# Compressive Strength Prediction of Alkali-Activated Slag Concretes by Using Artificial Neural Network (ANN) and Alternating Conditional Expectation (ACE)

Authors: Xiaoyu Qin; Qianmin Ma; Rongxin Guo; Zhigang Song; Zhiwei Lin; Haoxue Zhou
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

Compressive strength of alkali-activated slag (AAS) concrete is influenced by multi-factors in a nonlinear way. Both artificial neural network (ANN) and alternating conditional expectation (ACE) models of 3-day (3 d) and 28-day (28 d) compressive strength of AAS were established in this study by using the data reported in related literature, where alkali concentration of activator (Na2O%), modulus of activator (Ms), water/binder ratio (W/B), surface area of slag (SA), and basicity index of slag (Kb) were taken as input parameters. The models were employed later to predict 3 d and 28 d compressive strength of AAS concretes, respectively, and the results were validated by experimental work. The results show that both the ANN and the ACE models had adequate accuracy, no matter 3 d or 28 d compressive strength was considered. Compared to the 3 d compressive strength, due to data scattering that increased with the increase of data size, both the models did not yield a higher accuracy in the case of 28 d strength. However, also due to the increase in data size, both the models were more feasible to implement 28 d strength prediction as a result of sufficient learning and training during modeling. In addition, based on ACE analysis, the weight-influencing compressive strength of AAS decreased in a sequence of Na2O% > Ms > W/B > Kb > SA. If data size was sufficiently large, it was more suitable to establish an ANN model for compressive strength prediction of AAS concretes. Otherwise, ACE could be considered as an alternative to yield an acceptable result.


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## Body

## 1. Introduction

Alkali-activated slag (AAS), in which alkali activator (such as sodium silicate solution, known as water glass, WG) blends with ground granulated blast-furnace slag, has received widespread attention due to its extremely low CO2 emission and superior performance [1]. Concrete manufactured by using AAS instead of Portland cement (PC) is potentially employed in structural construction. On the other hand, performance testing of concrete is usually time-consuming via experimental work. In this context, prediction based on mathematic models has shown its practical significance. As one of the most basic and the most important performances of concrete, compressive strength is largely dependent on material components and their characteristics. Different from PC, whose compressive strength mainly depends on water-binder ratio, compressive strength dependence of AAS comes from both alkali activator and slag, as well as water-binder ratio. Such multi-factor conditions will certainly bring much more challenges for compressive strength prediction of AAS.Bagheri et al. [2] established an artificial neural network (ANN) by using the data obtained from the authors’ experimental work, followed by using genetic programming (GP) to conduct a prediction for compressive strength of boron-based alkali-activated fly ash-slag system. To develop the ANN model, percentages of fly ash and slag, as well as ratios of B, Si, and Na in the alkali activator were taken as input variables. Totally 114 series of data were collected and 70%, 15%, and 15% of the data were used for training, testing, and validation, respectively. A very low error value of less than 0.1 confirmed the high accuracy of the model. After a GP based on 20 series of experiments, R2 of 0.95 and root mean square error (RMSE) of 0.07 were obtained, respectively, implying a good feasibility of the model for such a prediction. Also, an ANN model was developed for compressive strength of alkali-activated fly ash-slag concretes in the study carried out by Nagajothi and Elavenil [3]. Twenty groups of data obtained from their own experiment were used for establishment of the model, where slag-fly ash ratio and river sand–manufactured sand ratio were used as input parameters. Finally, mean absolute error (MAE), RMSE, and mean absolute percentage error (MAPE) of 0.042, 0.094, and 0.001 were obtained, respectively, exhibiting that the model had high accuracy. Faridmehr et al. [4] also developed an ANN model for compressive strength of alkali-activated fly ash-slag self-compacting concretes, where contents of fly ash and slag, as well as curing age were taken as input parameters. Within the total 6 groups of data based on their own experiment, 70% and 30% of the data were used for training and testing, respectively. Reliability of the model was evaluated by comparing its error to the ones obtained from multiple linear regression (MLR) model and genetic algorithm combined with ANN (GA-ANN) model. Finally, relatively lower MAE of 1.78, mean squared error (MSE) of 5.98, RMSE of 2.45, and average absolute error (AAE) of 0.04 were obtained, respectively. Shariatmadari et al. [5] used alkali-activated volcanic ash-slag-PC to stabilize sandy soil, and developed ANN and evolutionary polynomial regression (EPR) models based on their own experimental results. Replacements of volcanic ash and slag in PC, concentration of alkali activator, alkali to binder ratio, Na/Al, Si/Al, curing time, and curing temperature were employed as input parameters. Training, testing, and validation used 75%, 10%, and 15% of data, respectively. After several trials, based on RMSE and MAE of 0.0439 and 0.0336, respectively, the ANN model with architecture of 8-5-10-1 was proved as the most accurate one. Zhang et al. [6] proposed a chemical-informed machine learning model for compressive strength of alkali-activated fly ash-slag system. To build the model, relatively comprehensive features were considered as input parameters, including contents of fly ash, slag, NaOH, WG, water, fine aggregates and coarse aggregates, reactivity modulus, hydraulic modulus, silica modulus, alumina modulus, lime modulus, Na2O in WG, SiO2 in WG, water in WG, relative humidity, as well as age. Training and testing used 70% and 30% of data (676 groups in total from literature), respectively. Eventually, high accuracy was achieved with a low MAE of 3.228 MPa.From the above, it can be seen that ANN has been successfully used to estimate compressive strength of alkali-activated materials. Most studies have been carried out on alkali-activated fly ash-slag and other alkali-activated systems rather than AAS, which, however, has more important significance in engineering practice currently. Furthermore, the data used in most studies were from their own experimental work. This could have resulted in a relatively small data size and then followed by a decrease in accuracy and feasibility when using the local optimum model to solve a global issue.In this context, this study will focus on compressive strength of AAS concretes by using the ANN approach. In the development of the ANN model, data will be collected as fully as possible from literature. After the model with sufficient accuracy has been established, its feasibility will be evaluated by using own experimental work. For comparison, alternating conditional expectation (ACE) analysis will also be conducted and the weight of the influencing factors on the compressive strength of AAS concretes will be determined elementarily by using such method.


## 2. Data Collection and Modeling

### 2.1. Data Collection

ANN and ACE models were established in this study to predict compressive strength of AAS concretes with WG as alkali activator. Data used for the model establishment was collected from related literature published publicly. The influence on strength of AAS should be from both alkali activator and slag, as well as their proportion. Considering the importance of the influencing parameters, alkali concentration of WG (Na2O%), modulus of WG (Ms), water/binder ratio (W/B), surface area of slag (SA), and basicity index of slag (Kb) were taken as the input parameters of the models [7–13]. Other parameters, such as binder content, which are less important and then not typically considered in the literature, are not adopted in this study for model establishment. Na2O%, Ms, W/B, and Kb should be calculated according to formulae (1)–(4) [14–17]. If NaOH was used in the alkali activator as well together with WG, NaOH should be treated as a part of WG. Therefore, “WG” in the formulae means the WG after NaOH adjustment. Compressive strengths of AAS at curing ages of 3 d and 28 d were considered as output parameters. Finally, 171 and 309 sets of data were successfully selected for 3 d and 28 d compressive strength prediction, respectively. Literature used and input/output parameter values listed in Tables 1 and 2 gives the number of tests, range of variation, and average and standard deviation values for each of the references presented in Table 1. Parts of the data in the Table 1 have same inputs but different output values. This is because other influencing factors rather than the five mentioned above were also considered in the literature, but here only the five factors were concerned.(1)Na2O%=Na2OinWGslag∗100%,(2)Ms=SiO2inWGNa2OinWG,(3)WB=additionalwater+waterinWGslag+SiO2inWG+Na2OinWG,(4)Kb=CaO+MgOSiO2+Al2O3.Table 1
Literatures and input/output parameters.
Ref.Input parametersOutput parametersNa2O%MsW/BSA (m²/kg)KbCompressive strength (MPa)3 d28 d[18]4.00.750.475270.9625.1643.804.01.000.475270.9616.4448.964.01.500.475270.96—48.054.02.000.475270.96—33.446.00.750.475270.9631.1546.716.01.000.475270.9635.6053.946.01.500.475270.9632.2960.726.02.000.475270.9612.3159.828.00.750.475270.9634.6251.698.01.000.475270.9632.6054.988.01.500.475270.9623.6658.448.02.000.475270.96—54.83[19]4.01.500.284850.99—81.204.01.500.324850.9950.1079.104.01.500.374850.9929.1074.104.01.500.414850.99—62.204.01.500.324850.9940.3079.504.01.500.324850.9946.0078.104.01.500.324850.9951.4082.404.01.500.324850.9952.1080.504.01.500.324850.9948.6077.104.01.500.324850.9952.3077.903.01.500.334850.99—55.105.01.500.294850.9954.3097.606.01.500.274850.9946.20102.604.01.000.334850.9938.2073.204.02.000.334850.9946.1086.504.01.500.323130.9941.3075.804.01.500.326790.9955.1085.20[20]5.01.500.465231.1410.7220.747.01.500.465231.14—27.579.01.500.465231.1414.7325.115.01.800.465231.14—27.297.01.800.465231.1419.0940.199.01.800.465231.1428.7857.735.02.000.465231.14—28.497.02.000.465231.1424.5746.039.02.000.465231.1450.6858.92[21]5.01.500.354621.00—79.605.01.500.404621.00—69.405.01.500.454621.00—61.305.01.500.504621.00—47.205.01.500.554621.00—31.605.01.500.354621.00—82.205.01.500.404621.00—72.505.01.500.454621.00—63.505.01.500.504621.00—52.705.01.500.554621.00—42.105.01.500.354621.00—84.005.01.500.404621.00—59.205.01.500.454621.00—57.105.01.500.504621.00—45.905.01.500.554621.00—36.30[22]7.01.800.465230.94—40.509.01.800.465230.94—60.109.02.000.465230.94—62.70[23]10.01.500.334501.2818.7025.0012.01.500.334501.2819.6027.2014.01.500.334501.2822.5029.6010.01.200.334501.2830.2040.4012.01.200.334501.2836.0046.8014.01.200.334501.2842.8050.4010.01.000.334501.2835.6050.4012.01.000.334501.2849.1061.0014.01.000.334501.2850.4064.4010.00.800.334501.2840.1055.7012.00.800.334501.2844.6064.6014.00.800.334501.2849.1065.40[24]8.01.400.284551.0428.6057.60[25]4.00.400.515251.10—33.274.00.800.515251.10—38.954.01.200.505251.10—46,776.00.400.505251.10—44.076.00.800.495251.10—52.366.01.200.485251.10—79.708.00.400.485251.10—36.768.00.800.475251.10—82.688.01.200.465251.10—75.26[26]4.01.000.445151.0831.4956.566.01.000.365151.0844.3073.008.01.000.335151.0854.3376.904.01.250.305151.0824.2459.916.01.250.355151.0842.6376.078.01.250.315151.0850.4377.464.01.500.255151.0817.8362.416.01.500.345151.0839.2978.028.01.500.295151.0841.2479.41[27]4.01.000.354350.99—24.444.01.000.504350.99—20.194.01.000.654350.99—18.32[28]4.02.060.443000.84—14.406.02.060.473000.84—20.308.02.060.453000.8410.5024.004.02.060.443000.8410.9038.006.02.060.363000.8428.5053.908.02.060.313000.8429.5052.504.02.060.273500.84—15.906.02.060.473500.84—22.208.02.060.453500.8410.8025.004.02.060.443500.84—51.706.02.060.363500.8427.6067.108.02.060.313500.8429.2068.204.02.060.274000.84—16.706.02.060.474000.8410.3023.908.02.060.454000.8411.0027.304.02.060.444000.8411.4054.406.02.060.374000.8426.8070.108.02.060.314000.8433.8072.40[29]2.01.250.404000.9965.5267.632.00.750.404000.9944.0351.081.51.670.404000.9951.4373.091.51.000.404000.9936.4658.83[30]5.02.400.233991.0144.3059.455.02.000.233991.0154.3568.645.02.000.473991.0154.3968.445.02.400.473991.0144.3759.26[31]5.02.400.533001.01—49.755.02.400.534001.01—67.645.02.400.535001.01—73.09[32]6.00.500.474461.0556.2542.036.01.000.474461.0568.0154.066.01.500.474461.0584.1458.986.02.000.474461.0587.9768.558.00.500.474461.0574.6655.758.01.000.474461.0582.0563.158.01.500.474461.0592.4770.558.02.000.474461.05100.4078.49[33]6.01.000.474850.93—87.304.91.500.474850.93—81.114.12.000.474850.93—85.31[34]4.32.000.443851.24—39.50[35]5.01.200.443250.92—83.13[36]10.83.200.454000.9940.1159.359.63.200.504000.9939.2551.6210.03.200.554000.9928.5145.6510.53.200.604000.9925.8636.13[37]6.01.200.354240.9097.66118.008.01.200.354240.90101.30123.2010.01.200.354240.9084.41108.706.01.400.354240.9090.68111.508.01.400.354240.9091.30113.1010.01.400.354240.9089.96110.106.01.600.354240.9089.34114.408.001.600.354240.9095.40118.2010.01.600.354240.9087.29109.00[38]4.01.250.403700.88—60.10[39]4.00.800.504350.9929.8042.075.00.800.504350.9932.4348.106.00.800.504350.9937.6851.05[40]10.01.000.454980.91—54.8210.01.000.454350.93—29.6610.01.000.454500.94—34.55[41]9.21.250.553850.8032.9239.55[42]4.01.500.504501.08—48.026.01.500.504501.08—68.8910.01.500.504501.08—78.71[43]4.00.500.405151.06—45.094.01.000.405151.06—50.414.01.500.405151.06—56.456.00.500.405151.06—55.386.01.000.405151.06—55.746.01.500.405151.06—63.208.00.500.405151.06—47.998.01.000.405151.06—56.058.01.500.405151.06—61.31[44]8.00.480.553451.22—18.1012.00.480.553451.22—34.0016.00.480.553451.22—39.10[45]0.40.500.334300.9938.9941.110.40.800.334300.9941.7848.860.41.200.334300.9927.9130.020.41.500.334300.9948.7855.860.41.800.334300.9943.7753.330.42.100.334300.9942.3151.870.42.300.334300.9927.7241.540.41.500.334300.9926.4250.530.61.500.334300.9945.5878.290.81.500.334300.9935.5060.901.01.500.334300.9949.3681.97[46]4.30.410.445011.14—28.003.91.220.445011.14—46.40[47]4.00.750.285270.66—26.084.01.000.285270.66—36.324.01.500.285270.66—36.804.02.000.285270.66—25.656.00.750.285270.66—15.576.01.000.285270.66—8.916.01.500.285270.66—60.006.02.000.285270.66—41.208.00.750.285270.66—1.288.01.000.285270.66—6.248.01.500.285270.66—39.688.02.000.285270.66—23.73[48]3.01.000.414050.5538.39—4.01.000.404050.5553.05—[49]3.71.400.303381.1667.1099.403.01.700.303381.1652.5086.502.61.990.303381.1632.6077.002.32.290.303381.16—65.202.02.390.303381.16—44.201.82.940.303381.16—53.801.63.270.303381.16—55.501.43.600.303381.16—52.20[50]4.00.500.454531.0743.4784.004.00.800.454531.0751.58107.604.01.000.454531.0753.05123.804.01.200.454531.0756.00126.004.01.500.454531.0757.47128.204.01.800.454531.0747.16127.504.02.000.454531.0746.42126.704.02.200.454531.0736.8476.634.02.500.454531.07—34.632.01.500.454531.07—30.923.01.500.454531.0727.83105.904.01.500.454531.0758.74128.305.01.500.454531.0772.66140.706.01.500.454531.0781.16151.507.01.500.454531.0764.15116.70[51]4.02.500.294580.9730.8863.954.02.000.294580.9749.2383.254.01.500.294580.9761.58102.904.00.500.294580.9770.8890.254.01.000.294580.9768.5399.10[52]2.40.500.284611.01—33.382.41.000.294611.01—48.482.42.000.324611.01—70.132.40.500.284201.03—51.262.41.000.294201.03—69.142.42.000.324201.03—87.02[53]5.01.000.404871.0330.9454.545.01.500.404871.0338.3561.765.02.000.404871.0341.2670.99[54]4.00.750.505201.10—44.976.00.750.505201.10—84.094.01.000.505201.10—41.726.01.000.505201.10—79.69[55]2.30.550.494201.01—16.002.70.750.504201.0111.9018.302.70.750.506151.0815.3023.602.70.750.508171.0717.3025.903.10.850.514201.0112.9020.405.40.550.504201.0122.3035.206.60.750.504201.0126.7041.906.60.750.506151.0828.7044.606.60.750.508171.0731.4048.607.90.850.514201.0133.5049.60[8]8.00.750.504250.84—81.108.01.000.504250.84—80.908.01.250.504250.84—58.908.01.500.504250.84—57.50[56]4.00.600.434281.0334.6562.464.00.900.434281.0340.1569.884.01.200.434281.0333.6876.984.01.500.434281.0345.3381.813.00.600.434281.0328.7049.013.00.900.434281.0327.2862.353.01.200.434281.0323.0268.033.01.500.434281.03—68.32[57]4.00.750.504600.9311.5524.234.01.000.504600.9311.7033.844.01.250.504600.9311.9934.514.01.500.504600.9311.8828.846.00.750.504600.9314.3624.956.01.000.504600.9312.9625.516.01.250.504600.93—27.466.01.500.504600.93—22.168.00.750.504600.9314.2536.028.01.000.504600.9314.2536.788.01.250.504600.9311.8039.088.01.500.504600.9310.5732.64[58]5.81.000.474101.0242.3067.805.81.000.474101.0245.3085.005.81.500.474101.0255.0098.00[59]5.01.000.284651.04—82.7510.01.000.284651.04—71.2315.01.000.284651.04—48.125.01.500.284651.04—85.0410.01.500.284651.04—65.855.02.000.394651.04—86.8310.02.000.394651.04—48.84[60]3.01.000.256001.1452.0767.083.01.000.258001.1462.2191.393.01.000.2510001.1457.6277.08[61]6.00.800.384130.91—86.006.01.200.384130.91—80.80[62]2.91.000.425020.90—45.002.91.000.425030.97—36.922.91.000.404990.87—44.622.91.000.405070.93—71.152.91.000.405010.98—78.852.91.000.405020.95—39.622.91.000.404960.81—38.082.91.000.404990.77—37.69[63]4.00.750.504600.9335.0739.89[64]5.11.500.514601.0564.25100.00[65]4.00.400.444100.81—54.704.00.800.444100.81—59.704.01.200.444100.81—58.504.01.600.444100.81—52.306.00.400.444100.81—62.406.00.800.444100.81—78.406.01.200.444100.81—74.106.01.600.444100.81—71.008.00.400.444100.81—75.208.00.800.444100.81—76.108.01.200.444100.81—87.208.01.600.444100.81—88.30[66]4.01.650.484010.9831.3857.486.01.650.484010.9849.2778.894.01.000.484010.9829.0347.806.01.000.484010.9844.2860.70Table 2
Analysis of input/output parameters.
Ref.Input parametersOutput parametersNa2O%MsW/BSA (m2/kg)KbCompressive strength (MPa)3 d28 d[18]Number of tests912Range[4.00–8.00][0.75–2.00]0.47527.000.96[12.31–35.60][33.44–60.72]Average6.001.310.47527.000.9627.0951.28Standard deviation1.710.500.000.000.008.297.73[19]Number1417Range[3.00–6.00][1.00–2.00][0.27–0.41][313–679]0.99[29.10–55.10][55.10–102.60]Average4.121.500.32487.000.9946.5179.30Standard deviation0.600.180.0364.800.007.2311.02[20]Number69Range[5.00–9.00][1.50–2.00]0.46523.001.14[10.72–50.68][20.74–58.92]Average7.001.770.46523.001.1424.7636.90Standard deviation1.730.220.000.000.0014.2714.42[21]Number—15Range5.001.50[0.35–0.55]462.001.00—[31.60–84.00]Average5.001.500.45462.001.00—58.97Standard deviation0.000.000.070.000.00—16.50[22]Number—3Range[7.00–9.00][1.80–2.00]0.46523.000.94—[40.50–62.70]Average8.331.870.46523.000.94—54.43Standard deviation1.150.120.000.000.00—12.14[23]Number1212Range[10.00–14.00][0.80–1.50]0.33450.001.28[18.70–50.40][25.00–65.40]Average12.001.130.33450.001.2836.5648.41Standard deviation1.710.270.000.000.0011.5514.91[24]Number11Range8.001.400.28455.001.0428.6057.60Average8.001.400.28455.001.0428.6057.60Standard deviation0.000.000.000.000.000.000.00[25]Number—9Range[4.00–8.00][0.40–1.20][0.46–0.51]525.001.10—[33.27–82.68]Average6.000.800.49525.001.10—52.42Standard deviation1.730.350.020.000.00—19.49[26]Number99Range[4.00–8.00][1.00–1.50][0.25–0.44]515.001.08[17.83–54.33][56.56–79.41]Average6.001.250.33515.001.0838.4271.08Standard deviation1.730.220.050.000.0011.898.88[27]Number—3Range4.001.00[0.35–0.65]455.001.04—[18.32–24.44]Average4.001.000.50455.001.04—20.98Standard deviation0.000.000.150.000.00—3.14[28]Number12Range[4.00–8.00]2.06[0.27–0.47][300–400]0.84[10.30–33.80][14.40–72.40]Average6.002.060.39350.000.8420.0239.89Standard deviation1.680.000.0742.000.009.7621.10[29]Number44Range[1.50–2.00][0.75–1.67]0.40400.000.99[36.46–65.52][51.08–73.09]Average1.751.170.40400.000.9949.3662.66Standard deviation0.290.390.000.000.0012.399.70[30]Number22Range5.00[2.00–2.40]0.23399.001.01[44.30–54.35][59.45–68.64]Average5.002.200.23399.001.0149.3364.05Standard deviation0.000.280.000.000.007.116.50[31]Number—3Range5.002.400.53[300–500]1.01—[49.75–73.09]Average5.002.400.53400.001.01—63.49Standard deviation0.000.000.00100.000.00—12.21[32]Number88Range[6.00–8.00][0.50–2.00]0.47446.001.05[56.25–100.40][42.03–78.49]Average7.001.250.47446.001.0580.7461.45Standard deviation1.070.600.000.000.0014.0811.32[33]Number—3Range[4.10–6.00][1.00–2.00]0.47485.000.93—[81.11–87.30]Average5.001.500.47485.000.93—84.57Standard deviation0.950.500.000.000.00—3.16[34]Number—1Range4.302.000.44385.001.24—39.50Average4.302.000.44385.001.24—39.50Standard deviation0.000.000.000.000.00—0.00[35]Number—1Range5.001.200.44325.000.92—83.13Average5.001.200.44325.000.92—83.13Standard deviation0.000.000.000.000.00—0.00[36]Number44Range[9.60–10.80]3.20[0.45–0.60]400.000.99[25.86–40.11][36.13–59.35]Average10.233.200.53400.000.9933.4348.19Standard deviation0.530.000.060.000.007.309.80[37]Number99Range[6.00–10.00][1.20–1.60]0.35424.000.90[84.41–101.30][108.70–123.20]Average8.001.400.35424.000.9091.93114.02Standard deviation1.730.170.000.000.005.284.92[38]Number—1Range4.001.250.40370.000.88—60.10Average4.001.250.40370.000.88—60.10Standard deviation0.000.000.000.000.00—0.00[39]Number33Range[4.00–6.00]0.800.50435.000.99[29.80–37.68][42.07–51.05]Average5.000.800.50435.000.9933.3047.07Standard deviation1.000.000.000.000.004.014.58[40]Number—3Range10.001.000.45[435–498][0.91–0.94]—[29.66–54.82]Average4.001.000.45461.000.93—39.68Standard deviation0.000.000.0032.910.02—13.34[41]Number11Range9.201.250.55385.000.8032.9239.55Average9.201.250.55385.000.8032.9239.55Standard deviation0.000.000.000.000.000.000.00[42]Number—3Range[4.00–10.00]1.500.50450.001.08—[48.02–78.71]Average6.671.500.50450.001.08—65.21Standard deviation3.060.000.000.000.00—15.67[43]Number—9Range[4.00–8.00][0.50–1.50]0.40515.001.06—[45.09–61.31]Average6.001.000.40515.001.06—54.62Standard deviation1.730.430.000.000.00—5.90[44]Number—3Range[8.00–16.00]0.480.55345.001.22—[18.10–39.10]Average12.000.480.55345.001.22—30.40Standard deviation4.000.000.000.000.00—10.95[45]Number1111Range[0.40–1.00][0.50–2.30]0.33430.000.99[26.42–49.36][30.02–81.97]Average0.511.470.33430.000.9938.9254.03Standard deviation0.210.520.000.000.008.4215.37[46]Number—2Range[3.90–4.30][0.41–1.22]0.44501.001.14—[28.00–46.40]Average4.100.820.44501.001.14—37.20Standard deviation0.280.570.000.000.00—13.01[30]Number—2Range5.00[2.00–2.40]0.47399.001.01—[59.26–68.44]Average5.002.200.47399.001.01—63.85Standard deviation0.000.280.000.000.00—6.49[47]Number—12Range[4.00–8.00][0.75–2.00]0.28527.000.66—[1.28–60.00]Average6.001.310.28527.000.66—26.79Standard deviation1.710.500.000.000.00—17.05[48]Number2—Range[3.00–4.00]1.00[0.40–0.41]405.000.55[38.39–53.05]—Average3.501.000.41405.000.5545.72—Standard deviation0.710.000.010.000.0010.37S—[49]Number38Range[1.40–3.70][1.40–3.60]0.30338.001.16[32.60–67.10][44.20–99.40]Average2.302.450.30338.001.1650.7366.73Standard deviation0.770.770.000.000.0017.3219.19[50]Number1315Range[2.00–7.00][0.50–2.50]0.45453.001.07[27.83–81.16][30.92–151.50]Average4.201.500.45453.001.0753.58107.27Standard deviation1.150.510.000.000.0014.2235.90[51]Number55Range4.00[0.50–2.50]0.29458.000.97[30.88–70.88][63.95–102.90]Average4.001.500.29458.000.9756.2287.89Standard deviation0.000.790.000.000.0016.4815.42[52]Number—6Range2.40[0.50–2.00][0.28–0.32][420–461][1.01–1.03]—[33.38–87.02]Average2.401.170.30440.501.02—59.91Standard deviation0.000.680.0222.460.01—19.15[53]Number33Range5.00[1.00–2.00]0.40487.001.03[30.94–41.26][54.54–70.99]Average5.001.500.40487.001.0336.8562.43Standard deviation0.000.500.000.000.005.328.25[54]Number—4Range[4.00–6.00][0.75–1.00]0.50520.001.10—[41.72–84.09]Average5.000.880.50520.001.10—62.62Standard deviation1.150.140.000.000.00—22.37[55]Number910Range[2.30–7.90][0.55–0.85][0.49–0.51][420–817][1.01–1.08][11.90–33.50][16.00–49.60]Average4.660.730.50538.401.0422.2232.41Standard deviation2.160.100.01167.030.038.2113.07[8]Number—4Range8.00[0.75–1.50]0.50425.000.84—[57.50–81.10]Average8.001.130.50425.000.84—69.60Standard deviation0.000.320.000.000.00—13.18[56]Number78Range[3.00–4.00][0.60–1.50]0.43428.001.03[23.02–45.33][62.35–81.81]Average3.501.050.43428.001.0333.2667.36Standard deviation0.530.360.000.000.007.719.96[57]Number1012Range[4.00–8.00][0.75–1.50]0.50460.000.93[11.55–14.36][22.16–39.08]Average6.001.130.50460.000.9312.5330.50Standard deviation1.710.290.000.000.001.345.66[58]Number33Range5.80[1.00–1.50]0.47410.001.02[42.30–55.00][67.80–98.00]Average5.801.170.47410.001.0247.5383.60Standard deviation0.000.290.000.000.006.6415.15[59]Number—7Range[5.00–10.00][1.00–2.00][0.28–0.39]465.001.04—[48.12–86.83]Average8.571.430.31465.001.04—69.81Standard deviation3.780.450.050.000.00—16.42[60]Number33Range3.001.000.25[600–1000]1.14[52.07–62.21][67.08–91.39]Average3.001.000.25800.001.1457.3078.52Standard deviation0.000.000.00200.000.005.0812.22[61]Number—2Range6.00[0.80–1.20]0.38413.000.91—[80.80–86.00]Average6.001.000.38413.000.91—83.40Standard deviation0.000.280.000.000.00—3.68[62]Number—8Range2.901.00[0.40–0.42][496–503][0.77–0.98]—[36.92–78.85]Average2.901.000.41501.130.90—48.99Standard deviation0.000.000.013.270.08—16.47[63]Number11Range4.000.750.50460.000.9335.0739.89Average4.000.750.50460.000.9335.0739.89Standard deviation0.000.000.000.000.000.000.00[64]Number11Range5.101.500.51460.001.0564.25100.00Average5.101.500.51460.001.0564.25100.00Standard deviation0.000.000.000.000.000.000.00[65]Number—12Range[4.00–8.00][0.40–1.60]0.44410.000.81—[52.30–88.30]Average6.001.000.44410.000.81—69.83Standard deviation1.710.470.000.000.00—12.16[66]Number44Range[4.00–6.00][1.00–1.65]0.48401.000.98[29.03–49.27][47.80–78.89]Average5.001.330.48401.000.9838.4961.22Standard deviation1.150.380.000.000.009.8312.993 d totalNumber171—Range[0.40–14.00][0.50–3.20][0.23–0.60][300–1000][0.55–1.28][10.30–101.30]—Average5.651.390.40457.371.0141.62—Standard deviation2.910.540.0884.700.1221.40—28 d totalNumber—309Range[0.40–16.00][0.40–3.60][0.23–0.65][300–1000][0.66–1.28]—[1.28–151.50]Average5.591.370.41459.050.99—59.70Standard deviation2.720.570.0874.840.12—25.96


### 2.2. ANN Modeling

ANN is a kind of general mathematical model to solve nonlinear system problems. It processes information by imitating human neural network [67]. Due to its strong generalization ability, it has been applied successfully in the field of civil engineering in recent years [68–72]. ANN models consist of three layers: input layer, hidden layer(s), and output layer. The number of neurons in both the input and the output layers is just the number of parameters in the corresponding layers. Determination of the number of layers and number of neurons in each layer is relatively complex for the hidden layer(s), which is generally done by trial-and-error. Connection between neurons should be implemented by using a linear/nonlinear transfer function. Input parameters in the input layer are fed to the output layer through the hidden layer(s). If outputs were not desired, they would bring error signals to back-propagate into the input layer to minimize the error by modifying the weight of each neuron there. In this context, training is very important in ANN modeling, and sufficient data size is needed to guarantee its accuracy.In this study, the five parameters, Na2O%, Ms, W/B, SA, and Kb, were treated as the neutrons in the input layer, and compressive strength of AAS was the neutron in the output layer. The determination of the hidden layer was made by trial and error. Both single-layer and double-layer were tried in this study. For both cases, number of the neutrons in the hidden layer was equal to root of the sum of input and output node numbers, plus a constant value less than 10 in general [73]. After several trials (a sample of performance comparison is given in Table 3), one hidden layer was determined to be used, and the number of the neutrons in the hidden layer was 10 and 13 for 3 d and 28 d compressive strength, respectively, according to the MAE and the RMSE error evaluations (to be described in section 2.4). Therefore, ANN model structures of 5-10-1 and 5-13-1 were used eventually in this study for compressive strength prediction of AAS at curing ages of 3 d and 28 d, respectively, as shown in Figure 1. For both the networks, 70%, 15%, and 15% of the data collected from literature were randomly selected for training, testing, and validation, respectively. Number of training period, learning rate, and minimum error of the training were set as 1000, 0.01, and 0.00001, respectively. After a comparison between Gradient Descent method and Levenberg-Marquardt algorithm, the latter was used for training due to its higher accuracy. The results to be reported were the optimum solution after 50 times of training.Table 3
Performance comparison between different network structures (MPa).
5-10-15-13-15-(6, 6)-1TrainingTestingTrainingTestingTrainingTesting3 d compressive strengthMAE7.476.7811.289.898.017.23RMSE14.8918.2116.3417.1116.4119.6228 d compressive strengthMAE19.737.9815.645.7916.2610.15RMSE17.2513.9914.8910.9515.0311.76Figure 1
ANN model structures used in this study: (a) 5-10-1 structure for 3 d compressive strength. (b) 5-13-1 structure for 28 d compressive strength.
(a)(b)


### 2.3. ACE Modeling

ACE nonparametric regression technique, which has strong feasibility and high accuracy, is essentially a kind of response surface function. It is usually used to establish a mapping relationship between inputs and outputs which are already known by the approach of data fitting, as given in Ref. [74].(5)θY=φX1+φX2+⋅⋅⋅⋅⋅⋅φXn+ε1,(6)Y=θ−1φX1+φX2+⋅⋅⋅⋅⋅⋅φXn+ε2,where X1, X2⋅⋅⋅⋅⋅⋅Xnare input parameters; φX1,φX2⋅⋅⋅⋅⋅⋅φXn are response surface functions of X1, X2⋅⋅⋅⋅⋅⋅Xn; Y is output parameter; θY is response surface function of Y; θ−1 is inverse function of θ; ε1 and ε2 are accuracy errors.As the accuracy errorε is difficult to be determined, correction coefficient λ is usually introduced to modify formula (6), and finally, formula (7) is obtained as given below.(7)Y=λθ−1φX1+φX2+⋅⋅⋅⋅⋅⋅φXn.Furthermore, influencing weight of each input parameter on the output parameter could be analyzed elementarily by using ACE approach as well during the calculation.In this study,X1, X2⋅⋅⋅⋅⋅⋅X5were nominated as Na2O%, Ms, W/B, SA, and Kb, respectively, as input parameters. Their values were collected from literature as detailed in Section 2.1. Input parameters were imported in ACE calculation software S-PLUS to calculate their corresponding response surface function φX1, φX2⋅⋅⋅⋅⋅⋅φX5. After that, a mapping relationship was established between the response surface functions and output parameters, namely, compressive strength of AAS at curing ages of 3 d and 28 d, respectively, by data fitting regression. The values of the strength were also collected from literature as detailed in Section 2.1.


### 2.4. Error Evaluation

Both mean absolute error (MAE) and root mean square error (RMSE) were used in this study to evaluate accuracy of both the ANN and the ACE models. MAE and RMSE values are to be zero when the values predicted and tested are exactly the same. Error increases with the increase of MAE and RMSE values. Calculations of MAE and RMSE are given in formulae (8) and (9) according to the literature [2–6]. Furthermore, agreement between predicted and measured values together with coefficient of determination was also applied to better assess the applicability of the proposed networks.(8)MAE=∑i=1nyi−zin(9)RMSE=∑i=1nyi−yi2n1/2where yi (y1, y2, ......yn) are the values tested; zi (z1, z2, ......zn) are the values predicted; n is the number of data.


### 2.5. Experimental Validation

Eleven AAS concrete mixes were prepared in this study, their compressive strength was tested at curing ages of 3 d and 28 d, respectively, to validate the results predicted by using both the ANN and the ACE models.The slag used in the experimental work was from Qujing, Yunnan Province, China, whoseKb and SA were 0.96 and 405 m2/kg, respectively. Its chemical compositions are given in Table 4.Table 4
Chemical compositions of slag (%).
CaOSiO2Al2O3MgOTiO2SO3MnONa2OK2OFe2O338.2631.4015.716.902.941.431.230.960.530.38Industrial water glass (with Na2O% and SiO2% of 11.49% and 31.25%, respectively) supplied by Kunming, Yunnan Province was used as activator. NaOH (with purity above 96%) from Fuchen (Tianjin) Chemical Reagent Co., Ltd. was used to adjust the modulus of the WG to the values required. Crushed limestone with size of 5–25 mm (continuous grading) and manufactured sand with fineness modulus of 2.82 were used as coarse and fine aggregates, respectively. Tap water was used for mixing.By using the mix proportion given in Table5, concrete specimens were manufactured according to Chinese standard JGJ/T 439–2018 [75]. After mixing, the concrete mixture was cast into molds with size of 100 mm × 100 mm × 100 mm in two layers. Vibration was carried out after each layer was cast. When the concrete surface was stiff, the specimens with molds were moved into curing room with temperature of 20 ± 2°C and RH ≥ 95%. The specimens were de-molded one day after mixing, and then were moved into the curing room again for continuous curing to the ages required.Table 5
Mix proportions of concrete.
Mix no.Na2O%MsW/BMix proportions (kg/m3)SlagWGNaOHWaterCoarse aggregatesFine aggregates14.001.000.45349.7460.9312.15128.191123.24748.8324.001.500.45344.2189.959.05107.791138.80759.2034.002.000.45338.85118.066.0588.041153.87769.2546.001.000.45336.3587.8917.52109.241142.65761.7756.001.500.45328.73128.8512.9680.451164.49776.3366.002.000.45321.45168.008.6152.951185.36790.2478.001.000.45323.94112.8722.5091.691160.62773.7588.001.500.45314.58164.4116.54555.471187.97791.9898.002.000.45305.74213.0610.9121.291213.78809.19106.001.500.40328.73128.8512.9661.451175.89783.93116.001.500.50328.73128.8512.9699.451153.09768.73When the specimens reached curing ages of 3 d and 28 d, respectively, compressive strength test was carried out according to Chinese national standard GB/T 50081- 2019 [76]. The strength results to be reported are an average value of three duplicated specimens.


## 2.1. Data Collection

ANN and ACE models were established in this study to predict compressive strength of AAS concretes with WG as alkali activator. Data used for the model establishment was collected from related literature published publicly. The influence on strength of AAS should be from both alkali activator and slag, as well as their proportion. Considering the importance of the influencing parameters, alkali concentration of WG (Na2O%), modulus of WG (Ms), water/binder ratio (W/B), surface area of slag (SA), and basicity index of slag (Kb) were taken as the input parameters of the models [7–13]. Other parameters, such as binder content, which are less important and then not typically considered in the literature, are not adopted in this study for model establishment. Na2O%, Ms, W/B, and Kb should be calculated according to formulae (1)–(4) [14–17]. If NaOH was used in the alkali activator as well together with WG, NaOH should be treated as a part of WG. Therefore, “WG” in the formulae means the WG after NaOH adjustment. Compressive strengths of AAS at curing ages of 3 d and 28 d were considered as output parameters. Finally, 171 and 309 sets of data were successfully selected for 3 d and 28 d compressive strength prediction, respectively. Literature used and input/output parameter values listed in Tables 1 and 2 gives the number of tests, range of variation, and average and standard deviation values for each of the references presented in Table 1. Parts of the data in the Table 1 have same inputs but different output values. This is because other influencing factors rather than the five mentioned above were also considered in the literature, but here only the five factors were concerned.(1)Na2O%=Na2OinWGslag∗100%,(2)Ms=SiO2inWGNa2OinWG,(3)WB=additionalwater+waterinWGslag+SiO2inWG+Na2OinWG,(4)Kb=CaO+MgOSiO2+Al2O3.Table 1
Literatures and input/output parameters.
Ref.Input parametersOutput parametersNa2O%MsW/BSA (m²/kg)KbCompressive strength (MPa)3 d28 d[18]4.00.750.475270.9625.1643.804.01.000.475270.9616.4448.964.01.500.475270.96—48.054.02.000.475270.96—33.446.00.750.475270.9631.1546.716.01.000.475270.9635.6053.946.01.500.475270.9632.2960.726.02.000.475270.9612.3159.828.00.750.475270.9634.6251.698.01.000.475270.9632.6054.988.01.500.475270.9623.6658.448.02.000.475270.96—54.83[19]4.01.500.284850.99—81.204.01.500.324850.9950.1079.104.01.500.374850.9929.1074.104.01.500.414850.99—62.204.01.500.324850.9940.3079.504.01.500.324850.9946.0078.104.01.500.324850.9951.4082.404.01.500.324850.9952.1080.504.01.500.324850.9948.6077.104.01.500.324850.9952.3077.903.01.500.334850.99—55.105.01.500.294850.9954.3097.606.01.500.274850.9946.20102.604.01.000.334850.9938.2073.204.02.000.334850.9946.1086.504.01.500.323130.9941.3075.804.01.500.326790.9955.1085.20[20]5.01.500.465231.1410.7220.747.01.500.465231.14—27.579.01.500.465231.1414.7325.115.01.800.465231.14—27.297.01.800.465231.1419.0940.199.01.800.465231.1428.7857.735.02.000.465231.14—28.497.02.000.465231.1424.5746.039.02.000.465231.1450.6858.92[21]5.01.500.354621.00—79.605.01.500.404621.00—69.405.01.500.454621.00—61.305.01.500.504621.00—47.205.01.500.554621.00—31.605.01.500.354621.00—82.205.01.500.404621.00—72.505.01.500.454621.00—63.505.01.500.504621.00—52.705.01.500.554621.00—42.105.01.500.354621.00—84.005.01.500.404621.00—59.205.01.500.454621.00—57.105.01.500.504621.00—45.905.01.500.554621.00—36.30[22]7.01.800.465230.94—40.509.01.800.465230.94—60.109.02.000.465230.94—62.70[23]10.01.500.334501.2818.7025.0012.01.500.334501.2819.6027.2014.01.500.334501.2822.5029.6010.01.200.334501.2830.2040.4012.01.200.334501.2836.0046.8014.01.200.334501.2842.8050.4010.01.000.334501.2835.6050.4012.01.000.334501.2849.1061.0014.01.000.334501.2850.4064.4010.00.800.334501.2840.1055.7012.00.800.334501.2844.6064.6014.00.800.334501.2849.1065.40[24]8.01.400.284551.0428.6057.60[25]4.00.400.515251.10—33.274.00.800.515251.10—38.954.01.200.505251.10—46,776.00.400.505251.10—44.076.00.800.495251.10—52.366.01.200.485251.10—79.708.00.400.485251.10—36.768.00.800.475251.10—82.688.01.200.465251.10—75.26[26]4.01.000.445151.0831.4956.566.01.000.365151.0844.3073.008.01.000.335151.0854.3376.904.01.250.305151.0824.2459.916.01.250.355151.0842.6376.078.01.250.315151.0850.4377.464.01.500.255151.0817.8362.416.01.500.345151.0839.2978.028.01.500.295151.0841.2479.41[27]4.01.000.354350.99—24.444.01.000.504350.99—20.194.01.000.654350.99—18.32[28]4.02.060.443000.84—14.406.02.060.473000.84—20.308.02.060.453000.8410.5024.004.02.060.443000.8410.9038.006.02.060.363000.8428.5053.908.02.060.313000.8429.5052.504.02.060.273500.84—15.906.02.060.473500.84—22.208.02.060.453500.8410.8025.004.02.060.443500.84—51.706.02.060.363500.8427.6067.108.02.060.313500.8429.2068.204.02.060.274000.84—16.706.02.060.474000.8410.3023.908.02.060.454000.8411.0027.304.02.060.444000.8411.4054.406.02.060.374000.8426.8070.108.02.060.314000.8433.8072.40[29]2.01.250.404000.9965.5267.632.00.750.404000.9944.0351.081.51.670.404000.9951.4373.091.51.000.404000.9936.4658.83[30]5.02.400.233991.0144.3059.455.02.000.233991.0154.3568.645.02.000.473991.0154.3968.445.02.400.473991.0144.3759.26[31]5.02.400.533001.01—49.755.02.400.534001.01—67.645.02.400.535001.01—73.09[32]6.00.500.474461.0556.2542.036.01.000.474461.0568.0154.066.01.500.474461.0584.1458.986.02.000.474461.0587.9768.558.00.500.474461.0574.6655.758.01.000.474461.0582.0563.158.01.500.474461.0592.4770.558.02.000.474461.05100.4078.49[33]6.01.000.474850.93—87.304.91.500.474850.93—81.114.12.000.474850.93—85.31[34]4.32.000.443851.24—39.50[35]5.01.200.443250.92—83.13[36]10.83.200.454000.9940.1159.359.63.200.504000.9939.2551.6210.03.200.554000.9928.5145.6510.53.200.604000.9925.8636.13[37]6.01.200.354240.9097.66118.008.01.200.354240.90101.30123.2010.01.200.354240.9084.41108.706.01.400.354240.9090.68111.508.01.400.354240.9091.30113.1010.01.400.354240.9089.96110.106.01.600.354240.9089.34114.408.001.600.354240.9095.40118.2010.01.600.354240.9087.29109.00[38]4.01.250.403700.88—60.10[39]4.00.800.504350.9929.8042.075.00.800.504350.9932.4348.106.00.800.504350.9937.6851.05[40]10.01.000.454980.91—54.8210.01.000.454350.93—29.6610.01.000.454500.94—34.55[41]9.21.250.553850.8032.9239.55[42]4.01.500.504501.08—48.026.01.500.504501.08—68.8910.01.500.504501.08—78.71[43]4.00.500.405151.06—45.094.01.000.405151.06—50.414.01.500.405151.06—56.456.00.500.405151.06—55.386.01.000.405151.06—55.746.01.500.405151.06—63.208.00.500.405151.06—47.998.01.000.405151.06—56.058.01.500.405151.06—61.31[44]8.00.480.553451.22—18.1012.00.480.553451.22—34.0016.00.480.553451.22—39.10[45]0.40.500.334300.9938.9941.110.40.800.334300.9941.7848.860.41.200.334300.9927.9130.020.41.500.334300.9948.7855.860.41.800.334300.9943.7753.330.42.100.334300.9942.3151.870.42.300.334300.9927.7241.540.41.500.334300.9926.4250.530.61.500.334300.9945.5878.290.81.500.334300.9935.5060.901.01.500.334300.9949.3681.97[46]4.30.410.445011.14—28.003.91.220.445011.14—46.40[47]4.00.750.285270.66—26.084.01.000.285270.66—36.324.01.500.285270.66—36.804.02.000.285270.66—25.656.00.750.285270.66—15.576.01.000.285270.66—8.916.01.500.285270.66—60.006.02.000.285270.66—41.208.00.750.285270.66—1.288.01.000.285270.66—6.248.01.500.285270.66—39.688.02.000.285270.66—23.73[48]3.01.000.414050.5538.39—4.01.000.404050.5553.05—[49]3.71.400.303381.1667.1099.403.01.700.303381.1652.5086.502.61.990.303381.1632.6077.002.32.290.303381.16—65.202.02.390.303381.16—44.201.82.940.303381.16—53.801.63.270.303381.16—55.501.43.600.303381.16—52.20[50]4.00.500.454531.0743.4784.004.00.800.454531.0751.58107.604.01.000.454531.0753.05123.804.01.200.454531.0756.00126.004.01.500.454531.0757.47128.204.01.800.454531.0747.16127.504.02.000.454531.0746.42126.704.02.200.454531.0736.8476.634.02.500.454531.07—34.632.01.500.454531.07—30.923.01.500.454531.0727.83105.904.01.500.454531.0758.74128.305.01.500.454531.0772.66140.706.01.500.454531.0781.16151.507.01.500.454531.0764.15116.70[51]4.02.500.294580.9730.8863.954.02.000.294580.9749.2383.254.01.500.294580.9761.58102.904.00.500.294580.9770.8890.254.01.000.294580.9768.5399.10[52]2.40.500.284611.01—33.382.41.000.294611.01—48.482.42.000.324611.01—70.132.40.500.284201.03—51.262.41.000.294201.03—69.142.42.000.324201.03—87.02[53]5.01.000.404871.0330.9454.545.01.500.404871.0338.3561.765.02.000.404871.0341.2670.99[54]4.00.750.505201.10—44.976.00.750.505201.10—84.094.01.000.505201.10—41.726.01.000.505201.10—79.69[55]2.30.550.494201.01—16.002.70.750.504201.0111.9018.302.70.750.506151.0815.3023.602.70.750.508171.0717.3025.903.10.850.514201.0112.9020.405.40.550.504201.0122.3035.206.60.750.504201.0126.7041.906.60.750.506151.0828.7044.606.60.750.508171.0731.4048.607.90.850.514201.0133.5049.60[8]8.00.750.504250.84—81.108.01.000.504250.84—80.908.01.250.504250.84—58.908.01.500.504250.84—57.50[56]4.00.600.434281.0334.6562.464.00.900.434281.0340.1569.884.01.200.434281.0333.6876.984.01.500.434281.0345.3381.813.00.600.434281.0328.7049.013.00.900.434281.0327.2862.353.01.200.434281.0323.0268.033.01.500.434281.03—68.32[57]4.00.750.504600.9311.5524.234.01.000.504600.9311.7033.844.01.250.504600.9311.9934.514.01.500.504600.9311.8828.846.00.750.504600.9314.3624.956.01.000.504600.9312.9625.516.01.250.504600.93—27.466.01.500.504600.93—22.168.00.750.504600.9314.2536.028.01.000.504600.9314.2536.788.01.250.504600.9311.8039.088.01.500.504600.9310.5732.64[58]5.81.000.474101.0242.3067.805.81.000.474101.0245.3085.005.81.500.474101.0255.0098.00[59]5.01.000.284651.04—82.7510.01.000.284651.04—71.2315.01.000.284651.04—48.125.01.500.284651.04—85.0410.01.500.284651.04—65.855.02.000.394651.04—86.8310.02.000.394651.04—48.84[60]3.01.000.256001.1452.0767.083.01.000.258001.1462.2191.393.01.000.2510001.1457.6277.08[61]6.00.800.384130.91—86.006.01.200.384130.91—80.80[62]2.91.000.425020.90—45.002.91.000.425030.97—36.922.91.000.404990.87—44.622.91.000.405070.93—71.152.91.000.405010.98—78.852.91.000.405020.95—39.622.91.000.404960.81—38.082.91.000.404990.77—37.69[63]4.00.750.504600.9335.0739.89[64]5.11.500.514601.0564.25100.00[65]4.00.400.444100.81—54.704.00.800.444100.81—59.704.01.200.444100.81—58.504.01.600.444100.81—52.306.00.400.444100.81—62.406.00.800.444100.81—78.406.01.200.444100.81—74.106.01.600.444100.81—71.008.00.400.444100.81—75.208.00.800.444100.81—76.108.01.200.444100.81—87.208.01.600.444100.81—88.30[66]4.01.650.484010.9831.3857.486.01.650.484010.9849.2778.894.01.000.484010.9829.0347.806.01.000.484010.9844.2860.70Table 2
Analysis of input/output parameters.
Ref.Input parametersOutput parametersNa2O%MsW/BSA (m2/kg)KbCompressive strength (MPa)3 d28 d[18]Number of tests912Range[4.00–8.00][0.75–2.00]0.47527.000.96[12.31–35.60][33.44–60.72]Average6.001.310.47527.000.9627.0951.28Standard deviation1.710.500.000.000.008.297.73[19]Number1417Range[3.00–6.00][1.00–2.00][0.27–0.41][313–679]0.99[29.10–55.10][55.10–102.60]Average4.121.500.32487.000.9946.5179.30Standard deviation0.600.180.0364.800.007.2311.02[20]Number69Range[5.00–9.00][1.50–2.00]0.46523.001.14[10.72–50.68][20.74–58.92]Average7.001.770.46523.001.1424.7636.90Standard deviation1.730.220.000.000.0014.2714.42[21]Number—15Range5.001.50[0.35–0.55]462.001.00—[31.60–84.00]Average5.001.500.45462.001.00—58.97Standard deviation0.000.000.070.000.00—16.50[22]Number—3Range[7.00–9.00][1.80–2.00]0.46523.000.94—[40.50–62.70]Average8.331.870.46523.000.94—54.43Standard deviation1.150.120.000.000.00—12.14[23]Number1212Range[10.00–14.00][0.80–1.50]0.33450.001.28[18.70–50.40][25.00–65.40]Average12.001.130.33450.001.2836.5648.41Standard deviation1.710.270.000.000.0011.5514.91[24]Number11Range8.001.400.28455.001.0428.6057.60Average8.001.400.28455.001.0428.6057.60Standard deviation0.000.000.000.000.000.000.00[25]Number—9Range[4.00–8.00][0.40–1.20][0.46–0.51]525.001.10—[33.27–82.68]Average6.000.800.49525.001.10—52.42Standard deviation1.730.350.020.000.00—19.49[26]Number99Range[4.00–8.00][1.00–1.50][0.25–0.44]515.001.08[17.83–54.33][56.56–79.41]Average6.001.250.33515.001.0838.4271.08Standard deviation1.730.220.050.000.0011.898.88[27]Number—3Range4.001.00[0.35–0.65]455.001.04—[18.32–24.44]Average4.001.000.50455.001.04—20.98Standard deviation0.000.000.150.000.00—3.14[28]Number12Range[4.00–8.00]2.06[0.27–0.47][300–400]0.84[10.30–33.80][14.40–72.40]Average6.002.060.39350.000.8420.0239.89Standard deviation1.680.000.0742.000.009.7621.10[29]Number44Range[1.50–2.00][0.75–1.67]0.40400.000.99[36.46–65.52][51.08–73.09]Average1.751.170.40400.000.9949.3662.66Standard deviation0.290.390.000.000.0012.399.70[30]Number22Range5.00[2.00–2.40]0.23399.001.01[44.30–54.35][59.45–68.64]Average5.002.200.23399.001.0149.3364.05Standard deviation0.000.280.000.000.007.116.50[31]Number—3Range5.002.400.53[300–500]1.01—[49.75–73.09]Average5.002.400.53400.001.01—63.49Standard deviation0.000.000.00100.000.00—12.21[32]Number88Range[6.00–8.00][0.50–2.00]0.47446.001.05[56.25–100.40][42.03–78.49]Average7.001.250.47446.001.0580.7461.45Standard deviation1.070.600.000.000.0014.0811.32[33]Number—3Range[4.10–6.00][1.00–2.00]0.47485.000.93—[81.11–87.30]Average5.001.500.47485.000.93—84.57Standard deviation0.950.500.000.000.00—3.16[34]Number—1Range4.302.000.44385.001.24—39.50Average4.302.000.44385.001.24—39.50Standard deviation0.000.000.000.000.00—0.00[35]Number—1Range5.001.200.44325.000.92—83.13Average5.001.200.44325.000.92—83.13Standard deviation0.000.000.000.000.00—0.00[36]Number44Range[9.60–10.80]3.20[0.45–0.60]400.000.99[25.86–40.11][36.13–59.35]Average10.233.200.53400.000.9933.4348.19Standard deviation0.530.000.060.000.007.309.80[37]Number99Range[6.00–10.00][1.20–1.60]0.35424.000.90[84.41–101.30][108.70–123.20]Average8.001.400.35424.000.9091.93114.02Standard deviation1.730.170.000.000.005.284.92[38]Number—1Range4.001.250.40370.000.88—60.10Average4.001.250.40370.000.88—60.10Standard deviation0.000.000.000.000.00—0.00[39]Number33Range[4.00–6.00]0.800.50435.000.99[29.80–37.68][42.07–51.05]Average5.000.800.50435.000.9933.3047.07Standard deviation1.000.000.000.000.004.014.58[40]Number—3Range10.001.000.45[435–498][0.91–0.94]—[29.66–54.82]Average4.001.000.45461.000.93—39.68Standard deviation0.000.000.0032.910.02—13.34[41]Number11Range9.201.250.55385.000.8032.9239.55Average9.201.250.55385.000.8032.9239.55Standard deviation0.000.000.000.000.000.000.00[42]Number—3Range[4.00–10.00]1.500.50450.001.08—[48.02–78.71]Average6.671.500.50450.001.08—65.21Standard deviation3.060.000.000.000.00—15.67[43]Number—9Range[4.00–8.00][0.50–1.50]0.40515.001.06—[45.09–61.31]Average6.001.000.40515.001.06—54.62Standard deviation1.730.430.000.000.00—5.90[44]Number—3Range[8.00–16.00]0.480.55345.001.22—[18.10–39.10]Average12.000.480.55345.001.22—30.40Standard deviation4.000.000.000.000.00—10.95[45]Number1111Range[0.40–1.00][0.50–2.30]0.33430.000.99[26.42–49.36][30.02–81.97]Average0.511.470.33430.000.9938.9254.03Standard deviation0.210.520.000.000.008.4215.37[46]Number—2Range[3.90–4.30][0.41–1.22]0.44501.001.14—[28.00–46.40]Average4.100.820.44501.001.14—37.20Standard deviation0.280.570.000.000.00—13.01[30]Number—2Range5.00[2.00–2.40]0.47399.001.01—[59.26–68.44]Average5.002.200.47399.001.01—63.85Standard deviation0.000.280.000.000.00—6.49[47]Number—12Range[4.00–8.00][0.75–2.00]0.28527.000.66—[1.28–60.00]Average6.001.310.28527.000.66—26.79Standard deviation1.710.500.000.000.00—17.05[48]Number2—Range[3.00–4.00]1.00[0.40–0.41]405.000.55[38.39–53.05]—Average3.501.000.41405.000.5545.72—Standard deviation0.710.000.010.000.0010.37S—[49]Number38Range[1.40–3.70][1.40–3.60]0.30338.001.16[32.60–67.10][44.20–99.40]Average2.302.450.30338.001.1650.7366.73Standard deviation0.770.770.000.000.0017.3219.19[50]Number1315Range[2.00–7.00][0.50–2.50]0.45453.001.07[27.83–81.16][30.92–151.50]Average4.201.500.45453.001.0753.58107.27Standard deviation1.150.510.000.000.0014.2235.90[51]Number55Range4.00[0.50–2.50]0.29458.000.97[30.88–70.88][63.95–102.90]Average4.001.500.29458.000.9756.2287.89Standard deviation0.000.790.000.000.0016.4815.42[52]Number—6Range2.40[0.50–2.00][0.28–0.32][420–461][1.01–1.03]—[33.38–87.02]Average2.401.170.30440.501.02—59.91Standard deviation0.000.680.0222.460.01—19.15[53]Number33Range5.00[1.00–2.00]0.40487.001.03[30.94–41.26][54.54–70.99]Average5.001.500.40487.001.0336.8562.43Standard deviation0.000.500.000.000.005.328.25[54]Number—4Range[4.00–6.00][0.75–1.00]0.50520.001.10—[41.72–84.09]Average5.000.880.50520.001.10—62.62Standard deviation1.150.140.000.000.00—22.37[55]Number910Range[2.30–7.90][0.55–0.85][0.49–0.51][420–817][1.01–1.08][11.90–33.50][16.00–49.60]Average4.660.730.50538.401.0422.2232.41Standard deviation2.160.100.01167.030.038.2113.07[8]Number—4Range8.00[0.75–1.50]0.50425.000.84—[57.50–81.10]Average8.001.130.50425.000.84—69.60Standard deviation0.000.320.000.000.00—13.18[56]Number78Range[3.00–4.00][0.60–1.50]0.43428.001.03[23.02–45.33][62.35–81.81]Average3.501.050.43428.001.0333.2667.36Standard deviation0.530.360.000.000.007.719.96[57]Number1012Range[4.00–8.00][0.75–1.50]0.50460.000.93[11.55–14.36][22.16–39.08]Average6.001.130.50460.000.9312.5330.50Standard deviation1.710.290.000.000.001.345.66[58]Number33Range5.80[1.00–1.50]0.47410.001.02[42.30–55.00][67.80–98.00]Average5.801.170.47410.001.0247.5383.60Standard deviation0.000.290.000.000.006.6415.15[59]Number—7Range[5.00–10.00][1.00–2.00][0.28–0.39]465.001.04—[48.12–86.83]Average8.571.430.31465.001.04—69.81Standard deviation3.780.450.050.000.00—16.42[60]Number33Range3.001.000.25[600–1000]1.14[52.07–62.21][67.08–91.39]Average3.001.000.25800.001.1457.3078.52Standard deviation0.000.000.00200.000.005.0812.22[61]Number—2Range6.00[0.80–1.20]0.38413.000.91—[80.80–86.00]Average6.001.000.38413.000.91—83.40Standard deviation0.000.280.000.000.00—3.68[62]Number—8Range2.901.00[0.40–0.42][496–503][0.77–0.98]—[36.92–78.85]Average2.901.000.41501.130.90—48.99Standard deviation0.000.000.013.270.08—16.47[63]Number11Range4.000.750.50460.000.9335.0739.89Average4.000.750.50460.000.9335.0739.89Standard deviation0.000.000.000.000.000.000.00[64]Number11Range5.101.500.51460.001.0564.25100.00Average5.101.500.51460.001.0564.25100.00Standard deviation0.000.000.000.000.000.000.00[65]Number—12Range[4.00–8.00][0.40–1.60]0.44410.000.81—[52.30–88.30]Average6.001.000.44410.000.81—69.83Standard deviation1.710.470.000.000.00—12.16[66]Number44Range[4.00–6.00][1.00–1.65]0.48401.000.98[29.03–49.27][47.80–78.89]Average5.001.330.48401.000.9838.4961.22Standard deviation1.150.380.000.000.009.8312.993 d totalNumber171—Range[0.40–14.00][0.50–3.20][0.23–0.60][300–1000][0.55–1.28][10.30–101.30]—Average5.651.390.40457.371.0141.62—Standard deviation2.910.540.0884.700.1221.40—28 d totalNumber—309Range[0.40–16.00][0.40–3.60][0.23–0.65][300–1000][0.66–1.28]—[1.28–151.50]Average5.591.370.41459.050.99—59.70Standard deviation2.720.570.0874.840.12—25.96


## 2.2. ANN Modeling

ANN is a kind of general mathematical model to solve nonlinear system problems. It processes information by imitating human neural network [67]. Due to its strong generalization ability, it has been applied successfully in the field of civil engineering in recent years [68–72]. ANN models consist of three layers: input layer, hidden layer(s), and output layer. The number of neurons in both the input and the output layers is just the number of parameters in the corresponding layers. Determination of the number of layers and number of neurons in each layer is relatively complex for the hidden layer(s), which is generally done by trial-and-error. Connection between neurons should be implemented by using a linear/nonlinear transfer function. Input parameters in the input layer are fed to the output layer through the hidden layer(s). If outputs were not desired, they would bring error signals to back-propagate into the input layer to minimize the error by modifying the weight of each neuron there. In this context, training is very important in ANN modeling, and sufficient data size is needed to guarantee its accuracy.In this study, the five parameters, Na2O%, Ms, W/B, SA, and Kb, were treated as the neutrons in the input layer, and compressive strength of AAS was the neutron in the output layer. The determination of the hidden layer was made by trial and error. Both single-layer and double-layer were tried in this study. For both cases, number of the neutrons in the hidden layer was equal to root of the sum of input and output node numbers, plus a constant value less than 10 in general [73]. After several trials (a sample of performance comparison is given in Table 3), one hidden layer was determined to be used, and the number of the neutrons in the hidden layer was 10 and 13 for 3 d and 28 d compressive strength, respectively, according to the MAE and the RMSE error evaluations (to be described in section 2.4). Therefore, ANN model structures of 5-10-1 and 5-13-1 were used eventually in this study for compressive strength prediction of AAS at curing ages of 3 d and 28 d, respectively, as shown in Figure 1. For both the networks, 70%, 15%, and 15% of the data collected from literature were randomly selected for training, testing, and validation, respectively. Number of training period, learning rate, and minimum error of the training were set as 1000, 0.01, and 0.00001, respectively. After a comparison between Gradient Descent method and Levenberg-Marquardt algorithm, the latter was used for training due to its higher accuracy. The results to be reported were the optimum solution after 50 times of training.Table 3
Performance comparison between different network structures (MPa).
5-10-15-13-15-(6, 6)-1TrainingTestingTrainingTestingTrainingTesting3 d compressive strengthMAE7.476.7811.289.898.017.23RMSE14.8918.2116.3417.1116.4119.6228 d compressive strengthMAE19.737.9815.645.7916.2610.15RMSE17.2513.9914.8910.9515.0311.76Figure 1
ANN model structures used in this study: (a) 5-10-1 structure for 3 d compressive strength. (b) 5-13-1 structure for 28 d compressive strength.
(a)(b)


## 2.3. ACE Modeling

ACE nonparametric regression technique, which has strong feasibility and high accuracy, is essentially a kind of response surface function. It is usually used to establish a mapping relationship between inputs and outputs which are already known by the approach of data fitting, as given in Ref. [74].(5)θY=φX1+φX2+⋅⋅⋅⋅⋅⋅φXn+ε1,(6)Y=θ−1φX1+φX2+⋅⋅⋅⋅⋅⋅φXn+ε2,where X1, X2⋅⋅⋅⋅⋅⋅Xnare input parameters; φX1,φX2⋅⋅⋅⋅⋅⋅φXn are response surface functions of X1, X2⋅⋅⋅⋅⋅⋅Xn; Y is output parameter; θY is response surface function of Y; θ−1 is inverse function of θ; ε1 and ε2 are accuracy errors.As the accuracy errorε is difficult to be determined, correction coefficient λ is usually introduced to modify formula (6), and finally, formula (7) is obtained as given below.(7)Y=λθ−1φX1+φX2+⋅⋅⋅⋅⋅⋅φXn.Furthermore, influencing weight of each input parameter on the output parameter could be analyzed elementarily by using ACE approach as well during the calculation.In this study,X1, X2⋅⋅⋅⋅⋅⋅X5were nominated as Na2O%, Ms, W/B, SA, and Kb, respectively, as input parameters. Their values were collected from literature as detailed in Section 2.1. Input parameters were imported in ACE calculation software S-PLUS to calculate their corresponding response surface function φX1, φX2⋅⋅⋅⋅⋅⋅φX5. After that, a mapping relationship was established between the response surface functions and output parameters, namely, compressive strength of AAS at curing ages of 3 d and 28 d, respectively, by data fitting regression. The values of the strength were also collected from literature as detailed in Section 2.1.


## 2.4. Error Evaluation

Both mean absolute error (MAE) and root mean square error (RMSE) were used in this study to evaluate accuracy of both the ANN and the ACE models. MAE and RMSE values are to be zero when the values predicted and tested are exactly the same. Error increases with the increase of MAE and RMSE values. Calculations of MAE and RMSE are given in formulae (8) and (9) according to the literature [2–6]. Furthermore, agreement between predicted and measured values together with coefficient of determination was also applied to better assess the applicability of the proposed networks.(8)MAE=∑i=1nyi−zin(9)RMSE=∑i=1nyi−yi2n1/2where yi (y1, y2, ......yn) are the values tested; zi (z1, z2, ......zn) are the values predicted; n is the number of data.


## 2.5. Experimental Validation

Eleven AAS concrete mixes were prepared in this study, their compressive strength was tested at curing ages of 3 d and 28 d, respectively, to validate the results predicted by using both the ANN and the ACE models.The slag used in the experimental work was from Qujing, Yunnan Province, China, whoseKb and SA were 0.96 and 405 m2/kg, respectively. Its chemical compositions are given in Table 4.Table 4
Chemical compositions of slag (%).
CaOSiO2Al2O3MgOTiO2SO3MnONa2OK2OFe2O338.2631.4015.716.902.941.431.230.960.530.38Industrial water glass (with Na2O% and SiO2% of 11.49% and 31.25%, respectively) supplied by Kunming, Yunnan Province was used as activator. NaOH (with purity above 96%) from Fuchen (Tianjin) Chemical Reagent Co., Ltd. was used to adjust the modulus of the WG to the values required. Crushed limestone with size of 5–25 mm (continuous grading) and manufactured sand with fineness modulus of 2.82 were used as coarse and fine aggregates, respectively. Tap water was used for mixing.By using the mix proportion given in Table5, concrete specimens were manufactured according to Chinese standard JGJ/T 439–2018 [75]. After mixing, the concrete mixture was cast into molds with size of 100 mm × 100 mm × 100 mm in two layers. Vibration was carried out after each layer was cast. When the concrete surface was stiff, the specimens with molds were moved into curing room with temperature of 20 ± 2°C and RH ≥ 95%. The specimens were de-molded one day after mixing, and then were moved into the curing room again for continuous curing to the ages required.Table 5
Mix proportions of concrete.
Mix no.Na2O%MsW/BMix proportions (kg/m3)SlagWGNaOHWaterCoarse aggregatesFine aggregates14.001.000.45349.7460.9312.15128.191123.24748.8324.001.500.45344.2189.959.05107.791138.80759.2034.002.000.45338.85118.066.0588.041153.87769.2546.001.000.45336.3587.8917.52109.241142.65761.7756.001.500.45328.73128.8512.9680.451164.49776.3366.002.000.45321.45168.008.6152.951185.36790.2478.001.000.45323.94112.8722.5091.691160.62773.7588.001.500.45314.58164.4116.54555.471187.97791.9898.002.000.45305.74213.0610.9121.291213.78809.19106.001.500.40328.73128.8512.9661.451175.89783.93116.001.500.50328.73128.8512.9699.451153.09768.73When the specimens reached curing ages of 3 d and 28 d, respectively, compressive strength test was carried out according to Chinese national standard GB/T 50081- 2019 [76]. The strength results to be reported are an average value of three duplicated specimens.


## 3. Results and Discussion

### 3.1. ANN

Regression of ANN modeling for prediction of 3 d and 28 d compressive strength of AAS is given in Figures2 and 3, respectively. Correlation coefficient R is usually used to evaluate the correlation between the data samples. The closer the R-value is to 1, the stronger the correlation. From the figures, it can be seen that both the predictions have a good correlation between the data samples in general no matter training, testing, validation, or all of them are considered as the R-values are higher than 0.8. However, the correlation in the case of 28 d compressive strength is relatively lower in comparison with the 3 d one. It is known that 28 d compressive strength is the most elementary property of concrete, and therefore has been extensively reported in the literature. Consequently, large amounts of data samples on the 28 d compressive strength of AAS have been collected in this study, namely, 309 sets. This could have increased the scattering of the data as a result of different conditions of the specimen, such as different types and sizes of the specimen, different sources of slag, different aggregates, different curing conditions, used in the different studies.Figure 2
Regression of ANN modeling for prediction of 3 d compressive strength of AAS. (a) Training. (b) Testing. (c) Validation. (d) All.
(a)(b)(c)(d)Figure 3
Regression of ANN modeling for prediction of 28 d compressive strength of AAS. (a) Training. (b) Testing. (c) Validation. (d) All.
(a)(b)(c)(d)Also, from MAE and RMSE error evaluation results, as given in Table6, it can be seen that the error of the ANN models is at a low level, with MAE and RMSE values less than 20 MPa, in both the cases of 3 d and 28 d compressive strength, which means the models have sufficient accuracy.Table 6
Error evaluation (MPa).
ANNACETrainingTestingTrainingTesting3 d compressive strengthMAE7.476.788.995.39RMSE14.8918.2112.0014.0028 d compressive strengthMAE15.645.7914.877.32RMSE14.8910.9518.7015.79Later, 3 d and 28 d compressive strengths of the 11 AAS concrete mixes were experimentally measured. Simultaneously, the material parameters used in the experimental work were put in the ANN model to run a prediction modeling. Comparison of the results measured and predicted is reported in Table7, together with the error between them (100% × |predicted value-measured value|/measured value). From the table, it can be seen that in comparison to 28 d compressive strength, although the ANN model of 3 d compressive strength had an equivalent accuracy as discussed previously, it is less feasible to be employed to run the prediction. As stated previously, compared to the 309 sets of data that have been collected for the establishment of the 28 d compressive strength model, only 171 sets were available in the case of 3 d strength. Furthermore, the material parameters reported in the 171 data sets may not have covered the ones used in the experimental work, resulting in a lack of corresponding training, and finally in a high error between measurement and prediction. As can be seen from Table 1, few literatures consider the effects of 5 parameters on the 3D compressive strength of AAS at the same time. Therefore, as a result of insufficient training, the error of the mix 11 at 3 days is as high as 77.1%, while the larger database of 28 d compressive strength has supported effective training. Consequently, the error decreases dramatically to a low value of 4.6%. In this context, in order to improve feasibility of the ANN model for prediction, it is necessary to enlarge the scale of database enabling which could cover circumstances as full as possible, to ensure that a sufficient training could be implemented.Table 7
Comparison between the strength measured and predicted.
Mix no.3 d compressive strength (MPa)28 d compressive strength (MPa)MeasuredANNACEMeasuredANNACEPredictedError (%)PredictedError (%)PredictedError (%)PredictedError (%)124.227.312.823.33.750.547.46.151.41.8221.229.237.723.711.851.053.03.959.416.5323.031.235.628.423.551.256.29.857.211.7427.729.46.132.216.254.451.45.558.77.9533.731.85.632.63.360.057.14.865.79.5635.135.10.038.08.359.660.10.863.87.0737.827.527.236.53.461.054.910.061.71.1833.829.413.032.63.662.360.62.768.29.5938.230.220.942.511.260.263.55.566.410.31044.139.410.620.553.565.959.99.168.43.81113.123.277.110.916.856.253.64.660.78.0Mean error (%)22.414.15.77.9Max. error (%)77.153.510.016.5Min. error (%)0.03.30.81.1


### 3.2. ACE

Relationship between input parametersX1, X2⋅⋅⋅⋅⋅⋅X5 and their corresponding response surface function φX1, φX2⋅⋅⋅⋅⋅⋅φX5 is shown in Figures 4 and 5. ACE fitting curves of compressive strength of AAS at curing ages of 3 d and 28 d were plotted in Figure 6, which have been adjusted by introducing correction coefficientλ as stated in Section 2.3. After trial-and-error, the values of λ were determined to be 0.90 and 0.85, respectively, for 3 d and 28 d compressive strength. Eventually, fitting goodness R2 of 0.986 and 0.950 were obtained, respectively, in the case of 3 d and 28 d compressive strength, indicating that the ACE model has very high accuracy for both the cases. While probably due to the much bigger data size and the resulting increase in scattering, the ACE model for 28 d compressive strength is less accurate compared to the 3 d case, which could be seen from MAE and RMSE error evaluations as given in Table 6. However, the value is still acceptable for practical application.Figure 4
Relationship between input parameters and their corresponding response surface functions in the case of 3 d compressive strength. (a)X1 (Na2O%) and φX1. (b) X2 (Ms) and φX2. (c) X3 (W/B) and φX3. (d) X4 (SA) and φX4. (e) X5 (Kb) and φX5.
(a)(b)(c)(d)(e)Figure 5
Relationship between input parameters and their corresponding response surface functions in the case of 28 d compressive strength. (a)X1 (Na2O%) and φX1. (b)X2 (Ms) and φX2. (c)X3 (W/B) and φX3. (d)X4 (SA) and φX4. (e)X5 (Kb) and φX5.
(a)(b)(c)(d)(e)Figure 6
ACE fitting curves of compressive strength of AAS. (a) 3 d compressive strength. (b) 28 d compressive strength.
(a)(b)In addition, from Figures4 and 5, it can be seen that the relationship between X1 (Na2O%) and φX1 is much clearer compared to the others, and with the change of X1 (Na2O%), φX1 varies to a considerable scale. These indicate that among the five influencing factors, Na2O%, Ms, W/B, SA, and Kb, Na2O% took the largest weight-influencing compressive strength of AAS, followed by Ms > W/B > Kb > SA.Similar to the ANN prediction, the ACE model was also run to predict the 3 d and 28 d compressive strength of the 11 AAS concrete mixes by inputting the material parameters used in the experimental work into the model. Comparison of the results measured and predicted is reported in Table6, together with the error between them. Similarly, it is also found that no matter the mean error, max. error, or min. error, the value for 28 d compressive strength is lower than that for 3 d compressive strength, which indicates that compared to 3 d compressive strength, the ACE modeling was much more feasible to predict 28 d compressive strength, although the model for the latter was less accurate than the model for the former.


### 3.3. Comparison between ANN and ACE

From the discussion above it can be seen that when data size is relatively small, such as in the case of 3 d compressive strength (171 sets of data), although ANN model with a high precision could be established based on the given data size, its feasibility to predict nontrained data would be limited as ANN is a kind of statistics of known information in essence. While ACE is based on fitting technique, its function could be close to the true values by adjusting the coefficient of the input parameters. As a result, from Table6 it can be seen that in the case of 3 d compressive strength, nearly half of the error values of ACE prediction is at a very low level and the average one is also acceptable although very few predictions have yielded a high error value.When data size is sufficiently large, such as in the case of 28 d compressive strength (309 sets of data), the error value between the results predicted and measured dramatically decreases as shown in Table7, for both ANN and ACE, indicating a great improvement of their feasibility for the prediction. When applying ANN, there are more samples to train the model more efficiently. When a prediction is being processed, the related memory could be aroused to give a precise prediction. On the other hand, an increase in data size is also helpful to improve the precision of fitting, as a result of which the ACE error value decreases as well. However, it seems that there is an optimum data size for the fitting of ACE. When the size is beyond the upper bound, the increase in fitting precision would be limited. Consequently, in this study, ACE performed not as well as ANN for the prediction of 28 d compressive strength, but it is worthy to note that the ACE error values are still in an acceptable range for practical application. Therefore, from the discussion above it can be seen that when massive data are available, it is more suitable to establish an ANN model for compressive strength prediction of AAS concretes. If data size was insufficient to support a precise ANN modeling, ACE could be considered as an alternative to yield an acceptable result.


## 3.1. ANN

Regression of ANN modeling for prediction of 3 d and 28 d compressive strength of AAS is given in Figures2 and 3, respectively. Correlation coefficient R is usually used to evaluate the correlation between the data samples. The closer the R-value is to 1, the stronger the correlation. From the figures, it can be seen that both the predictions have a good correlation between the data samples in general no matter training, testing, validation, or all of them are considered as the R-values are higher than 0.8. However, the correlation in the case of 28 d compressive strength is relatively lower in comparison with the 3 d one. It is known that 28 d compressive strength is the most elementary property of concrete, and therefore has been extensively reported in the literature. Consequently, large amounts of data samples on the 28 d compressive strength of AAS have been collected in this study, namely, 309 sets. This could have increased the scattering of the data as a result of different conditions of the specimen, such as different types and sizes of the specimen, different sources of slag, different aggregates, different curing conditions, used in the different studies.Figure 2
Regression of ANN modeling for prediction of 3 d compressive strength of AAS. (a) Training. (b) Testing. (c) Validation. (d) All.
(a)(b)(c)(d)Figure 3
Regression of ANN modeling for prediction of 28 d compressive strength of AAS. (a) Training. (b) Testing. (c) Validation. (d) All.
(a)(b)(c)(d)Also, from MAE and RMSE error evaluation results, as given in Table6, it can be seen that the error of the ANN models is at a low level, with MAE and RMSE values less than 20 MPa, in both the cases of 3 d and 28 d compressive strength, which means the models have sufficient accuracy.Table 6
Error evaluation (MPa).
ANNACETrainingTestingTrainingTesting3 d compressive strengthMAE7.476.788.995.39RMSE14.8918.2112.0014.0028 d compressive strengthMAE15.645.7914.877.32RMSE14.8910.9518.7015.79Later, 3 d and 28 d compressive strengths of the 11 AAS concrete mixes were experimentally measured. Simultaneously, the material parameters used in the experimental work were put in the ANN model to run a prediction modeling. Comparison of the results measured and predicted is reported in Table7, together with the error between them (100% × |predicted value-measured value|/measured value). From the table, it can be seen that in comparison to 28 d compressive strength, although the ANN model of 3 d compressive strength had an equivalent accuracy as discussed previously, it is less feasible to be employed to run the prediction. As stated previously, compared to the 309 sets of data that have been collected for the establishment of the 28 d compressive strength model, only 171 sets were available in the case of 3 d strength. Furthermore, the material parameters reported in the 171 data sets may not have covered the ones used in the experimental work, resulting in a lack of corresponding training, and finally in a high error between measurement and prediction. As can be seen from Table 1, few literatures consider the effects of 5 parameters on the 3D compressive strength of AAS at the same time. Therefore, as a result of insufficient training, the error of the mix 11 at 3 days is as high as 77.1%, while the larger database of 28 d compressive strength has supported effective training. Consequently, the error decreases dramatically to a low value of 4.6%. In this context, in order to improve feasibility of the ANN model for prediction, it is necessary to enlarge the scale of database enabling which could cover circumstances as full as possible, to ensure that a sufficient training could be implemented.Table 7
Comparison between the strength measured and predicted.
Mix no.3 d compressive strength (MPa)28 d compressive strength (MPa)MeasuredANNACEMeasuredANNACEPredictedError (%)PredictedError (%)PredictedError (%)PredictedError (%)124.227.312.823.33.750.547.46.151.41.8221.229.237.723.711.851.053.03.959.416.5323.031.235.628.423.551.256.29.857.211.7427.729.46.132.216.254.451.45.558.77.9533.731.85.632.63.360.057.14.865.79.5635.135.10.038.08.359.660.10.863.87.0737.827.527.236.53.461.054.910.061.71.1833.829.413.032.63.662.360.62.768.29.5938.230.220.942.511.260.263.55.566.410.31044.139.410.620.553.565.959.99.168.43.81113.123.277.110.916.856.253.64.660.78.0Mean error (%)22.414.15.77.9Max. error (%)77.153.510.016.5Min. error (%)0.03.30.81.1


## 3.2. ACE

Relationship between input parametersX1, X2⋅⋅⋅⋅⋅⋅X5 and their corresponding response surface function φX1, φX2⋅⋅⋅⋅⋅⋅φX5 is shown in Figures 4 and 5. ACE fitting curves of compressive strength of AAS at curing ages of 3 d and 28 d were plotted in Figure 6, which have been adjusted by introducing correction coefficientλ as stated in Section 2.3. After trial-and-error, the values of λ were determined to be 0.90 and 0.85, respectively, for 3 d and 28 d compressive strength. Eventually, fitting goodness R2 of 0.986 and 0.950 were obtained, respectively, in the case of 3 d and 28 d compressive strength, indicating that the ACE model has very high accuracy for both the cases. While probably due to the much bigger data size and the resulting increase in scattering, the ACE model for 28 d compressive strength is less accurate compared to the 3 d case, which could be seen from MAE and RMSE error evaluations as given in Table 6. However, the value is still acceptable for practical application.Figure 4
Relationship between input parameters and their corresponding response surface functions in the case of 3 d compressive strength. (a)X1 (Na2O%) and φX1. (b) X2 (Ms) and φX2. (c) X3 (W/B) and φX3. (d) X4 (SA) and φX4. (e) X5 (Kb) and φX5.
(a)(b)(c)(d)(e)Figure 5
Relationship between input parameters and their corresponding response surface functions in the case of 28 d compressive strength. (a)X1 (Na2O%) and φX1. (b)X2 (Ms) and φX2. (c)X3 (W/B) and φX3. (d)X4 (SA) and φX4. (e)X5 (Kb) and φX5.
(a)(b)(c)(d)(e)Figure 6
ACE fitting curves of compressive strength of AAS. (a) 3 d compressive strength. (b) 28 d compressive strength.
(a)(b)In addition, from Figures4 and 5, it can be seen that the relationship between X1 (Na2O%) and φX1 is much clearer compared to the others, and with the change of X1 (Na2O%), φX1 varies to a considerable scale. These indicate that among the five influencing factors, Na2O%, Ms, W/B, SA, and Kb, Na2O% took the largest weight-influencing compressive strength of AAS, followed by Ms > W/B > Kb > SA.Similar to the ANN prediction, the ACE model was also run to predict the 3 d and 28 d compressive strength of the 11 AAS concrete mixes by inputting the material parameters used in the experimental work into the model. Comparison of the results measured and predicted is reported in Table6, together with the error between them. Similarly, it is also found that no matter the mean error, max. error, or min. error, the value for 28 d compressive strength is lower than that for 3 d compressive strength, which indicates that compared to 3 d compressive strength, the ACE modeling was much more feasible to predict 28 d compressive strength, although the model for the latter was less accurate than the model for the former.


## 3.3. Comparison between ANN and ACE

From the discussion above it can be seen that when data size is relatively small, such as in the case of 3 d compressive strength (171 sets of data), although ANN model with a high precision could be established based on the given data size, its feasibility to predict nontrained data would be limited as ANN is a kind of statistics of known information in essence. While ACE is based on fitting technique, its function could be close to the true values by adjusting the coefficient of the input parameters. As a result, from Table6 it can be seen that in the case of 3 d compressive strength, nearly half of the error values of ACE prediction is at a very low level and the average one is also acceptable although very few predictions have yielded a high error value.When data size is sufficiently large, such as in the case of 28 d compressive strength (309 sets of data), the error value between the results predicted and measured dramatically decreases as shown in Table7, for both ANN and ACE, indicating a great improvement of their feasibility for the prediction. When applying ANN, there are more samples to train the model more efficiently. When a prediction is being processed, the related memory could be aroused to give a precise prediction. On the other hand, an increase in data size is also helpful to improve the precision of fitting, as a result of which the ACE error value decreases as well. However, it seems that there is an optimum data size for the fitting of ACE. When the size is beyond the upper bound, the increase in fitting precision would be limited. Consequently, in this study, ACE performed not as well as ANN for the prediction of 28 d compressive strength, but it is worthy to note that the ACE error values are still in an acceptable range for practical application. Therefore, from the discussion above it can be seen that when massive data are available, it is more suitable to establish an ANN model for compressive strength prediction of AAS concretes. If data size was insufficient to support a precise ANN modeling, ACE could be considered as an alternative to yield an acceptable result.


## 4. Conclusions

Based on the data collected and modeling used in this study, the following conclusions could be drawn:(1)
Both the ANN and the ACE models had adequate accuracy, no matter 3 d or 28 d compressive strength was considered.(2)
Compared to the 3 d compressive strength, due to increased data scattering and data size, both the ANN and the ACE models did not yield a higher accuracy in the case of 28 d strength. However, also due to the increase in data size, both the models were more feasible to implement a 28 d strength prediction as a result of sufficient learning and training during modeling.(3)
Based on the ACE analysis, among the five influencing factors, Na2O%, Ms, W/B, SA, and Kb,, Na2O% took the largest weight-influencing compressive strength of AAS, followed by Ms > W/B > Kb > SA.(4)
When massive data are available, it is more suitable to establish an ANN model for compressive strength prediction of AAS concretes. If data size was insufficient to support a precise ANN modeling, ACE could be considered as an alternative to yield an acceptable result.



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*Source: 8214859-2022-08-02.xml*