CN104261742A - Non-linear optimization method for mix proportion of concrete - Google Patents

Abstract

The invention discloses a non-linear optimization method for mix proportion of concrete. The non-linear optimization method is carried out according to the following steps: firstly, establishing a neural network model for predicting the performance of concrete; secondly, determining the target and constraint conditions of an optimization model for mix proportion; thirdly, establishing the optimization model for mix proportion by virtue of a particle swarm optimization algorithm; and fourthly, carrying out particle reduction, namely, respectively reducing optimal fitness values obtained by calculation and positions of the optimal fitness values into the lowest cost value and the corresponding mix proportion of concrete and completing the method. The non-linear optimization method has the beneficial effects that (1) the non-linear prediction model of the performance of concrete and the non-linear optimization model of the mix proportion are established; (2) the problem of over-fitting control in the non-linear prediction of the performance of concrete is solved; and (3) the global optimization of the mix proportion of concrete is achieved and the optimization efficiency is relatively high.

Description

The nonlinear optimization method of concrete mix

Technical field

The invention belongs to technical field of concrete production, be mainly used in mix-design and the optimization, the particularly mixtures optimal design of polynary cementitious material concrete of (as commerical ready-mixed concrete company, ready mixed concrete factory) in mass-producing concrete production.

Background technology

The inorganic non-metal composite material that concrete is made up of cement, water, sand, stone and adulterant, admixture is consumption one of material of construction the most widely in modern capital construction projects.In the production of concrete material, mix-design is as " formula ", and direct impact even determines concrete performance.From that time that concrete material produces, mix-design problem just becomes a critical technical problem.Traditional Four composition concrete (only being formed by cement, water, sand and stone mix) meets Borrow's rice formula of cement-water ratio-intensity, and its mix-design is relatively simple.In recent years; along with mixing of adulterant and the admixtures such as water reducer, retardant such as flyash, granulated blast-furnace slag pulverized powder, silicon ash; and concrete performance is to high-strength, high-performance future development, Borrow's rice formula has been difficult to meet design requirement, must seek new approach.Current Chinese code of practice (JGJ55-2011) and in the world similar specification take the method to Borrow's rice formula is revised to carry out mix-design more, except precision, efficiency are relatively low, also there is the shortcoming cannot carrying out mixtures optimal design.The full computing method that Beijing University of Technology professor Chen Jiankui proposes be a breakthrough on Proportion Design Method of High Performance Concrete, but computational effort is relatively large, and does not consider the cost optimization implementing proportioning.

Relevant concrete mix optimization method, is proposed in the 1970's by people such as Cannon the earliest, and it uses the simplicial method of linear programming.Consider to exist certain non-linear between starting material and concrete performance, various countries expert adopts different nonlinear algorithms to improve thereafter, and relevant representative work is seen in Publication about Document:

[1] Li Rongxiang, Li Yuejun. concrete mix real time control for multi-objective optimization [J]. Journal of Hydraulic Engineering, 1996 (4): 34-39.

[2]YEH I-Chen.Design of high-performance concrete mixtureusing neural networks and nonli near programming[J].Journal of Computing in Civil Engineering,1999,13(1):36-42.

[3] Wang Jizong, Liang Xiaoying. based on the design optimization of high performance concrete [J] of Matlab language. Industrial buildings, 2005 (1): 67-68.

[4] Liu Guohua, Chen Bin, Wang Shuyu etc. based on the concrete mix optimization design research [J] of artificial neural network and Monte-Carlo method. water power journal, 2003 (4): 45-53.

[5] Chen Bin, Li Fuqiang. Nonlinear Multiobjective optimized algorithm research [J] of concrete mix. journal of Zhejiang university (engineering version), 2005,39 (1): 16-19.

[6] Chen Xiaodong, Chen Bin, Liu Guohua. based on the concrete mix optimization design research [J] of BP ANN-GA mingled algorithm. water generating journal, 2007 (5): 59-63,52.

Conclude above document, concrete performance prediction is two kinds of methods nothing more than, i.e. polynomial regression and artificial neural network (ANNs) method; Optimization method comprises replica, Monte-Carlo method and genetic algorithm (GA) etc.

Aforementioned prior art, employing linear programming method, fail to consider the nonlinear relationship between starting material-concrete performance; Adopt the optimization of Monte-Carlo method, efficiency is lower, consuming time longer; Employing genetic algorithm, there is many uncertainties in parameter choose, therefore perfect all not enough.In addition, the over-fitting of artificial neural network controls relative difficulty, makes method be subject to certain limitation in actual applications, still has area for improvement.

Summary of the invention

For realizing mixtures optimal design, the present invention, using minimum as optimization aim for concrete for unit volume material cost, to improve the economic benefit of concrete production enterprise, proposes a kind of nonlinear optimization method of design of new concrete mix.

The present invention adopts BP artificial neural network, establishes concrete performance (comprising intensity, workability, weather resistance) predictive model; Based on the concrete performance prediction model of aforementioned foundation, adopt particle cluster algorithm (PSO), establish concrete mix Optimized model.

The present invention: (1) establishes the Nonlinear Prediction Models of concrete performance, the Non-linear Optimal Model of proportioning; (2) the over-fitting control problem in concrete performance nonlinear prediction is solved; (3) achieve the global optimization of concrete mix, and optimization efficiency is higher.

The present invention takes following technical scheme:

The nonlinear optimization method of concrete mix, it carries out as follows:

Step one: the neural network model setting up concrete performance prediction.Adopt three layers of BP artificial neural network, network input layer is quality index and the consumption of concrete raw material; Output layer is the performance requriements intending optimized mix-proportion, mainly comprises the intensity of concrete different larval instar, the slump, and the durability index such as displacement flux, chloride diffusion coefficient.Network training adopts " error tracking strategy ".Optional input block is in table 1.

The BP network input block that table 1 is conventional

When mix-design requires to determine, the quantity of network input, output unit is determined, only remaining Hidden unit number, training stop criterion two parameters are uncertain.In the present invention, last parameter is recommended as 18, also can by experience, or by tentative calculation from Row sum-equal matrix; Training stop criterion is divided into again maximum frequency of training, allows worst error two kinds, and the present invention is recommended as maximum frequency of training 20000 times respectively, or allows worst error 5%.

Over-fitting control is the intrinsic difficult point of all nonlinear algorithms.For solving the over-fitting control problem of predictive model, the present invention proposes one " error tracking strategy " in BP neural network fit procedure, that is: first carry out first time network training and prediction, using its predicated error as the initial value of Optimal error.Then network is often trained once, predicts immediately to forecast sample group, if predicated error is less than initial value, then get it for optimum value also record generation position, so constantly double counting, till network training error or frequency of training reach preset value.

Step 2: determine the target of mixtures optimal design model, constraint condition.The optimization aim that algorithm is given tacit consent to is that the production cost of unit volume concrete is minimum, can calculate by formula (1):

C _cost＝C _w·W _w+C _c·W _c+C _s·W _s+C _g·W _g+C _f·W _f+C _sl·W _sl+C _aa·W _aa+C _pl·W _pl (1)

In formula, C _cost, C _w, C _s, C _g, C _f, C _sl, C _aaand C _plrepresent the unit price of water, cement, sand, stone and flyash, breeze, other adulterant and admixture respectively, W _w, W _s, W _g, W _f, W _sl, W _aaand W _plit is correspondingly each raw-material unit dose.

The constraint function of mix-design, except intensity (be typically 7 days, 28 days ultimate compression strength), workability (being typically initial slump) and durability index, also comprise the restriction of various empirical ratios and the restriction of concrete gross weight, shown in (2) ~ formula (7):

$S_{\mathrm{cr}}^7>f_{\mathrm{cr}}^7---\left(2\right)$

$S_{\mathrm{cr}}^{28}>f_{\mathrm{cr}}^{28}---\left(3\right)$

$S_{\mathrm{slump}}^0>S_{\mathrm{slump}}^0---\left(4\right)$

$R_1^{\min }<W_w/(W_c+W_f+W_{\mathrm{sl}}+W_{\mathrm{aa}})<R_1^{\max }---\left(5\right)$

$R_2^{\min }<W_s/(W_s+W_g)<R_2^{\max }---\left(6\right)$

$R_3^{\min }<W_w+W_c+W_f+W_{\mathrm{sl}}+W_{\mathrm{aa}}+W_s+W_g+W_{\mathrm{pl}}<R_3^{\max }---\left(7\right).$

With the difference that Concrete Design requires, also can other constraint condition of corresponding increase.

Step 3: adopt particle cluster algorithm, set up mixtures optimal design model:

(1) initialize population.Note pbest _iand P _i=(p _i1, p _i2p _iD) ^tbe respectively the optimal adaptation angle value that particle i once reached and the position corresponded in D dimension space thereof, gbest and P _g=(p _g1, p _g2..., p _gD) ^tbe respectively optimal adaptation angle value and correspondence position thereof that all particles in colony once reached.The evolution equation (dynamic conditioning rule) that particle cluster algorithm adopts is:

v _id(t+1)＝v _id(t)+C ₁r ₁(t)(p _id(t)-x _id(t))+C ₂r ₂(t)(p _gd(t)-x _id(t))i＝1,…N (8)

x _id(t+1)＝x _id(t)+v _id(t+1)i＝1,…N (9)

In formula, subscript i represents i-th particle, and d represents the d dimension of particle, and t represents t generation, C ₁, C ₂for study constant, be called cognitive parameter and social parameter, usually 0 ~ 2 value, r ₁~ ∪ (0,1) and r ₂~ ∪ (0,1) is two separate randomized numbers.

Now setting population number is 20 (adjustable), namely in given each concrete raw material amount ranges (search volume), produces 20 assembly composition and division in a proportion by random rule.Raw material types number and particle dimension, the volume coordinate of its consumption and particle.Calculate position and the speed of each particle, calculate the fitness value of each particle in current position:

fitness _i＝f(X _i) (10)

Correspondingly initialize pbest _iand gbest:

pbest _i＝fitness _i (11)

gbest＝min(fitness ₁,fitness ₂,…fitness _N) (12)

In the present invention, so-called optimal adaptation angle value, that is meet the minimum unit cost value in constraint condition situation.

(2) velocity of particle and position is upgraded.In each iterative process, each particle upgrades position and the speed of oneself by (8), (9) formula, namely upgrades concrete mix, makes it to advance and reconnoiter towards cost descending direction.

If $v_{\mathrm{id}}>v_d^{\max },$ Get $v_{\mathrm{id}}=v_d^{\max };$ If $v_{\mathrm{id}}<{-v}_d^{\max }$ Get $v_{\mathrm{id}}=-v_d^{\max }.$

Equally when trying to achieve $x_{\mathrm{id}}>x_d^{\max }$ Or $<-x_d^{\max },$ Get respectively $x_{\mathrm{id}}=x_d^{\max }$ Or $x_{\mathrm{id}}=x_d^{\max }.$

(3) pbest is upgraded _iand gbest.To each particle, its fitness value and the best fitness value (unit volume Cost of Concrete value) lived through are compared, if better (lower), upgrade individual history desired positions P by current position _i, namely upgrade the optimum mix proportion representated by this particle by current proportioning.

To each particle in colony, by its history optimal-adaptive angle value and colony or the fitness value of the desired positions experienced in neighborhood compare, if better, then upgrade gbest.And it can be used as current overall desired positions P _g, namely it can be used as current global optimum's proportioning.

(4) judge, stop.If met stopping criterion (this algorithm is set as reaching given maximum iteration time), namely stop calculating; Otherwise jump to step 3 they (2).

Step 4: particle reduces.The optimal-adaptive angle value and position thereof that calculate gained are reduced to respectively least cost value and corresponding concrete mix, terminate.

Adopt technical solution of the present invention, concrete mixing proportion design method, can raw material types, performance needed for user, and the requirement of mix-design, at cost minimum target, Design and optimization goes out concrete mix.Raw material types contains water, cement, sand, stone, flyash, breeze, silicon ash, water reducer etc.; Concrete performance comprises intensity, workability, weather resistance etc., and wherein, strength range contains C15-C70 slump range and contains 50mm-250mm.

Accompanying drawing explanation

Fig. 1 is the schema of algorithm involved by the present invention.

Embodiment

Below the preferred embodiment of the present invention is elaborated.

Below provide application example of the present invention.Certain company need design the concrete of C30, C40 two labels, and the slump requires to be 150-170mm.Raw material selection water, cement, river sand, rubble, flyash, breeze and water reducer.Each raw material quality index is respectively: cement is P.O42.5 level, and within 3 days, 28 days, ultimate compression strength is 23.7MPa, 47MPa, unit price 315 yuan/t; River grain fineness number modulus is 2.7, unit price 85 yuan/t; The maximum particle of crushed stone 31.5mm, crush index is 6.3, unit price 55 yuan/t; Flyash is II grade, water demand ratio 99, unit price 110 yuan/t; Breeze is S95 level, 28 days activity indexs 101, unit price 250 yuan/t; Water reducer volume is 1%, and water-reducing rate is 25%, and unit price 1980 yuan/t, water price is disregarded.Adopt " design of common concrete proportioning code " (JGJ55-2011) and the present invention's two kinds of methods respectively, the score of design concrete match ratio is in table 2 and table 3.

Table 2 application example of the present invention (C30) unit: Kg

* the maximum spike of adulterant is defined as and is no more than 30%.When adopting JGJ55-2011 design mixture proportion, flyash Replacement rate is 20%, and breeze Replacement rate is 10%.

Table 3 application example of the present invention (C40) unit: Kg

* the maximum spike of adulterant is defined as and is no more than 30%.When adopting JGJ55-2011 design mixture proportion, flyash Replacement rate is 20%, and breeze Replacement rate is 10%.

Claims (8)

1. the nonlinear optimization method of concrete mix, is characterized in that carrying out as follows:

Step one: with the consumption of each concrete raw material and quality index for independent variable(s), concrete strength, workability and/or durability index are dependent variable, set up the neural network model of concrete performance prediction;

Step 2: according to given mix-design requirement, determine the target of mixtures optimal design model, constraint condition;

Step 3: adopt particle cluster algorithm, set up mixtures optimal design model:

(1) initialize population, namely press random rule and produce n initial engagement ratio, this n proportioning all meets constraint condition;

(2) calculate, upgrade velocity of particle and position, namely upgrade proportioning;

(3) pbest is upgraded _iand gbest;

(4) judge, stop: if meet stopping criterion, namely stop calculating; Otherwise jump to step 3 they (2);

Step 4: particle reduces: the optimal-adaptive angle value and position thereof that calculate gained are reduced to respectively least cost value and corresponding concrete mix, terminate.

2. the nonlinear optimization method of concrete mix as claimed in claim 1, it is characterized in that: in step one, adopt three layers of BP artificial neural network, network input layer is quality index and the consumption of concrete raw material; Output layer is the performance requriements intending optimized mix-proportion, comprises the intensity of concrete different larval instar, the slump, displacement flux, chloride diffusion coefficient.

3. the nonlinear optimization method of concrete mix as claimed in claim 2, it is characterized in that: in step one, the input block of network input layer comprises cement consumption, fine aggregate consumption, coarse aggregate consumption, water consumption, flyash consumption, breeze consumption, water-reducing rate, and above-mentioned raw-material corresponding Key Quality Indicator.

4. the nonlinear optimization method of the concrete mix as described in any one of claim 1-3, is characterized in that: in step 2, and the optimization aim of acquiescence is that the production cost of unit volume concrete is minimum, calculates by formula (1):

C _cost＝C _w·W _w+C _c·W _c+C _s·W _s+C _g·W _g+C _f·W _f+C _sl·W _sl+C _aa·W _aa+C _pl·W _pl (1)

In formula (1), C _cost, C _w, C _s, C _g, C _f, C _sl, C _aaand C _plrepresent the unit price of water, cement, sand, stone, flyash, breeze, other adulterant and admixture respectively, W _w, W _s, W _g, W _f, W _sl, W _aaand W _plit is correspondingly each raw-material unit dose;

The constraint function of mix-design, except intensity, workability and durability index, also comprises the restriction of various empirical ratios and the restriction of concrete gross weight, shown in (2) ~ formula (7):

$S_{\mathrm{cr}}^7>f_{\mathrm{cr}}^7---\left(2\right)$

$S_{\mathrm{cr}}^{28}>f_{\mathrm{cr}}^{28}---\left(3\right)$

$S_{\mathrm{slump}}^0>S_{\mathrm{slump}}^0---\left(4\right)$

$R_1^{\min }<W_w/(W_c+W_f+W_{\mathrm{sl}}+W_{\mathrm{aa}})<R_1^{\max }---\left(5\right)$

$R_2^{\min }<W_s/(W_s+W_g)<R_2^{\max }---\left(6\right)$

$R_3^{\min }<W_w+W_c+W_f+W_{\mathrm{sl}}+W_{\mathrm{aa}}+W_s+W_g+W_{\mathrm{pl}}<R_3^{\max }---\left(7\right).$

5. the nonlinear optimization method of concrete mix as claimed in claim 4, is characterized in that: in step 3, note pbest _iand P _i=(p _i1, p _i2p _iD) ^tbe respectively the optimal adaptation angle value that particle i once reached and the position corresponded in D dimension space thereof, gbest and P _g=(p _g1, p _g2..., p _gD) ^tbe respectively optimal adaptation angle value and correspondence position thereof that all particles in colony once reached; The evolution equation that particle cluster algorithm adopts is:

v _id(t+1)＝v _id(t)+C ₁r ₁(t)(p _id(t)-x _id(t))+C ₂r ₂(t)(p _gd(t)-x _id(t))i＝1,…N (8)

x _id(t+1)＝x _id(t)+v _id(t+1)i＝1,…N (9)

In formula (8), (9), subscript i represents i-th particle, and d represents the d dimension of particle, and t represents t generation, C ₁, C ₂for study constant, be called cognitive parameter and social parameter, usually 0 ~ 2 value, r ₁~ ∪ (0,1) and r ₂~ ∪ (0,1) is two separate randomized numbers;

Setting population number is an integer, namely in given each concrete raw material amount ranges, produces integer assembly composition and division in a proportion by random rule; Raw material types number and particle dimension, the volume coordinate of its consumption and particle; Calculate position and the speed of each particle, calculate the fitness value of each particle in current position:

fitness _i＝f(X _i) (10)

Correspondingly initialize pbest _iand gbest:

pbest _i＝fitness _i (11)

gbest＝min(fitness ₁,fitness ₂,…fitness _N)(12)。

6. the nonlinear optimization method of concrete mix as claimed in claim 5, it is characterized in that: in step 3, in each iterative process, each particle upgrades position and the speed of oneself by (8), (9) formula, namely upgrade concrete mix, make it to advance and reconnoiter towards cost descending direction;

If $v_{\mathrm{id}}>v_d^{\max },$ Get $v_{\mathrm{id}}=v_d^{\max };$ If $v_{\mathrm{id}}<-v_d^{\max }$ Get $v_{\mathrm{id}}=-v_d^{\max }.$

Equally, when trying to achieve $x_{\mathrm{id}}>x_d^{\max }$ Or $<-x_d^{\max },$ Get respectively $x_{\mathrm{id}}=x_d^{\max }$ Or $x_{\mathrm{id}}=-x_d^{\max }.$

7. the nonlinear optimization method of concrete mix as claimed in claim 6, it is characterized in that: in step 3, to each particle, its fitness value and the best fitness value lived through are compared, if lower, then using its individual history optimum value pbest as this particle _i, upgrade individual history desired positions P by current position _i, namely upgrade the optimum mix proportion representated by this particle by current proportioning;

To each particle in colony, by its history optimal-adaptive angle value and colony or the fitness value of the desired positions experienced in neighborhood compare, if better, then upgrade gbest; And it can be used as current overall desired positions P _g, namely it can be used as current global optimum's proportioning.

8. the nonlinear optimization method of concrete mix as claimed in claim 2 or claim 3, it is characterized in that: in step one, " error tracking strategy " is adopted in BP neural network fit procedure, that is: first time network training and prediction is first carried out, using its predicated error as the initial value of Optimal error; Then network is often trained once, predicts immediately to forecast sample group, if predicated error is less than initial value, then get it for optimum value also record generation position, so constantly double counting, till network training error or frequency of training reach preset value.