Improving Cost Contingency Estimation in Infrastructure Projects with Artificial Neural Networks and a Complexity Index
Abstract
:1. Introduction
- (1)
- To select high-performing ML models for cost contingency prediction;
- (2)
- To investigate whether integrating a complexity index can improve prediction performance;
- (3)
- To develop interval predictions and assess whether the incorporation of a complexity index improves their accuracy.
2. Literature Review
2.1. Cost Contingency Prediction
2.2. Traditional Approaches to Contingency Estimation
2.3. Machine Learning Applications in Contingency Estimation
Algorithms | Theoretical Underpinnings | Strengths |
---|---|---|
Linear regression | Linear regression assumes a linear relationship between the input variables and the target: where is the predicted target, represents the input variables, are the coefficients (weights) that quantify the influence of each input on the target, and is the intercept. The optimal coefficients are achieved by minimizing the ordinary least squares [11]: , where is the actual value, is the predicted value, and is the number of observations. The coefficients in the linear regression model quantify the influence of each input variable on the target. | Simplicity, interpretability, and computational efficiency |
SVR | Similar to linear regression, SVR fits the function WTX + b while allowing a margin of tolerance . To handle non-linear relations, it performs the kernel trick, which maps data to a higher-dimensional space where linear separation is achievable. Common kernel options include linear (), polynomial, and radial basis function [27]. | Capability to address outliers and model non-linear relationships |
Decision trees | Decision trees split data into branches based on features that best reduce impurity. Impurity is a measure of the homogeneity of the data within a node, aiming to make each split as “pure” as possible. It can be calculated using metrics like Gini impurity and entropy for classification and variance for regression models [25]. Specifically, Gini impurity is calculated as: , where is the proportion of class in the node ; and entropy is measured as: . | Capability to model non-linear relationship and effectively identify important features |
Random forest | Random forest improves predictive accuracy by combining multiple decision trees. Each tree is trained on a random subset of data and features, reducing variance and overfitting [26]. The final prediction is the average outcome across all trees: , where is the total number of trees. | Robustness to overfitting |
Gradient boosting | Gradient boosting builds an ensemble of decision trees sequentially, with each new tree focused on reducing the errors of the previous one [36]. At each step , the model updates predictions as: , where is the learning rate controlling the contribution of each tree. The final model combines these sequentially trained trees, each contributing based on its ability to minimize prior errors. | Promising predictive accuracy through interactive error correction |
XGBoost | XGBoost employs regularization and optimization techniques to enhance model performance. Regularization, which prevents overfitting by penalizing model complexity, includes two techniques: L1 and L2 [31]. L1 regularization applies a penalty based on the absolute magnitude of coefficients, given by , while L2 uses the squared magnitude, i.e., , where are model parameters, and and control the strength of L1 and L2 regularization, respectively. XGBoost also uses optimization techniques, like second-order approximation and shrinkage. | High predictive accuracy through optimization |
ANN | An ANN consists of interconnected neuron layers: input, hidden, and output. Each neuron in layer l receives weighted inputs from the previous layer : , where and refer to the weight and bias, respectively. The activation function introduces non-linearity: . During training, the ANN adjusts these weights using backpropagation which calculates the gradient of the loss function (a measure of prediction error) with respect to each weight [28]. | Ability to model complex relationships |
2.4. Interval Estimation in Machine Learning
2.5. Project Complexity and Estimation Accuracy
2.6. Research Gap
3. Materials and Methods
3.1. Stage 1: Data Collection and Preprocessing
3.2. Stage 2: Project Contingency Prediction Models
3.3. Stage 3: Point Estimation and Complexity Index
3.4. Stage 4: Interval Predictions and Complexity Index
- (a)
- Monte Carlo dropout
- (i)
- Train the model using the original training dataset, with dropout enabled during both training and inference;
- (ii)
- Perform multiple stochastic forward passes (n passes) through the trained model for the same test case x, with dropout activated to introduce randomness in each pass;
- (iii)
- Generate a set of n predictions for the test case x from the stochastic forward passes;
- (iv)
- Calculate the lower and upper bounds of the prediction interval, using the formulas presented below [61]:
- (b)
- Bootstrapping
4. Results
4.1. Feature Selection
4.2. Development of Cost Contingency Prediction Models
4.3. Integrating the Complexity Index into Point Estimation
4.4. Integrating the Complexity Index into Interval Estimation
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Research | Algorithm | Input Variables | Target | Advantages/Disadvantages |
---|---|---|---|---|
Lhee et al. (2014) [1] | ANN | Number of bidders, project letting year, project duration, and contract value | Predicted contingency amount | The ANN model demonstrated promising accuracy in predicting cost contingency. However, the input variables are limited, and the lack of consideration for project complexity factors restricts the model’s generalizability to infrastructure projects. |
Islam et al. (2021) [5] | Fuzzy Bayesian belief networks | Cost overrun-related risks, including 27 independent risks and 14 dependent risks | Probability of cost overrun | It predicted the probability of cost overrun. However, limited project cases (12 cases) used for prediction model, computational complexity, and reliance on subjective data constrain its application. |
El-Kholy et al. (2022) [10] | ANN | Sensitivity analysis ratio of steel reinforcement prices, ratio of the direct cost of steel reinforcement to the total project cost, probability distribution types for risk variables (triangular and normal), and contractor trend in dealing with risk (gambler, neutral, and conservative) | Predicted cost contingency percentage | This study demonstrated that the ANN model outperformed regression-based models in predictive accuracy. However, the limited number of project cases (30 cases) and the focus on the influence of steel reinforcement prices on cost contingency, constrain its broader applicability. |
Ammar et al. (2024) [11] | Linear regression | Cost overrun-related factors, such as inaccurate cost estimate, design changes, scope changes, and variation orders | Predicted contingency amount | This study revealed promising predictive performance for linear regression. However, it lacks diverse project features as input variables and relies on subjective input data. |
Prediction Models | Hyperparameters |
---|---|
Linear regression | ElasticNet (‘alpha’ = 1, ‘l1_ratio’ = 1) |
SVM | SVR(‘C’ = 500, ‘degree’ = 2, ‘epsilon’ = 2, ‘gamma’ = ‘scale’, ‘kernel’ = ‘linear’) |
Decision tree | DecisionTreeRegressor (‘criterion’ = ‘poisson’, ‘max_depth’ = None, ‘max_features’ = None, ’min_samples_split’ = 2) |
Random forest | RandomForestRegressor (n_estimators = 100, criterion = ‘squared_error’, max_depth = None, min_samples_split = 2, min_samples_leaf = 1) |
Gradient boosting | GradientBoostingRegressor (‘learning_rate’ = 0.1, ‘loss’ = ‘huber’, ‘n_estimators’ = 100) |
XGBoosting | XGBRegressor (objective = ‘reg:squarederror’, n_estimators = 300, learning_rate = 0.01, max_depth = 3, subsample = 0.8, colsample_bytree = 1, gamma = 0, min_child_weight = 20, reg_alpha = 0, reg_lambda = 0, random_state = 31) |
ANN | MLPRegressor (hidden_layer_sizes = (256, 128), activation = ‘relu’, solver = ‘adam’, alpha = 0.0001, max_iter = 600, random_state = 0, learning_rate = ‘constant’, learning_rate_init = 0.001, shuffle = True, verbose = True, validation_fraction = 0.1, momentum = 0.9) |
Model Variables | Description | Value | ||||
---|---|---|---|---|---|---|
Data Type | Min. | Max. | Mean | Standard Deviation | ||
Input | ||||||
Project estimate (PE) (HKD) | A cost estimate prepared by a client before receiving any bids from contractors for a construction project. It is based on the design, specifications, and other known factors. | Numerical value | 32.55 million | 44,878.95 million | 1508.99 million | 4701.69 million |
Contract contingency allowed in PE (HKD) | A specific allowance to cover unforeseen costs or risks (e.g., design changes or unexpected site conditions) that might arise during the construction project. | Numerical value | 2.35 million | 2665.22 million | 114.16 million | 308.88 million |
Approved PE (HKD) | The officially sanctioned project estimate that has been reviewed and endorsed by the client. | Numerical value | 34.00 million | 44,798.40 million | 1826.55 million | 5167.11 million |
Project type | Project type refers to the category of public infrastructure projects classified by their purpose. Five main types are identified: land development projects (LDPs), roads and highways (RH), water treatment projects (WTPs), sewage treatment projects (STPs), and other public functional projects (PFPs, e.g., hospitals, schools, and government offices) | Five string values: LDPs (26%), RH (11%), WTPs (7%), STPs (11%), PFPs (45%) | -- | -- | -- | -- |
Starting year | The year in which the construction work for a project begins on site. | Integer | 1998 | 2021 | -- | -- |
Completion year | The year when all construction activities are finished, and the project is considered complete. | Integer | 2002 | 2024 | -- | -- |
Output | ||||||
Materialized cost contingency (HKD) | The portion of the allocated cost contingency that has actually been used to cover unforeseen risks or changes during the project construction process. | Numerical value | −7518.71 million | 1418.48 million | −233.66 million | 784.91 million |
Prediction Targets | Metrics | Linear Regression | SVM | Decision Tree | Random Forest | Gradient Boosting | XGBoosting | ANN |
---|---|---|---|---|---|---|---|---|
Materialized cost contingency | R2 | 0.397 | 0.360 | 0.084 | 0.725 | 0.782 | 0.785 | 0.808 |
MAE | 156 | 141 | 156 | 94 | 86 | 86 | 93 | |
MSE | 66,709 | 70,870 | 101,470 | 30,412 | 24,095 | 23,876 | 21,236 | |
RMSE | 258 | 266 | 318 | 174 | 155 | 157 | 145 |
Prediction Target | Metrics | Without Complexity Index | With Complexity Index |
---|---|---|---|
Materialized cost contingency | R2 | 0.808 | 0.889 |
MAE | 93 | 68 | |
MSE | 21,236 | 11,080 | |
RMSE | 145 | 105 |
Features | Value | Rank |
---|---|---|
Approved project estimate | 151,976.32 | 1 |
Complexity index | 121,533.38 | 2 |
Contract contingency | 46,223.72 | 3 |
Starting year | 14,185.36 | 4 |
Completion year | 6729.28 | 5 |
Project type | 1650.03 | 6 |
Project estimate | 803.49 | 7 |
Prediction Target | Methods | Without Complexity Index (Uncertainty Accuracy, %) | With Complexity Index (Uncertainty Accuracy, %) |
---|---|---|---|
Cost contingency prediction | Monte Carlo dropout | 60 | 76 |
Bootstrapping | 80 | 88 |
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Sing, M.C.P.; Ma, Q.; Gu, Q. Improving Cost Contingency Estimation in Infrastructure Projects with Artificial Neural Networks and a Complexity Index. Appl. Sci. 2025, 15, 3519. https://doi.org/10.3390/app15073519
Sing MCP, Ma Q, Gu Q. Improving Cost Contingency Estimation in Infrastructure Projects with Artificial Neural Networks and a Complexity Index. Applied Sciences. 2025; 15(7):3519. https://doi.org/10.3390/app15073519
Chicago/Turabian StyleSing, Michael C. P., Qiuwen Ma, and Qinhuan Gu. 2025. "Improving Cost Contingency Estimation in Infrastructure Projects with Artificial Neural Networks and a Complexity Index" Applied Sciences 15, no. 7: 3519. https://doi.org/10.3390/app15073519
APA StyleSing, M. C. P., Ma, Q., & Gu, Q. (2025). Improving Cost Contingency Estimation in Infrastructure Projects with Artificial Neural Networks and a Complexity Index. Applied Sciences, 15(7), 3519. https://doi.org/10.3390/app15073519