CN103514370A - Optimization construction algorithm for aggregate grading of resin concrete - Google Patents

Abstract

The invention discloses an optimization construction algorithm for aggregate grading of resin concrete. The optimization construction algorithm comprises the following steps that (1) particle diameter intervals are chosen according to an actual aggregate situation; (2) grading orders are chosen according to needs, and particle diameter ranges of the intervals are determined according to the grading orders; (3) according to the selected grading basic parameters, an actual distribution function FF(D) of aggregate grading is established; (4) according to the established actual distribution function and a theoretical distribution function, a target optimization function of the aggregate grading is established; (6) a modern optimization algorithm is adopted to carry out iteration solving on a target, and distribution results of the intervals are obtained. The optimization construction algorithm can be suitable for different aggregate grading orders, grading precision of the aggregate of resin concrete is improved, mechanical performance of produced resin concrete materials is improved, and the manufactured materials can serve as an excellent machine tool structural component.

Description

A kind of optimization of resin concrete grading of aggregates builds algorithm

Technical field

The present invention relates to concrete manufacturing technology field, specifically, relate to the construction method of the multistage grading of aggregates ratio of a kind of high-accuracy resin concrete.

Background technology

Ultraprecision Machining just develops to nanoscale from micron, submicron order, and this just requires processing and measuring equipment etc. to have higher precision, static and dynamic performance and thermal stability.Traditional cast iron materials can not meet the designing requirement of new machine structure, the silica sand etc. of take is aggregate, and resin is made the resin concrete material of cementing agent, has high damping, good anti-vibration, the features such as thermal stability is strong have obtained certain application on ultra-precision machine tool.Because the composition of the resin concrete overwhelming majority is aggregate, so aggregate produces extremely important impact to the performance of resin concrete.

Particle packing theory is used for solving grading of aggregates problem, can be divided into discontinuous particle diameter and pile up theoretical and Continuous Particle Size accumulation theory.Two kinds of theories connect each other, and are all to pursue large as far as possible bulk density and the least possible porosity.

Present particle packing theoretical standard is much applied to prepare asphalt for building and concrete, yet, these grating standards are more is for building concrete but not the resin concrete of manufacture precision machine tool structural member, though there is reference, both have this significantly to distinguish; On the other hand, domestic research of grade-suit theory and the standard that is exclusively used in resin concrete is almost blank, grading distribution scheme is just chosen arbitrarily in many research, these experience schemes there is no correlation theory support, the grading distribution scheme that other utilize test method to obtain, the dynamic data base of the hundreds of thousands kind scheme of even having set up certain grade of grating having, this not only takes time and effort, and applicability is limited.

Summary of the invention

For the problems of the prior art, the optimization that the invention provides a kind of resin concrete grading of aggregates builds algorithm, solves the resin concrete grading distribution scheme gear shaper without theoretical support of manufacturing at present precision machine tool structural member, the problem that applicability is low.

The present invention is achieved through the following technical solutions:

The optimization of grading of aggregates builds an algorithm, comprises the following steps:

(1) according to actual aggregate situation, select grain diameter interval;

(2) select as required grating exponent number, and determine each interval particle size range according to grating exponent number;

(3), according to selected grating basic parameter, set up the actual distribution function F of grading of aggregates _f(D);

(4), according to selected grating basic parameter, set up the theoretic distribution function F of grading of aggregates _e(D);

(5), according to actual distribution function and the theoretic distribution function set up, set up the objective optimization function of grading of aggregates;

(6) adopt modern optimization algorithm, such as genetic algorithm is carried out iterative to targeted, obtain each interval distribution results.

In described step (1), actual aggregate situation refers to the aggregate size scope of factory's actual production, can directly buy or can directly with experimental facilities, process, and scope is [d ₀, d _n], d in formula ₀for particle minimum grain size, d _nfor maximum particle diameter.

In described step (2), selected grating exponent number refers to selected grating exponent number according to actual needs as required, can be Huo Qi rank, ,Liu rank, quadravalence ,Wu rank.

In described step (2), according to grating exponent number, determine each interval particle size range, described particle size range is decided by the screening scope of the sieve of factory's actual production, and when selected grating exponent number is n, having each particle size interval is d ₀～d ₁, d ₁～d ₂..., d _n-1～d _n.

Actual grain size distribution function F in described step (3) _f(D) refer to the accumulative total percent of pass of each particle diameter, monotonic nondecreasing, and have the F of being _f(d ₀)=0, F _f(d _n)=1;

$F_F\left(D\right)=\frac{1}{V_F}[\underset{i=1}{\overset{n-1}{\mathrm{\Σ}}}{w}_i{\∫}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_n{\∫}_{d_{n-1}}^D{f}_{\mathrm{Fn}}\left(D\right)\mathrm{dD}],(d_{n-1}\≤D\≤d_n)$

W in formula _ifor every grade particles amount of choosing, %;

$f_{\mathrm{Fi}}\left(D\right)=\frac{d}{\mathrm{dD}}\left(F_{\mathrm{Fi}}\left(D\right)\right),(i=1~n)$

$V_F=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i{\∫}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD},(i=1~n)$

According to described step, can generate the actual distribution of particles of aggregate under n level grating.

Theoretical particle size distribution function F in described step (4) _e(D) refer to the accumulative total percent of pass of each particle diameter, i.e. F _e(d ₀)=0, F _e(d _n)=1;

$F_E\left(D\right)=\frac{1}{V_E}[\underset{i=1}{\overset{n-1}{\mathrm{\Σ}}}{w}_i{\∫}_{d_{i-1}}^{d_i}{f}_{\mathrm{Ei}}\left(D\right)\mathrm{dD}+w_n{\∫}_{d_{n-1}}^D{f}_{\mathrm{En}}\left(D\right)\mathrm{dD}],(d_{n-1}\≤D\≤d_n)$

W in formula _ifor every grade particles amount of choosing, %;

$f_{\mathrm{Ei}}\left(D\right)=\frac{d}{\mathrm{dD}}\left(F_{\mathrm{Ei}}\left(D\right)\right),(i=1~n)$

$V_E=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i{\∫}_{d_{i-1}}^{d_i}{f}_{\mathrm{Ei}}\left(D\right)\mathrm{dD},(i=1~n)$

According to described step, can generate the theoretical distribution of particles of aggregate under n level grating.

In described step (5), objective optimization function is the variance minimum of theoretical distribution and actual distribution, guarantees that each interval grain amount is all greater than zero simultaneously, and function is:

$\left\{\begin{array}{c}s=\min \left\{{\∫}_{d_0}^{d_n}{[F_F\left(D\right)-F_E\left(D\right)]}^2\mathrm{dD}\right\}\\ w_i\≥0,(i=1~n)\end{array}\right.$

In formula, every implication as hereinbefore.

In described step (6), utilize modern optimization algorithm to calculate and refer to that the objective function building in step (5) belongs to nonlinear problem, traditional algorithm cannot solve, and utilizes modern optimization algorithm genetic algorithm to solve, and solves s w hour simultaneously _i, then use (i=1～n) can obtain grating result:

$p_i=w_i/\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i$

P in formula _ifor interval aggregate distributed weight number percent.

Beneficial effect of the present invention is: compared with prior art, an innovation of maximum of the present invention is exactly the general-purpose algorithm that has proposed a kind of optimization of resin concrete material grading of aggregates, has the following advantages:

1) filled up to a certain extent the vacancy of resin concrete grading of aggregates theory, the grading of aggregates that is applicable to different rank is calculated, and actual production is had to directive significance;

2) the multistage grading of aggregates that the present invention optimizes is theoretical, has improved the grating precision of aggregate, to improving the mechanical property tool of resin concrete part, has certain effect.

Algorithm of the present invention can be applicable to different grading of aggregates exponent numbers, improves resin concrete grading of aggregates precision, improves the mechanical property of the resin concrete material of producing, and makes the material of manufacturing can be used as good machine tool structure part.

Accompanying drawing explanation

Fig. 1 is 7 grades of grating Different Size Fractions particle diameters;

Fig. 2 is 4 grades of grating Different Size Fractions particle diameters;

Fig. 3 is 5 grades of grating Different Size Fractions particle diameters;

Fig. 4 is 6 grades of grating Different Size Fractions particle diameters;

Fig. 5 is F _f1(D) matched curve;

Fig. 6 is F _f2(D) matched curve;

Fig. 7 is F _f3(D) matched curve;

Fig. 8 is F _f4(D) matched curve;

Fig. 9 is F _f5(D) matched curve;

Figure 10 is F _f6(D) matched curve;

Figure 11 is F _f7(D) matched curve;

Figure 12 is three kinds of theory gradation curves comparison (horizontal ordinate is particles of aggregates particle diameter, and ordinate is accumulation percent of pass).

Embodiment

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

First so that the size-grade distribution of actual aggregate as far as possible approximation theory model be that core concept re-establishes mathematical model.

The particle shape of supposing accumulation system is spherical.When the grading of aggregates exponent number of design is n, be located at grain diameter interval [d0, dn] upper, between each graded region, be d0～d1, d1～d2 ..., dn-1～dn, the every grade particles amount of choosing w1, w2 ..., wn.Establishing actual particle size distribution is FF (D) again, and the size-grade distribution of theoretical model is FE (D), and FF (D) and FE (D) be monotonic nondecreasing and FF (d0)=FE (d0)=0 continuously, FF (dn)=FE (dn)=1.And then establish the probability density that fF (D) and fE (D) are respectively FF (D) and FE (D), i.e. fF (D)=FF (D), fE (D)=FE (D).What wherein should be noted that has:

1) in practical application, classification is generally that the multiple particle size range by manufacturer production aggregate determines, user only need therefrom select the classification of own needs.If user needs tailor-make classification, just aggregate again must be carried out to fragmentation and sieves with standard sieve.When classification is special, even also need the screen cloth of customized special type.This can increase cost and the production cycle of preparing resin concrete material undoubtedly greatly.

2) fF (D) in different grain size interval may be different, respectively with fF1 (D), and fF2 (D) ..., fFn (D) represents, need to sample respectively and draw screening table, and with in addition differentiate and obtaining after matching of smooth curve.

3) fE (D) uses classical theoretical equation continuously to D differentiate conventionally.

Therefore can obtain mathematical model as follows:

$F_F\left(D\right)=\frac{1}{V_F}[\underset{i=1}{\overset{n-1}{\mathrm{\Σ}}}{w}_i{\∫}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_n{\∫}_{d_{n-1}}^D{f}_{\mathrm{Fn}}\left(D\right)\mathrm{dD}],(d_{n-1}\≤D\≤d_n)$

$F_E\left(D\right)={\∫}_{d_{i-1}}^{d_i}{f}_E\left(D\right)\mathrm{dD}+{\∫}_{d_i}^D{f}_E\left(D\right)\mathrm{dD},(d_{n-1}\≤D\≤d_n)$

Wherein $V_F=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i{\∫}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD},(i=1~n)$

Objective function:

$\left\{\begin{array}{c}s=\min \left\{{\∫}_{d_0}^{d_n}{[F_F\left(D\right)-F_E\left(D\right)]}^2\mathrm{dD}\right\}\\ w_i\≥0,(i=1~n)\end{array}\right.$

Solve

can obtain the number percent of aggregates at different levels.

Resin concrete grading of aggregates of the present invention can have multiple embodiments, is described in more detail below with embodiment, and the present invention be take embodiment by example but by the following example, do not limited.

Embodiment 1

This example adopts 7 gratings to pile up, i.e. d ₀=0.076mm, d ₁=0.15mm, d ₂=0.22mm, d ₃=0.5mm, d ₄=0.9mm, d ₅=1.6mm, d ₆=2.5mm, d ₇=4mm, as shown in Figure 1.

Actual distribution F _f(D) as shown in the formula:

$F_F\left(D\right)=\left\{\begin{array}{cc}\frac{1}{V_F}{w}_1{\∫}_{d_0}^D{f}_{F1}\left(D\right)\mathrm{dD}& (d_0\≤D\≤d_1)\\ \frac{1}{V_F}[w_1{\∫}_{d_0}^{d_1}{f}_{F1}\left(D\right)\mathrm{dD}+w_2{\∫}_{d_1}^D{f}_{F2}\left(D\right)\mathrm{dD}]& (d_1\≤D\≤d_2)\\ \frac{1}{V_F}[\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{w}_i{\∫}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_3{\∫}_{d_2}^D{f}_{F3}\left(D\right)\mathrm{dD}]& (d_2\≤D\≤d_3)\\ \frac{1}{V_F}[\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{w}_i{\∫}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_4{\∫}_{d_3}^D{f}_{F4}\left(D\right)\mathrm{dD}]& (d_3\≤D\≤d_4)\\ \frac{1}{V_F}[\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{w}_i{\∫}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_5{\∫}_{d_4}^D{f}_{F5}\left(D\right)\mathrm{dD}]& (d_4\≤D\≤d_5)\\ \frac{1}{V_F}[\underset{i=1}{\overset{5}{\mathrm{\Σ}}}{w}_i{\∫}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_6{\∫}_{d_5}^D{f}_{F6}\left(D\right)\mathrm{dD}]& (d_5\≤D\≤d_6)\\ \frac{1}{V_F}[\underset{i=1}{\overset{6}{\mathrm{\Σ}}}{w}_i{\∫}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_7{\∫}_{d_6}^D{f}_{F7}\left(D\right)\mathrm{dD}]& (d_6\≤D\≤d_7)\end{array}\right.$

Wherein $V_F=\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{w}_i{\∫}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD},f_{\mathrm{Fi}}\left(D\right)=\frac{d}{\mathrm{dD}}\left(F_{\mathrm{Fi}}\left(D\right)\right),(i=1~7)$

The granularity of every grade of aggregate has been carried out respectively to actual sampling Detection.With standard sieve screening, draw screening table, as shown in table 1.By Curve Fitting Tool in Matlab software, data measured is carried out curve fitting subsequently, obtained aggregate size distribution F _fi(D).It should be noted that:

1) in actual screening, the particle diameter of every grade of aggregate generally has 2% left and right and exceeds particle size range at the corresponding levels, due to this part aggregate seldom, so ignore;

2) to want the function of matching be distribution function in the present invention, is monotonic nondecreasing, so can not use

deng curve.By more various matched curves, the present invention has chosen Power curve y=ax ^b+ c carries out matching, as accompanying drawing 5～11.This curve monotonic nondecreasing, and error of fitting is very little.F _f1(D)～F _f7(D) coefficient a, b, c and error term are square as table 2.

Table 1 Different Size Fractions sieve aperture percent of pass

Table 2 actual distribution function F _fi(D) the every coefficient of expression formula and error of fitting

Theoretical model F _e(D) as shown in the formula:

$F_E\left(D\right)=\left\{\begin{array}{cc}{\∫}_{d_0}^D{f}_E\left(D\right)\mathrm{dD}& (d_0\≤D\≤d_1)\\ {\∫}_{d_0}^{d_1}{f}_E\left(D\right)\mathrm{dD}+{\∫}_{d_1}^D{f}_E\left(D\right)\mathrm{dD}& (d_1\≤D\≤d_2)\\ \underset{i=1}{\overset{2}{\mathrm{\Σ}}}{\∫}_{d_{i-1}}^{d_i}{f}_E\left(D\right)\mathrm{dD}+{\∫}_{d_2}^D{f}_E\left(D\right)\mathrm{dD}& (d_2\≤D\≤d_3)\\ \underset{i=1}{\overset{3}{\mathrm{\Σ}}}{\∫}_{d_{i-1}}^{d_i}{f}_E\left(D\right)\mathrm{dD}+{\∫}_{d_3}^D{f}_E\left(D\right)\mathrm{dD}& (d_3\≤D\≤d_4)\\ \underset{i=1}{\overset{4}{\mathrm{\Σ}}}{\∫}_{d_{i-1}}^{d_i}{f}_E\left(D\right)\mathrm{dD}+{\∫}_{d_4}^D{f}_E\left(D\right)\mathrm{dD}& (d_4\≤D\≤d_5)\\ \underset{i=1}{\overset{5}{\mathrm{\Σ}}}{\∫}_{d_{i-1}}^{d_i}{f}_E\left(D\right)\mathrm{dD}+{\∫}_{d_5}^D{f}_E\left(D\right)\mathrm{dD}& (d_5\≤D\≤d_6)\\ \underset{i=1}{\overset{6}{\mathrm{\Σ}}}{\∫}_{d_{i-1}}^{d_i}{f}_E\left(D\right)\mathrm{dD}+{\∫}_{d_6}^D{f}_E\left(D\right)\mathrm{dD}& (d_6\≤D\≤d_7)\end{array}\right.$

With Dinger-Funk equation description theory model, during n=0.37, bulk density is maximum

$f_E\left(D\right)\frac{d}{\mathrm{dD}}\left(\frac{D^{0.37}-{d_s}^{0.37}}{{d_l}^{0.37}-{d_s}^{0.37}}\right)$

Objective function:

$\left\{\begin{array}{c}s=\min \left\{{\∫}_{d_0}^{d_7}{[F_F\left(D\right)-F_E\left(D\right)]}^2\mathrm{dD}\right\}\\ w_i\≥0,(i=1~n)\end{array}\right.$

Solve $p_i=w_i/\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i,(i=1~7)$ Can obtain grating result.

While utilizing in Matlab this objective function of genetic algorithm for solving, in Matlab software, the present invention is as follows by genetic algorithm relative parameters setting: TolCon=1e-40, TolFun=1e-40, Generation=200, Population Size=50, has added up genetic algorithm result altogether 100 times, and partial results is in Table 3.

Table 3 genetic algorithm optimization result

Each variance of organizing pi data is very little, and the result that genetic algorithm is described is reliable and accurate, meanwhile, secondly, the F in the present invention's acquiescence _a1(D)～F _a7(D) be being uniformly distributed on intervals at different levels.The present invention calculates grating result in this case, and by it during with table 3 and n=0.37 the result of Dinger-Funk equation compare after discovery, three kinds of results are difference slightly, as shown in table 4 and Figure 12.

The comparison of three kinds of theory gradation results of table 4

It is 7 o'clock that this example can obtain grading of aggregates exponent number, and umber proportionings at different levels are as table 5:

Table 57 grade grading of aggregates parameter

Embodiment 2

This example adopts 4 gratings to pile up, d ₀=0.5mm, d ₁=0.9mm, d ₂=2mm, d ₃=2.36mm, d ₄=4mm, as shown in Figure 2.

Actual distribution F _f(D) as shown in the formula:

$F_F\left(D\right)=\left\{\begin{array}{cc}\frac{1}{V_F}{w}_1{\&Integral;}_{d_0}^D{f}_{F1}\left(D\right)\mathrm{dD}& (d_0\&le;D\&le;d_1)\\ \frac{1}{V_F}[w_1{\&Integral;}_{d_0}^{d_1}{f}_{F1}\left(D\right)\mathrm{dD}+{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="2013104303827100003DEST\_PATH\_IMAGE005.png"\; state="\{\{state\}\}">w</figure-callout>}}_2{\&Integral;}_{d_1}^D{f}_{F2}\left(D\right)\mathrm{dD}]& (d_1\&le;D\&le;d_2)\\ \frac{1}{V_F}[\underset{i=1}{\overset{2}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_3{\&Integral;}_{d_2}^D{f}_{F3}\left(D\right)\mathrm{dD}]& ({\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="2013104303827100003DEST\_PATH\_IMAGE005.png"\; state="\{\{state\}\}">d</figure-callout>}}_2\&le;D\&le;d_3)\\ \frac{1}{V_F}[\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_4{\&Integral;}_{d_3}^D{f}_{F4}\left(D\right)\mathrm{dD}]& (d_3\&le;D\&le;d_4)\end{array}\right.$

Wherein $V_F=\underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD},f_{\mathrm{Fi}}\left(D\right)=\frac{d}{\mathrm{dD}}\left(F_{\mathrm{Fi}}\left(D\right)\right),(i=1~4)$

Theoretical model F _e(D) as shown in the formula:

$F_E\left(D\right)=\left\{\begin{array}{cc}{\&Integral;}_{d_0}^D{f}_T\left(D\right)\mathrm{dD}& (d_0\&le;D\&le;d_1)\\ {\&Integral;}_{d_0}^{d_1}{f}_T\left(D\right)\mathrm{dD}+{\&Integral;}_{d_1}^D{f}_T\left(D\right)\mathrm{dD}& (d_1\&le;D\&le;d_2)\\ \underset{i=1}{\overset{2}{\mathrm{\&Sigma;}}}{\&Integral;}_{d_{i-1}}^{d_i}{f}_T\left(D\right)\mathrm{dD}+{\&Integral;}_{d_2}^D{f}_T\left(D\right)\mathrm{dD}& ({\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="2013104303827100003DEST\_PATH\_IMAGE005.png"\; state="\{\{state\}\}">d</figure-callout>}}_2\&le;D\&le;d_2)\\ \underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{\&Integral;}_{d_{i-1}}^{d_i}{f}_T\left(D\right)\mathrm{dD}+{\&Integral;}_{d_3}^D{f}_T\left(D\right)\mathrm{dD}& (d_3\&le;D\&le;d_4)\end{array}\right.$

With Dinger-Funk equation description theory model, during n=0.37, bulk density is maximum

$f_F\left(D\right)=\frac{d}{\mathrm{dD}}\left(\frac{D^{0.37}-{d_s}^{0.37}}{{d_l}^{0.37}-{d_s}^{0.37}}\right)$

Objective function:

$\left\{\begin{array}{c}s={\&Integral;}_{d_0}^{d_4}{[F_F\left(D\right)-F_E\left(D\right)]}^2\mathrm{dD}\}\\ w_i\&GreaterEqual;0,(i=1~4)\end{array}\right.$

Solve $p_i=w_i/\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i,(i=1~4)$ Can obtain grating result.

While utilizing in Matlab this objective function of genetic algorithm for solving, in Matlab software, the present invention is as follows by genetic algorithm relative parameters setting: TolCon=1e-40, TolFun=1e-40, Generation=200, Population Size=50, has added up genetic algorithm result altogether 100 times, and net result is as shown in table 6.

Table 6 genetic algorithm optimization result

It is 4 o'clock that this example can obtain grading of aggregates exponent number, and umber proportionings at different levels are as shown in table 7:

Table 74 grade grading of aggregates parameter

Embodiment 3

This example adopts 5 gratings to pile up, i.e. d ₀=0.22mm, d ₁=0.5mm, d ₂=0.9mm, d ₃=1.6mm, d ₄=2.5mm, d ₅=4mm, as shown in Figure 3.

Actual distribution F _f(D) as shown in the formula:

$F_F\left(D\right)=\left\{\begin{array}{cc}\frac{1}{V_F}{w}_1{\&Integral;}_{d_0}^D{f}_{F1}\left(D\right)\mathrm{dD}& (d_0\&le;D\&le;d_1)\\ \frac{1}{V_F}[w_1{\&Integral;}_{d_0}^{d_1}{f}_{F1}\left(D\right)\mathrm{dD}+{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="2013104303827100003DEST\_PATH\_IMAGE005.png"\; state="\{\{state\}\}">w</figure-callout>}}_2{\&Integral;}_{d_1}^D{f}_{F2}\left(D\right)\mathrm{dD}]& (d_1\&le;D\&le;d_2)\\ \frac{1}{V_F}[\underset{i=1}{\overset{2}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_3{\&Integral;}_{d_2}^D{f}_{F3}\left(D\right)\mathrm{dD}]& ({\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="2013104303827100003DEST\_PATH\_IMAGE005.png"\; state="\{\{state\}\}">d</figure-callout>}}_2\&le;D\&le;d_3)\\ \frac{1}{V_F}[\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_4{\&Integral;}_{d_3}^D{f}_{F4}\left(D\right)\mathrm{dD}]& (d_3\&le;D\&le;d_4)\\ \frac{1}{V_F}[\underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_5{\&Integral;}_{d_4}^D{f}_{F5}\left(D\right)\mathrm{dD}]& (d_4\&le;D\&le;d_5)\end{array}\right.$

Wherein $V_F=\underset{i=1}{\overset{5}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD},f_{\mathrm{Fi}}\left(D\right)=\frac{d}{\mathrm{dD}}\left(F_{\mathrm{Fi}}\left(D\right)\right),(i=1~5)$

The granularity of every grade of aggregate has been carried out respectively to actual sampling Detection.With standard sieve screening, draw screening table, as table 1.By Curve Fitting Tool in Matlab software, data measured is carried out curve fitting subsequently, obtained aggregate size distribution F _fi(D).

Theoretical model FE (D) as shown in the formula:

$F_E\left(D\right)=\left\{\begin{array}{cc}{\&Integral;}_{d_0}^D{f}_E\left(D\right)\mathrm{dD}& (d_0\&le;D\&le;d_1)\\ {\&Integral;}_{d_0}^{d_1}{f}_E\left(D\right)\mathrm{dD}+{\&Integral;}_{d_1}^D{f}_E\left(D\right)\mathrm{dD}& (d_1\&le;D\&le;d_2)\\ \underset{i=1}{\overset{2}{\mathrm{\&Sigma;}}}{\&Integral;}_{d_{i-1}}^{d_i}{f}_E\left(D\right)\mathrm{dD}+{\&Integral;}_{d_2}^D{f}_E\left(D\right)\mathrm{dD}& ({\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="2013104303827100003DEST\_PATH\_IMAGE005.png"\; state="\{\{state\}\}">d</figure-callout>}}_2\&le;D\&le;d_3)\\ \underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{\&Integral;}_{d_{i-1}}^{d_i}{f}_E\left(D\right)\mathrm{dD}+{\&Integral;}_{d_3}^D{f}_E\left(D\right)\mathrm{dD}& (d_3\&le;D\&le;d_4)\\ \underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}{\&Integral;}_{d_{i-1}}^{d_i}{f}_E\left(D\right)\mathrm{dD}+{\&Integral;}_{d_4}^D{f}_E\left(D\right)\mathrm{dD}& (d_4\&le;D\&le;d_5)\end{array}\right.$

With Dinger-Funk equation description theory model, during n=0.37, bulk density is maximum

$f_E\left(D\right)\frac{d}{\mathrm{dD}}\left(\frac{D^{0.37}-{d_s}^{0.37}}{{d_l}^{0.37}-{d_s}^{0.37}}\right)$

Objective function:

$\left\{\begin{array}{c}s=\min \left\{{\&Integral;}_{d_0}^{d_5}{[F_F\left(D\right)-F_E\left(D\right)]}^2\mathrm{dD}\right\}\\ w_i\&GreaterEqual;0,i=1~5\end{array}\right.$

Solve $p_i=w_i/\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i,(i=1~5)$ Can obtain grating result.

While utilizing in Matlab this objective function of genetic algorithm for solving, in Matlab software, the present invention is as follows by genetic algorithm relative parameters setting: TolCon=1e-40, TolFun=1e-40, Generation=200, Population Size=50, has added up genetic algorithm result altogether 100 times, and partial results is in Table 8.

Table 8 genetic algorithm optimization result

It is 5 o'clock that this example can obtain grading of aggregates exponent number, and umber proportionings at different levels are as table 9:

Table 95 grade grading of aggregates parameter

Embodiment 4

This example adopts 6 gratings to pile up, i.e. d ₀=0.15mm, d ₁=0.22mm, d ₂=0.5mm, d ₃=0.9mm, d ₄=1.6mm, d ₅=2.5mm, d ₆=4mm, as shown in Figure 4.

Actual distribution F _f(D) as shown in the formula:

$F_F\left(D\right)=\left\{\begin{array}{cc}\frac{1}{V_F}{w}_1{\&Integral;}_{d_0}^D{f}_{F1}\left(D\right)\mathrm{dD}& (d_0\&le;D\&le;d_1)\\ \frac{1}{V_F}[w_1{\&Integral;}_{d_0}^{d_1}{f}_{F1}\left(D\right)\mathrm{dD}+w_2{\&Integral;}_{d_1}^D{f}_{F2}\left(D\right)\mathrm{dD}]& (d_1\&le;D\&le;d_2)\\ \frac{1}{V_F}[\underset{i=1}{\overset{2}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_3{\&Integral;}_{d_2}^D{f}_{F3}\left(D\right)\mathrm{dD}]& (d_2\&le;D\&le;d_3)\\ \frac{1}{V_F}[\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_4{\&Integral;}_{d_3}^D{f}_{F4}\left(D\right)\mathrm{dD}]& (d_3\&le;D\&le;d_4)\\ \frac{1}{V_F}[\underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_5{\&Integral;}_{d_4}^D{f}_{F5}\left(D\right)\mathrm{dD}]& (d_4\&le;D\&le;d_5)\\ \frac{1}{V_F}[\underset{i=1}{\overset{5}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_6{\&Integral;}_{d_5}^D{f}_{F6}\left(D\right)\mathrm{dD}]& (d_5\&le;D\&le;d_6)\end{array}\right.$

Wherein $V_F=\underset{i=1}{\overset{6}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD},f_{\mathrm{Fi}}\left(D\right)=\frac{d}{\mathrm{dD}}\left(F_{\mathrm{Fi}}\left(D\right)\right),(i=1~6)$

The granularity of every grade of aggregate has been carried out respectively to actual sampling Detection.With standard sieve screening, draw screening table, as table 1.By Curve Fitting Tool in Matlab software, data measured is carried out curve fitting subsequently, obtained aggregate size distribution F _fi(D).

Theoretical model F _e(D) as shown in the formula:

$F_E\left(D\right)=\left\{\begin{array}{cc}{\&Integral;}_{d_0}^D{f}_E\left(D\right)\mathrm{dD}& (d_0\&le;D\&le;d_1)\\ {\&Integral;}_{d_0}^{d_1}{f}_E\left(D\right)\mathrm{dD}+{\&Integral;}_{d_1}^D{f}_E\left(D\right)\mathrm{dD}& (d_1\&le;D\&le;d_2)\\ \underset{i=1}{\overset{2}{\mathrm{\&Sigma;}}}{\&Integral;}_{d_{i-1}}^{d_i}{f}_E\left(D\right)\mathrm{dD}+{\&Integral;}_{d_2}^D{f}_E\left(D\right)\mathrm{dD}& ({\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="2013104303827100003DEST\_PATH\_IMAGE005.png"\; state="\{\{state\}\}">d</figure-callout>}}_2\&le;D\&le;d_3)\\ \underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{\&Integral;}_{d_{i-1}}^{d_i}{f}_E\left(D\right)\mathrm{dD}+{\&Integral;}_{d_3}^D{f}_E\left(D\right)\mathrm{dD}& (d_3\&le;D\&le;d_4)\\ \underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}{\&Integral;}_{d_{i-1}}^{d_i}{f}_E\left(D\right)\mathrm{dD}+{\&Integral;}_{d_4}^D{f}_E\left(D\right)\mathrm{dD}& (d_4\&le;D\&le;d_5)\end{array}\right.$

With Dinger-Funk equation description theory model, during n=0.37, bulk density is maximum

$f_E\left(D\right)\frac{d}{\mathrm{dD}}\left(\frac{D^{0.37}-{d_s}^{0.37}}{{d_l}^{0.37}-{d_s}^{0.37}}\right)$

Objective function:

$\left\{\begin{array}{c}s=\min \left\{{\&Integral;}_{d_0}^{d_6}{[F_F\left(D\right)-F_E\left(D\right)]}^2\mathrm{dD}\right\}\\ w_i\&GreaterEqual;0,i=1~6\end{array}\right.$

Solve $p_i=w_i/\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i,(i=1~6)$ Can obtain grating result.

While utilizing in Matlab this objective function of genetic algorithm for solving, in Matlab software, the present invention is as follows by genetic algorithm relative parameters setting: TolCon=1e-40, TolFun=1e-40, Generation=200, Population Size=50, has added up genetic algorithm result altogether 100 times, and partial results is in Table 10.

Table 10 genetic algorithm optimization result

It is 6 o'clock that this example can obtain grading of aggregates exponent number, and umber proportionings at different levels are as table 11:

Table 116 grade grading of aggregates parameter

Claims (8)

1. the optimization of resin concrete grading of aggregates builds an algorithm, it is characterized in that, comprises the following steps:

(1) according to actual aggregate situation, select grain diameter interval;

(2) select as required grating exponent number, and determine each interval particle size range according to grating exponent number;

(3), according to selected grating basic parameter, set up the actual distribution function F of grading of aggregates _f(D);

(4), according to selected grating basic parameter, set up the theoretic distribution function F of grading of aggregates _e(D);

(5), according to actual distribution function and the theoretic distribution function set up, set up the objective optimization function of grading of aggregates;

(6) adopt modern optimization algorithm to carry out iterative to targeted, obtain each interval distribution results.

2. the optimization of a kind of resin concrete grading of aggregates according to claim 1 builds algorithm, it is characterized in that: in described step (1), actual aggregate situation refers to the aggregate size scope of factory's actual production, can directly buy or can directly with experimental facilities, process, scope is [d ₀, d _n], d in formula ₀for particle minimum grain size, d _nfor maximum particle diameter.

3. the optimization of a kind of resin concrete grading of aggregates according to claim 1 builds algorithm, it is characterized in that: in described step (2), selected grating exponent number refers to selected grating exponent number according to actual needs as required, can be Huo Qi rank, ,Liu rank, quadravalence ,Wu rank.

4. the optimization of a kind of resin concrete grading of aggregates according to claim 1 builds algorithm, it is characterized in that: in described step (2), according to grating exponent number, determine each interval particle size range, described particle size range is decided by the screening scope of the sieve of factory's actual production, when selected grating exponent number is n, having each particle size interval is d ₀～d ₁, d ₁～d ₂..., d _n-1～d _n.

5. the optimization of a kind of resin concrete grading of aggregates according to claim 1 builds algorithm, it is characterized in that: actual grain size distribution function F in described step (3) _f(D) refer to the accumulative total percent of pass of each particle diameter, monotonic nondecreasing, and have the F of being _f(d ₀)=0, F _f(d _n)=1;

$F_F\left(D\right)=\frac{1}{V_F}[\underset{i=1}{\overset{n-1}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD}+w_n{\&Integral;}_{d_{n-1}}^D{f}_{\mathrm{Fn}}\left(D\right)\mathrm{dD}],(d_{n-1}\&le;D\&le;d_n)$

W in formula _ifor every grade particles amount of choosing, %;

$f_{\mathrm{Fi}}\left(D\right)=\frac{d}{\mathrm{dD}}\left(F_{\mathrm{Fi}}\left(D\right)\right),(i=1~n)$

$V_F=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Fi}}\left(D\right)\mathrm{dD},(i=1~n)$

According to described step, can generate the actual distribution of particles of aggregate under n level grating.

6. the optimization of a kind of resin concrete grading of aggregates according to claim 1 builds algorithm, it is characterized in that: theoretical particle size distribution function F in described step (4) _e(D) refer to the accumulative total percent of pass of each particle diameter, i.e. F _e(d ₀)=0, F _e(d _n)=1;

$F_E\left(D\right)=\frac{1}{V_E}[\underset{i=1}{\overset{n-1}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Ei}}\left(D\right)\mathrm{dD}+w_n{\&Integral;}_{d_{n-1}}^D{f}_{\mathrm{En}}\left(D\right)\mathrm{dD}],(d_{n-1}\&le;D\&le;d_n)$

W in formula _ifor every grade particles amount of choosing, %;

$f_{\mathrm{Ei}}\left(D\right)=\frac{d}{\mathrm{dD}}\left(F_{\mathrm{Ei}}\left(D\right)\right),(i=1~n)$

$V_E=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i{\&Integral;}_{d_{i-1}}^{d_i}{f}_{\mathrm{Ei}}\left(D\right)\mathrm{dD},(i=1~n)$

According to described step, can generate the theoretical distribution of particles of aggregate under n level grating.

7. the optimization of a kind of resin concrete grading of aggregates according to claim 1 builds algorithm, it is characterized in that: in described step (5), objective optimization function is the variance minimum of theoretical distribution and actual distribution, guarantee that each interval grain amount is all greater than zero, function is simultaneously:

$\left\{\begin{array}{c}s=\min \left\{{\&Integral;}_{d_0}^{d_n}{[F_F\left(D\right)-F_E\left(D\right)]}^2\mathrm{dD}\right\}\\ w_i\&GreaterEqual;0,(i=1~n)\end{array}\right.$

In formula, every implication as hereinbefore.

8. the optimization of a kind of resin concrete grading of aggregates according to claim 1 builds algorithm, it is characterized in that: in described step (6), utilize modern optimization algorithm to calculate and refer to that the objective function building in step (5) belongs to nonlinear problem, traditional algorithm cannot solve, utilize modern optimization algorithm genetic algorithm to solve preferably, solve s w hour simultaneously _i, then use (i=1～n) can obtain grating result:

$p_i=w_i/\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i$

P in formula _ifor interval aggregate distributed weight number percent.

Images