CN101382473A - 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

Due to bridge structure itself and the complicacy of environment of living in and the singularity of safety appraisement of structure, there is larger limitation in existing safety appraisement of structure method, fails to obtain gratifying progress in practical application, be mainly reflected in following some:

(1) the 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 definite system incentive; Yet the continuous variation in operational process of the serious disappearance of old bridge data and bridge structure parameter makes the foundation of structure accurate model very difficult, the not intellectual that adds random environment excitation in bridge structural health monitoring, makes the safety appraisement of structure based on model run into the obstacle that is difficult to go beyond.

(2), though the evaluation method based on statistical study has obtained attention progressively, its research and application are still in the initial stage; Bridge enormous size, complex structure, vibration amplitude is very low, common the adopted dynamic characteristics 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 cannot engineering demands.

(3) although neural network has good performance when processing nonlinear problem, owing to lacking complete training sample, cannot between structural response and safe condition, set up effective causal relation.

(4) current safety evaluation mostly adopts single method or single parameter to analyze, 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, makes also not have at present a kind of gratifying bridge security overall evaluation system.

From the above analysis, because the formation of bridge structure itself is very complicated, its performance is easily subject to the impact of the various factors of structure environment of living in, and the appraisal that makes structural safety is very complicated and difficult also.Although the evaluation method for bridge structure safe has much at present, due to a variety of causes, these evaluation methods have itself intrinsic defect, in practical application, not yet achieve satisfactory results.

Along with deepening continuously of bridge structure monitoring system application, 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, because excitation is unknown, while utilizing traditional method that has model to evaluate, will run into great obstacle.Therefore, according to this outstanding feature, how by the statistical study to this mass data, therefrom extract the characteristic information of related structure safety, the development law of mining structure performance, the effective evaluation of implementation structure safety, more and more obtains people's attention.Due to not accurate model and the known excitation of Structure of need of its evaluation procedure, there is versatility widely, and the mixing together that it processes subject and branch of mechanics for signal provides fabulous opportunity.Therefore there is important learning value and realistic meaning.

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

EWMA control chart is a kind of in conventional control chart, has now been widely used in the 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 nearer historical information of adjusting the distance gives larger weight, and distance information far away is given less weight.This feature is applicable to describing the Evolution of bridge structure response mobile load effect information and deteriorating effect information very much.

EWMA control chart is defined as follows:

To a certain average, be

, the statistic processes that standard deviation is 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 positive integer; λ is smoothing parameter, and 0< λ≤1;

it is i group observations; Z ₀for initial value.

Weight distribution feature according to EWMA control chart statistic, can obtain its statistical nature: establishing each got sample size is n, and the mathematical expectation E of statistic Z (Z) is:

$E\left(Z\right)=E\left(\stackrel{\&RightArrow;}{X}\right)=\stackrel{\&OverBar;}{Z}$

The variance D of statistic Z (Z) is:

$D\left(Z\right)=\frac{\mathrm{\&lambda;}}{n(2-\mathrm{\&lambda;})}[1-{(1-\mathrm{\&lambda;})}^{2i}]D\left(\stackrel{\&RightArrow;}{X}\right)$

Standard deviation sigma _rfor:

${\mathrm{\&sigma;}}_R=\sqrt{D\left(Z\right)}=\frac{\mathrm{\&sigma;}}{\sqrt{n}}\sqrt{\left(\frac{\mathrm{\&lambda;}}{2-\mathrm{\&lambda;}}\right)[1-{(1-\mathrm{\&lambda;})}^{2i}]}$

The control of EWMA control chart is limited to:

$\mathrm{UCL}=\stackrel{\&OverBar;}{Z}+k{\mathrm{\&sigma;}}_R=\stackrel{\&OverBar;}{Z}+k\frac{\mathrm{\&sigma;}}{\sqrt{n}}\sqrt{\left(\frac{\mathrm{\&lambda;}}{2-\mathrm{\&lambda;}}\right)[1-{(1-\mathrm{\&lambda;})}^{2i}]}$

$\mathrm{LCL}=\stackrel{\&OverBar;}{Z}-k{\mathrm{\&sigma;}}_R=\stackrel{\&OverBar;}{Z}-k\frac{\mathrm{\&sigma;}}{\sqrt{n}}\sqrt{\left(\frac{\mathrm{\&lambda;}}{2-\mathrm{\&lambda;}}\right)[1-{(1-\mathrm{\&lambda;})}^{2i}]}$

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

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

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

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

Wherein: λ and k are the controlled ARL of procurement process (Average Run Length: parameter average run length), the size that n is sample set: the at this moment control of EWMA control chart 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 for bridge structure safe monitoring system, adopt EWMA control chart to set up elementary early warning limit and the security alarm limit of bridge structure safe, as criterion, bridge structure assessed and reported to the police.

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

Usining on the basis of elementary early warning limit and security alarm limit as criterion, further combined with the alteration trend characteristic WRI index of monitoring information and the secondary of RSI index or three assessment results, again bridge structure assessed and reported to the police, it comprises: as the value of structure Real-Time Monitoring information control chart statistic reaches interior control limit [LCL, UCL] or the outer limit [VCL that controls, 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 interior control limit [LCL, UCL], directly send elementary early warning.

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

(1) historical information of arbitrary Real-Time Monitoring parameter of bridge structure is set up to a stochastic process, is expressed as:

Z _i＝

+ξ _i

In formula: i is positive integer;

Z _ifor the data of this monitoring information i value within the cycle;

process Mean for the data of this monitoring information;

ξ _iparameter for random variation;

(2) determine σ, d and ARL ₀value

Data analysis to monitoring information, calculates the standard deviation sigma of these data and minimum offset d=η σ (wherein | η |≤1); Again according to the specific requirement of the actual conditions of bridge structure and evaluation, choose 10 times～20 times of cycle basic time of data variation, as the average operation duration ARL of false alarm does not occur in 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, determine the value of λ and k;

(4) optimize the value of λ and k

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

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

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

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

In formula: the size that n is sample set, n=ARL ₀/ Δ t, Δ t is sampling interval.

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

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

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

$P_f=2\&CenterDot;\frac{1}{\sqrt{2\mathrm{\&pi;}}}{\&Integral;}_{-\&infin;}^{-x}{e}^{\frac{-{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A200810232825E00182.png,A200810232825E00183.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}{2}}\mathrm{dt}$

(3) according to following formula, determine the outer limit of controlling: [VCL, HCL]=[

-x σ,

+ x σ]

In formula:

process Mean for the data of monitoring information;

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

The value of aforesaid structure Real-Time Monitoring information control chart statistic reaches interior control limit [LCL, UCL] or the outer limit [VCL that controls, 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 (n) <125, do not send elementary early warning or security alarm, otherwise, elementary early warning or security alarm sent.

The aforesaid value as structure Real-Time Monitoring information control chart statistic reaches interior 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 simultaneously satisfy condition-25<WRI of assessment result (n) <125 and 45≤RSI (n)≤55, do not send elementary early warning; If wherein arbitrary condition does not meet, send elementary early warning.

Wherein, the alteration trend characteristic WRI index of the Real-Time Monitoring information of bridge structure safe refers to that the current fluctuating range of data of Real-Time Monitoring information accounts for the percentage of its last cycle maximum fluctuation amplitude, and circular is:

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

In formula: Z _maxfor the data of the Real-Time Monitoring information maximal value within the last cycle;

Z _minfor the data of Real-Time Monitoring information within the last cycle minimum value;

Z is the current value of the data of Real-Time Monitoring information;

N is the measuring point quantity in the Cycle Length of actual measurement data result;

Wherein, the maximal value Z of the data of Real-Time Monitoring information within the last cycle _maxwith minimum value Z _minbe respectively measuring point in the last cycle and count n and deduct apart from maximal value and the minimum value of amplitude after a current detection point m measuring point, m value can be 3～6.

The unidirectional undulate quantity of the data that the alteration trend characteristic RSI index of the Real-Time Monitoring information of bridge structure safe refers to Real-Time Monitoring information within a certain cycle accounts for the relative percentage of total undulate quantity, and circular is:

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

In 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 formula: Z _ifor the data of this Real-Time Monitoring information i value in one-period;

Z _i-1for the data of this Real-Time Monitoring information i-1 value in one-period;

I is the data of the Real-Time Monitoring information value numbers in one-period;

I is positive integer.

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

Accompanying drawing explanation

Accompanying drawing 1, bridge structural state schematic 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, the search procedure block diagram of optimum (λ, k) combination;

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, the 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, the simulation that strain 30 is out of control and evaluation map;

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 accompanying drawing, Fig. 2 to Fig. 5 is (λ, k) build-up curve figure, is and quotes 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 the time-domain information of the structural response that wavelet analysis and regretional analysis can collect bridge health monitoring system to be separated into independently deteriorating effect information and mobile load effect information.Wherein, deteriorating effect message reflection the slow variation tendency of structural behaviour, mobile load effect information has 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 mobile load effect information and the deteriorating effect information of monitoring of structures parameter, the effectively security situation of monitoring of structures.Due to the randomness of live load and the stochastic error of temperature effect rejecting process, mobile load effect information and the deteriorating effect information of structural response are all random variation, and in structure during in normal condition, its mean approximation is a constant, can regard respectively a stochastic process as, be equivalent to the controlled change of statistic processes; And when safety problem appears in structure, its numerical value is by the unidirectional variation (increase or reduce) that occurs continuing, and its fluctuating range will continue to increase, and depart from equilibrium point (being average), 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 change procedure of the mobile load effect information of the bridge structure of each measuring point and deteriorating effect information be monitored the distribution according to the statistic of each data point on control chart, whether deterministic process is out of control, thereby completes the safety evaluation of structure.

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

When concrete structure EWMA control chart, first the historical information of the mobile load effect of bridge structure and deteriorating effect is formed respectively to a stochastic process z={z ₀, z ₁, z ₂..., z _n... }, be expressed as: Z _i=μ+ξ _i, μ is Process Mean, ξ _ifor the parameter of random variation, (when structure is during in normal condition, μ is constant, ξ _ibe random variation, whole process does not have obvious trend.When there is damage or having safety problem in structure, Z _iamplitude of variation continue to increase, there is the expendable unidirectional variation tendency continuing in Process Mean; Therefore, by the statistical study to this process, monitor this Process Mean and whether occur expendable unidirectional variation tendency, can evaluate the security situation of bridge structure).

Embodiment 1:

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

Take amount of deflection as example, and under normal circumstances, concrete shrinkage and creep effect mainly occurs in the First Year that bridge builds up, and therefore, for becoming the bridge of bridge after 1 year, this factor can be ignored.So, in the situation that not considering unexpected disaster, on 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 _vfor the amount of deflection that the hydraulic performance decline of structure own causes, this value is approximately 0 under normal condition; y _mvertical deflection for live load generation; y _tfor temperature affects the amount of deflection producing.

The deteriorating effect that the action effect (structural response) of girder point is mainly caused by temperature effect, mobile load effect and structural damage or performance change forms.Therefore, above 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) are also the functions of time, and the structural response therefore being caused by them can be expressed as:

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 formula, z _v(t) be structure deterioration effect, only relevant with structural behaviour variation, z _t(t) be temperature effect, by structure temperature and thermal expansivity, determined z _m(t) be mobile load effect, change relevant with live load and structural behaviour.Visible, the structural response information relevant with structural behaviour V parameter (t) only has deteriorating effect z _vand mobile load effect z (t) _m, and the variation of temperature effect and structural behaviour is irrelevant (t).

Temperature effect z _t(t) mainly by Sunshine Temperature Difference Effect, abrupt temperature drop and Seasonal Temperature Difference, caused, its main time scale is 1 day and 1 year.In being less than the time span of 1 year, can be further organized as cycle changing unit z _t1with changing unit z non-periodic _t2.That 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.Therefore 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 by abrupt temperature drop and Nian Wen, changed and partially restrained causes, it changes the length of span in time and season and difference, 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 obtaining also constantly increases, and it can be considered as to a process.Due to the cyclical variation feature 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:

$z_M\left(t\right)=f_3[V\left(t\right),P(x,t)]=\underset{k=<{\mathrm{<figure-callout\; id="0"\; label="N"\; filenames="A200810232825E00183.png,A200810232825E00191.png"\; state="\{\{state\}\}">N</figure-callout>}}_0>}{\mathrm{\&Sigma;}}{c}_k\&CenterDot;\exp (\mathrm{<figure-callout\; id="2"\; label="jk"\; filenames="A200810232825E00182.png,A200810232825E00183.png"\; state="\{\{state\}\}">jk</figure-callout>}2\mathrm{n\&pi;}/N_0)$

K=<N in formula ₀> represents that summation only need comprise N ₀, desirable k=0,1,2 ..., N ₀-1; c _kfor the coefficient of each harmonic component, by concrete load situation, determined; N represents the time.Visible mobile load effect itself has the formation feature of Spatial multi scale.

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

as time goes on will occur lasting decline, similarly changing also will appear in its elastic modulus E.To there is a unidirectional variation tendency in the V parameter (t) that is to say reflect structure performance change.Therefore,, when structure is normal, because V (t) is constant, mobile load effect is by only by live load P _ndetermine.And live load is random variation, the effect that it causes must be carried out fluctuation up and down by a small margin around some equilibrium points, and when live load disappears, girder returns to its normal state, and equilibrium point is now the average of process.

And there is damage when structure, and for example, during Damages in Stay Cables, its sectional area A _nor elastic modulus E _gcontinue to reduce, therefore the inevitable continuous decrease of the elasticity coefficient K of girder, the effect now being caused by live load is inevitable constantly to be increased, and finally departs from the equilibrium point of normal condition.Equally, when not damage of drag-line, and main beam structure is while having damage, the elastic modulus E of girder _gthere is lasting reducing, therefore also can cause the action effect under mobile load constantly to increase.And even if 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 that whether structure is in a safe condition.

In like manner, structural behaviour is changed to caused deteriorating effect z _v(t), in structure during in normal condition, because V (t) is constant, its variation is almost 0, but due to the impact 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 Process Mean is a fixing constant; And when damage or safety problem appear in structure, unidirectional variation tendency appears in V (t), under the effect of dead load, structural response will have an expendable growth slowly.Therefore, as long as this process of monitoring is not constant value in the average of a certain setting cycle, but there is unidirectional expendable trend, can judge that structure has entered unsafe condition.

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

Z _i＝

+ξ _i

In formula,

for Process Mean, ξ _iparameter for random variation.

Referring to accompanying drawing 1, when structure is during in normal condition,

constant, ξ _ibe random variation, whole process does not have obvious trend.When there is damage or having safety problem in structure, Z _iamplitude of variation continue to increase, there is the expendable unidirectional variation tendency continuing in Process Mean.Therefore, by the statistical study to this process, monitor this Process Mean and whether occur expendable unidirectional variation tendency, can evaluate the security situation of bridge structure.

Obtain mobile load effect and the deteriorating effect information of structural response, can design the EWMA control chart of response, according to the statistic of each information, drop on and control the inside and outside situation deterministic process of limit whether in normal range, thereby realize the safety evaluation to bridge construction.For obtaining optimum evaluation effect, the present invention adopts " optimum control limit " in conjunction with the method for designing based on reliability of bridge structure standard.Control [the VCL of the fiduciary level proper calculation of conjugative bridge girder construction, 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 used separately, due to after structural damage and do not reach in this period of time of inefficacy without any warning information, there is the situation of leaking activating alarm, likely can incur loss through delay correct diagnosis and the impact of structure and safeguard decision-making, even can cause more serious consequence; And " optimum control limit " [LCL, UCL] actual conditions while being normal according to process determine, it requires process to occur carrying out as early as possible alarm after unusual fluctuations, therefore its control range line from the statistic of normal condition close to, its width is than [VCL, HCL] smaller, if used separately, due to the complicacy of bridge structure environment of living in and the uncertainty of influence factor, likely appear at that structure is not damaged and have the situation of controlling limit that surpasses during statistic, miss activating alarm, and improved thus the cost of process monitoring, reduced the Monitoring Performance of control chart.So for fear of the defect of a certain control limit of independent use, the present invention adopts two kinds to control the method that limit combines, adopt two-stage alarming mechanism: when the statistic of control chart surpasses [LCL, UCL] scope time, just provide elementary early warning, remind supvr to note; When statistic surmounts two-stage, control in limited time, just provide security alarm, now must show great attention to the ruuning situation of bridge structure, and make further examination and maintenance decision-making.At this, [LCL, UCL] can be described as interior 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 interior control limit [LCL, UCL] of EWMA control chart, comprising:

(1) historical information of arbitrary Real-Time Monitoring parameter of bridge structure is set up to a stochastic process, is expressed as:

Z _i＝

+ξ _i

In formula: i is positive integer;

Z _ifor the data of this monitoring information i value within the cycle;

process Mean for the data of this monitoring information;

ξ _iparameter for random variation;

(2) determine σ, d and ARL ₀value

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

ARL ₀definite be to carry out according to the specific requirement of the actual conditions of bridge structure and evaluation.For this large scale structure of bridge, the cost causing due to its monitoring system mistake activating alarm is relatively high, therefore in structure, during in normal condition, wishes not occur in a long time the situation of mistake activating alarm.The monitoring of the Chongqing Coriaria sinica small stream Yangtze Bridge of take is example, and structure measurement information is to gather once for every ten minutes, and a certain measurement point for structure, just has 144 data points within one day.For this reason, ARL ₀may be selected to be 2000 points, mistake activating alarm does not occur 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, determine 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.D determines that need to consider security of system requires the maximum offset allowing, and is finally expressed as the size of d the multiple of normal observation sample standard deviation σ.Once 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) optimize the value of λ and k

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

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

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

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

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

In formula: the size that n is sample set, n=ARL ₀/ Δ t, Δ t is sampling interval.

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

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

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

$P_f=2\&CenterDot;\frac{1}{\sqrt{2\mathrm{\&pi;}}}{\&Integral;}_{-\&infin;}^{-x}{e}^{\frac{-{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A200810232825E00182.png,A200810232825E00183.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}{2}}\mathrm{dt}$

(3) according to following formula, determine the outer limit of controlling: [VCL, HCL]=[

-x σ,

+ x σ]

In formula:

process Mean for the data of monitoring information;

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

3) control the formation " dual control system limit " that combines of limit [VCL, HCL] and interior control limit [LCL, UCL] outward, as criterion, bridge structure assessed and reported to the police:

After inside and outside control limit is all determined, control chart designs complete, can be used to monitor the mobile load effect of bridge each point structural response and the situation of change of deteriorating effect information.Once the value of control chart statistic exceeds the scope of interior control limit [LCL, UCL], i.e. expression process has sign out of control, can carry out elementary early warning; Once and the value of statistic surmounts after interior control limit [LCL, UCL], surmount fast again outer control limit [VCL, HCL], reflected that the safe condition of bridge structure has been 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 in engineering reality, and evaluation result is as follows:

1. the evaluation result of transient information control chart

It is below the result that certain large bridge portion measuring point amount of deflection and strain transient information are evaluated with EWMA control chart.When the transient information of mid-span deflection measuring point n5 and s5 is set up to control chart, by analysis and iterative computation to the process of its historical information formation, 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 be [4.32,4.32] according to reliability of bridge structure proper calculation resulting [HCL, VCL].So far, the control chart design of evaluating for bridge structure safe is complete, can be by it for practical application.

The situation that occurs safety problem in order to simulate bridge structure, by amount of deflection s5 July 1 below information add that continues the stochastic variable increasing, then evaluate with EWMA control chart.Control limit for all the other each points, also can obtain the result of similar span centre measuring point by calculating, and just because the standard deviation sigma of normal condition is different, and concrete control limit numerical value is different.

Referring to the control chart that is respectively the amount of deflection transient information of span centre measuring point n5, s5 in accompanying drawing 7 to 9, figure, evaluate situation.From evaluation result, can see, when structure is during in normal condition, the value of the transient information control chart statistic of amount of deflection all drops on to be controlled between limit.There is the lasting average evaluation increasing in the fluctuating range that Fig. 9 is simulation measuring point s5 amount of deflection transient information after July 1, it is visible when safety problem appears in structure, also there is the increase continuing in the fluctuating range of the statistic of its control chart, and drops on two-stage and control outside 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 parameters such as skew that allow are also different, thereby the width that the corresponding control 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, therefore the design of the control chart of this Bridge Structure strain should be carried out according to the concrete condition in each cross section, consider respectively the deployment scenarios of lower edge measuring point on each cross section, and press the design procedure complete design of control chart.

Be below that the lower edge measuring point 20 of above-mentioned Bridge beam cross section IV ' and O cross section upper limb measuring point 30 were started to have designed corresponding control chart 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.λ=0.18 of each control chart, 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 cross section is when different, the fluctuation situation of controlled quentity controlled variable is obviously different.In structure, during in normal condition, the value of controlled quentity controlled variable all drops on to be controlled between limit.

Equally, for the situation of safety problem appears in model configuration, start to add one continue the stochastic variable increasing 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 adding of additional stochastic variable, the value fluctuating range of controlled quentity controlled variable constantly increases, and exceeds rapidly control limit.Now from the interval of the minimum offset that occurs setting, count and only have 6 points.Visible, control chart has good performance.

2. the evaluation result of deteriorating effect control chart

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

For further improving the accuracy of the EWMA control chart method safety early warning of bridge structure safe early warning of the present invention, as the value of structure Real-Time Monitoring information control chart statistic reaches interior control limit [LCL, UCL] or the outer limit [VCL that controls, 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 (described alteration trend characteristic WRI index and RSI index are in fact the unidirectional intensity of variations of monitored parameters in the time period according to assessment result, to judge whether to send elementary early warning or security alarm, by quantitative test, can evaluate the safety of bridge structure equally).

Concrete operations are as follows:

When directly reaching or surmounting interior control limit [LCL, UCL] or outer control limit [VCL, HCL] as the value of structure Real-Time Monitoring information control chart statistic, directly send elementary early warning or security alarm.

As the value of structure Real-Time Monitoring information control chart statistic reaches interior control limit [LCL, UCL] or the outer limit [VCL that controls, 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 (n) is <125, do not send elementary early warning or security alarm, otherwise, elementary early warning or security alarm sent.

As the value of structure Real-Time Monitoring information control chart statistic reaches interior 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 simultaneously satisfy condition-25<WRI of assessment result (n) <125 and 45≤RSI (n)≤55, do not send elementary early warning; If wherein arbitrary condition does not meet, send elementary early warning.

The alteration trend characteristic WRI index of the Real-Time Monitoring information of bridge structure safe refers to 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 securities market technical Analysis index, circular is:

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

In formula: Z _maxfor the data of the Real-Time Monitoring information maximal value within the last cycle;

Z _minfor the data of Real-Time Monitoring information within the last cycle minimum value;

Z is the current value of the data of Real-Time Monitoring information;

N is the measuring point quantity in the Cycle Length of actual measurement data result;

Wherein, the maximal value Z of the data of Real-Time Monitoring information within the last cycle _maxwith minimum value Z _minbe respectively measuring point in the last cycle and count n and deduct apart from maximal value and the minimum value of amplitude after a current detection point m measuring point, m value can be 3～6.

The unidirectional undulate quantity of the data that the alteration trend characteristic RSI index of the Real-Time Monitoring information of bridge structure safe refers to Real-Time Monitoring information within a certain cycle accounts for the relative percentage of total undulate quantity, and circular is:

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

In 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 formula: Z _ifor the data of this Real-Time Monitoring information i value in one-period;

Z _i-1for the data of this Real-Time Monitoring information i-1 value in one-period;

I is the data of the Real-Time Monitoring information value numbers in one-period;

I is 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 interior control limit [LCL, UCL] or the outer limit [VCL that controls, HCL] more than 80%, here it needs to be noted: for different bridge structures, in the value of the Real-Time Monitoring information control chart statistic of the bridge structure safe of choosing accounts for, the critical value of the ratio of outer control limit is also different, some bridge comparatively robusts, the time of operation is shorter, so just can this critical value be established highlyer, such as 90% or 95%, and the time of some bridge operations is long, structure is aging must be more severe, just can critical value be established lowlyer so to this bridge, such as 80% or 85%, the benefit of doing is like this, for the bridge structure compared with firm, can reduce the situation that false alarm occurs as far as possible, to frailish bridge structure, would rather report by mistake also and not fail to report.

Claims (9)

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

2, the EWMA control chart method of bridge structure safe early warning according to claim 1, it is characterized in that: using elementary early warning limit and security alarm limit as criterion, bridge structure is assessed and reported to the police, comprise: the interior control limit [LCL, UCL] of EWMA control chart is elementary early warning limit outer control limit [VCL, HCL] be security alarm limit, when the value of the Real-Time Monitoring information control chart statistic of bridge structure surpasses interior control limit [LCL, UCL], send elementary early warning; While surmounting outer control limit [VCL, HCL] as the value of real-time monitoring information control chart statistic, send security alarm.

3, the EWMA control chart method of bridge structure safe early warning according to claim 2, it is characterized in that: usining on the basis of elementary early warning limit and security alarm limit as criterion, further combined with the alteration trend characteristic WRI index of monitoring information and the secondary of RSI index or three assessment results, again bridge structure assessed and reported to the police, it comprises: as the value of structure Real-Time Monitoring information control chart statistic reaches interior control limit [LCL, UCL] or the outer limit [VCL that controls, 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 interior control limit [LCL, UCL], directly send elementary early warning.

4, the EWMA control chart method of bridge structure safe early warning according to claim 2, is characterized in that: the computing method of the interior control limit [LCL, UCL] of EWMA control chart, comprising:

(1) historical information of arbitrary Real-Time Monitoring parameter of bridge structure is set up to a stochastic process, is expressed as:

Z _i＝

+ξ _i

In formula: i is positive integer;

Z _ifor the data of this monitoring information i value within the cycle;

process Mean for the data of this monitoring information;

ξ _iparameter for random variation;

(2) determine σ, d and ARL ₀value

Data analysis to monitoring information, calculates the standard deviation sigma of these data and minimum offset d=η σ (wherein | η |≤1); Again according to the specific requirement of the actual conditions of bridge structure and evaluation, choose 10 times～20 times of cycle basic time of data variation, as the average operation duration ARL of false alarm does not occur in 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, determine the value of λ and k;

(4) optimize the value of λ and k

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

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

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

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

In formula: the size that n is sample set, n=ARL ₀/ Δ t, Δ t is sampling interval.

5, the EWMA control chart method of bridge structure safe early warning according to claim 2, is characterized in that: outer control limit [VCL, HCL] computing method of EWMA control chart, comprising:

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

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

$P_f=2\&CenterDot;\frac{1}{\sqrt{2\mathrm{\&pi;}}}{\&Integral;}_{-\&infin;}^{-x}{e}^{\frac{-t^2}{2}}\mathrm{dt}$

(3) according to following formula, determine the outer limit of controlling: [VCL, HCL]=[

-x σ,

+ x σ]

In formula:

process Mean for the data of monitoring information;

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

6, the EWMA control chart method of bridge structure safe early warning according to claim 3, it is characterized in that: as the value of structure Real-Time Monitoring information control chart statistic reaches interior control limit [LCL, UCL] or the outer limit [VCL that controls, 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 (n) <125, do not send elementary early warning or security alarm, otherwise, send elementary early warning or security alarm.

7, the EWMA control chart method of bridge structure safe early warning according to claim 3, it is characterized in that: as the value of structure Real-Time Monitoring information control chart statistic reaches interior 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 simultaneously satisfy condition-25<WRI of assessment result (n) <125 and 45≤RSI (n)≤55, do not send elementary early warning; If wherein arbitrary condition does not meet, send elementary early warning.

8, the EWMA control chart method of bridge structure safe early warning according to claim 3, it is characterized in that: the alteration trend characteristic WRI index of the Real-Time Monitoring information of bridge structure safe refers to that the current fluctuating range of data of Real-Time Monitoring information accounts for the percentage of its last cycle maximum fluctuation amplitude, and circular is:

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

In formula: Z _maxfor the data of the Real-Time Monitoring information maximal value within the last cycle;

Z _minfor the data of Real-Time Monitoring information within the last cycle minimum value;

Z is the current value of the data of Real-Time Monitoring information;

N is the measuring point quantity in the Cycle Length of actual measurement data result;

Wherein, the maximal value Z of the data of Real-Time Monitoring information within the last cycle _maxwith minimum value Z _minbe respectively measuring point in the last cycle and count n and deduct apart from maximal value and the minimum value of amplitude after a current detection point m measuring point, m value can be 3～6.

9, the EWMA control chart method of bridge structure safe early warning according to claim 3, it is characterized in that: the unidirectional undulate quantity of the data that the alteration trend characteristic RSI index of the Real-Time Monitoring information of bridge structure safe refers to Real-Time Monitoring information within a certain cycle accounts for the relative percentage of total undulate quantity, and circular is:

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

In 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 formula: Z _ifor the data of this Real-Time Monitoring information i value in one-period;

Z _i-1for the data of this Real-Time Monitoring information i-1 value in one-period;

I is the data of the Real-Time Monitoring information value numbers in one-period;

I is positive integer.

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