CN105157588A - Multi-dimensional synchronous optimized measurement method for strain localization band interval evolution rule - Google Patents

Abstract

The invention provides an observation method of an evolution rule of a strain localization band interval with a stress or strain. The method comprises: a digital image of a testing sample during a loading process is obtained by using a shooting device; a strain field with high smoothness is obtained by using a sub-pixel digital image correlation method and a bicubic spline interpolation method; strain data of each tested strain localization band are obtained; an initial value of iteration is set and one more dimension of any initial value is set than the number of strain localization bands, synchronous iteration is carried out continuously by using a swarm intelligence algorithm to reduce deviation between data and test solutions of all strain localization bands gradually, and then a unique strain localization band angle and respective different intercepts are obtained; and an interval between any two adjacent strain localization bands is calculated based on a distance formula between two parallel lines. The method has the following beneficial effects: accuracy and uniqueness of a measurement result can be guaranteed; a strain localization band interval evolution rule can be obtained; and automatic batch high-efficiency measurement can be realized.

Description

The multidimensional Synchronous fluorimetry measuring method of a kind of strain localization belt distance development law

Technical field

The present invention relates to a kind of strain localization band distance measurement technology, belong to the fields such as rock-soil mechanics, Geotechnical Engineering, Experimental Mechanics, geomechanics, engineering material mechanics performance test.

Background technology

Strain localization is the phenomenon that the strain observed before material damage concentrates in narrow belt-like zone, and strain localization can be divided into shear strain localization, tensile strain localization and compressive strain localization by load type.Strain localization's phenomenon can be observed on different levels, such as, netted tectonic structure on the minor fault of the netted skid wire on crystal particle scale, the intersection on engineering yardstick and earth's crust yardstick and seismic zone all can ascribe strain localization phenomenon (Wang Xuebin to, Pan Yishan. the strain localization's phenomenon in geologic hazard. Journal of Geological Hazards and Environment Preservation, 2001,12 (4): 1-5; Wang Xuebin, Zhao Yangfeng, Dai Shuhong etc. the conjugated shear joins band numerical simulation of Seismic Block Model. Journal of Disaster Prevention and Mitigation Engineering, 2004,24 (2): 119-125).Strain localization's phenomenon often exists with latticed form, and like this, the measurement of strain localization's belt distance just becomes unavoidable major issue in strain localization's phenomenal research.

At present, the measurement of strain localization's belt distance mainly adopts two kinds of methods: employing ruler and Digital image technology measure the spacing between macroscopic crack surface, in this, as the spacing of strain localization band.In fact, the error of this measuring method is very large, and measurement result varies with each individual, and workload is large, and be difficult to realize robotization, in batches, high-level efficiency measures, the data volume obtained is limited, and, measurement be the spacing of crack surface, the not spacing of strain localization band.Strain localization band is in startup and evolution, and due to the difference of deformation stage and the adjustment of stress field, the direction of strain localization and position suitable change will occur.Without any theoretical proof, strain localization's belt distance is equal to crack surface spacing.For Measurement accuracy strain localization belt distance, strain field must be conceived to, before crackle occurs, strain field has become uneven, and this change only is generally not easy to observe with naked eyes, the Digital Image Correlation Method (Wang Xuebin of development, Du Yazhi, Pan Yishan. based on DIC thick-Strain Distribution of uniaxial compression sand sample of fine searching method and the experimental study of strain gradient. Geotechnical Engineering journal, 2012,34 (11): 2050-2057; Wang Xuebin, Du Yazhi, Pan Yishan. consider the comparison of the Digital Image Correlation Method of single order and Second Order Displacements gradient in shear zone is measured. engineering mechanics, 2013,30 (7): 282-287; Wang Xuebin, Du Yazhi, Pan Yishan. the Digital Image Correlation Method observation of uniaxial compression damp sand sample local and overall volume strain. Geotechnical Engineering journal, 2014,36 (9): 1648-1656) to provide convenience condition for the accurate measurement of strain field.Digital Image Correlation Method is a kind of optical measurement mechanics method, has the advantage that measuring equipment is simple, low to measurement environment requirement, measuring accuracy is high.

The present invention proposes the spacing adopting Digital Image Correlation Method monitor strain localization band.The good strain field of slickness obtained using sub-pix Digital Image Correlation Method and bicubic spline interpolation method is as foundation, by the measurement problem arises of unique strain localization belt distance in a multidimensional Synchronous fluorimetry problem, utilize swarm intelligence algorithm, by continuous synchronous iteration, reduce each bar strain localization band data gradually and sound out the deviation answered between (each line segment), final realization takes into account unique strain localization band angle of all data and the measurement of strain localization's belt distance.

Summary of the invention

In order to the precision solving existing strain localization band measurement method for distance is low, efficiency is low, obtain the problem that data volume is limited and acquired results is not unique, the invention provides a kind of multidimensional Synchronous fluorimetry measuring method of the strain localization's belt distance development law based on Digital Image Correlation Method, improve the efficiency of measurement, precision, can obtain abundant data volume, acquired results is unique.

The invention is characterized in, comprise the steps:

Step 1: utilize capture apparatus (digital camera or CCD camera) to obtain one, sample under loaded conditions and comprise the digital picture on speckle surface;

Step 2: utilize sub-pix Digital Image Correlation Method, obtains the deformation field of specimen surface: horizontal line strain stress _x, perpendicular line strain stress _y, shear strain γ _xyand maximum shear strain γ _max;

Step 3: zoning is set, obtain every bar strain localization band central authorities and neighbouring strain data thereof, this zoning can be 1 quadrilateral area comprising many strain localization bands, may also be the set of the quadrilateral area comprising 1 strain localization band;

The situation of 1 quadrilateral area comprising many strain localization bands for zoning:

First, 1 the quadrilateral zoning comprising many strain localization bands is set;

Afterwards, according to strain field, determine to move towards the number m of consistent strain localization band;

Afterwards, utilize interpolation method, obtain the good various strain field of slickness in zoning;

Finally, utilize tested strain localization band angle and the width of rough estimate, arrange multiple long and narrow quadrilateral area, each long and narrow quadrilateral area only comprises 1 strain localization band, obtains every bar strain localization band central authorities and neighbouring strain data thereof;

The situation of the set of the quadrilateral area comprising 1 strain localization band for zoning:

First, according to strain field, determine to move towards the number m of consistent strain localization band;

Afterwards, utilize tested strain localization band angle and the width of rough estimate, arrange multiple long and narrow quadrilateral area as zoning, each long and narrow quadrilateral area only comprises 1 strain localization band;

Afterwards, utilize interpolation method, obtain the good various strain field of slickness in zoning;

Finally, every bar strain localization band central authorities and neighbouring strain data thereof is obtained;

Step 4: for every bar strain localization band, n iterative initial value and relevant iteration parameter are set, for arbitrary initial value (series of parallel line segment), the dimension of initial value is m+1, comprising 1 slope and m intercept, utilize swarm intelligence algorithm, by continuous synchronous iteration, obtain the common slope of each bar line segment and intercepts different separately;

Step 5: utilize range formula between parallel lines, calculates the spacing of any two adjacent strain localization bands.

Further, wherein, the described acquisition digital picture that one, sample comprises speckle surface is under loaded conditions further: if the native texture of specimen surface can be used as speckle field, then need not manual manufacture speckle field, otherwise, utilize the artificial speckle fields of spraying such as paint, pigment, ink, utilize testing machine or charger to load sample, meanwhile, the image of capture apparatus record speckle field is utilized.

Further, wherein, describedly utilize sub-pix Digital Image Correlation Method, the deformation field obtaining specimen surface is further: the image selecting some records, relevant calculating parameter and computation schema are set, use displacement field and the strain field of sub-pix Digital Image Correlation Method computed image, strain field is by carrying out central difference acquisition to displacement field, and maximum shear strains γ _maxby ε _x, ε _yand γ _xyobtain

${\mathrm{\γ}}_{\max }=\sqrt{{({\mathrm{\ϵ}}_x-{\mathrm{\ϵ}}_y)}^2+{{\mathrm{\γ}}_{xy}}^2}---\left(1\right)$

Further, wherein, the strain localization band that described trend is consistent refers to the set of some strain localization bands that its angle is substantially identical in strain localization band network.

Further, wherein, described acquisition every bar strain localization band central authorities and neighbouring strain data thereof are further: arrange critical strain parameter, will exceed the data of data as tested strain localization band of this parameter.

Further, wherein, the Width size of described long and narrow quadrilateral area can be taken as 20 ~ 60 times of material mean particle diameter, i.e. 1 ~ 3 times of strain localization's bandwidth; Described critical strain parameter is determined by experience, generally can be taken as γ in zoning _maxmore than 60% of maximal value.

Further, wherein, described iterative initial value comprises the initial value of the common slope of line segment corresponding to each bar strain localization band and the initial value of different intercept, therefore the dimension of initial value is than the number m many 1 of strain localization band, if any one iterative initial value is Ω _i={ k _i, b _1i, b _2i..., b _mi, wherein, k _ifor the initial value of common slope, { b _1i, b _2i..., b _miit is the initial value of different intercept.

Further, wherein, described swarm intelligence algorithm can be selected in particle swarm optimization algorithm, genetic algorithm, differential evolution algorithm scheduling algorithm.

Further, wherein, the slope that described each bar line segment is common and intercepts different separately refer to that the m bar line segment determined by these parameters and each bar strain localization band central authorities and neighbouring strain data thereof are the most close, and namely deviation reaches minimum

$min\left(J\right)=min\left\{{\mathrm{\Σ}}_{i=1}^m{\mathrm{\Σ}}_{j=1}^{c_i}{\[s_{ij}-f_{ij}(k_l,b_{il})\]}^2\right\}---\left(2\right)$

Wherein, subscript l represents any one in n iterative initial value, l=1 ~ n; c _irepresent the data number of i-th strain localization band, usually, the data number of differently strained localization band is different, i=1 ~ m; s _ijrepresent the ordinate of a jth data of i-th strain localization band, i=1 ~ m, j=1 ~ c _i, s _ij=s _ij(x _ij), x _ijfor the horizontal ordinate of these data; f _ijthe ordinate of line segment at a jth data place that representative and i-th strain localization band approach, due to f _ijlinear function, so, f _ij=(k _l, b _il)=k _lx _ij+ b _il, k _lthe common slope of 1 initial value (each line segment), b _ilthe different intercepts of 1 initial value, (s _ij-f _ij) ²represent the deviation between 1 dependent variable strong point and 1 line segment square, to all data c on a strain localization band _isummation, represent the deviation between the strain data of a strain localization band and 1 line segment square, again to every bar strain localization band summation, represent the deviation between the strain data of each bar strain localization band and each bar line segment square, by continuous synchronous iteration, it is made to reach minimum vectorial Ω _*={ k _*, b _1*, b _2*..., b _m*be described unique and optimum.

Further, wherein, described synchronous iteration is iterative initial value or the process souning out answer continuous renewal, for different swarm intelligence algorithms, the more new principle souning out answer is not identical, but substantially all consider difference sound out information sharing, the mutually study between answer and affect and the strategy such as the survival of the fittest and the survival of the fittest, the condition that iteration terminates comprises two kinds: 1) iterations reaches maximum algebraically; 2) iteration result tends towards stability (although iterations does not reach maximum algebraically).

Further, wherein, described iteration parameter comprises: the threshold condition that the number of maximum algebraically, iterative initial value, iteration terminate and the iteration parameter required by distinct group intelligent algorithm, such as, for particle swarm optimization algorithm, need the parameters such as the maximal rate of particle flight, Studying factors, inertia constant.

Further, wherein, the spacing d of described any two adjacent strain localization bands _iformula is

d _i＝|b _(i+1)*-b _i*|sinθ _*＝|b _(i+1)*-b _i*|sin[arctan(k _*)],i＝1～(m-1)(3)

The multidimensional Synchronous fluorimetry measuring method of a kind of strain localization's belt distance development law based on Digital Image Correlation Method of the present invention, the robotization of strain localization's belt distance, quick, Measurement accuracy can be realized, the abundant information obtained, can ensure the uniqueness of measurement result.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the multidimensional Synchronous fluorimetry measuring method of a kind of strain localization belt distance development law;

Fig. 2 is the schematic diagram of digital image acquisition device under loaded conditions; In figure, 1-sample, 2-comprise the surface of speckle, 3-light source, 4-capture apparatus, 5-computing machine;

Fig. 3 is the Digital Image Correlation Method program interface figure based on particle group optimizing and Newton-Raphson alternative manner of independent development;

Fig. 4 is the schematic diagram of multidimensional Synchronous fluorimetry process, and wherein Fig. 4-a is for arranging zoning; Fig. 4-b is the scope determining to move towards consistent strain localization band; Fig. 4-c obtains every bar strain localization band central authorities and neighbouring strain data thereof; Fig. 4-d is for arranging iterative initial value and iteration parameter; Fig. 4-e is the net result (only giving the true answer making objective function minimum) of iteration; In figure, 6-zoning, 7-strain localization band, 7-1-move towards consistent strain localization band (tested strain localization band), 7-2-move towards consistent strain localization band, 8-long and narrow quadrilateral area, 9-arbitrary data point, 10-a certain iterative initial value (such iterative initial value have n), 11-unique true answer;

Fig. 5 is the process flow diagram of the multidimensional Synchronous fluorimetry process based on particle swarm optimization algorithm;

Fig. 6 is the schematic diagram of the spacing calculating any two adjacent strain localization bands;

Fig. 7 is different longitudinal strain ε _atime Uniaxial Compression sand sample maximum shear strain γ _maxdistribution plan, wherein, Fig. 7-a is ε _aresult figure when=0.08; Fig. 7-b is ε _aresult figure when=0.09; Fig. 7-c is ε _aresult figure when=0.11; Fig. 7-d is ε _aresult figure when=0.13; Fig. 7-e is ε _aresult figure when=0.14; Fig. 7-f is ε _aresult figure when=0.15; Fig. 7-g is ε _aresult figure when=0.16; In figure, 3 quadrilateral areas of 12-restriction, 3 strain localization bands;

Fig. 8 is ε _athe data of 3 consistent strain localization bands, iterative initial value and multidimensional Synchronous fluorimetry procedure chart is moved towards when=0.16, wherein, result figure when Fig. 8-a is iteration algebraically N=1; Result figure when Fig. 8-b is iteration algebraically N=10; Result figure when Fig. 8-c is iteration algebraically N=30; Result figure when Fig. 8-d is iteration algebraically N=100; In figure, 13-15-iterative initial value; The data of 16-strain localization band; 17-truly answer; 17-1-for the true answer of the 1st band; 17-2-for the true answer of the 2nd band; 17-3-for the true answer of the 3rd band;

Fig. 9 is ε _a=0.16 and different iteration algebraically time objective function J evolution diagram;

Figure 10 is different longitudinal strain ε _atime tested strain localization band the evolution diagram of spacing.

Embodiment

Be described below in conjunction with the embodiment of accompanying drawing to the method.

The multidimensional Synchronous fluorimetry measuring method of a kind of strain localization of the present invention belt distance development law, its process flow diagram as shown in Figure 1, comprises the steps:

Step 1: as shown in Figure 2, utilize capture apparatus 4 (digital camera or CCD camera) to obtain 1 one, sample under loaded conditions and comprise the digital picture on the surface 2 of speckle, light source 3 is arranged at the front of capture apparatus 4, and the Image Saving of shooting is in the hard disk of computing machine 5;

This step is implemented specific as follows: first, at the surperficial manufacturing artificial speckle field of 1 one, sample, if the native texture of specimen surface can reach the condition as speckle field, then need not manual manufacture speckle field; Then, utilize testing machine or charger to load sample 1, meanwhile, utilize capture apparatus 4 to record the image of speckle field.

Described artificial speckle field refers to the random speckle shape pattern adopting the sprayings such as paint, pigment, ink at specimen surface.

Step 2: utilize sub-pix Digital Image Correlation Method (Fig. 3), obtains the deformation field of specimen surface: horizontal line strain stress _x, perpendicular line strain stress _y, shear strain γ _xyand maximum shear strain γ _max;

This step is specifically implemented as follows: first, from the great amount of images of record, selects somely typically to calculate for strain field; Afterwards, relevant calculating parameter and computation schema are set, use the displacement field of sub-pix Digital Image Correlation Method computed image; Afterwards, strain field is obtained by carrying out central difference to displacement field; Finally, according to horizontal line strain, perpendicular line strain and the strain of inplane shear strain calculation maximum shear.

Described calculating parameter comprises: subarea size, measuring point spacing, measure-point amount, number of particles and particle maximum flying speed etc.

Described computation schema comprises: incremental mode and full dose pattern, and so-called incremental mode refers to that the displacement field of gained and strain field are increments using last image as distortion front image; So-called full dose pattern refers to that the displacement field of gained and strain field are full doses using first image as distortion front image.

Described sub-pix Digital Image Correlation Method can select the Digital Image Correlation Method (Du Yazhi based on particle group optimizing and Newton-Raphson alternative manner, Wang Xuebin. based on the Digital Image Correlation Method of Newton-Raphson iteration and PSO algorithm. computer engineering and application, 2012,48 (34): 184-189), the method can avoid traditional Newton-Raphson alternative manner to be easy to be absorbed in the drawback of local optimum, and the initial value of iteration also can be avoided to be not easy the drawback determined.Although the method can carry out relevant search to displacement field and strain field simultaneously, consider that the precision of strain field is general not high, thus abandon the data of strain field, usual employing is carried out central difference to displacement field and is obtained new strain field.

Described maximum shear strain field is obtained by 3 kinds of strain fields, this maximum shear strain field is always greater than zero, and along with the continuation of distortion, the distortion of strain localization band inside is further obvious, and distortion increase outside band is comparatively slow, thus strain localization's process can be characterized well.

Step 3: arrange zoning, obtains every bar strain localization band central authorities and neighbouring strain data thereof;

This step is implemented specific as follows: first, by observing strain field, arrange one and comprise the zoning of many strain localization bands 7 (, to comprise 1 quadrilateral area of many strain localization bands as zoning 6, as depicted in fig. 4-a) here; Afterwards, according to strain field, determine to move towards the number m (Fig. 4-b) of consistent strain localization band 7; Afterwards, the strain field limited to the data volume of above-mentioned zoning carries out bicubic spline interpolation, and to improve data volume and the slickness of strain field, do not need to carry out whole sample, this can reduce interpolation workload, improves the efficiency of interpolation; Finally, as shown in Fig. 4-b and Fig. 4-c, utilize angle and the width of the tested strain localization band 7-1 of rough estimate, reject the data outside tested strain localization band 7-1, obtain every bar tested strain localization band 7-1 central authorities and neighbouring strain data thereof.

The strain localization band that described trend is consistent refers to the set of some localization bands that its angle is substantially identical in strain localization band network, usually, strain localization band 7 in strain localization band network exists in the mode of conjugation, namely two bunches, wherein arbitrary bunch is strain localization band 7-1 or 7-2 moving towards consistent, herein, to move towards consistent strain localization band 7-1 as tested strain localization band.

The every bar of described acquisition tested strain localization band central authorities and neighbouring strain data thereof are further: first, arrange suitable critical strain parameter, will exceed the data of data as tested strain localization band 7-1 of this parameter; Afterwards, rule of thumb, determine the scope of the tested strain localization band 7-1 of each bar, give up the data outside these scopes.

The scope of the tested strain localization band of described each bar is limited by 1 long and narrow quadrilateral area 8, long and narrow quadrilateral area 8 is all positioned within zoning 6, the longer limit of two of long and narrow quadrilateral area 8 is parallel, its angle is by virtue of experience arranged, for rock-soil material, the direction of shear strain localization band and major principal stress (σ ₃) angle between direction is generally at 55 ° ~ 80 °; The distance on the limit that two of long and narrow quadrilateral area 8 are longer, namely the size of its Width can be taken as 1 ~ 3 times of shear strain localization bandwidth, i.e. 20 ~ 60 times of material mean particle diameter.

Described critical strain parameter can be taken as γ in zoning 6 _maxmaximal value more than 60%.

Step 4: as shown in Fig. 4-d, for the tested strain localization band 7-1 of every bar, n iterative initial value and relevant iteration parameter are set, for a certain iterative initial value 10, i.e. series of parallel line segment, the dimension of initial value is m+1, comprising 1 slope and m intercept, utilize swarm intelligence algorithm, by continuous synchronous iteration, obtain the common slope of each bar line segment and intercepts different separately.

Described iterative initial value refers to a series of line segments within zoning 6, and every bar line segment is for 1 strain localization band 7, and iterative initial value is determined completely by the slope of these line segments and intercept, and true origin can be taken at the center of zoning 6; For a certain iterative initial value 10, its line segment comprised is parallel to each other, and like this, the dimension of initial value is by the number m many 1 than strain localization band; For different initial values, usually, its whole line segments comprised do not meet the requirement be parallel to each other.

Described arbitrary iterative initial value is set to Ω _i={ k _i, b _1i, b _2i..., b _mi, wherein, i=1 ~ n, n are the number of iterative initial value; It should be pointed out that the number of this iterative initial value is not equal to the dimension of initial value, dimension is relevant with the number of strain localization band 7, and the number of initial value is relevant with the complexity of problem, and for the optimization problem easily solved, the number of initial value does not need too much; k _ifor the common slope of arbitrary iterative initial value, { b _1i, b _2i..., b _mibe the different intercepts of arbitrary iterative initial value; In an iterative process, iterative initial value will be upgraded by exploration answer, but sound out the feature that answer still meets iterative initial value: sound out answer for any one, its line segment comprised is parallel to each other.

Described swarm intelligence algorithm comprises particle swarm optimization algorithm, genetic algorithm, differential evolution algorithm etc.Different swarm intelligence algorithms has different performances and origin, which dictates that and sound out the different more new principle of answer, but these swarm intelligence algorithms have following general character: have stronger overall parallel search capabilities, this root is soundd out information sharing, the mutually study between answer in considering difference and affects and the strategy such as the survival of the fittest and the survival of the fittest.

Described synchronous iteration process refers to sounds out answer constantly to truly answering the process of approaching, in the process, m bar line segment is synchronous with the deviation between m bar strain localization band central authorities and neighbouring strain data to be reduced gradually, and above-mentioned iteration or searching process can ascribe to and make objective function J reach minimum, namely

$min\left(J\right)=min\left\{{\mathrm{\Σ}}_{i=1}^m{\mathrm{\Σ}}_{j=1}^{c_i}{\[s_{ij}-f_{ij}(k_l,b_{il})\]}^2\right\}---\left(1\right)$

Wherein, subscript l represents any one in n iterative initial value, l=1 ~ n; c _irepresent the data number of i-th strain localization band, usually, the data number of differently strained localization band is different, i=1 ~ m; s _ijrepresent the ordinate of a jth data of i-th strain localization band, i=1 ~ m, j=1 ~ c _i, s _ij=s _ij(x _ij), x _ijfor the horizontal ordinate of these data; f _ijthe ordinate of line segment at a jth data place that representative and i-th strain localization band approach, due to f _ijlinear function, so, f _ij=(k _l, b _il)=k _lx _ij+ b _il, k _lthe common slope of 1 initial value (each line segment), b _ilthe different intercepts of 1 initial value, s _ij-f _ijrepresent 1 data point 9 and 1 sound out answer in deviation between 1 line segment, for obtain all data points 9 and one sound out answer in all line segments deviation square, need to carry out twice read group total: the 1st time, to square summation of the deviation of all data in 1 strain localization band 7,2nd time, to square summation of the deviation of each bar strain localization band 7; By continuous synchronous iteration, the minimum exploration answer that square to reach of above-mentioned deviation is made to be designated as Ω _*, Ω _*={ k _*, b _1*, b _2*..., b _m*, it has uniqueness, is required true answer 13.If to the data matching respectively of each bar strain localization band 7, then cannot ensure that the angle of every bar strain localization band 7 is identical, like this, for the slightly differentiated some line segments of some angles, be difficult to the unique consequence of the formula acquisition strain localization belt distance that employing 1 is determined.By arranging the number m many 1 of dimension than strain localization band of iterative initial value, and, wherein only comprise a slope, this is uniqueness and the accuracy of iteration result in order to ensure strain localization band 7 spacing, and it is that iteration result due to strain localization band 7 angle has taken into account consistent strain localization band 7 central authorities of all trends and neighbouring all data thereof that its uniqueness and accuracy are protected.

Described iteration parameter comprises: the design parameter of the threshold condition that the number of maximum algebraically, iterative initial value, iteration terminate and distinct group intelligent algorithm.Below, the process flow diagram (Fig. 5) and the calculation procedure that adopt particle swarm optimization algorithm to carry out iteration is provided:

(1) initialization particle is in zoning 6, according to the form of tested strain localization band 7, provides the estimated value of its centerline angles degree and intercept, the initial value of n particle is produced with this, the dimension of each initial value is m+1, and current particle is 1st generation particle, N=1;

(2) evaluate each particle and utilize formula (1), calculate the quality of each particle, namely evaluate the departure degree of each particle and strain localization band data;

(3) find arbitrary particle optimum and sound out answer p _bestfor arbitrary particle, in all iteration algebraically, find optimum exploration and answer p _id, i.e. p _best, subscript i is particle numbering, and i=1 ~ n, d are a certain dimension, d=1 ~ (m+1);

(4) optimum found in all particles sounds out answer g _bestin all iteration algebraically, the optimum found in all particles sounds out answer g _best;

(5) upgrade and sound out the flying speed that answer utilizes following formula more new particle and reposition

$v_{id}^{N+1}={\mathrm{wv}}_{id}^N+c_1{r}_1(g_{best}^N-{\stackrel{\‾}{x}}_{id}^N)+c_2{r}_2(p_{id}^N-{\stackrel{\‾}{x}}_{id}^N)---\left(2\right)$

$w=w_{max}-N\frac{w_{max}-w_{\min }}{N_{max}}---\left(3\right)$

${\stackrel{\‾}{x}}_{id}^{N+1}={\stackrel{\‾}{x}}_{id}^N+v_{id}^{N+1}---\left(4\right)$

Wherein, represent the speed of i-th particle when N+1 generation in d dimension; c ₁, c ₂for aceleration pulse, generally get c ₁=c ₂=2; r ₁and r ₂be respectively the random number of value between [0,1]; W is inertia constant, and value is linear decrease along with the increase of iteration algebraically N, its maximal value w _maxwith minimum value w _minbe respectively 1.4 and 0; N _maxfor the maximum iteration time preset; represent the coordinate of i-th particle when N+1 generation in d dimension.If particle upgrade after speed certain dimension on beyond scope [-v _max, v _max], be then limited on the border of this dimension.If the coordinate after particle upgrades, beyond region of search, is also limited on border.

(6) if meet the condition that iteration terminates, namely iteration result tends towards stability, then stop iteration.Otherwise iteration algebraically increases by 1, get back to (2) and continue to calculate, until meet the condition that iteration terminates.

Step 5: as shown in Figure 6, utilizes range formula between two parallel lines, calculates the spacing d of any two adjacent strain localization bands 7 _i, its formula easily pushes away

d _i＝|b _(i+1)*-b _i*|sinθ _*,i＝1～(m-1)(5)

Wherein, θ _*for the angle of line segment, θ _*with k _*relevant, so

d _i＝|b _(i+1)*-b _i*|sin[arctan(k _*)],i＝1～(m-1)(6)

As i=1, d ₁represent the 1st article with the spacing of the 2nd article of strain localization band, by that analogy.Also distance between beeline and dot formulae discovery d can be adopted _i, but require point point-blank.

Fig. 7 is different longitudinal strain ε _atime Uniaxial Compression sand sample maximum shear strain γ _maxdistribution plan, this result adopts the Digital Image Correlation Method based on particle group optimizing and Newton-Raphson alternative manner of independent development to obtain.Can find, along with ε _aincrease, strain localization band is more and more clear, and network situation is more and more obvious, therefrom chooses 3 and moves towards consistent strain localization band as measurand, wherein, using 3 quadrilateral areas 12 of restriction 3 strain localization bands as zoning.Fig. 8 is ε _amove towards the data of 3 consistent strain localization bands, iterative initial value and multidimensional Synchronous fluorimetry procedure chart when=0.16, wherein population is taken as 3, and namely iterative initial value 13-15 amounts to 3, as space is limited, does not provide other ε _atime procedure chart.Can find, along with the increase of iteration algebraically N, each answer of souning out constantly is drawn close to the data 16 of each bar strain localization band, and finally, the same target of each exploration answer trend, is required true answer 17.Fig. 9 is ε _a=0.16 and different iteration algebraically time objective function J evolution diagram, can find, along with the increase of iteration algebraically N, objective function J constantly reduces, and this illustrates that souning out answer constantly approaches to true answer, and when N=60 ~ 100, iteration result tends towards stability.Figure 10 is different longitudinal strain ε _atime tested strain localization band the evolution diagram of spacing, can find, different ε _atime, the distance between strain localization band is different, along with ε _aincrease, for the 1st band true answer 17-1 with for the true spacing d answering 17-2 of the 2nd band ₁there is the trend of reduction, for true answer 17-2 and the true spacing d answering 17-3 for the 3rd band of the 2nd band ₂there is the trend of increase.

Claims (8)

1. a multidimensional Synchronous fluorimetry measuring method for strain localization's belt distance development law, the method concrete steps are as follows:

Step 1: utilize capture apparatus to obtain one, sample under loaded conditions and comprise the digital picture on speckle surface;

Step 2: utilize sub-pix Digital Image Correlation Method, obtains the deformation field of specimen surface: horizontal line strain stress _x, perpendicular line strain stress _y, shear strain γ _xyand maximum shear strain γ _max;

Step 3: zoning is set, obtain every bar strain localization band central authorities and neighbouring strain data thereof, this zoning can be 1 quadrilateral area comprising many strain localization bands, may also be the set of the quadrilateral area comprising 1 strain localization band;

The situation of 1 quadrilateral area comprising many strain localization bands for zoning:

First, 1 the quadrilateral zoning comprising many strain localization bands is set;

Afterwards, according to strain field, determine to move towards the number m of consistent strain localization band;

Afterwards, utilize interpolation method, obtain the good various strain field of slickness in zoning;

Finally, utilize tested strain localization band angle and the width of rough estimate, arrange multiple long and narrow quadrilateral area, each long and narrow quadrilateral area only comprises 1 strain localization band, obtains every bar strain localization band central authorities and neighbouring strain data thereof;

The situation of the set of the quadrilateral area comprising 1 strain localization band for zoning:

First, according to strain field, determine to move towards the number m of consistent strain localization band;

Afterwards, utilize tested strain localization band angle and the width of rough estimate, arrange multiple long and narrow quadrilateral area as zoning, each long and narrow quadrilateral area only comprises 1 strain localization band;

Afterwards, utilize interpolation method, obtain the good various strain field of slickness in zoning;

Finally, every bar strain localization band central authorities and neighbouring strain data thereof is obtained;

Step 4: for every bar strain localization band, n iterative initial value and relevant iteration parameter are set, for arbitrary initial value, i.e. series of parallel line segment, the dimension of initial value is m+1, comprising 1 slope and m intercept, utilizes swarm intelligence algorithm, by continuous synchronous iteration, obtain the common slope of each bar line segment and intercepts different separately;

Step 5: utilize range formula between parallel lines, calculates the spacing of any two adjacent strain localization bands.

2. the multidimensional Synchronous fluorimetry measuring method of a kind of strain localization according to claim 1 belt distance development law, it is characterized in that, by strain localization band distance measurement problem arises in multidimensional Synchronous fluorimetry problem, by continuous synchronous iteration, reduce strain localization band data gradually and sound out the deviation between answering, until meet iteration termination condition.

Described synchronous iteration refers to sounds out answer to truly answering the process of approaching, in the process, m bar line segment is synchronous with the deviation between m bar strain localization band central authorities and neighbouring strain data thereof to be reduced gradually, and above-mentioned iteration or searching process can ascribe to and make objective function J reach minimum, namely

$min\left(J\right)=min\left\{{\mathrm{\Σ}}_{i=1}^m{\mathrm{\Σ}}_{j=1}^{c_i}{\[s_{ij}-f_{ij}(k_l,b_{il})\]}^2\right\}---\left(1\right)$

Wherein, subscript l represents any one in n iterative initial value, l=1 ~ n; c _irepresent the data number of i-th strain localization band, usually, the data number of differently strained localization band is different, i=1 ~ m; s _ijrepresent the ordinate of a jth data of i-th strain localization band, j=1 ~ c _i, s _ij=s _ij(x _ij), x _ijfor the horizontal ordinate of these data; f _ijthe ordinate of line segment at a jth data place that representative and i-th strain localization band approach, due to f _ijlinear function, so, f _ij=(k _l, b _il)=k _lx _ij+ b _il, k _lthe common slope of 1 initial value (each line segment), b _ilthe different intercepts of 1 initial value, s _ij-f _ijrepresent 1 data point and 1 sound out answer in deviation between 1 line segment; For obtain all data points and one sound out answer in all line segments deviation square, need to carry out twice read group total: the 1st time, to square summation of the deviation of all data in 1 strain localization band, the 2nd time, to square summation of the deviation of each bar strain localization band; The minimum exploration answer that square to reach of above-mentioned deviation is made to be designated as Ω _*, Ω _*={ k _*, b _1*, b _2*..., b _m*, it has uniqueness, is required true answer.

3. the multidimensional Synchronous fluorimetry measuring method of a kind of strain localization according to claim 1 belt distance development law, it is characterized in that, sound out answer for any one, its dimension, than strain localization band number m many 1, wherein comprises the common slope of each bar line segment and intercepts different separately.

4. the multidimensional Synchronous fluorimetry measuring method of a kind of strain localization according to claim 1 belt distance development law, it is characterized in that, utilize the overall parallel search capabilities of swarm intelligence algorithm, the different intercept and common slope of souning out each bar parallel segment of answering synchronously are searched for, take into account the data of all strain localization bands, ensure that correctness and the uniqueness of acquired results.

5. the multidimensional Synchronous fluorimetry measuring method of a kind of strain localization according to claim 1 belt distance development law, it is characterized in that, interpolation method is utilized to carry out interpolation to the strain field that the data volume obtained by sub-pix Digital Image Correlation Method in described zoning is limited, to obtain smooth strain field, according to the feature of strain field, obtain the data of tested strain localization band;

The feature of described strain field comprises: the statistical information of (1) maximum shear strain field, line strain field or shear strain field; (2) each scope of bar strain localization band and the estimated value of angle, above-mentioned estimated value is by directly observing or by virtue of experience determining.

6. the multidimensional Synchronous fluorimetry measuring method of a kind of strain localization according to claim 1 belt distance development law, is characterized in that, the spacing d of any two adjacent strain localization bands _icomputing formula be

d _i＝|b _(i+1)*-b _i*|sinθ _*＝|b _(i+1)*-b _i*|sin[arctan(k _*)],i＝1～(m-1)(2)

Wherein, the subscript * of parameter represents the parameter making objective function reach minimum, also can adopt the spacing of distance between beeline and dot formulae discovery two adjacent strain localization bands, but requires point point-blank.

7. the multidimensional Synchronous fluorimetry measuring method of a kind of strain localization according to claim 1 belt distance development law, it is characterized in that, tested strain localization band moves towards consistent, and namely its angle is substantially identical.

8. the multidimensional Synchronous fluorimetry measuring method of a kind of strain localization according to claim 1 belt distance development law, it is characterized in that, by calculating the spacing between adjacent strain localization band under different stress or strained condition in sample, the development law of strain localization's belt distance with stress or strain can be obtained.