The application of Fourier series in forecasting construction project completion: a case study

Purpose Predicting project completion time is a crucial aspect of construction management for mitigating delays and supporting effective project control. However, existing forecasting methods still rely on extensive historical data and lack optimality in capturing the cyclical and non-linear patterns of project progress. Therefore, an accurate and adaptive prediction model is required to support decision-making under conditions of limited data. Accurate prediction of construction completion remains challenging due to the cyclicality and nonlinearity of progress data, especially when historical datasets are frequently scarce or unavailable. This study develops and validates Optimum Fourier Series–Polynomial Regression (Optimum.FSPR), a hybrid prediction model designed to provide reliable completion forecasts under conditions of data scarcity or high volatility. Design/methodology/approach The Optimum.FSPR technique integrates Fourier Series (FS) to model cyclic patterns with Polynomial Regression (PR) to capture nonlinear long-term trends. Model performance is evaluated using weekly project progress data, with Autoregressive Integrated Moving Average (ARIMA), eXtreme Gradient Boosting (XGBoost) and Long Short-Term Memory (LSTM) serving as benchmark models and Mean Absolute Error, Mean Absolute Percentage Error and Root Mean Squared Error as evaluation metrics. Additionally, 2,000 Monte Carlo simulations were utilized to generate a probabilistic distribution of the S-curve regarding project completion time. Findings Traditional forecasting models proved ineffective for this application due to instability and heavy data requirements. Conversely, Optimum.FSPR demonstrated superior accuracy, consistency and stability. Optimum.FSPR produced lower errors compared to ARIMA, XGBoost and LSTM. An integrated simulation approach identifies a 94.5% probability of project completion by the 49th week. These results confirm the model’s reliability for application in practical construction project scenarios characterized by data limitations. Practical implications This research offers a robust, data-driven tool for project managers and stakeholders to monitor progress in real-time. By facilitating accurate forecasting with minimal data, the model enables proactive decision-making to mitigate delays and optimize resource allocation throughout the project lifecycle. Originality/value The study introduces a novel application of Fourier analysis in construction management. By merging spectral analysis with regression, the research advances predictive methodologies for handling complex datasets, effectively capturing both cyclic variations and nonlinear trends, thereby addressing a significant gap in the literature regarding methodologies for predicting the progress and completion of construction projects.