Concrete corrosion in wastewater systems: Prediction and sensitivity analysis using advanced extreme learning machine

Abstract

The implementation of novel machine learning models can contribute remarkably to simulating the degradation of concrete due to environmental factors. This study considers the sulfuric acid corrosive factor in wastewater systems to simulate concrete mass loss using five machine learning models. The models include three different types of extreme learning machines, including the standard, online sequential, and kernel extreme learning machines, in addition to the artificial neural network, classification and regression tree model, and statistical multiple linear regression model. The reported values of concrete mass loss for six different types of concrete are the target values of the machine learning models. The input variability was assessed based on two scenarios prior to the application of the predictive models. For the first assessment, the machine learning models were developed using all the available cement and concrete mixture input variables; the second assessment was conducted based on the gamma test approach, which is a sensitivity analysis technique. Subsequently, the sensitivity analysis of the most effective parameters for concrete corrosion was tested using three different approaches. The adopted methodology attained optimistic and reliable modeling results. The online sequential extreme learning machine model demonstrated superior performance over the other investigated models in predicting the concrete mass loss of different types of concrete.

Graphical abstract

Keywords

sewer systems / environmental engineering / data-driven methods / sensitivity analysis

Introduction

In wastewater systems and sewers, sulfuric acid corrosion occurs because of the sulfur cycle that typically occurs in wastewater collectors, sewer networks, and sewage system structures [1]. The aquatic form of hydrogen sulfide (H₂S) is generated under anaerobic conditions from the sulfur compounds present in the sewage. Upon emission to the air, gaseous H₂S is converted to sulfur, and as a result of microbiological action, to sulfuric acid [2]. Concrete degradation and corrosion caused by biogenic sulfuric acid (BSA) attacks are considered to primarily influence the durability of concrete structures, such as municipal wastewater systems [3]. Therefore, the lifetime of the wastewater collectors and network is directly influenced by the rate of concrete corrosion. In this respect, simulating and predicting the concrete corrosion rate of wastewater systems will tremendously help designers to optimize sewer systems considering both the hydraulic and economic aspects.

Accordingly, various direct methods have been used to simulate concrete corrosion. Some direct methods (e.g., linear polarization resistance) are based on corrosion rate estimation, which is realized via methods such as corrosion current density measurement. However, the main drawback of these direct methods is that they are destructive, which means that some parts of the concrete cover must be broken out [4]. Accordingly, several researchers have used indirect and non-destructive methods for concrete corrosion estimation and prediction, including hard computing (such as numerical methods) and soft computing (such as different types of artificial neural networks (ANNs)). Sadowski [4] used both direct methods (such as the resistivity four-probe method) and the indirect soft computing method of ANN to assess the corrosion rate of steel in concrete. The results implied the successful use of ANNs for the prediction of corrosion current density. Alani and Faramarzi [5] applied the evolutionary polynomial regression (EPR) soft computing technique for corrosion prediction of concrete subjected to sulfuric acid attack. The outcomes of the study confirmed the appropriateness of using EPR in predicting the degradation of concrete exposed to sulfuric acid. Jiang et al. [6] challenged the potential of ANNs for predicting concrete corrosion processes in sewers in terms of the corrosion initiation time and corrosion rate. They reported that the ANN model outperformed the conventional multiple linear regression (MLR) model.

Xu et al. [7] developed a numerical model as a hard computing approach to predict the corrosion rate of steel reinforcements in cracked reinforced concrete. Assessment of the obtained corrosion values between the observational test and predicted numerical results proved the capability of the numerical model to predict the corrosion rate with acceptable accuracy. Qian et al. [8] applied several soft computing models, including ANN, support vector machine (SVM), and decision tree (DT), to predict and evaluate the degradation of concrete strength in a marine environment. The results indicated that the SVM model performed better than the ANN and DT models in predicting concrete degradation. Li et al. [9] assessed the prediction potential of three different data-driven models, including MLR, the adaptive neuro-fuzzy inference system (ANFIS), and ANN for modeling the corrosion initiation time and corrosion rate in sewers. The ANN and ANFIS models were concluded to perform better than the nonlinear mathematical MLR model.

Different approaches have been introduced and developed to cope with the BSA corrosion problem in wastewater networks as follows: (i) reduction in the magnitude of H₂S emission using chemical or biological technologies [10]; (ii) application of acid-resistant types of cement and concrete admixtures [11]; (iii) utilization of protective coatings and linings that prevent the chemical attack of the underlying concrete [12]; (iv) application of antimicrobial admixtures and coatings to control or decrease microbial activity [13]. One of the major attempts to reduce the rate of deterioration and correspondingly increase the optimum lifetime of the concrete used in wastewater systems has been to improve the durability of concrete by changing the concrete composition. Through a BSA attack on concrete, Yang et al. [14] compared the strength and corrosion rate of ordinary Portland cement concrete (OPCC) and a new artificial reef concrete (NARC). The results showed that the compressive strength, corrosion magnitudes, and corrosion rates of OPCC were higher than those of NARC. Ramezanianpour et al. [15] conducted an experimental study on the durability of different types of concrete mixtures containing ordinary Portland cement (PC), natural pozzolan (NP), and blast furnace slag immersed in a sulfuric acid solution. The findings of this study proved that concretes with admixtures were more durable in acidic solutions. In addition, the results showed that incorporating NP in the concrete mixture can enhance the concrete quality against acid sulfuric attacks. Zhang and Song [16] attempted to predict the sulfuric acid corrosion of concrete based on an SVM soft computing model. They considered five influencing factors, including the water–cement ratio (W/C), pH value of the solution, quantity of cement and fly ash, and fluidity of the specimens for predicting the corrosion rate. The findings of the study indicated that the employed SVM model could be introduced as an effective method to predict concrete corrosion. Based on a database of 78 concrete mixtures, Hewayde et al. [17] developed ANN models to predict the degradation of concrete subjected to sulfuric acid attacks. The outcomes of their study confirmed the high capability of the applied ANNs to predict the mass loss of concrete specimens.

Soft computing methods such as neural computing and fuzzy sets have also been employed to analyze the durability-based service life of concrete structures under different conditions, such as the corrosive environment of sewer systems [18–21]. Sobhani and Ramezanianpour [21] utilized fuzzy interfaces as an artificial intelligence model to compute the service life of reinforced concrete; to this end, the physical characteristics of concrete were quantified. The results of their study indicated that the proposed artificial intelligence system could accurately estimate the service life of concrete; however, the estimated period was longer than that obtained by the applied probabilistic method. Taffese and Sistonen [18] reviewed the capability of various machine learning (ML) models, such as ANNs and SVMs, to address the limitations of classical prediction models. Research has shown that ML models based on in-service data (e.g., using wireless sensors) are increasingly being used to evaluate the durability and service life of concrete structures. Zounemat-Kermani et al. [22] evaluated various ML eNSEmble learning, including bagging, boosting, and modified bagging (random forest), to predict concrete corrosion in sewers. The results indicated that the random forest model provided more accurate predictions than the other ML models.

Based on the reported literature, the introduction of soft computing implementation for modeling concrete corrosion is still a new research area. The exploration of new robust and reliable intelligence models highly motivates this research scope and contributes to the basic knowledge of environmental engineering materials and sustainability. The viability of ML models for material science engineering has been revealed by optimistic outcomes [23–28]. To the best of our knowledge, relatively new soft computing models have been investigated for the prediction of concrete corrosion (with various mixtures of PC, slag, silica fume, and fly ash) with sulfuric acid used as the corrosive agent. To this end, three types of extreme learning machines (ELMs), including the standard ELM, online sequential ELM (OS-ELM), and kernel-ELM (K-ELM), are employed, along with the multi-layer perceptron neural network (MLPNN) and the classification and regression tree (CART). The methodology of this study contributes to the modeling of concrete corrosion corresponding to various concrete mixtures (both for the prediction process and a comprehensive sensitivity analysis of the effective parameters). In addition, three different sensitivity analysis techniques, including the gamma test (GT), leave-one-out analysis, and regressional relief F (RReliefF) algorithm, were inspected to determine the most effective factors for decreasing the corrosion of concrete subjected to sulfuric acid.

Methods

Applied machine learning models

In this study, three different categories of ML models (three types of self-tuning ELMs, ANNs, and CART modes) were applied to model the corrosion of concrete subjected to sulfuric acid attacks. In addition, GT was used to determine the optimum combination of the input vector. The models are described below.

Extreme learning machine model

ELM is a new version of the basic ANN, which was developed by [29]. The main advantages of ELM are fast learning and self-internal parameter tuning [30–32]. The ELM model exhibits a robust and reliable predictive methodology for multiple engineering problems [33–37]. The model was developed based on a single-layer feed-forward neural network (SLFN). The ELM model has undergone several modifications and enhancements [38,39]. The random generation of the magnitudes of the weights and bias is the core innovation of the ELM model performance [40]. The target function of the model for N samples

{{\displaystyle \{{{\displaystyle x}}_i,{{\displaystyle t}}_i;{{\displaystyle x}}_i\in R^d,{{\displaystyle x}}_i\in R^m\}}}_{i=\mathrm{1}}^N

can be expressed in the following form:

(1)f(x)={\displaystyle \sum _{i=\mathrm{1}}^L{{\displaystyle \beta }}_i}G({{\displaystyle w}}_i,{{\displaystyle b}}_i,{{\displaystyle x}}_i)={{\displaystyle h}}_{(x)}\beta

where h_{\mathrm{(x)}} represents the hidden layer output matrix. {\beta }_i=\{{\beta }_1{\mathrm{,\beta }}_2,\mathrm{...}{\mathrm{,\beta }}_L\} denotes the weight between the output and the hidden layer connections; w_i is the input weight; and b_i is the bias. Conceptually, the ELM goal aims to minimize the training error with the minimal magnitude of the output norm weight [41]:

(2)\mathrm{Minimize:}{\Vert H\beta -T\Vert }^{\mathrm{2}}\mathrm{and}\Vert \beta \Vert ,

The least-squares method can be applied to Eq. (1)to obtain the output weights:

(3)\beta =H^{T}T,

where H^T presents the Moore–Penrose inverse [42].

The output function of Eq. (1) can be given as follows:

(4)f(x)=h_{\mathrm{(x)}}{(\mathrm{1}/C+H^{T}H)}^{-\mathrm{1}}{H}^{T}T,

and the output function can be written as follows:

(5)f(x)=h_{\mathrm{(x)}}{H}^T{(\mathrm{1}/C+H{H}^T)}^{-\mathrm{1}}T.

Kernel extreme learning machine (K-ELM) model

Based on the discussion in the current research [43], the feature mapping of h_{\mathrm{(x)}} is unknown, as described in Eq. (5). Hence, the K-ELM model is defined using Mercer’s condition [44]:

(6){\Omega }_{\mathrm{ELM}}=h_{\mathrm{(xi)}}\cdot h_{\mathrm{(xj)}}=K(x_i,x_j).

The kernel formulation of the ELM model can be expressed based on Eq. (5), as follows:

(7)f(x)=\left[\begin{array}{l}K(x_i,x_{\mathrm{1}})\\ .\\ K(x_i,x_N)\end{array}\right]{(\mathrm{1}/C+{\Omega }_{\mathrm{ELM}})}^{-\mathrm{1}}T.

In Eq. (7), the required information is only forK(x_i,x_j), whereas h_{\mathrm{(x)}} can remain unknown. No requirement exists for any interaction by the developer for the hidden neurons; instead, they are randomly assigned.

Online sequential extreme learning machine (OS-ELM) model

OS-ELM is an extended version of the basic ELM model, which was developed by adding a radial basis function (RBF) to the SLFN for the hidden nodes [45]. Mathematically, when the RBF is incorporated with hidden nodes,

G(w_i,b_i,x_i)=g(b_i{w}_i-x_i),b_i\in R^{+}

Note that w_i and b_i denotes the center and impact width of the RBF node, respectively, where R^{+} is the positive real value.

For a simple learning network with L hidden layer nodes and x_i input variables, t_i is assigned to the network sequentially. Herein, the OS-ELM is processed based on two stages: initialization and sequential processes.

1) Initialization: The learning phase is initiated based on a small set of training data.

a) Random assignment of input parameters: The parameters for the RBF are assigned randomly.

b) Calculation of the matrix of the hidden layer output [46].

c) Estimation of the initial output weights.

2) Sequential learning process: Herein, the new observations are briefly discussed.

a) Computations of the partial hidden layer output matrix [46].

b) Output weight calculation.

c) Set up of sequential learning process.

The processes of the OS-ELM model are presented in Fig. 1.

Classification and regression trees

The initial development of the CART was proposed by Ref. [47] as an explanatory approach that can read the data structure and highlight the important data characteristics in a bid to develop the governing rules [48]. As a non-parametric approach, CART can be applied to predict dependencies from input data [49,50]. Different DT models have been developed over time; however, the performance of the CART model in nonlinear regression problem modeling has been remarkable [51,52]. Therefore, the CART model is often selected based on its capability to perform well in a process that involves internal heterogeneity and nonlinear structures [53]. The CART is also applicable for the partitioning of dependent variables into classes considering the level of internal homogeneity required and for constructing a simple model for each set of variables.

The construction of a classification tree requires several repetitive splits associated with the target variable as the following: If X is<A value or Y is in the range of [C, D], then the sample is classified as normal with P probability. These splits are terminated when the splitting procedure cannot be implemented. Such a condition occurs when all observations are in the same group or when the same node has a small number of observations (based on a predefined value). The CART as a predictive model has several advantages, such as the ease of understanding the resulting algorithms because it signifies a sequential approach that results in the establishment of an optimal algorithm. Another advantage is that the related risk of a case in each of the steps of the produced algorithm that belongs to the targeted groups is known.

Multi-layer perceptron neural network (MLPNN)

ANNs are complex computational models that were developed based on the human nervous system [54]. ANNs can perform ML tasks and provide the outcomes of a new data set by learning from previous experiences [55]. Therefore, ANNs are suitable for practical applications in several simulation studies [56]. Another attribute of ANNs, which supports their application in complex data pattern processing, is their nonlinear nature, which is lacking in most traditional linear techniques [57,58]. The structure of an ANN comprises several interlinked neurons, and each neuron sums the weighted inputs (“summation of the inputs products and their weights”) [59]. The outcome of this summation is passed through a transfer/activation function. The interconnection model generally entails a defined structure, even though most of the common interconnection models are built following a layered methodology to ensure simplicity in the algorithm development. An ANN model consists of one input phase of neurons for the input variables, a hidden layer for the learning process, and a final layer that provides the network output [60].

Gamma test

For modeling a continuous nonlinear model for uNSEen data, the GT can be used, which is operated based on the minimum mean square error metric. The GT was initially developed by [61] but later modified by several researchers [62]. The GT is only introduced briefly in this research, as further details regarding are presented in the aforementioned articles [63–66]. The basic concept of the GT is different from that of earlier attempts entailing nonlinear analyses. Assume a data set \{(x_i,y_i),\mathrm{1}\le i\le M\} in which the input vectors x_i\in R^m are within m-dimensional vectors of a certain range C\in R^m, whereas the associated outputs y_i\in R^m are scalars. In addition, assume that vector x contains factors that help predict output y. Then, the fundamental system relationship is y=f(x_i,\dots ,x_m)+r, where f represents the smooth function and r represents the noise (i.e., the associated random variables). The mean of the r’s distribution can also be assumed to be zero, whereas the variance of r, Var(r), is bounded. Regarding the model that can be potentially developed, its domain is now bounded to the class of smooth functions with bounded first partial derivatives. The model output variance, which cannot be explained by a smooth data model, is better estimated by the gamma statistic (Г). The GT is reliant on N[i, k], which are the kth (\mathrm{1}\le k\le p) nearest neighbors X_{N[i, k]} (\mathrm{1}\le k\le p) for each vector X_i(\mathrm{1}\le k\le M).

Methodology development

The methodology of the current study consists of the following two main phases.

Phase (I): Prediction phase: The objective of this phase is associated with the assessment of the applied ML models and the statistical MLR model in predicting concrete corrosion in wastewater systems. To achieve this, three types of ELM models (the standard ELM, OS-ELM, and K-ELM), along with two prevailing types of artificial intelligence-based models (MLPNN and CART), are applied. The modeling procedure was accomplished through two different input scenarios. Detailed information regarding the modeling scenarios is provided in Section 5.1. The final evaluation of the models' performances was accomplished using several statistical measures given in the following sections.

Phase (II): Sensitivity analysis phase: In this phase, the degree of effectiveness of each individual independent parameter for the cement properties and concrete mixture on the amount of corrosion is specified. Three different sensitivity analysis methods, including two preprocessing techniques (GT and RReliefF analysis) and one post-processing technique (leave-one-out method), are implemented to achieve this goal. Figure 2 depicts the schematic plan applied as the methodology of this study.

Data set description

In the present study, the concrete degradation corresponding to the mass loss of six different reinforced concrete mix samples with water–cementitious ratio (W/C) equal to 0.4 and 0.5 (Portland concrete with W/C ratio equals to 0.4 (PC50); Portland concrete with W/C ratio equals to 0.5 (PC40); sulfate resisting cement (SR); slag concrete (SC); silica fume concrete (SFC); and silica fume and slag concrete (SFSC)) is investigated. In this regard, 96 data sets were gathered from the reports of Abdelmseeh et al. [67,68]. The corrosion tests were conducted on concrete discs 0.025 m thick and 0.1 m in diameter. All the disc-shaped samples were exposed to 2 cm³ of 7% sulfuric acid on a regular basis three times per week for 150 applications over a period of one year. The mix proportions and materials used for all six concrete treatments are listed in Table 1. Moreover, Table 2 includes a statistical description of the concrete mass loss for the various implemented concrete mixtures.

To estimate the concrete corrosion, the mass loss of the concrete samples at the end of each acid application test was measured. The mass loss calculated from the H₂SO₄ corrosion tests versus the number of applications is shown in Fig. 3. As shown in the figure, after 150 applications of H₂SO₄, the PC50 concrete experienced the greatest mass loss, approximately equal to 35 g (approximately 8.2% of the original dry mass); however, the same type of concrete, PC40, with a lower W/C ratio and higher CW values, showed less corrosion (28.6 g). The least mass loss is related to the SR concrete (sulfate-resistant cement specimen) with a 27.5 g mass loss (approximately 5.8% of the original dry mass).

As can be seen in Fig. 3, for a specific number of acid applications (approximately after 30 applications), no mass loss is observed for some time (approximately 10 weeks), which is called the corrosion initiation period. After the initiation period, the concrete corrosion process begins and normally continues at a uniform rate. Both the corrosion initiation period and the subsequent corrosion rate are functions of various local environmental conditions in wastewater networks, together with the physical properties of construction materials [69].

Evaluation of the models

The prediction capability of the corrosion concrete from the five ML models was statistically evaluated using four measures (score metrics): root mean square error (RMSE) and mean absolute error (MAE) as deviance measures, Nash–Sutcliffe efficiency (NSE) as the efficiency measure, and Akaike information criterion (AIC) as the estimator of out-of-sample prediction error [70,71]. The mathematical formulae of the measures used can be written as follows:

(8)RMSE=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=\mathrm{1}}^N{({{\displaystyle C}}_p-{{\displaystyle C}}_{\mathrm{0}})}^{\mathrm{2}}}}{N}}},

(9)MAE={\displaystyle \frac{\mathrm{1}}{N}}{\displaystyle \sum _{i=\mathrm{1}}^N\left|{{\displaystyle C}}_p-{{\displaystyle C}}_{\mathrm{0}}\right|},

(10)NSE=\mathrm{1}-\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=\mathrm{1}}^N{({{\displaystyle C}}_p-{{\displaystyle C}}_{\mathrm{0}})}^{\mathrm{2}}}}{{\displaystyle \sum _{i=\mathrm{1}}^N{{\displaystyle \left({{\displaystyle C}}_p-\overline{{{\displaystyle C}}_{\mathrm{0}}}\right)}}^{\mathrm{2}}}}}},

(11)AIC=N\cdot \mathit{log}(\sqrt{{\displaystyle \sum _{i=\mathrm{1}}^N{({{\displaystyle C}}_p-{{\displaystyle C}}_{\mathrm{0}})}^{\mathrm{2}}}}+\mathrm{2}\cdot k,

where C_o is the observed value of concrete corrosion in terms of mass loss (g); C_p denotes the predicted value of concrete corrosion in terms of mass loss (g) in the testing set, along with the simulated values in the training set; N is the number of data samples, bar indicates the mean value; and k denotes the number of variables [72,73].

In this study, the random stratification method was applied for the train-test split, such that 80% of the total data were allocated for the training set and the remaining 20% were used for testing the models. The training and testing sets were examined for data distributions, and the results of the Anderson–Darling normality test indicated that both sets follow a non-normal distribution (p-value<0.05).

Application results and assessment

Input selection and tuning parameters

As mentioned in the previous sections, two modeling scenarios were used for the prediction phase in this study. Scenario (I) considers all potential independent parameters for predicting the target value. In other words, each data set consisted of nine input factors: acid application number (AA), weight of cement in concrete (CW, kg/m³), W/C ratio, percentage of slag in the concrete mixture (Sl %), percentage of silica fume in the concrete mixture (SF %), tricalcium silicate (C₃S %), dicalcium silicate (C₂S %), tricalcium aluminate (C₃A %), and tetra calcium aluminoferrite (C₄AF %). Further, the mass loss amount served as the concrete corrosion (C) target.

In scenario (II), the most effective input parameters are selected based on the GT. First, the gamma value of the combination of all variables (scenario I) was calculated (Table 3, Г = 0.051). After the continuous process, at each step, one of the input parameters was omitted, and the corresponding gamma values were calculated (Table 3). Thus far, these results were also used for the sensitivity analysis, such that a higher gamma value shows more effectiveness of the omitted parameter. Finally, the best combination corresponding to the lowest value for gamma was selected as the best input vector. In this study, several combinations of input parameters were tested with the GT, and it appeared that three of the independent parameters, AA, CW (kg/m³), and Sl %, were the most interconnected parameters with concrete mass loss (Г = − 0.008).

After specifying the input structure of the models, the tuning parameters related to the architecture of the network of the ML models should be determined. However, finding the optimal effective parameters in data-driven models is one of the most crucial steps in model establishment. In the present study, the trial-and-error process was applied, and different coefficients and values were explored to minimize the difference between the observed and estimated values. This process has been extensively used in the literature to obtain the best structure and related parameters [74,75].

In Table 4, detailed information regarding the tuning parameters of the developed ML models is given.

Prediction of concrete corrosion using all inputs- Scenario I

In this section, the performance of the five ML computing techniques, together with the modeling results of the MLR model, which were used for concrete corrosion using nine input variables, is discussed. The statistical performance measures for each model are summarized in Table 5 for both the training and testing sets. The results in Table 4 demonstrate that, in the first scenario (when all the acid application, cement, and concrete data are included), the OS-ELM and standard ELM exhibits flawless performance in the training phase (RMSE and MAE<0.001 g and NSE= 1.00). In addition, all the extreme learning ML models surpassed the conventional ML models and the statistical MLR model in both the training and testing phases. The OS-ELM model achieved the best performance in the training and testing phases, according to the statistical measures.

Figure 4 displays the relationship between the measured and simulated/predicted concrete mass losses in the training and testing phases. All the circular marks in Fig. 4 are situated near the line of agreement (1:1 line) in the ELM models; the arrangement of these marks is different in the conventional ML models (MLPNN and CART). The diagnostic analysis of the filled circular marks (corresponding to the testing data set) also revealed that the OS-ELM and ELM could predict the concrete corrosion rate with small errors.

The concrete loss variability of the standard ELM and OS-ELM models was very close to the measured values. This outcome was verified by the ELM model yielding significantly small magnitudes of MAE, RMSE, and AIC, and high values for the Nash–Sutcliffe criteria.

To show the performance of the applied models explicitly in terms of the entire simulated and predicted data points relative to the measured values, the box plots of the results are provided in Fig. 5. The top and bottom whiskers represent the maximum and minimum values, respectively. The top and bottom of the rectangular boxes denote the quartiles of the 25th and 75th percentiles, respectively, and the median is shown inside the rectangle.

Figure 5 shows that, on average, the simulated results (in the training set) and predicted results (in the testing set) using OS-ELM and ELM are better than those from the other applied models. According to Fig. 5, the standard ELM model was superior to the other models in terms of predicting the minimum values (bottom whisker) and median values (middle line in the rectangle).

Figure 6 summarizes the general performances of the applied models in the form of the Taylor diagram and displays the predicted values in the testing set [76]. This diagram simply expresses three main statistics including the correlation coefficient between the predicted values and measured data (as an angle in the polar plot), RMSE (as a radial distance from the observation point), and the ratio of the standard deviation of the predicted values (as a radial distance from the origin). As can be observed in Fig. 6, the K-ELM and OS-ELM represented the predicted values well, whereas the CART model exhibited low prediction performance.

Prediction of concrete corrosion using gamma test- Scenario II

In this section, to assess the effectiveness of the GT approach in selecting the optimum combination of input parameters, models applied based on just three of the nine available variables (including AA, CW, SI%) were employed for the concrete corrosion prediction phase. Table 6 summarizes the results of the training and testing phases of the models with the proposed optimum combination.

According to this table, although the accuracy of the standard ELM was higher than that of the other models (RMSE= 0.208 g and NSE= 0.999), this model performed worse than the combined ELM models (OS-ELM and K-ELM) in the testing phase. The performances of the OS-ELM, K-ELM, and CART models are relatively similar; however, the K-ELM model yielded slightly better results based on the trivial improvement in RMSE (RMSE= 1.349 g in the testing phase). The applied MLPNN model failed to provide acceptable results, similar to its other predictive model counterparts. This implies that the MLPNN model is considerably more susceptible to the number of input variables than the CART and ELM models. The results in Table 5 also help verify the fair potential of the MLR model (as a statistical model) in predicting corrosion values; thus, the MLR model provided a better prediction than the MLPNN model in the testing phase. Although the MLR model was better than the CART model in the training set, the MLR model could not maintain its superiority in the testing phase.

The corrosion rates estimated and predicted by the ML models are compared in Fig. 7, in the form of scatter plots. A favorable correlation exists between the measured and estimated values using the standard ELM and combined ELM models for the training phase. Nonetheless, the dispersion of the data points of the predicted results of the CART model in the testing phase is substantially less than that of the standard ELM model. This clearly indicates the higher potential of the CART model than that of the standard ELM to predict concrete corrosion based on limited data. This confirms the statistical measures listed in Table 6 for the testing phase.

The box plots of the simulated and predicted results of the applied models are shown in Fig. 5. Compared with the size and shape of the measured box plot, the MLPNN performed poorly for both the training and testing sets and did not follow the same distribution for the median and quartiles. This finding corroborates the results summarized in Table 6. In addition, the comparison between the performances of the models is provided through the Taylor diagram presented in Fig. 6, which clearly indicates that the CART model performed better in the second scenario compared with the other models.

Sensitivity analyses results

In this study, to evaluate the importance of each independent contributing factor, two preprocessing sensitivity analyses (based on the data sets), including the GT and RReliefF algorithm, and a post-processing analysis (based on the modeling outcomes of an ML model), named the leave-one-out method, were used. Employing various sensitivity methods will aid researchers in attaining a more comprehensive awareness of the most effective cement/concrete parameters to cope with the corrosion problem. In the following section, the results obtained from each method are presented.

Preprocessing sensitivity analysis: gamma test

In the present research, the GT was primarily employed for the input selection procedure (see Section 5.1). On the one hand, employing the GT reduces the computational cost and provides input data guidance before constructing data-driven models. On the other hand, the GT can also be employed to determine the influence of each independent variable on the target value (here the corrosion mass) as a sensitivity analysis tool. The results for the GT are summarized in Table 3, which indicate that omitting the AA parameter resulted in the highest value of gamma (Г = 0.269). In other words, AA is the most effective variable for simulating concrete corrosion. Figure 8(a) shows the gamma values corresponding to the eight cement/concrete input combinations, each of which lacks one of the independent input variables. This conclusion was expected because the total corrosion process was caused by direct contact of sulfuric acid on the concrete with sulfuric acid. However, one question remains: what are the most effective cement and concrete mixture parameters in dealing with concrete corrosion? According to the results of the GT (Table 3), the three most important parameters are CW (Г = 0.075), Sl % (Г = 0.072), and magnitude of silicate and aluminates in the cement (Г = 0.046), respectively. The GT results also imply that varying the Sf % does not have a direct effect on the reduction of corrosion.

Preprocessing sensitivity analysis: RReliefF algorithm

At this stage, the RReliefF algorithm is utilized to determine the importance of the cement and concrete characteristic input variables used, including CW (kg/m³), W/C, Sl %, SF %, C₃S %, C₂S %, C₃A %, and C₄AF %. RReliefF is a regression method that approximates the quality of parameters based on how their weighted values distinguish between parameters that are close to each other [77]. RReliefF was implemented for eight cement/concrete variables that were expected to have direct effects on concrete corrosion; the results obtained are shown in Fig. 8(b). As can be observed in the figure, CW (kg/m³) (with the highest value) followed by W/C and Sl % have more influence on the concrete corrosion rate than other factors. Similar to the results of the GT, the silicates and aluminates parameters have the same effect on the corrosion rate.

Post-processing sensitivity analysis: leave-one-out method

Under the leave-one-out sensitivity analysis evaluation scheme, the base predictive model (ELM) was selected to determine the importance of each input parameter. In this seNSE, the ELM model was trained nine times by removing one input parameter at each time using the data set previously described to predict concrete corrosion. The results of the leave-one-out procedure are summarized in Table 7.

The RMSE and NSE values calculated by the models relying on eight input combinations based on omitting one parameter at a time (Table 7) were compared, demonstrating that the weakest performance corresponds to the removal of the CW parameter. In other words, the CW is by far the most significant cement/concrete input parameter in the acid-induced concrete corrosion process (with 299% effectiveness). Similarly, based on the results of Table 7, C₂S % (with 38% effectiveness) and SF % (with 31% effectiveness) are the second and third most important input parameters, respectively.

In this study, local sensitivity analyses were conducted. However, some researchers have applied global sensitivity analyses, such as variance-based methods (e.g., the analysis of variance with Sobol’s sensitivity indices) in their studies [78–81]. Therefore, global sensitivity analysis methods should be considered in future studies.

Discussions

Concrete corrosion induced by sulfuric acid is a major concern for most wastewater collectors and sewer systems. The corrosion rate is a function of two main factors: 1) local environmental conditions in sewers and 2) the physical properties of concrete as the major construction material [69]. This study focused on modeling the latter factors using six types of data-driven models and three sensitivity analysis methods. Based on the obtained results, the combined ELM models (particularly the OS-ELM) were observed to enhance the prediction skill of the corrosion rate over the MLR, standard ELM, and conventional neural network and DT models (MLPNN and CART). Further, the CART and combined ELM models can be applied to overcome deficiencies in the prediction process when applied to corrosion modeling with restricted input data (the second modeling scenario). The statistical MLR model provided better results than the conventional ML models (MLPNN and CART). This confirms that the ELM models surpassed not only the conventional ML models but were also superior to the MLR model, which was built based on the statistical approach. This is due to the high ability of ELM models to capture the complex physicochemical process of concrete corrosion subject to the sulfuric acid mechanism. The comparison of the results obtained from the first (introducing the entire parameters to the models) and second (the most effective ones based on the GT) modeling scenarios showed that the general performance of the developed predictive models was better in the first scenario. Among the applied models, the MLPNN model was highly dependent on the inclusion of sufficient input data parameters so that in the second scenario, it failed to present promising results.

The most effective input parameters for the sensitivity analyses using the three different methods of GT, RReliefF algorithm, and leave-one-out method are introduced in different manner, with the exception of the CW parameter as the most cement/concrete characteristic influential variable. Having explored the most important factor, Table 1 indicates that the SR and PC40 concretes had the highest amount of cement weight in concrete (CW= 425 kg/m³) compared with the other concrete samples (CW<425 kg/m³). As expected, sulfate-resistant cement is assumed to be the main factor in coping with the acid sulfuric corrosion process subjected to equivalent values for CW= 425 kg/m³ and W/C= 0.4.

As can be observed in Fig. 3, the SR, SFC, and PC40 concrete samples were less corroded than the other concrete types. Compared with the SR and PC40 concrete mixtures, less cement was used in the SFC mixture (CW= 391 kg/m³), although this mixture managed to cope with the corrosion process as well as the other two. In other words, iNSErting 8% silica fume as an additive cementing material resulted in a decrease in the amount of cement (34 kg/m³) in terms of resisting concrete degradation (the resistance characteristic of the SFC concrete was better than that of PC40) . These findings agree with those of Monteny et al. (2003) [82]. They claimed that, compared to the reference mixture, a concrete mixture with silica fume subjected to sulfuric acid attacks exhibited better potential for coping with corrosion.

Subsequently, the same conclusion can be derived by adding slag to the concrete (SC). As summarized in Table 1, the SC mixture has the lowest weight of cement (CW= 276 kg/m³) among all the other mixtures. The sensitivity analyses showed that CW plays the most important role in the corrosion process, which implies that the SC should have had the highest values for mass loss. Nevertheless, replacing 35% of slag instead of cement with the PC40 mixture improved the resistance characteristic of the SC concrete by inducing a 16% decreased in the final weight of the concrete mass loss.

Because the ranking results of the applied sensitivity analysis methods are not similar, the ranks of each independent parameter using different analyses are listed in Table 8.

One of the main reasons for the dissimilar outcomes of sensitivity analysis techniques can be related to the restricted available database for concrete samples. Despite this contrast, the results of different sensitivity analyses unanimously confirmed that the cement weight in concrete (kg/m³) ratio plays the most important role in decreasing the concrete corrosion rate. Further, changing the percentage of the additive cementing material (i.e., slag and silica fume) in the concrete mixture directly affects the durability of concrete deterioration. Nonetheless, by integrating the outcomes of the three sensitivity analysis methods, it was indicated that the W/C ratio and slag had a major influence on concrete corrosion resistance, followed by CW.

Future research can be further extended to study and examine various related data sets for a more informative explanation of the actual behavior of concrete corrosion, which might enhance the predictability performance. In addition, the application of other types of novel ML methods, such as deep neural networks, is highly recommended for evaluating the capability of sophisticated soft computing approaches in modeling complex engineering problems [83–86].

Conclusions

This paper presents the results of soft computing modeling of the corrosion of concrete samples with six different substituents: 35% slag, 8% silica fume, 31% slag and silica fume, and three references without slag or silica fume but different types of PC. This study aims to develop and challenge proper prediction ML models using two conventional models, MLPNN and CART, along with three types of ELM, namely the standard ELM, OS-ELM, and K-ELM. The prediction procedure was accomplished in two scenarios: I) considering all the potential input variables (AA, cement characteristics, and concrete mixture), and II) considering the most effective parameters by using the GT. The RMSE, MAE, NSE, and AIC statistical measures were considered for the model evaluation. In addition to the prediction process, three different sensitivity methods (i.e., GT, RReliefF algorithm, and leave-one-out method) were utilized to determine the most effective parameters in the corrosion mechanism based on three different analysis methods. In summary, the following conclusions were drawn.

1) Applying the GT to choose an effective input vector enhanced the performance of the CART model to 31% of the RMSE in the testing phase. Although the input selection by the GT reduced the computational time, it failed to improve the prediction capability of the MLPNN and ELM (standard ELM, OS-ELM, and K-ELM) models.

2) In terms of the match between the predicted and measured values of the concrete mass loss, a significant improvement was observed in the ELM models for capturing the variability of concrete mass loss over the conventional neural network (MLPNN), statistical MLR model, and DT (CART) models.

3) Among the three applied ELM models, the OS-ELM model was selected as the best model because it had the best performance in both the training and testing phases.

4) In the case of limited input independent data for predicting the concrete corrosion rate, the use of combined ELM models (OS-ELM and K-ELM) over the standard ELM model is suggest.

5) The results of the sensitivity analyses indicated that CW plays the most important role in coping with the decrease in corrosion. In addition, the addition of slag and silica fume as additive cementing materials in concrete mixtures has a greater effect than the W/C ratio for coping with the concrete corrosion problem.

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