CN104133960A - Improved optimal arranging method of static sensors - Google Patents

Abstract

The invention discloses an improved optimal arranging method of static sensors. The method comprises the following steps that: 1, a whole-bridge solid finite element model is built and is modified; 2, the modified model is used for building finite element damage models under n kinds of damage conditions, and stress prediction values in potential positions under each damage condition are extracted; 3, according to the measurement precision of the sensors, the stress prediction values are divided into a plurality of intervals, and damage models with the corresponding stress prediction values in the same interval are unrecognizable damage models; and intervals including the models are set into sets b<ik>, elements in the sets b<ik> are in the unrecognizable damage state, and a plurality of sets b<ik> form a set B<i>; and 4, the potential position number of each sensor is m, the number of the sensors is s, and calculation is carried out according to a formula shown in the accompanying drawing; and the number of the fewest elements in a subset is the minimum number Y<min> of the unrecognizable damage models, and the sensor arrangement corresponding to the Y<min> is the optimal sensor arrangement. The improved optimal arranging method has the advantage that the goal of distinguishing various kinds of possible damage to bridge structures to the maximum degree by using the fewest sensors can be achieved.

Description

A kind of optimization distribution method of improved static(al) sensor

Technical field

The optimization distribution method that the present invention relates to a kind of improved static(al) sensor, belongs to bridge field.

Background technology

The strainometer of test strain, stress etc. is taken into account in the displacement that in science of bridge building, adoptable static(al) sensor kind mainly contains test amount of deflection.Reason due to aspects such as economy and structure running statuses, it is impossible structurally settling too much sensor, therefore need to be optimized laying to the position of sensor, can apply the various possible degree of impairment of the minimum maximum specification configuration of sensor.

It is a major issue in bridge structural health monitoring process that the optimization of sensor is laid, in monitoring in the past, the method of taking for the information of obtaining bridge diverse location as much as possible is generally to imbed more sensor in bridge inside, yet this way can be brought following adverse consequences: the cost that, has increased monitoring system; Two, too much sensor itself also can cause adverse influence to the structure of bridge.Therefore should accomplish to use less sensor to obtain structural health information as much as possible as far as possible.

The > > of < < North China Electric Power University (Hebei) 2008 discloses a kind of sensor fault diagnosis method based on Multi-source Information Fusion, it adopts sensor to diagnosing malfunction, but the method is not the fault diagnosis for bridge, and algorithm is laid in its optimization that does not also relate to sensor, Park, jae-Hyung, Ho, Duc-Duy, Ryu, Yeon-Sun, et al.Damage detection algorithm-embedded smart sensor node system for bridge structural health monitoring[C] //Proceedings of SPIE-The International Society for Optical Engineering, 2009 (7292), this article adopts autonomous smart sensor node to analyze Prestressed Concrete Bridges health monitoring (SHM), designed the intelligent sensor node based on acceleration and impedance, set up special operating system, use intelligent sensor node to use the method for the overall situation and local mixing to carry out purpose monitoring to it, but this article does not relate to the optimization of sensor yet to be laid, Lee, Soon Gie, Yun GunJin Real-time health monitoring of bridge structures using a reference-free damage detection algorithm[C] //Proceedings of SPIE-The International Society for Optical Engineering, 2011 (7981), this article has proposed continuous real-time structure control monitoring (SHM) and a damage monitoring system, adopt WAVELET PACKET DECOMPOSITION (WPD) to set up sensitive indicator (DSI) to caused bridge damnification, adopt benchmark model correcting principle instrument and acceleration transducer for the test of monitoring system, this article has adopted correcting principle instrument and acceleration transducer, for damage detection system, and set up sensitive indicator, but its optimization that does not also relate to static(al) sensor is laid.Therefore also need the optimization of the static(al) sensor for bridge health monitoring to lay and further study.

Summary of the invention

The object of the invention is to, a kind of optimization distribution method of improved static(al) sensor is provided, it can effectively solve problems of the prior art, especially the optimization distribution method that there is no a kind of ready-made bridge static(al) sensor senses device, realizes the problem that the minimum static(al) sensor of application is farthest distinguished the various possible degree of impairment of bridge structure.

For solving the problems of the technologies described above, the present invention adopts following technical scheme: a kind of optimization distribution method of improved static(al) sensor, is characterized in that: comprise the following steps:

S1. set up the entity finite element model of full-bridge, this entity finite element model is revised;

S2. adopt the stressing conditions of bridge diverse location under the different load situation of revised entity finite element modeling, set up the finite element damage model under n kind degree of impairment, and extract the strain predicted value p at each sensor potential site i place under various degree of impairments _ij, wherein, the potential site that i is sensor, j is degree of impairment, 1≤j≤n;

S3, according to the measuring accuracy of sensor, by the stress prediction value p at sensor potential site i place _ibe divided into some intervals, the damage model of corresponding stress prediction value in same interval is can not identification of damage model; The interval that comprises two or more models is made as to set b _ik, wherein, k is can not identification of damage number, 0≤k < j; Set b _ikin element be various unrecognizable faulted conditions and a plurality of b _ikform set B _i, B _i={ b _i1∪ b _i2... ∪ b _ik;

S4, if the potential site number of each sensor is m, the number of sensor is s, calculates Y={B ₁∩ B ₂... ∩ B _s; In subset, the minimum number of number of elements is the number Y of minimum not recognizable pattern _min, Y _minthe installation position of corresponding sensor is optimum sensor and lays.

Preferably, in step S1, described revises and comprises this entity finite element model: adopt uniform design once to revise this entity finite element model.

Specifically, described employing uniform design is once revised and is comprised the following steps this entity finite element model:

X1, chooses objective function Q (x) and m parametric variable X to be revised;

X2, is divided into n level by the value of each parametric variable; The number n of described level determines according to the precision of engine request;

X3, tests according to uniform designs table and use table Selecting All Parameters horizontal combination thereof;

X4, brings the static(al) data that obtain of test at every turn and actual measurement static(al) data in objective function and error criterion function, to obtain the result of test at every turn into;

X5, each test findings relatively, obtains objective function and error criterion function parameter level hour, and the finite element model based on this parameter level i.e. revised baseline finite element model once.

Objective function Q (x) described in aforesaid step X1 is specially:

$Q\left(x\right)=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_i{\left(\frac{{\mathrm{\&epsiv;}}_i\left(X\right)-{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}_i}{{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}_i}\right)}^2$

Wherein, Q (x) is objective function, r _ifor weight coefficient, ε _i(X) be the strain value that i is ordered, mean value for i strain.

Error criterion function described in step X4 of the present invention is:

The error rate of single measuring point data:

$P\left(x_i\right)=\left|\frac{x_i-{\stackrel{\&OverBar;}{x}}_i}{{\stackrel{\&OverBar;}{x}}_i}\right|;$

The average error rate of all measuring point datas:

$P\left(x\right)=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left|\frac{x_i-{\stackrel{\&OverBar;}{x}}_i}{{\stackrel{\&OverBar;}{x}}_i}\right|;$

In formula, x _i, be respectively the measuring point data that measuring point data that finite element model calculates and field measurement obtain.

In the present invention, the experiment number of described uniform design is 3～5 times of parametric variable number.

In the optimization distribution method of aforesaid improved static(al) sensor, described also revises and comprises this entity finite element model: utilize uniform design to choose testing site and generate response surface, adopt response surface method to carry out second-order correction to this entity finite element model.

Specifically, the described uniform design that utilizes is chosen testing site generation response surface, adopts response surface method to carry out second-order correction to this finite element damage model and comprises:

A, obtains the n of bridge stray parameter variable X by uniform designs table _sindividual sample point, obtains the sample point numerical value Y of response surface objective function, Y={y by Uniform Design ₁, y ₂..., y _ns;

B, utilizes the sample point numerical value Y regretional analysis of parametric variable X and objective function to obtain the least-squares estimation value of undetermined multipliers, and then obtains response surface function;

C, is optimized response surface function, obtains response surface objective function and error criterion function parametric variable value hour, and the structural finite element model based on this parametric variable is the finite element model after bridge second-order correction.

Parametric variable X=[E described in the present invention, ρ, μ], wherein, E is modulus of elasticity of concrete, and ρ is concrete density, and μ is Poisson ratio.

The present invention also comprises: the entity finite element model according to revised full-bridge, judges the stress loss amount of its acquisition or the early warning value whether elastic modulus loss amount reaches setting.

Program Y of the present invention _minrealization:

Owing to solving Y _minprocess in, when i=s, needing the number of times of set of computations Y is C (m, s), calculated amount is huge, thereby solves Y _min, need the corresponding optimized algorithm of establishment.Because seek common ground, there is law of association, i.e. (A ∩ B) ∩ C=A ∩ (B ∩ C), so while calculating the Y of s=i+1 at every turn, can utilize the Y of s=i, with each element in the Y of s=i, intersect with the Y of s=1, by enumerating, can not repeat to calculate each element in Y, thereby save a large amount of computing times.

According to this principle, can adopt following method to realize Y _mincalculating:

Y while first calculating s=1, supposes to have m capable, and in Y, element representation is { Y ₁, Y ₂... Y _m; The number of calculating the maximal subset element in each set Yi (is expressed as Y _{i, max}) and all Y _{i, max}in minimum value (be expressed as Y _{s=k, min}), wherein, the number that s is sensor, Y is the number of recognizable pattern not, the potential site number that m is each sensor;

Secondly, the Y when Y when Y during according to s=i and s=1 intersects to calculate s=i+1, the like iteration.

Y for example ₁=B ₁∩ B ₂={ (5,6); (9,0) }, its not recognizable pattern be at most 2; And be empty set, recognizable pattern is not zero, and Y is now required.

According to above algorithm idea, the program flow diagram of establishment as shown in Figure 1.

Adopt matlab language establishment relative program to calculate, the strain value under each faulted condition that simulation is obtained, as input, obtains corresponding output.

In order to verify validity and the superiority of optimization distribution method of the present invention, inventor has carried out following test:

The preferred arrangement of the sensor based on damage identifiability is mainly divided into three large steps: the evaluation that the foundation of the foundation of bridge structure finite element model and correction, damage model and sensor are laid.

One, the foundation of bridge structure finite element model and correction

1. science of bridge building overview:

It is domestic that stone river bridge is positioned at Funing County, Qinhuangdao, in November, 2012, is open to the traffic, and starting point pile No. is K254+142, and terminal pile No. is K254+388,246 meters of total lengths.Bridge deck width is 17 meters, and clear span is 16 meters, and cross fall is 2%.Bridge is to consist of 20 meters of continuous prestressed concrete box girders after the four first freely-supporteds in hole one, totally 3 12 holes, adopt six single box single chamber case beams of trapezoidal box-type section, monolithic case beam is divided into four kinds of different cross sections, is respectively termination central sill B-B1, termination side bar B-B2, central sill C-C1 and side bar C-C2.Little case beam, wet seam and bridge floor in-situ layer all adopt concrete C50 in length and breadth.As Fig. 2, Fig. 3 are respectively longitudinal sketch and the bridge standard cross-section figure of the drawing of full-bridge, Fig. 4 is the real figure general picture of full-bridge.

Choose solid45 unit simulation C50 concrete, the constant of each unit and material properties are chosen according to the design load of Bridge Design offering of materials, and it is worth in Table 1:

Table 1 material properties

2. bridge finite element model is set up

Stone river bridge consists of 3 12 bridge beams, and each across structure and material therefor all the same, therefore only analyze a wherein bridge beam, but still set up the whole bridge that comprises bridge pier while setting up model.

The cell type that this test adopts has the three-dimensional beam element beam44 of the linear beam element beam188 of the three-dimensional of simulation girder and the wet seam of simulation, and Beam188 supports the grid in custom cross section and cross section to divide.According to the drawing of bridge, defined 4 kinds of box-type sections herein and be rendered as three-dimensional model.Beam44 unit is used for connecting girder, be a kind ofly there is the pressure of bearing, draw, the single shaft beam of bending and torsion ability.This unit allows end face node to depart from the asymmetry of position of form center and the end face structure in cross section.Beam44 unit can carry out loosening of cell node, and the rotation of J node is loosened in this test by the value of keyopt is set, to reach the actual conditions of the bridge that coincide.

To sum up, the bridge of this test is comprised of six beams, and every girder is simulated with beam188, and its springform measures Ec=3.45 * 10 ⁴mpa, hinged with beam44 unit simulation between six horizontal beams, four kinds of cross sections are self-defined figure, its model cross section is as shown in Fig. 5～Fig. 8.

Utilize the command stream of ANSYS software to set up bridge finite element model:

(1) utilize secwrite, sectype, secoffset and secread order to set up four kinds of cross sections shown in Fig. 5～Fig. 8, grid division also records cross section number; Set up simultaneously bridge pier and support cylinder cross section grid division, record cross section number;

(2) choose cell type beam188 and beam44, and elastic modulus, Poisson ratio and the density of difference definition unit type;

(3) select in the actual bridge of suitable unit definition one across node and unit, and compose upper section in corresponding position, by stretching cross section, complete the foundation of a cross-module type;

(4) on the basis of a cross-module type, by ngen and egen order, complete the foundation of all the other five cross-module types;

(5) by nsym and esym order, complete the foundation of 12 bridge beam models.

Below just completed the foundation of bridge model, totally six beams, for hereinafter narration is convenient, define and are respectively from left to right 1-6 beam.Fig. 9 is the cross-sectional view of bridge, and bridge pier and cylinder support has also all well divided grid.

Because Fig. 9 does not see the characteristic (cross fall etc.) in Chu cross section, and only need set at the corresponding bridge of pier location place degree of freedom (translation displacement and swing offset) while analyzing, therefore Figure 10 is the cross-sectional view that stone river bridge only has bridge, in this figure, can find out clearly 2% cross fall.

Figure 11 is the model of whole bridge, containing bridge pier.

As seen from Figure 11: bridge have 12 across, every 4 across being one, have 3, model consists of bridge pier and bridge, but because bridge deck width is 17 meters, full-bridge length is 240 meters, ratio is far short of what is expected, does not therefore see the inside of Chu Qiaoliang, so provided again Figure 12, Figure 12 is the partial model (containing termination) of bridge model, can be found out clearly the model of bridge by Figure 12.

3, bridge finite element model correction

First, adopt the uniform design in the present invention once to revise this entity finite element model; Secondly, on this basis, utilize uniform design to choose testing site and generate response surface, adopt response surface method to carry out second-order correction to this entity finite element model; Finally, utilize measured data to revise this entity finite element model.

Bridge finite element model correction is the correction of model being carried out based on measured data, thus the measuring error of measured data and precision larger on the impact of finite element model correction result; In order to reduce the impact of measuring error, under static load operating mode, the response of structure wants enough large, can reflect the true response under work structuring state, facilitate the measurement of measuring point data simultaneously, under considering, set following actual static load operating mode: operating mode 1:0 load, only consider in the situation of bridge deadweight, the deformation of each point of bridge structure, in the strain of 1 time bridge of operating mode as shown in figure 13; The in the situation that of operating mode 1, the stress of bridge as shown in figure 14; Shade in Figure 13 and Figure 14 represents respectively the big or small degree of stress and strain; Figure 13 and Figure 14 are strain and the stress diagraies under operating mode 1, in order to contrast with the measured data under this operating mode, thereby draw the precision of finite element model correction.Operating mode 2: the vehicle with 26 tons of gross weights carries out loading test, front axle weighs 8 tons, and axis and rear axle weight average are 9 tons; Wherein wheelspan is 1.4m, single span bridge deck width is 2.4m, during Vehicle Driving Cycle, both sides wheel tracks remains on 0.5m left and right from the distance at the edge, both sides of bridge floor, the data that when recording car and being parked in the middle of every beam, (the now strain of the generation of bridge is maximum) each sensor obtains; The in the situation that of operating mode 2, the strain of bridge as shown in figure 15; The in the situation that of operating mode 2, the stress of bridge as shown in figure 16.Shade in Figure 15 and Figure 16 represents respectively the big or small degree of stress and strain; Figure 15 and Figure 16 are strain and the stress diagraies under operating mode 2, in order to contrast with the measured data under this operating mode, thereby draw the precision of finite element model correction.

The measuring point that simultaneously the present invention is actual while measuring distributes and adopts the arrangement as shown in Figure 17～Figure 22, the position of these measuring points is respectively: the 0m of No. 2 beams, 0.6m (left side), 0.6m (right side) locate, the 5m of No. 3 beams, 10m (left side), 10m (right side), 15m place, these corresponding measuring points represent with A1, A2, A3, B1, B2, B3, B4 respectively, and these positions also can represent the strained situation of 4, No. 5 beams in symmetric position.

Two, the foundation of damage model

The potential site that the position that can lay sensor in structure is called to sensor.Suppose that structure has occurred damage in certain position, utilize above revised bridge finite element model under degree of impairment, to set up its finite element model, then obtain structure in the effect value at sensor potential site place.These effect value can be obtained by the sensor measurement at this place.The object that sensor optimization of the present invention is laid is utilized these effect value exactly, uses minimum sensor, farthest distinguishes each degree of impairment.The citation form that can simulate damage generally has area of section to reduce, unitary elasticity modulus lost, support damage sedimentation etc.

Due to the actual damage form combination of several damages often of structure, it is also impossible simulating all degree of impairments and be unrealistic.Therefore, in actual applications, can to some possible degree of impairments, carry out finite element analogy according to slip-stick artist's experience.

In the preferred arrangement of static(al) sensor, sensor must be made sensitive reaction to different degree of impairments, and, when placement sensor, the numerical value that the sensor under different simulation degree of impairments is measured should be different.Suppose under certain degree of impairment, set up the damage finite element model of structure, the prediction effect value that can obtain any sensor potential site i place is p _i, suppose that all potential sensing stations are m, all damage status are n.

Three, the evaluation that sensor is laid

The final purpose that sensor optimization of the present invention is laid is to distinguish to greatest extent each damage model predicted value.The present invention will make unrecognizable damage model decreased number be called optimal case to minimum layout scheme, with the minimum number Y of recognizable pattern not _minas objective function, in given number of probes s, minimum not recognizable pattern is counted Y _min.

The three Span Continuous free beams of take are example, and the application of method of the present invention in sensor optimization is arranged is described.Three Span Continuous free beams as shown in figure 23, often across being divided into three unit.Damage is set as wherein a certain unitary elasticity modulus lost 60%, and because unit adds up to 9, damage status amounts to 9 kinds, adds that therefore harmless situation is n=10.Suppose the damage that adopts strain transducer recognition unit.

In the situation that utilizing bridge finite element model to apply evenly load, by finite element simulation calculation, the strain predicted value obtaining under each unit nondestructive state and each damage status is as shown in table 2:

Table 2 strain prediction

Note: Biao Zhong strain unit is μ ε, 1 damages the 1 elastic modulus loss 60% of expression unit, the like.9 unit all can arrange strain transducer, therefore m=9.

Drawing unit 1 is to unit 9 under each degree of impairment and nondestructive state, and the histogram of strain predicted value p1 to p9 as shown in figure 24.

(1) damage model: the potential site that the position that can lay sensor in structure is called to sensor.Suppose that structure has occurred damage in certain position, under degree of impairment, set up its finite element model, then obtain structure in the effect value at sensor potential site place; These effect value can be obtained by the sensor measurement at this place.Due to the actual damage form combination of several damages often of structure, it is also impossible simulating all degree of impairments and be unrealistic.Therefore, in actual applications, can to some possible degree of impairments, carry out finite element analogy according to slip-stick artist's experience, also need in addition the actual load situation such as vehicle to add up, according to the cumulative effect of load, derive bridge load situation.When placement sensor, the numerical value that the sensor under different simulation degree of impairments is measured should be different.

(2) supposition, under certain degree of impairment, is set up the damage finite element model of structure.The prediction effect value that can obtain any sensor potential site i place is p _i, suppose that all potential sensing stations are m, all damage status are n.The strain value of prediction is through finite element model, the strain value producing under average load according to actual bridge.

The accuracy of identification of supposing strain transducer is 1 μ ε, each unit strain predicted value p _ijinterval demarcation interval (interval size can be determined according to sensor accuracy of identification) with 1 μ ε.Can obtain sensor potential site i place can not identification of damage model set b _ikand the element (scope that can detect according to sensor itself, hypothesis is placed in the situation of a sensor, two sensors respectively again, for example, when two sensors are set, suppose that respectively sensor is placed on each position in 9 unit, can obtain unrecognizable position element) as table 3:

Not recognizable pattern list of table 3

As can be known from Table 3: when s=1, a sensor is only set, because set B ₅in all subset elements at most and its subset elements be 2, i.e. unrecognizable damage model Y _minit is 2, so sensor is arranged in to unit 5 for the optimum layout.

When s=2, sensor can be arranged on any two positions in each position, 1 to 9 of unit.From B ₁to B ₉in appoint and to get two set and do and occur simultaneously, Y for example ₁=B ₁∩ B ₂={ (5,6); (9,0) }, its not recognizable pattern be at most 2; And be empty set, recognizable pattern is not zero.

In this experimental example, sensing station is got unit 3 and unit 5, and unit 4 waits arrangement form with unit 5 combinations, all can obtain Y _min, can be so that can not identification of damage model be zero.

Compared with prior art, the present invention, under static(al) test, can realize and utilize the farthest various possible degree of impairment of specification configuration of minimum sensor and energy, thereby better bridge be carried out to health monitoring; The present invention simultaneously revises the entity finite element model of bridge, adopt the stressing conditions of bridge diverse location under the different load situation of revised entity finite element modeling, and set up the finite element damage model under n kind degree of impairment, thereby can extract more accurately the strain predicted value p at each sensor potential site i place under various degree of impairments _ij, and then when realizing the various possible degree of impairment utilize the minimum maximum specification configuration of sensor, the quantity of the sensor calculating is also point-device.Sensor optimization distribution method principle of the present invention is clear and definite, simple to operate, has very strong practicality on science of bridge building.In addition, in the present invention, stress prediction value is divided into each interval, can not recognizing site in order to judge targetedly, and sensor measurement obtains is stress value, and in model, also can directly obtain the estimated value of stress, thereby stress prediction value is divided into each interval with respect to the repeatability of direct judgement range of predicted value, seem more direct; Meanwhile, stress prediction value is divided into each interval, has in fact also avoided the problem of interval coincidence.In addition, the present invention has verified that Uniform ity Design Method is as the obvious assay optimization method for designing of a kind of superiority, and it is feasible applying in the correction of bridge structure finite element model; Finite element model correction based on Uniform ity Design Method has advantages of that FEM (finite element) calculation number of times is few, although this method is difficult to find optimum solution, but it can utilize the shorter time to find a more correct result from efficiency, avoided iterative computation long drawback consuming time repeatedly in the large-scale finite element model makeover process of bridge; The efficiency that has improved the large-scale finite element model correction of bridge, has reduced repetitive work amount.Adopting the error rate of main measuring point after Uniform ity Design Method correction is below 10%, and most of measuring point error rate is lower than 3%, thereby can reach higher accuracy requirement, in addition, the present invention adopts uniform design to carry out model optimization, model correction has not only been improved in precision, and comprise in calculated amount and also having reduced much choosing of point, because the model optimization that further adopts response surface method to carry out on the basis of uniform Design optimization, that the adjusting point that correction is chosen based on uniform design further carries out response surface optimization, suppose not pass through the optimization prerequisite of uniform design, need so the quantity of the point revised will be considerably beyond in this, that is to say, the uniform Design optimization method of model in the present invention, not only improved the precision of model, and reduced calculated amount.The Mathematical Method that response surface method described in the present invention combines with mathematical statistics as a kind of test design, it is also feasible applying in the finite element model correction of large complicated bridge structure; Because the correction method for finite element model based on Uniform ity Design Method is just chosen less group of parameter horizontal combination and is tested, the correction result obtaining sometimes may be unsatisfactory, do not reach accuracy requirement, need to increase the precision that parameter value level improves model correction, mean and increase finite element model calculation times (one or many), reduced the efficiency of model correction; And if now finite element model is further revised to (adopting the response surface method based on uniform Design) in conjunction with response surface method on the bridge finite element model modified basis based on Uniform ity Design Method, only needing to increase a finite element model calculates, the precision of further raising model correction that just can be simple and efficient, make bridge finite element model meet the accuracy requirement of engineering analysis, guarantee higher correction efficiency simultaneously; For thering is the finite element model correction of degree of precision requirement, provide a kind of simple possible efficient reference method.In the present invention, based on Uniform ity Design Method and the bridge finite element model modification method based on response surface method, can both overcome the deficiencies such as the structural sensitivity computational accuracy that the modification method that is directly based upon on structural finite element model basis exists is wayward, FEM (finite element) calculation iterations many and be not easy to develop on common finite element software platform, save a large amount of computing times, improve the efficiency of finite element model correction, can provide good experience and reference for the development of bridge complex Finite Element Model Updating later.The finite element model correction that simultaneously the present invention is based on uniform Design response surface method is the correction to initial finite element model for strain data, has higher precision and specific aim.Finally, in the present invention, set up the entity finite element model of full-bridge, this entity finite element model is revised, while then adopting the stressing conditions of bridge diverse location under the different load situation of revised entity finite element modeling, can determine more accurately the rapid wear position of bridge, and then optimize and lay sensor in the rapid wear position of bridge, can realize and utilize the more effective measurement of sensor of lesser amt to identify more rapid wear position.

Difficulty of the present invention is:

(1) static(al) sensor optimization is laid solution design and implementation method;

(2) novelty, utilizes uniform Design response surface method, can reduce calculated amount simultaneously and improve and revise precision;

(3) specific aim, what the present invention is directed to is large-scale complicated system, and for engineering, the research of large-scale complicated system itself is exactly a difficult matter, says nothing of large scale system is carried out to the further work such as correction.In fact, after a method puts forward, and may not be certain this method and itself have how difficultly, but be its practicality, the E=mc2 that for example einstein proposes, this expression formula is extremely bright and clear, but very practical.The bridge finite element model of the correction in the present invention also has good practicality.

Accompanying drawing explanation

Fig. 1 is Program Y of the present invention _minprocess flow diagram;

Fig. 2 is longitudinal sketch of the drawing of full-bridge;

Fig. 3 is bridge standard cross-section figure;

Fig. 4 is the real figure general picture of full-bridge;

Fig. 5 is termination central sill B-B1 sectional view;

Fig. 6 is termination side bar B-B2 sectional view;

Fig. 7 is central sill C-C1 sectional view;

Fig. 8 is side bar C-C2 sectional view;

Fig. 9 is the cross-sectional view of bridge;

Figure 10 is the cross-sectional view of bridge;

Figure 11 is the model of the whole bridge that comprises bridge pier;

Figure 12 is bridge portion illustraton of model;

Figure 13 is the strain figure at 1 time bridge of operating mode;

Figure 14 is the stress diagram of bridge in the situation that of operating mode 1;

Figure 15 is the strain figure of bridge in the situation that of operating mode 2;

Figure 16 is the stress diagram of bridge in the situation that of operating mode 2;

Figure 17～Figure 22 is measuring point distribution plan;

Figure 23 is the dividing elements figure of three Span Continuous free beams;

Figure 24 is strain predicted value p ₁to p ₉histogram;

Figure 25 is one across finite element model;

Figure 26 is one across finite element model vertical view;

Figure 27 is recognizable pattern number Y not _minchanging trend diagram;

Figure 28 considers noise Y _minchanging trend diagram.

Below in conjunction with the drawings and specific embodiments, the present invention is further illustrated.

Embodiment

Embodiments of the invention: a kind of optimization distribution method of improved static(al) sensor, specifically comprises the following steps:

S1. set up the entity finite element model of full-bridge, this entity finite element model is revised;

S2. adopt the stressing conditions of bridge diverse location under the different load situation of revised entity finite element modeling, set up the finite element damage model under n kind degree of impairment, and extract the strain predicted value p at each sensor potential site i place under various degree of impairments _ij, wherein, the potential site that i is sensor, j is degree of impairment, 1≤j≤n;

S3, according to the measuring accuracy of sensor, by the stress prediction value p at sensor potential site i place _ibe divided into some intervals, the damage model of corresponding stress prediction value in same interval is can not identification of damage model; The interval that comprises two or more models is made as to set b _ik, wherein, k is can not identification of damage number, 0≤k < j; Set b _ikin element be various unrecognizable faulted conditions and a plurality of b _ikform set B _i, B _i={ b _i1∪ b _i2... ∪ b _ik;

S4, if the potential site number of each sensor is m, the number of sensor is s, calculates Y={B ₁∩ B ₂... ∩ B _s; In subset, the minimum number of number of elements is the number Y of minimum not recognizable pattern _min, Y _minthe installation position of corresponding sensor is optimum sensor and lays.

In the application, also can, according to the entity finite element model of revised full-bridge, judge the stress loss amount of its acquisition or the early warning value whether elastic modulus loss amount reaches setting.

In step S1, described revises and comprises this entity finite element model: adopt uniform design once to revise this entity finite element model, specifically comprise the following steps:

X1, chooses objective function Q (x) and m parametric variable X to be revised; Described objective function Q (x) is specially:

$Q\left(x\right)=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_i{\left(\frac{{\mathrm{\&epsiv;}}_i\left(X\right)-{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}_i}{{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}_i}\right)}^2$

Wherein, Q (x) is objective function, r _ifor weight coefficient, ε _i(X) be the strain value that i is ordered, mean value for i strain; Described parametric variable X=[E, ρ, μ], wherein, E is modulus of elasticity of concrete, and ρ is concrete density, and μ is Poisson ratio;

X2, is divided into n level by the value of each parametric variable;

X3, tests according to uniform designs table and use table Selecting All Parameters horizontal combination thereof;

X4, brings the static(al) data that obtain of test at every turn and actual measurement static(al) data in objective function and error criterion function, to obtain the result of test at every turn into; Described error criterion function is:

The error rate of single measuring point data:

$P\left(x_i\right)=\left|\frac{x_i-{\stackrel{\&OverBar;}{x}}_i}{{\stackrel{\&OverBar;}{x}}_i}\right|;$

The average error rate of all measuring point datas:

$P\left(x\right)=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left|\frac{x_i-{\stackrel{\&OverBar;}{x}}_i}{{\stackrel{\&OverBar;}{x}}_i}\right|;$

In formula, x _i, be respectively the measuring point data that measuring point data that finite element model calculates and field measurement obtain;

X5, each test findings relatively, obtains objective function and error criterion function parameter level hour, and the finite element model based on this parameter level i.e. revised baseline finite element model once; The experiment number of this uniform design is 3～5 times of parametric variable number;

After entity finite element model is once revised, utilize uniform design to choose testing site and generate response surface, adopt response surface method to carry out second-order correction to this entity finite element model, specifically comprise the following steps:

A, obtains the n of bridge stray parameter variable X by uniform designs table _sindividual sample point, obtains the sample point numerical value Y of response surface objective function, Y={y by Uniform Design ₁, y ₂..., y _ns;

B, utilizes the sample point numerical value Y regretional analysis of parametric variable X and objective function to obtain the least-squares estimation value of undetermined multipliers, and then obtains response surface function;

C, is optimized response surface function, obtains response surface objective function and error criterion function parametric variable value hour, and the structural finite element model based on this parametric variable is the finite element model after bridge second-order correction.

Engineering example:

The large stone river bridge of take is research object, and the modal strain of extraction model is as input, adopts the optimization distribution method of improved static(al) sensor of the present invention to obtain the static(al) sensor optimization scheme of stone river bridge.

One, the foundation of bridge finite element model and correction

Utilize ANSYS software set up stone river Bridge Structure one across finite element model as shown in Figure 25, Figure 26, wherein bridge structure is divided into 40 unit; To this model carry out once, second-order correction.

Two, the foundation of damage model

Suppose that damage appears in the elastic modulus of unit because crack or local loss of prestress at the bottom of beam appear in bridge, set up according to this 40 unit damage finite element models.In structure, under harmless and degree of impairment, the strain data by monolithic beam one across 40 unit of structure proposes.

Three, the optimization of sensor is laid

Because the resolution of vibrating string extensometer is 1 μ ε, therefore carrying out when sensor optimization is arranged that burst length is decided to be to 1 μ ε, i.e. each unit strain predicted value p _ijinterval demarcation interval with 1 μ ε.Through computing, when number of sensors increases gradually, the variation of recognizable pattern is not as shown in table 4:

Table 4 bridge structural calculation result

Along with increasing of number of sensors s, recognizable pattern number Y not _minvariation tendency as shown in figure 27.

As shown in Figure 27, number of sensors is obvious on the impact of optimum results, along with increasing of number of sensors s, and recognizable pattern number Y not _minreduce rapidly.This explanation: sensor is all arranged in to the position sensitive to injury response, and a plurality of sensors is carried out in the situation of Combinatorial Optimization, sensing system can react, distinguish the various degree of impairments of supposition accurately.Utilize method of the present invention to carry out preferred arrangement to sensor and can be good at embodying set object.In this project example, only need to arrange 4 strain transducers, just can make can not identification of damage model number be zero, utilize 4 strain transducers after preferred arrangement, just can the 40 places supposition of stone river Bridge Structure be damaged and accurately be identified.At Y _min=0 o'clock, the setting position of sensor can be got following unit combination: { 6,14,23,32} buries sensor underground.(at Y _min=0 o'clock, first suppose that number of probes is 1, i.e. S=1, because set B ₅in all subset elements at most and its subset elements be 2, i.e. unrecognizable damage model Y _minit is 2, so sensor is arranged in to unit 5 for the optimum layout; If the unrecognizable damage model Y of accuracy requirement _minbe less than 2, dose again sensor, i.e. a S+1; Device number of probes is 2, i.e. S=2, the situation analysis listed according to table 3.Y for example ₁=B ₁∩ B ₂={ (5,6); (9,0) }, its not recognizable pattern be at most 2; And be empty set, recognizable pattern is not zero, and Y is now required.Utilize listed analysis form 4 and Figure 27 to learn that sensor burial place is now best.)

Consider noise effect, the accuracy of identification of sensor can decrease, and burst length is decided to be to 2 μ ε, recalculates and can obtain:

Table 5 is considered noise calculation result

Equally can be along with the increasing of number of sensors s, not recognizable pattern number Y _minvariation tendency as shown in figure 28.

As shown in Figure 28: in the situation that considering noise, sensor resolution (being accuracy of identification) declines to some extent, the result of optimization also changes to some extent.When 6 sensors need be set, just can make can not identification of damage model number be zero; When s=4 and s=5, Y _min=2, increase sensor and fail to make not recognizable pattern to reduce.

If sensor cost is comparatively expensive, (s=4, Y while still establishing 4 sensors _min=2), the setting position of sensor can take following unit combination 7,18,27,35} buries sensor underground, and concrete computation process is as follows:

Solving Y _minprocess in, when i=s, needing the number of times of set of computations Y is C (m, s), calculated amount is huge, solves Y _min, need the corresponding optimized algorithm of establishment.Because seek common ground, have law of association, (A ∩ B) ∩ C=A ∩ (B ∩ C) is so while calculating the Y of s=i+1, can utilize the Y of s=i at every turn.With each element in the Y of s=i, intersect with the Y of s=1, by enumerating, can not repeat to calculate each element in Y, thereby save a large amount of computing times.

This algorithm is according to this principle, and the program key step of establishment is as follows: the Y while first calculating s=1.Suppose to have m capable, in Y, element representation is { Y ₁, Y ₂... Y _m; Calculate each set Y _iin the number of maximal subset element (be expressed as Y _{i, max}); Calculate all Y _{i, max}in minimum value (be expressed as Y _{s=k, min}).The Y when Y when Y during then according to s=i and s=1 intersects to calculate s=i+1, the like iteration.According to above algorithm idea, work out process flow diagram as shown in Figure 1:

Adopt matlab language establishment relative program to calculate, under each faulted condition that simulation is obtained, the strain value of each effect value, as input, obtains corresponding output.In structure harmless and elastic modulus damage 60% in the situation that, strain data proposition (with 1 μ ε demarcation interval) by monolithic beam one across 40 unit of structure, as shown in following table 6～table 8, (wherein, table 6 is under 1～10 kind of degree of impairment to simulation result, 40 strains that unit is corresponding; Table 7 is under 11～20 kinds of degree of impairments, 40 strains that unit is corresponding; Table 8 is under 21～30 kinds of degree of impairments, 40 strains that unit is corresponding):

Table 6

Table 7

Table 8

If construction budget is well-to-do, (s=6, Y when preferred arrangement is carried out in the combination that can choose 6 sensors _min=0), consider noise effect, the accuracy of identification of sensor can decrease, and burst length is decided to be to 2 μ ε, recalculate and can obtain: number of probes S be 6 o'clock not recognizable pattern number be 0, in unit combination: { 6,11,17,24,30,35} buries sensor underground.

Static(al) sensor optimization distribution method of the present invention, for large stone river bridge engineering, is proved to the method principle is clear and definite, simple to operate, in engineering, there is very strong practicality.

Claims (10)

1. an optimization distribution method for improved static(al) sensor, is characterized in that: comprise the following steps:

S1. set up the entity finite element model of full-bridge, this entity finite element model is revised;

S2. adopt the stressing conditions of bridge diverse location under the different load situation of revised entity finite element modeling, and set up the finite element damage model under n kind degree of impairment; Extract the strain predicted value p at each sensor potential site i place under various degree of impairments _ij, wherein, the potential site that i is sensor, j is degree of impairment, 1≤j≤n;

S3, according to the measuring accuracy of sensor, by the stress prediction value p at sensor potential site i place _ibe divided into some intervals, the damage model of corresponding stress prediction value in same interval is can not identification of damage model; The interval that comprises two or more models is made as to set b _ik, wherein, k is can not identification of damage number, 0≤k < j; Set b _ikin element be various unrecognizable faulted conditions and a plurality of b _ikform set B _i, B _i={ b _i1∪ b _i2... ∪ b _ik;

S4, if the potential site number of each sensor is m, the number of sensor is s, calculates Y={B ₁∩ B ₂... ∩ B _s; In subset, the minimum number of number of elements is the number Y of minimum not recognizable pattern _min, Y _minthe installation position of corresponding sensor is optimum sensor and lays.

2. the optimization distribution method of improved static(al) sensor according to claim 1, is characterized in that, in step S1, described revises and comprise this entity finite element model: adopt uniform design once to revise this entity finite element model.

3. the optimization distribution method of improved static(al) sensor according to claim 2, is characterized in that, described employing uniform design is once revised specifically and comprised the following steps this entity finite element model:

X1, chooses objective function Q (x) and m parametric variable X to be revised;

X2, is divided into n level by the value of each parametric variable;

X3, tests according to uniform designs table and use table Selecting All Parameters horizontal combination thereof;

X4, brings the static(al) data that obtain of test at every turn and actual measurement static(al) data in objective function and error criterion function, to obtain the result of test at every turn into;

X5, each test findings relatively, obtains objective function and error criterion function parameter level hour, and the finite element model based on this parameter level i.e. revised baseline finite element model once.

4. the optimization distribution method of improved static(al) sensor according to claim 3, is characterized in that, the objective function Q (x) described in step X1 is specially:

$Q\left(x\right)=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_i{\left(\frac{{\mathrm{\&epsiv;}}_i\left(X\right)-{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}_i}{{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}_i}\right)}^2$

Wherein, Q (x) is objective function, r _ifor weight coefficient, ε _i(X) be the strain value that i is ordered, mean value for i strain.

5. the optimization distribution method of improved static(al) sensor according to claim 4, is characterized in that, the error criterion function described in step X4 is:

The error rate of single measuring point data:

$P\left(x_i\right)=\left|\frac{x_i-{\stackrel{\&OverBar;}{x}}_i}{{\stackrel{\&OverBar;}{x}}_i}\right|;$

The average error rate of all measuring point datas:

$P\left(x\right)=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left|\frac{x_i-{\stackrel{\&OverBar;}{x}}_i}{{\stackrel{\&OverBar;}{x}}_i}\right|;$

In formula, x _i, be respectively the measuring point data that measuring point data that finite element model calculates and field measurement obtain.

6. the optimization distribution method of improved static(al) sensor according to claim 2, is characterized in that, the experiment number of described uniform design is 3～5 times of parametric variable number.

7. according to the optimization distribution method of the arbitrary described improved static(al) sensor of claim 2～6, it is characterized in that, described also revises and comprises this entity finite element model: utilize uniform design to choose testing site and generate response surface, adopt response surface method to carry out second-order correction to this entity finite element model.

8. the optimization distribution method of improved static(al) sensor according to claim 7, it is characterized in that, the described uniform design that utilizes is chosen testing site generation response surface, adopts response surface method to carry out second-order correction to this finite element damage model and specifically comprises the following steps:

A, obtains the n of bridge stray parameter variable X by uniform designs table _sindividual sample point, obtains the sample point numerical value Y of response surface objective function, Y={y by Uniform Design ₁, y ₂..., y _ns;

B, utilizes the sample point numerical value Y regretional analysis of parametric variable X and objective function to obtain the least-squares estimation value of undetermined multipliers, and then obtains response surface function;

C, is optimized response surface function, obtains response surface objective function and error criterion function parametric variable value hour, and the structural finite element model based on this parametric variable is the finite element model after bridge second-order correction.

9. the optimization distribution method of improved static(al) sensor according to claim 8, is characterized in that, described parametric variable X=[E, ρ, μ], wherein, E is modulus of elasticity of concrete, and ρ is concrete density, and μ is Poisson ratio.

10. the optimization distribution method of improved static(al) sensor according to claim 9, it is characterized in that, also comprise: the entity finite element model according to revised full-bridge, judges the stress loss amount of its acquisition or the early warning value whether elastic modulus loss amount reaches setting.