Proper Orthogonal Decomposition for Performance Based Design and Modelling Concrete

Abstract

Reduction in the usage of Portland cement as the primary cementitious component in concrete has become a key driver for accomplishment of the UN sustainable development goals (SDGs). Utilization of secondary cementitious materials, recycled materials and performance-based design of concrete by innovative cement combinations are being attempted to make concrete the most versatile and widely used construction material and sustainable too. Nevertheless, achieving desired workability, strength and durability characteristics, is still challenging owing to the complex interaction of many variables. Performance-based design demands thorough qualitative and quantitative appraisal of concrete characteristics. Knowledge of significant variables will provide directions to performance-based design methods for accomplishing targeted levels. Data analytics help enhance state-of-the-art. Mathematically, in such complex systems, random experiments further add to sources of redundancy and lead to unnecessary complications, if all the variables are to be included in performance appraisal. Identification of significant variables, elimination of redundant helps in dimensionality reduction of data and meaningful representation of system’s behaviour. Statistical methods, group method of data handling, machine learning techniques are very popularly employed in modelling complex systems of this kind. Proper Orthogonal Decomposition (POD) has been considered in this work for dimensionality reduction in performance-based design of concrete. An account of employment of data handling techniques in performance-based design has been provided and utility of POD in such assignments has been demonstrated and highlighted. Sequential steps adopted in current research have been described. Available-published data sets have been adopted for study. Correlation matrix obtained from screened data has been decomposed to obtain eigenvalues and eigenvectors. Orthogonal components extracted from dimensionality reduction have been further used to draw inferences. A method to identify significant variables and their hierarchy has been ordered, which is of prime importance in performance-based design to for accomplishment of targets. A performance quality index has been proposed for evaluating relative quality of different mixes. Potential utility of POD in refinement of vi available concrete models to predict and project behaviour of concrete with inclusion of emerging data in decision-making for redefining such models have been investigated. General outcomes on utility of POD in concrete performance evaluation and specific conclusions on concrete workability, strength, durability and performance at elevated temperature exposure have been brought out as inferences. It is found that POD can be an effective tool in exploration of complex concrete data. Identification of crucial variables and ordering of hierarchy based on their significance can aid in quick calibration of concrete characteristics depending upon specific target requirements of performance-based design. Utilization of POD can open up new vistas to extend existing concrete capabilities and possibilities.