to the police, it comprises: the value as the real-time monitoring information control chart of structure statistic reaches inner control limit [LCL, UCL] or outer control limit [VCL, HCL] 80% when above, alteration trend characteristic WRI index and RSI index by real-time monitoring information are carried out secondary or three assessments, and judge whether to send elementary early warning or security alarm according to assessment result; When the real-time monitoring information state value of bridge structure reaches inner control limit [LCL, UCL], directly send elementary early warning.

Wherein, the computing method of the inner control of EWMA control chart limit [LCL, UCL] comprising:

(1) historical information of arbitrary real-time monitoring parameter of bridge structure is set up a stochastic process, is expressed as:

Z _i＝Z+ξ _i

In the formula: i is a positive integer;

Z _iI the value of data in the cycle for this monitoring information;

Z is the process average of the data of this monitoring information;

ξ _iParameter for random variation;

(2) determine σ, d and ARL ₀Value

Data to monitoring information are analyzed, and calculate the standard deviation sigma of these data and minimum offset d=η σ (wherein | η |≤1); Again according to the actual conditions of bridge structure and the specific requirement of evaluation, choose 10 times～20 times of cycle basic time of data variation, as the average operation duration ARL that false alarm does not take place in the section between at a time ₀(Average Run Length).

(3) determine the value of λ and k

By look-up table, from the optimum λ curve map of EWMA control chart and EWMA control chart, (λ, k) build-up curve figure determines the value of λ and k;

(4) value of optimization λ and k

According to the actual conditions of bridge structure monitoring, set up an iterative process, by the variation search of d value optimum (λ k) makes up, and makes the probability of mistake activating alarm of monitored process and the error minimum of predetermined probability;

(5) try to achieve the upper and lower limit of the inner control limit of EWMA control chart according to following formula:

$\mathrm{UCL}=\stackrel{\‾}{Z}+k\frac{\mathrm{\σ}}{\sqrt{n}}\sqrt{\frac{\mathrm{\λ}}{2-\mathrm{\λ}}}$

$\mathrm{LCL}=\stackrel{\‾}{Z}-k\frac{\mathrm{\σ}}{\sqrt{n}}\sqrt{\frac{\mathrm{\λ}}{2-\mathrm{\λ}}}$

In the formula: n is the size of sample subclass, n=ARL ₀/ Δ t, Δ t are sampling interval.

Outer control limit [VCL, HCL] computing method of EWMA control chart comprise:

(1) RELIABILITY INDEX that provides according to the reliability of bridge structure standard can obtain the permissible value P of structural failure probability _f

(2) limit coefficient [x, x], (x＞0) according to the outer control of following formula calculating EWMA control chart;

$P_f=2\&CenterDot;\frac{1}{\sqrt{2\mathrm{\&pi;}}}{\&Integral;}_{-\&infin;}^{-x}{e}^{\frac{-{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="H2008102328250E00012.png,H2008102328250E00013.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}{2}}\mathrm{dt}$

(3) determine outer control limit according to following formula:

In the formula: Process average for the data of monitoring information;

σ is the standard deviation of the data of monitoring information.

The value of the real-time monitoring information control chart of aforesaid structure statistic reaches inner control limit [LCL, UCL] or outer control limit [VCL, HCL] 80% when above, alteration trend characteristic WRI index and RSI index by real-time monitoring information are carried out secondary evaluation, comprise: if-25＜WRI (h)＜125, then do not send elementary early warning or security alarm, otherwise, elementary early warning or security alarm then sent.

Aforesaid value as the real-time monitoring information control chart of structure statistic reaches inner control limit [LCL, UCL] 80% when above, alteration trend characteristic WRI index and RSI index by real-time monitoring information are carried out three assessments, comprise: when assessment result satisfy condition simultaneously-when 25＜WRI (h)＜125 and 45≤RSI (h)≤55, then do not send elementary early warning; If wherein arbitrary condition does not satisfy, then send elementary early warning.

Wherein, the alteration trend characteristic WRI index of the real-time monitoring information of bridge structure safe is meant that the current fluctuating range of data of real-time monitoring information accounts for the percentage of its last cycle maximum fluctuation amplitude, and concrete computing method are:

$\mathrm{WRI}\left(h\right)=\frac{Z_{\max }-Z}{Z_{\max }-Z_{\min }}\&times;100$

In the formula: Z _MaxThe maximal value of data in the last cycle for real-time monitoring information;

Z _MinFor the data of real-time monitoring information in the last cycle minimum value;

Z is the current numerical value of the data of real-time monitoring information;

H is actual measurement data result's the interior measuring point quantity of Cycle Length;

Wherein, the maximal value Z of data in the last cycle of real-time monitoring information _MaxWith minimum value Z _MinBe respectively measuring point in the last cycle and count maximal value and the minimum value that h deducts amplitude behind the current detection point m measuring point, the m value can be 3～6.

The alteration trend characteristic RSI index of the real-time monitoring information of bridge structure safe is meant that the unidirectional undulate quantity of data in certain one-period of real-time monitoring information accounts for the relative percentage of total undulate quantity, and concrete computing method are:

$\mathrm{RSI}\left(h\right)=\frac{A}{A+B}\&times;100$

In the formula: A is the summation of data positive dirction recruitment in one-period of real-time monitoring information;

B is the summation of data negative direction recruitment absolute value in one-period of real-time monitoring information;

Wherein: $A=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}|Z_i-Z_{i-1}|,$ And Z _i-Z _I-1〉=0

$B=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}|Z_i-Z_{i-1}|,$ And Z _i-Z _I-1＜0

In the formula: Z _iI the value of data in one-period for this real-time monitoring information;

Z _I-1I-1 the value of data in one-period for this real-time monitoring information;

I is the value number of data in one-period of real-time monitoring information;

I is a positive integer.

Useful technique effect of the present invention is: by the statistical study to the bridge monitoring mass data, therefrom extract the characteristic information of relevant structural safety, the development law of mining structure performance, the effective evaluation of implementation structure safety, evaluation procedure does not need the accurate model and the known excitation of structure, has versatility widely.

Description of drawings

Accompanying drawing 1, the bridge structural state synoptic diagram;

Accompanying drawing 2, ARL ₀=50,100,250,370 o'clock, the optimum λ curve of EWMA control chart;

Accompanying drawing 3, ARL ₀=500,1000,1500,2000 o'clock, the optimum λ curve of EWMA control chart;

Accompanying drawing 4, ARL ₀=50,100,250,370 o'clock, EWMA control chart (λ, k) build-up curve;

Accompanying drawing 5, ARL ₀=500,1000,1500,2000 o'clock, EWMA control chart (λ, k) build-up curve;

Accompanying drawing 6, optimum (λ, k) Zu He search procedure block diagram;

Accompanying drawing 7, the mobile load effect E WMA control chart evaluation map of amount of deflection n5;

Accompanying drawing 8, the EWMA control chart evaluation map of amount of deflection s5 transition;

Accompanying drawing 9, simulation that amount of deflection s5 transient information is out of control and evaluation map;

Accompanying drawing 10, the EWMA control chart evaluation map of strain 20 transient informations;

Accompanying drawing 11, the EWMA control chart evaluation map of strain 30 transient informations;

Accompanying drawing 12, simulation and evaluation map that strain 30 is out of control;

Accompanying drawing 13, the evaluation map of amount of deflection s5 deteriorating effect information;

Accompanying drawing 14, the evaluation map of strain 30 deteriorating effect information;

In the accompanying drawing, Fig. 2 to Fig. 5 is that (λ, k) build-up curve figure are and quote figure, its source is: Crowder SV.Design ofexponentially weighted moving average schemes.Journal of Quality Technology 1989,21:155-162..

Embodiment

(1) health condition of bridge structure can be reflected in the variation (structural response) of structural parameters undoubtedly, by the variation of monitoring of structures parameter, can judge the safety case of structure.Utilize wavelet analysis and regretional analysis can with the bridge structural health monitoring system acquisition to the time-domain information of structural response be separated into independently deteriorating effect information and mobile load effect information.Wherein, the deteriorating effect message reflection the slow variation tendency of structural behaviour, mobile load effect information has then reflected the transient changing (being transient information) of configuration state under live load, they have all comprised the status information of reflect structure health status.Therefore, by the mobile load effect information and the deteriorating effect information of monitoring of structures parameter, the effectively security situation of monitoring of structures.Because the randomness of live load and temperature effect are rejected the stochastic error of process, the mobile load effect information and the deteriorating effect information of structural response all are random variation, and when structure is in normal condition, its mean approximation is a constant, can regard a stochastic process respectively as, be equivalent to the controlled change of statistic processes; And when safety problem appears in structure, the unidirectional variation that continuing will appear in its numerical value (increase or reduce), its fluctuating range will continue to increase, and depart from equilibrium point (being average), promptly broken the variation of original normal condition, the similar statistic processes of this change procedure out of control.Therefore, can adopt the method for control chart, respectively the mobile load effect information and the deteriorating effect change in information process of the bridge structure of each measuring point be monitored, according to the distribution of statistic on control chart of each data point, whether deterministic process is out of control, thereby finishes the safety evaluation of structure.

In addition, bridge structure in-service, the mobile load effect information of structural response is all relevant with the performance parameter of structured material with deteriorating effect information.Initial stage under arms, material property is stable, and the fluctuation range of mobile load effect information and deterioration information is certain substantially, but along with the prolongation of the phase of military service, slowly changing appears in material property parameter, thereby makes its fluctuation range corresponding variation also occur.For this variation of correct reflection in time, control chart must have corresponding characteristics, can make full use of historical information, and makes the information near more apart from current time, state variation that more can reflect structure, and the EWMA control chart has all above-mentioned characteristics just.

When specifically constructing the EWMA control chart, at first the mobile load effect of bridge structure and the historical information of deteriorating effect are constituted a stochastic process z={z respectively ₀, z ₁, z ₂..., z _n... }, be expressed as: Z _i=μ+ξ _i, μ is the process average, ξ _i(when structure was in normal condition, μ was constant, ξ for the parameter of random variation _iBe random variation, whole process does not have tangible trend.When structure damage occurs or safety problem is arranged, Z _iAmplitude of variation continue to increase, the expendable unidirectional variation tendency that continues appears in the process average; Therefore,, monitor this process average and expendable unidirectional variation tendency whether occurs, can estimate the Structure Safety for Bridge situation) by statistical study to this process.

Embodiment 1:

Having gathered a large amount of structural response historical datas that contained the structure safety state information in view of the bridge structural health monitoring system in the application that continues (is monitored parameters, also be the data of monitoring information), variation characteristics according to these data are carried out statistical study to it, can therefrom search and extract the characteristic information of reflect structure safe condition, excavate the development law of structural behaviour, thus the implementation structure safety evaluation.

With the amount of deflection is example, and under normal circumstances, the concrete shrinkage and the effect of creeping mainly occur in 1 year that bridge builds up, and therefore for becoming the bridge of bridge after 1 year, this factor can be ignored.So, under the situation of not considering unexpected disaster, on the cable-stayed bridge main-beam certain a bit, as can be known from the above analysis, its vertical deflection can be determined by following formula:

y＝y _V+y _M+y _T

Wherein, y _VBe the amount of deflection that the performance of structure own descends and causes, this value is approximately 0 under normal condition; y _MVertical deflection for the live load generation; y _TBe the amount of deflection that temperature effect produced.

The action effect (structural response) of girder point mainly is made up of the deteriorating effect that temperature effect, mobile load effect and structural damage or performance change cause.Therefore, following formula also can be expressed as:

z＝z _V+z _T+z _M＝f[V，T，P(x)]

Wherein: V is the parameter of reflect structure performance, can be elastic modulus E, moment of inertia I, the drag-line elastic modulus E of girder _g, drag-line sectional area A (if exist) or the combination of arbitrary parameter wherein.Because V is the function of time t, and temperature T and live load P (x) also are the functions of time, therefore the structural response that is caused by them can be expressed as respectively:

z _V(t)＝f ₁[V(t)]，z _T(t)＝f ₂[T(t)]，z _M(t)＝f ₃[V(t)，P(x，t)]

In the formula, z _V(t) be the structure deterioration effect, only relevant with the structural behaviour variation, z _T(t) be temperature effect, determine z by structure temperature and thermal expansivity _M(t) be the mobile load effect, change relevant with live load and structural behaviour.As seen, relevant with structural behaviour V parameter (t) structural response information has only deteriorating effect z _V(t) and mobile load effect z _MAnd the variation of temperature effect and structural behaviour is irrelevant (t).

Temperature effect z _T(t) mainly by sunshine the temperature difference, abrupt temperature drop and season the temperature difference and cause that its main time scale is 1 day and 1 year.In less than the time span in 1 year, can be further organized as cycle changing unit z _T1With changing unit z non-periodic _T2That is:

z _T(t)＝z _T1(t)+z _T2(t)

Wherein, z _T1Cycle identical with the time cycle of structure measuring point ambient atmosphere temperature, just for the variation of atmospheric temperature, the temperature effect of amount of deflection will postpone about 2 hours.Therefore, z _T1Sine or cosine function for time t.Might as well make:

z _T1＝Acos(ωt+Ψ ₀)

Its cycle is 1 day, and wherein, angular frequency is identical with temperature funtion.So z _T(t) also can be expressed as:

z _T(t)＝Acos(ωt+Ψ ₀)+y _T2(t)

The temperature effect z of aperiodic component _T2Mainly changed by abrupt temperature drop and Nian Wen and the part constraint causes, its length that changes span in time is with season and different, but also not obvious in intraday variation.

Obviously, to mobile load effect z _M(t), along with the continuous collection of monitoring system, the mobile load effect information of being obtained also constantly increases, and it can be considered as a process.Since the cyclical variation characteristics of live load itself, mobile load effect z _M(t) can be further organized as the primitive period is N ₀Sequence, therefore available N ₀The weighted sum of the complex exponential sequence of individual one-tenth harmonic relationships represents, that is:

$z_M\left(t\right)=f_3[V\left(t\right),P(x,t)]=\underset{k=\&lang;{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="H2008102328250E00012.png,H2008102328250E00013.png"\; state="\{\{state\}\}">N</figure-callout>}}_0\&rang;}{\mathrm{\&Sigma;}}{c}_k\&CenterDot;\exp (\mathrm{<figure-callout\; id="2"\; label="jk"\; filenames="H2008102328250E00012.png,H2008102328250E00013.png"\; state="\{\{state\}\}">jk</figure-callout>}2\mathrm{n\&pi;}/N_0)$

K=＜N in the formula ₀Represent that summation only need comprise N ₀, desirable k=0,1,2 ..., N ₀-1; c _kBe the coefficient of each harmonic component, determine by concrete load situation; The n express time.As seen mobile load effect itself has multiple dimensioned formation characteristics of time.

When structure was in normal operating condition, each physical parameter of bridge structure did not change, and for example concrete elastic modulus E is after through 1 year, and under normal condition, its variation is very slow, almost can think constant.And damage appears when structure, and for example during fatigue damage, the parameter of its reflect structure strength of materials performance

As time goes on lasting decline will occur, similarly changing also will appear in its elastic modulus E.A unidirectional variation tendency will appear in the V parameter (t) that is to say the reflect structure performance change.Therefore, when structure just often because V (t) is constant, the mobile load effect by only by live load P _nDetermine.And live load is a random variation, and its effect that causes must be carried out by a small margin fluctuation up and down around some equilibrium points, and when live load disappeared, girder promptly returned to its normal state, and equilibrium point at this moment is the average of process.

And when structure appearance damage, when for example drag-line damages, its sectional area A _nOr elastic modulus E _gContinue to reduce, so the elasticity coefficient K of girder must continue to descend, must constantly be increased by the effect that live load causes this moment, and finally depart from the equilibrium point of normal condition.Equally, when not damage of drag-line, and main beam structure is when having damage, then the elastic modulus E of girder _gWhat occur continuing reduces, so also can cause the action effect under the mobile load constantly to increase.And even load disappears, structure is also recovered less than original state.Therefore, as long as the current average of observation process departs from the degree of original normal condition equilibrium point, can judge whether structure is in a safe condition.

In like manner, structural behaviour is changed caused deteriorating effect z _V(t), when structure is in normal condition, because V (t) is constant, its variation is almost 0, but because the influence of the stochastic error of information access process and deteriorating effect leaching process, the concrete sample value of its process might not be constant, but the process average is a fixing constant; And when damage or safety problem appearred in structure, unidirectional variation tendency appearred in V (t), and under the effect of dead load, structural response will have an expendable growth slowly.Therefore,, but unidirectional expendable trend occurred, can judge that structure has entered unsafe condition as long as this process of monitoring is not constant value in the average of a certain setting cycle.

In sum, the historical information of the mobile load effect of bridge structure and deteriorating effect constitutes a stochastic process z={z respectively ₀, z ₁, z ₂..., z _n... }, might as well be expressed as:

Z _i＝Z+ξ _i

In the formula, Z is the process average, ξ _iParameter for random variation.

Referring to accompanying drawing 1, when structure was in normal condition, Z was constant, ξ _iBe random variation, whole process does not have tangible trend.When structure damage occurs or safety problem is arranged, Z _iAmplitude of variation continue to increase, the expendable unidirectional variation tendency that continues appears in the process average.Therefore,, monitor this process average and expendable unidirectional variation tendency whether occurs, can estimate the Structure Safety for Bridge situation by statistical study to this process.

Obtain the mobile load effect and the deteriorating effect information of structural response, can design the EWMA control chart of response, drop on the inside and outside situation deterministic process of control limit whether in normal range, thereby realize safety evaluation bridge construction according to the statistic of each information.For obtaining optimum evaluation effect, the present invention adopts " optimum control limit " in conjunction with the method for designing based on the reliability of bridge structure standard.Control [the VCL that the fiduciary level standard of conjugative bridge girder construction is calculated, HCL] what reflect is that structure has gone out the control limit of safety problem (being structural failure), and structure obviously also has one not short period from being damaged to lose efficacy, therefore [VCL, HCL] width often very wide, if use separately, because behind structural damage and this section that does not reach inefficacy in the period without any warning information, promptly there is the situation of leaking activating alarm, might incur loss through delay the correct diagnosis and the influence of structure and safeguard decision-making, even can cause more serious consequence; And " optimum control limit " [LCL, UCL] be to determine according to process actual conditions just often, it requires process to occur alarming as early as possible after the unusual fluctuations, therefore its control range line is nearer from the statistic of normal condition, its width is than [VCL, HCL] smaller, if use separately, because the complicacy of bridge structure environment of living in and the uncertainty of influence factor, might appear at that structure is not damaged and the situation that surpasses the control limit is arranged during statistic, promptly miss activating alarm, and improved the cost of process monitoring thus, reduced the monitoring performance of control chart.So, for fear of the defective of a certain control limit of independent use, the method that the present invention adopts two kinds of control limits to combine, promptly adopt the two-stage alarming mechanism: when the statistic of control chart surpasses [LCL, UCL] scope the time, just provide elementary early warning, remind the supvr to note; When statistic surmounts two-stage control in limited time, just provide security alarm, must show great attention to the ruuning situation of bridge structure this moment, and make further examination and maintenance decision-making.At this, [LCL, UCL] can be described as the inner control limit, and [VCL, HCL] can be described as outer control limit.Based on this, the specific design step of EWMA control chart is as follows:

1) computing method of the inner control of EWMA control chart limit [LCL, UCL] comprising:

(1) historical information of arbitrary real-time monitoring parameter of bridge structure is set up a stochastic process, is expressed as:

Z _i＝Z+ξ _i

In the formula: i is a positive integer;

Z _iI the value of data in the cycle for this monitoring information;

Z is the process average of the data of this monitoring information;

ξ _iParameter for random variation;

(2) determine σ, d and ARL ₀Value

Data to monitoring information are analyzed, and calculate the standard deviation sigma of these data and minimum offset d=η σ (wherein | η |≤1); Again according to the actual conditions of bridge structure and the specific requirement of evaluation, choose 10 times～20 times of cycle basic time of data variation, as the average operation duration ARL that false alarm does not take place in the section between at a time ₀(Average Run Length).

ARL ₀Determine to carry out according to the specific requirement of the actual conditions of bridge structure and evaluation.For this large scale structure of bridge,, therefore when structure is in normal condition, wish not take place in a long time the situation of mistake activating alarm because the cost that its monitoring system mistake activating alarm causes is higher relatively.Monitoring with the Chongqing Coriaria sinica small stream Yangtze Bridge is an example, and structure measurement information is to gather once in per ten minutes, for a certain measurement point of structure, 144 data points is arranged just within one day.For this reason, ARL ₀May be selected to be 2000 points, be i.e. the mistake activating alarm did not take place in 2 weeks.

(3) determine the value of λ and k

By look-up table, from the optimum λ curve map of EWMA control chart and EWMA control chart, (λ, k) build-up curve figure determines the value of λ and k;

ARL ₀After determining, in order to select λ, the size of the minimum offset d that the first deterministic process of needs can be monitored.Definite needs of d are taken all factors into consideration the maximum offset that the security of system requirement is allowed, and at last the size of d are expressed as the multiple of normal observation sample standard deviation σ.In case the size of d determines, can be according to it and ARL ₀Value, utilize Fig. 2 to Fig. 5 interpolation to determine the value of λ and k.

(4) value of optimization λ and k

According to the actual conditions of bridge structure monitoring, set up an iterative process, by the variation search of d value optimum (λ k) makes up, and makes the probability of mistake activating alarm of monitored process and the error minimum of predetermined probability;

Because the value of d is between 0-4, so optimum (λ, k) combination can be determined according to the analysis that bridge structure is in the actual monitoring process of normal condition.Detailed process is: according to the actual conditions of bridge structure response observation process, set up an iterative process, by the variation search of d value optimum (λ k) makes up, and makes the probability of mistake activating alarm of monitored process and the error minimum of predetermined probability.Its search procedure such as Fig. 6, the control limit of search gained is designated as [LCL, UCL].

(5) try to achieve the upper and lower limit of the inner control limit of EWMA control chart according to following formula:

$\mathrm{UCL}=\stackrel{\&OverBar;}{Z}+k\frac{\mathrm{\&sigma;}}{\sqrt{n}}\sqrt{\frac{\mathrm{\&lambda;}}{2-\mathrm{\&lambda;}}}$

$\mathrm{LCL}=\stackrel{\&OverBar;}{Z}-k\frac{\mathrm{\&sigma;}}{\sqrt{n}}\sqrt{\frac{\mathrm{\&lambda;}}{2-\mathrm{\&lambda;}}}$

In the formula: n is the size of sample subclass, n=ARL ₀/ Δ t, Δ t are sampling interval.

2) outer control limit [VCL, HCL] computing method of EWMA control chart comprise:

(1) RELIABILITY INDEX that provides according to the reliability of bridge structure standard can obtain the permissible value P of structural failure probability _f

(2) limit coefficient [x, x] according to the outer control of following formula calculating EWMA control chart, (x〉0);

$P_f=2\&CenterDot;\frac{1}{\sqrt{2\mathrm{\&pi;}}}{{\&Integral;}_{-\&infin;}^{-x}e}^{\frac{-{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="H2008102328250E00012.png,H2008102328250E00013.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}{2}}\mathrm{dt}$

(3) determine outer control limit: [VCL, HCL]=[Z-x σ, Z+x σ] according to following formula

In the formula: Z is the process average of the data of monitoring information;

σ is the standard deviation of the data of monitoring information.

3) outer control limit [VCL, HCL] and inner control limit [LCL, the UCL] formation " two control limit " that combines, bridge structure is assessed and reported to the police as criterion:

After inside and outside control limit was all determined, control chart promptly designed and finishes, and can be used to monitor the mobile load effect and the deteriorating effect change in information situation of bridge each point structural response.In case the value of control chart statistic exceeds the scope of inner control limit [LCL, UCL], i.e. expression process has sign out of control, can carry out elementary early warning; And after in case the value of statistic surmounts inner control limit [LCL, UCL], surmount outer control limit [VCL, HCL] fast, reflected that then the Structure Safety for Bridge state broken balance, at this moment need to provide security alarm information.Show great attention to the ruuning situation of bridge, and take further emergency measure.

Said method verifies that evaluation result is as follows in engineering reality:

1. the evaluation result of transient information control chart

Below be the result that certain big bridge portion measuring point amount of deflection and strain transient information are estimated with the EWMA control chart.When the transient information of mid-span deflection measuring point n5 and s5 is set up control chart, analysis and iterative computation by process that its historical information is constituted, can obtain optimum minimum offset is d=1.5 σ, thereby determine that according to Fig. 2 to Fig. 5 the value of λ is 0.21, the value of k is 3.4, and calculate resulting [HCL, VCL] according to the reliability of bridge structure standard is [4.32,4.32].So far, the control chart design that is used for the bridge structure safe evaluation finishes, and it can be used for practical application.

In order to simulate the situation that safety problem appears in bridge structure, with amount of deflection s5 July 1 back information add a stochastic variable that continues to increase, estimate with the EWMA control chart again.For the control limit of all the other each points, by calculating the result that also can obtain similar span centre measuring point, just because the standard deviation sigma of normal condition is different, and concrete control limit numerical value is different.

Referring to accompanying drawing 7 to 9, the control chart that is respectively the amount of deflection transient information of span centre measuring point n5, s5 among the figure is estimated situation.Can see that from evaluation result when structure was in normal condition, the value of the transient information control chart statistic of amount of deflection all dropped between the control limit.The average evaluation of increase appears continuing in Fig. 9 for the fluctuating range of simulation measuring point s5 amount of deflection transient information after July 1, as seen when safety problem appears in structure, the increase that continues also appears in the fluctuating range of the statistic of its control chart, and drops on outside the two-stage control limit.

The method for designing of the control chart of strain transient information and step are similar to amount of deflection information, just because raw information is different, its fluctuating range, standard deviation, the maximum parameter such as skew that allows are also different, thereby the width that the control corresponding of control chart is limit is different.

Because the influence factor of strain is various, and influence mode is very complicated, and strain is local parameter, dynamic load and other factors effect under, the situation of change of each cross section measuring point strain is different, but comparatively speaking, the situation of change of the same aspect in same cross section (upper limb or lower edge) strain is more consistent, so the design of the control chart of this bridge structural strain should be carried out according to the concrete condition in each cross section, consider the deployment scenarios of lower edge measuring point on each cross section respectively, and finish design by the design procedure of control chart.

Below be that lower edge measuring point 20 and O cross section upper limb measuring point 30 to above-mentioned bridge girder section IV ' began to have designed control corresponding figure to the transient information at 2 noon of July June 25, and carry out the situation of safety evaluation, referring to accompanying drawing 10 to 12.The λ of each control chart=0.18, k=3.4.

As seen from the figure, the same aspect in same cross section, the controlled quentity controlled variable of the control chart of two measuring points changes similar, and the cross section is not simultaneously, the fluctuation situation of controlled quentity controlled variable is obviously different.When structure was in normal condition, the value of controlled quentity controlled variable all dropped between the control limit.

Equally, for the situation of safety problem appears in model configuration, begin to add a stochastic variable that continues to increase at measuring point 30 in 20: 30 afternoon of July 1, its evaluation result is referring to accompanying drawing 12.As we can see from the figure, along with the adding that adds stochastic variable, the value fluctuating range of controlled quentity controlled variable constantly increases, and exceeds the control limit rapidly.Count from the interval of the minimum offset that occurs setting this moment and have only 6 points.As seen, control chart has preferable performance.

2. the evaluation result of deteriorating effect control chart

The control chart design of deteriorating effect information is similar to preceding method.Below be evaluation result, referring to accompanying drawing 13,14 to the deteriorating effect information of mid-span deflection measuring point s5 and IV ' cross section strain measuring point 20.The k value of inner control limit that can controlled figure through search be [3.1,3.1], and the value of λ is 0.25, and controlling the k value of limitting outward still is [4.32,4.32].Wherein, horizontal ordinate is the sampling instant by benchmark effect (subtrahend) in the effect difference.Δ y _AmWith Δ S _AmRepresent deterioration amount of deflection difference and strain differential in 12 hours respectively.As can be seen from the figure, when structure was in normal condition, the value of statistic all dropped in the inner control limit [LCL, UCL].

For further improving the accuracy of the EWMA control chart method safe early warning of bridge structure safe early warning of the present invention, value as the real-time monitoring information control chart of structure statistic reaches inner control limit [LCL, UCL] or outer control limit [VCL, HCL] 80% when above, alteration trend characteristic WRI index and RSI index by real-time monitoring information are carried out secondary or three assessments, and judge whether to send elementary early warning or security alarm (described alteration trend characteristic WRI index and RSI index come down to the unidirectional intensity of variation of monitored parameters in the time period, can estimate Structure Safety for Bridge equally by quantitative test) according to assessment result.

Concrete operations are as follows:

Directly reach or when surmounting inner control limit [LCL, UCL] or outer control limit [VCL, HCL], directly send elementary early warning or security alarm as the value of the real-time monitoring information control chart of structure statistic.

Value as the real-time monitoring information control chart of structure statistic reaches inner control limit [LCL, UCL] or outer control limit [VCL, HCL] 80% when above, alteration trend characteristic WRI index and RSI index by real-time monitoring information are carried out secondary evaluation, if-25＜WRI (h)＜125, then do not send elementary early warning or security alarm, otherwise, elementary early warning or security alarm then sent.

Value as the real-time monitoring information control chart of structure statistic reaches inner control limit [LCL, UCL] 80% when above, alteration trend characteristic WRI index and RSI index by real-time monitoring information are carried out three assessments, when assessment result satisfy condition simultaneously-when 25＜WRI (h)＜125 and 45≤RSI (h)≤55, then do not send elementary early warning; If wherein arbitrary condition does not satisfy, then send elementary early warning.

The alteration trend characteristic WRI index of the real-time monitoring information of bridge structure safe is meant that the current fluctuating range of data of real-time monitoring information accounts for the percentage of its last cycle maximum fluctuation amplitude, used the William's index technology in the securities market technical Analysis index, concrete computing method are:

$\mathrm{WRI}\left(h\right)=\frac{Z_{\max }-Z}{Z_{\max }-Z_{\min }}\&times;100$

In the formula: Z _MaxThe maximal value of data in the last cycle for real-time monitoring information;

Z _MinFor the data of real-time monitoring information in the last cycle minimum value;

Z is the current numerical value of the data of real-time monitoring information;

H is actual measurement data result's the interior measuring point quantity of Cycle Length;

Wherein, the maximal value Z of data in the last cycle of real-time monitoring information _MaxWith minimum value Z _MinBe respectively measuring point in the last cycle and count maximal value and the minimum value that h deducts amplitude behind the current detection point m measuring point, the m value can be 3～6.

The alteration trend characteristic RSI index of the real-time monitoring information of bridge structure safe is meant that the unidirectional undulate quantity of data in certain one-period of real-time monitoring information accounts for the relative percentage of total undulate quantity, and concrete computing method are:

$\mathrm{RSI}\left(h\right)=\frac{A}{A+B}\&times;100$

In the formula: A is the summation of data positive dirction recruitment in one-period of real-time monitoring information;

B is the summation of data negative direction recruitment absolute value in one-period of real-time monitoring information;

Wherein: $A=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}|Z_i-Z_{i-1}|,$ And Z _i-Z _I-1〉=0

$B=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}|Z_i-Z_{i-1}|,$ And Z _i-Z _I-1＜0

In the formula: Z _iI the value of data in one-period for this real-time monitoring information;

Z _I-1I-1 the value of data in one-period for this real-time monitoring information;

I is the value number of data in one-period of real-time monitoring information;

I is a positive integer.

In the EWMA control chart method of bridge structure safe early warning of the present invention, when the value of the real-time monitoring information control chart statistic of bridge structure safe reaches inner control limit [LCL, UCL] or outer control limit [VCL, HCL] more than 80%, here it needs to be noted: at different bridge structures, the critical value of ratio that the value of the real-time monitoring information control chart statistic of the bridge structure safe of choosing accounts for inside and outside control limit is also different, the bridge comparatively robust that has, the time of operation is shorter, so just can establish this critical value highlyer, such as 90% or 95%; And the time of the bridge that has operation is long, and structure is relatively more severely aging, just can establish critical value lowlyer to this bridge so, such as 80% or 85%; The benefit of doing like this is, for firmer bridge structure, can reduce the situation that false alarm takes place as far as possible, to frailish bridge structure, then would rather report by mistake also and not fail to report.

Claims (4)

1. the EWMA control chart method of a bridge structure safe early warning, it is characterized in that: all configuration state information of obtaining at the bridge structure safe monitoring system, adopt the EWMA control chart to set up the elementary early warning limit and the security alarm limit of bridge structure safe, bridge structure is assessed and reported to the police as criterion;

Wherein, limit as criterion with elementary early warning limit and security alarm, bridge structure is assessed and reported to the police, comprise: the inner control limit [LCL, UCL] of EWMA control chart is elementary early warning limit, outer control limit [VCL, HCL] be that security alarm is limit, when the value of the real-time monitoring information control chart statistic of bridge structure surpasses inner control limit [LCL, UCL], send elementary early warning; When surmounting outer control limit [VCL, HCL], send security alarm as the value of real-time monitoring information control chart statistic;

(1) computing method of the inner control of described EWMA control chart limit [LCL, UCL] comprising:

(1) historical information of arbitrary real-time monitoring parameter of bridge structure is set up a stochastic process, is expressed as:

In the formula: i is a positive integer;

Z _iI the value of data in the cycle for this monitoring information;

Process average for the data of this monitoring information;

ξ _iParameter for random variation;

(2) determine σ, d and ARL ₀Value

Data to monitoring information are analyzed, and calculate the standard deviation sigma of these data and minimum offset d=η σ (wherein | η |≤1); Again according to the actual conditions of bridge structure and the specific requirement of evaluation, choose 10 times～20 times of cycle basic time of data variation, as the average operation duration ARL that false alarm does not take place in the section between at a time ₀(Average Run Length);

(3) determine the value of λ and k

By look-up table, from the optimum λ curve map of EWMA control chart and EWMA control chart, (λ, k) build-up curve figure determines the value of λ and k;

(4) value of optimization λ and k

According to the actual conditions of bridge structure monitoring, set up an iterative process, by the variation search of d value optimum (λ k) makes up, and makes the probability of mistake activating alarm of monitored process and the error minimum of predetermined probability;

(5) try to achieve the upper and lower limit of the inner control limit of EWMA control chart according to following formula:

In the formula: n is the size of sample subclass, n=ARL ₀/ Δ t, Δ t are sampling interval;

(2) outer control limit [VCL, HCL] computing method of described EWMA control chart comprise:

(1) RELIABILITY INDEX that provides according to the reliability of bridge structure standard can obtain the permissible value P of structural failure probability _f

(2) limit coefficient [x, x], (x＞0) according to the outer control of following formula calculating EWMA control chart;

(3) determine outer control limit according to following formula:

In the formula:

Process average for the data of monitoring information;

σ is the standard deviation of the data of monitoring information.

2. according to the EWMA control chart method of the described bridge structure safe early warning of claim 1, it is characterized in that: on the basis as criterion with elementary early warning limit and security alarm limit, further combined with the alteration trend characteristic WRI index of monitoring information and secondary or three assessment results of RSI index, again bridge structure is assessed and reported to the police, it comprises: the value as the real-time monitoring information control chart of structure statistic reaches inner control limit [LCL, UCL] or outer control limit [VCL, HCL] 80% when above, alteration trend characteristic WRI index and RSI index by real-time monitoring information are carried out secondary or three assessments, and judge whether to send elementary early warning or security alarm according to assessment result; When the real-time monitoring information state value of bridge structure reaches inner control limit [LCL, UCL], directly send elementary early warning.

3. according to the EWMA control chart method of the described bridge structure safe early warning of claim 2, it is characterized in that: the value as the real-time monitoring information control chart of structure statistic reaches inner control limit [LCL, UCL] or outer control limit [VCL, HCL] 80% when above, alteration trend characteristic WRI index and RSI index by real-time monitoring information are carried out secondary evaluation, comprising: if-25＜WRI (h)＜125, then do not send elementary early warning or security alarm, otherwise, then send elementary early warning or security alarm;

Wherein, the alteration trend characteristic WRI index of the real-time monitoring information of bridge structure safe is meant that the current fluctuating range of data of real-time monitoring information accounts for the percentage of its last cycle maximum fluctuation amplitude, and concrete computing method are:

In the formula: Z _MaxThe maximal value of data in the last cycle for real-time monitoring information;

Z _MinFor the data of real-time monitoring information in the last cycle minimum value;

Z is the current numerical value of the data of real-time monitoring information;

H is actual measurement data result's the interior measuring point quantity of Cycle Length;

Wherein, the maximal value Z of data in the last cycle of real-time monitoring information _MaxWith minimum value Z _MinBe respectively measuring point in the last cycle and count maximal value and the minimum value that h deducts amplitude behind the current detection point m measuring point, the m value can be 3～6.

4. according to the EWMA control chart method of the described bridge structure safe early warning of claim 2, it is characterized in that: the value as the real-time monitoring information control chart of structure statistic reaches inner control limit [LCL, UCL] 80% when above, alteration trend characteristic WRI index and RSI index by real-time monitoring information are carried out three assessments, comprise: when assessment result satisfy condition simultaneously-when 25＜WRI (h)＜125 and 45≤RSI (h)≤55, then do not send elementary early warning; If wherein arbitrary condition does not satisfy, then send elementary early warning;

Wherein, 1) the alteration trend characteristic WRI index of the real-time monitoring information of bridge structure safe is meant that the current fluctuating range of data of real-time monitoring information accounts for the percentage of its last cycle maximum fluctuation amplitude, and concrete computing method are:

In the formula: Z _MaxThe maximal value of data in the last cycle for real-time monitoring information;

Z _MinFor the data of real-time monitoring information in the last cycle minimum value;

Z is the current numerical value of the data of real-time monitoring information;

H is actual measurement data result's the interior measuring point quantity of Cycle Length;

Wherein, the maximal value Z of data in the last cycle of real-time monitoring information _MaxWith minimum value Z _MinBe respectively measuring point in the last cycle and count maximal value and the minimum value that h deducts amplitude behind the current detection point m measuring point, the m value can be 3～6;

2) the alteration trend characteristic RSI index of the real-time monitoring information of bridge structure safe is meant that the unidirectional undulate quantity of data in certain one-period of real-time monitoring information accounts for the relative percentage of total undulate quantity, and concrete computing method are:

In the formula: A is the summation of data positive dirction recruitment in one-period of real-time monitoring information;

B is the summation of data negative direction recruitment absolute value in one-period of real-time monitoring information;

Wherein:

And Z _i-Z _I-1〉=0

And Z _i-Z _I-1＜0

In the formula: Z _iI the value of data in one-period for this real-time monitoring information;

Z _I-1I-1 the value of data in one-period for this real-time monitoring information;

I is the value number of data in one-period of real-time monitoring information;

I is a positive integer.

Images