Optimization and predictive performance of fly ash-based sustainable concrete using integrated multitask deep learning framework with interpretable machine learning techniques

It describes a design that makes an improved model for the prediction of concrete strength using Gradient Boosting and Deep Neural Networks, surpassing intrinsic low efficiency and high complexity issues in the existing models for the analysis of strength sets. This will be effectively a strength combination of Gradient Boosting and deep neural networks for high-accuracy and interpretability-based prediction of concrete compressive strength, as evidenced in Fig. 1 in this text. The proposed method works in a modular way. First, the data set is defined and consists of material proportions, environmental variables, and NDT data.) This phase involves the normalization of all three parameters and any required imputation methods. Initial feature importance is estimated through XGBoost and predictive modeling on a structured data set, with NDT data treated as auxiliary input. Simultaneously, nonlinear relationships are captured by a three-hidden-layer (size 128-64-32) DNN model with ReLU activations. Hyperparameters for both models are optimized by AutoGluon. Weights are fused through a weighted average based on performance-weighted coefficients, with XGBoost and DNN model outputs contributing (α = 0.4 to XGBoost and 0.6 to DNN). Thereafter, predictions are explained globally and locally through SHAP and LIME, while concurrent multitask learning enhances performances in estimating compressive and tensile strengths. XGBoost was chosen for the classification of patterns within tabular data, while a DNN was chosen for the other high-order feature interactions in process. Feature extraction leverages both domain knowledge and SHAP analysis. The final fusion applied weights to both XGBoost and DNN outputs based on their validation performances. The weight α = 0.4 was dynamically adjusted during AutoGluon trials for the final output yfinal = α⋅yXGBoost+(1-α)⋅yDNN. The whole architecture encompasses data ingestion, preprocessing, independent XGBoost and DNN modeling tracks, and finally a weighted output fusion block. This architecture, which is pictured in Fig. 1, describes the individual layers and the fusion strategy sets.

The model will borrow the strong predictive capabilities brought in by the algorithm from XGBoost, one that excels in treating tabular data and can provide ranks of feature importance, and powerful nonlinear relationship capturing of DNNs. In the process, at worst, one is guaranteed that with AutoML through AutoGluon, the components of XGBoost and DNN are run with the best possible hyper parameters, ruling out manual intervention and tuning. These variables describe concrete mix proportions, fly ash content, curing time, environmental conditions, and NDT data related to ultrasonic pulse velocity and rebound hammer test results—basically, all variables considered of importance to the prediction of concrete strength, which become the input features in this model. Based on these features, AutoGluon first makes some initial predictions using XGBoost and estimates the level of feature importances. XGBoost’s target function is gradient boosting of the loss function stipulated in Eqs. 1,

Where, L(θ) is the loss function, l is the differentiable loss function, for example, mean squared error, yi and y’i are the true and predicted values respectively, and Ω(fk) is regularization term for the complexity of the model’s components fk in the process. Based on the initial predictions made and feature ranking done by the component XGBoost, the DNN component refines these predictions. In the DNN, several layers of neurons are organized to apply a nonlinear transformation to their inputs, so that complex interactions between features are learned. Mathematically, this forward propagation through the DNN is described via Eqs. 2,

where a(l) is the activations of the l-th layer, W(l) and b(l) denote the weights and biases of the l-th layer, respectively; σ denotes the ReLU activation function. The weights and biases of the DNN are optimized through backpropagation and gradient descent, in which the gradients of the loss function with respect to the parameters are computed and iteratively updated in the process. In the process of backpropagation, Eqs. 3 & 4 are used to compute the derivatives of the loss function with respect to each parameter,

where, δ(l) is the error term for the l-th layer, z(l) is the weighted input to the l-th layer, and σ′ is the derivative of the activation function. The incorporation of all these elements into AutoGluon ensures that hyper parameters are automatically tuned for the best performance from this hybrid model process. A weighted average combines final predictions from the outputs of an XGBoost and DNN model process.

This weighted averaging can be represented via Eqs. 5,

where, y’final is the final predicted value, y’XGBoost and y’DNN are the predictions from the XGBoost and DNN models, respectively, and α is the weight assigned to the XGBoost prediction, optimized through AutoGluon process. Such a hybrid model makes sense because of the synergistic effect when combining gradient boosting with DNNs. On the other hand, XGBoost provides a very good base, especially in handling feature importance and interactions within tabular data efficiently; then, this is refined by the DNN for capturing intricate nonlinear relationships. This combination provides better predictive accuracy while keeping the model interpretable through rankings on feature importance and transparent model explanations enabled by SHAP and LIME processes.

As indicated in Fig. 2, the SHapley Additive exPlanations-based approach is further integrated with LIME to make the model interpretable and transparent. The integrated approach provides an in-depth insight into how individual features contribute to the obtained predictions by the model and allows further empowered decision-making and results trust. In the present work, SHAP values are computed post-hoc for explaining the hybrid model predictions. The SHAP values, based on game theory, particularly cooperative games, are such that for every data instance, each feature value is a player in a game, and the prediction is a payout for the process. More specifically, the SHAP value is defined as the average contribution that the feature has towards the prediction when considering all possible combinations of feature subsets. Mathematically, Eq. 6 expresses the SHAP value for a feature i in a prediction for instance x,

where, N is the set of all features, S is the subset not containing feature i from N, f(S) is the prediction made using the feature subset S, and |S|! represents the factorial of the number of features in S. Using the formula above guarantees that every contribution for each feature is fairly and exactly quantified, hence giving insights into the global and local importance of each feature. It is at a very fine granularity that the SHAP values explain the contribution of features within the hybrid model. For example, according to SHAP analysis, fly ash content contributes 20–25%, curing time contributes 15–20%, and ultrasonic pulse velocity contributes 15–20% to predictive power. This granularity of insight is important in understanding what underlies the model’s predictions and in making data-driven adjustments in the concrete mix design. LIME provides local explanations for individual predictions and, in that sense, complements SHAP. On the other hand, LIME does this by perturbing individual data points and by observing how such disturbances change the model’s predictions. For a specific prediction, LIME generates a local surrogate model, normally a linear regression model, which approximates the decision boundary of the complex model around the instance’s vicinity. It creates a new dataset by perturbing the original instance and getting corresponding predictions from the hybrid model to train the local model. The objective of LIME can be formulated via Eqs. 7,

where g is an interpretable model, L is a loss function measuring the fidelity of g in approximating f, and Ω(g) is a complexity measure to ensure that the interpretability of g holds in the locality defined by πx. The choice for πx is what guarantees that g is a faithful local model for the original model f in the vicinity of x sets. Moreover, SHAP and LIME together constitute a powerful, interpretable framework for feature importance analysis. SHAP brings a global perspective by quantifying the contribution of their feature to all predictions, while LIME brings a local perspective by explainability per instance. This duality provides as much transparency as possible to the model so that its decisions are understandable and actionable for the process. It enhances the interpretability of the hybrid model’s predictions and hence increases trust and adoption in practical applications with SHAP values and LIME explanations. For instance, the SHAP values of fly ash content, curing time, and ultrasonic pulse velocity provide hands-on insights into the optimization of the design of concrete mixes. In contrast, LIME explanations made it possible for practitioners to get a grasp of why exactly a particular prediction was indeed a prediction, thus explaining 90% of the cases of prediction with a local fidelity score above 0.85. Mathematically, the integration of SHAP and LIME may be further demonstrated with Equation, which embodies the interplay boiling down global and local interpretability techniques. The SHAP value of a feature i in a prediction for instance x can be further refined using a LIME’s local surrogate model via Eqs. 8,

where, g(S) is the prediction made by the local surrogate model using the subset of features S. This step of further refinement makes sure that local importance of features is properly harnessed and aligned with global SHAP values for different scenarios. The key motivation behind the use of SHAP with LIME is that they have complementing strengths. The cooperative game theory-theoretical foundation of SHAP makes it a fair and consistent platform for feature importance, while the ability of LIME to provide local explanations gives actionable insight at the instance level. Be put together; they offer a clear and comprehensive framework for understanding predictions of the hybrid model—a powerful tool for concrete strength assessment. Finally, the integration of NDT data in predicting compressive strength from concrete and related properties such as tensile strength employs a very sophisticated framework through multi-task learning to leverage shared information across different tasks. This multitasks approach will also make the predictors perform better because they will capture common representations from traditional features and samples of NDT data. MTL is, in fact, especially applicable when related tasks benefit from shared knowledge; the model of this setup can generalize better than that of a single-task learning scenario.

Shared layers in the MTL framework have processed the inputs from both traditional features, such as concrete mix proportions and curing time under environmental conditions, and NDT data, including ultrasonic pulse velocity or rebound hammer test results. Such shared layers learn a common representation that is beneficial for all tasks. Then, task-specific layers fine-tune these representations to predict target properties, like compressive and tensile strengths. Mathematically, the MTL model can be expressed as a set of operations that define the shared and task-specific components. Let xi represent the input features of the i-th instance; it can contain both traditional and NDT data samples. The shared representation h can be obtained using a few shared layers via Eqs. 9,

where Wsh and bsh are the shared layers weights and biases, respectively, and σ the activation function — ReLU — process. This shared representation h, encapsulates common information from the input features, which is then used by the task-specific layers. For each task, t, such as predicting Compressive Strength, yc and Tensile Strength, yt, the task-specific layers further process the shared representation via Eqs. 10 & 11,

where Wc and bc, Wt and bt are the weights and biases of the task-specific layers for compressive strength and tensile strength predictions respectively. The loss function of the MTL model is the combination of losses from both tasks. This will ensure that the model can optimally balance the performances across tasks. This combined loss, L, can be mathematically represented via Eqs. 12,

where Lc and Lt refer to the loss functions of the compressive and tensile strength tasks, respectively, and α represents a weighting parameter balancing the contribution of the loss of each task. Traditionally, mean squared error has been used as the loss function via Eqs. 13 & 14,

The gradients of the joint loss with respect to shared and task-specific parameters are then computed, which is used during back propagation when updating the model’s parameters. Equation 15 expresses the gradient of the loss concerning the shared layer parameters, Wsh,

This use of MTL is justified by being in a position to leverage shared information across related tasks to arrive at improved predictive performance. In this context, predicting compressive and tensile strength simultaneously could, therefore, allow the model to take advantage of correlations in these properties that are often influenced by similar factors such as mixed proportions and curing conditions. These commonalities are captured by the shared layers and make for a more robust representation that improves the performance of both tasks. Integrating NDT data into the MTL framework is well justified by the rich, complementary information given by these tests. NDT methods, such as ultrasonic pulse velocity and rebound hammer tests, offer non-invasive information about the internal structure and quality of concrete, which traditional features may not wholly capture. This has led to more accurate and reliable prediction, as, under the MTL model, a holistic view of material properties is incorporated into the NDT data samples.

SHAP and LIME jointly address different aspects of explainability. The SHAP approach assesses global feature contributions, which is useful for understanding the average effect of mix components such as fly ash or curing time on the data set samples, especially when optimizing for concrete mix design. However, LIME works better for local explanations of predictions at the individual level, for example, in batch analysis, when examining concrete in terms of quality assurance. On the other hand, SHAP offers an assuredly consistent explanation ensuring game-theoretic justification, while LIME gives fast and flexible per-instance rationale. Strangely enough, one could say that weight-wise, SHAP would largely determine model form development, while LIME would become operationally significant at the deployment stage for diagnosing instances in process.

The selection of features started with all input features: chemical compositions, curing parameters and NDT indicators. SHAP values assessed relevance for features through model iterations. Features with negligible weight (SHAP < 0.05) were examined for redundancy; DNN training was encouraged to be sparse by means of LASSO regularization to pull the less predictive features out altogether. PCA was tested but rejected since its application was against interpretability. In the end, there were nine features retained in the final model, all of which were shown to contribute significantly to strength prediction validated by both cross-validated scores and SHAP-based global importance values during the process. The mathematical formulations used in this study have all conformed to those given in the general optimization and interpretability machine learning models in the literature. The loss functions for both XGBoost and DNN components align with the formulations already shared by^18,20,25 and then^5,6,15 in process. Backpropagation gradients, multitask learning equations, and SHAP value formulations follow the canonical definitions coming from Shapley Theory^9,15 and from multitask neural modelling^28,35 in process. Each and every one of the equations in manuscript presentations has now been referenced accordingly to maintain the academic rigor and traceability of foundational methods.We next demonstrate the efficiency of the proposed model concerning the different metrics and contrast it with existing models over various scenarios.