Contents lists available at ScienceDirect Algal Research journal homepage: www.elsevier.com/locate/algal Direct estimation of microalgal flocs fractal dimension through laser reflectance and machine learning Patricio Lopez-Exposito, Carlos Negro, Angeles Blanco Chemical Engineering Department, Complutense University of Madrid. Avda. Complutense s/n, Madrid 28040, Spain ARTICLE INFO Keywords: Microalgae flocculation monitoring Direct estimation fractal dimension laser reflectance Flocs growth modelling Microalgal flocs geometry Machine learning regression ABSTRACT The pre-concentration of microalgal cultures through flocculation can be applied to reduce the harvesting costs of biomass. The microalgal flocs induced through flocculation must have the optimal size and geometry to enhance the performance of subsequent concentration operations. In this work, we propose a new method to estimate the average fractal dimension of Chlorella sorokiniana flocs based on correlating the suspension chord length distribution with the flocs average geometry through a machine learning random forest regression model. To obtain the data required for training the machine learning model, a set of virtual flocs of prescribed fractal dimension was generated through a computer software. The virtual flocs were subject to chord length data acquisition by means of another piece of software simulating the operation of a focused beam reflectance probe. With the chord length data generated the random forest regression model was trained and optimized and then satisfactorily validated with data of real suspensions of known average geometry. The method developed may be used to implement flocculation control systems capable of adjusting the geometry of flocs to the requirements of subsequent concentration operations by actuating on the process stirring intensity. 1. Introduction Biomass harvesting accounts for almost nearly 30% of the cost as- sociated to the production of microalgae [1]. The pre-concentration of biomass through flocculation has been recognised as a means to sig- nificantly reduce the cost and energy demand for microalgal harvesting [2]. Most studies in this line have focused on the effectiveness of the different flocculants and flocculating methods in relation to process yield [3] but few have concentrated on monitoring the physical char- acterization of the microalgal flocs produced. Nevertheless, the size and structure of flocs produced though flocculation are crucial factors for the subsequent downstream processes that integrate the separation or concentration train. Filtration performance, for example, has been re- ported to improve if the suspension to concentrate is composed of large floc sizes with open structures [4,5]. In the case of settling, on the other hand, the relationship between floc geometry and terminal velocity is somehow more complex but equally important [6,7]. The above leads us to conclude that floc size and structure should be considered in flocculation studies and, ideally, in industrial harvesting setups. Despite the relevance of the physical features of the flocs, the monitoring of flocculation processes is generally carried out through indirect mea- surements, such as turbidity, that take no account of the size distribution or shape of the flocs being formed. de Oliveira, Moreno, da Silva, De Julio and Moruzzi [8] acknowledged the need for direct flocculation monitoring methods that account for particle size and geometry in order to develop control systems capable of adjusting the stirring conditions to produce flocs with optimal physical features for the subsequent concentration processes. Among the available techniques to monitor the size distribution of particulate suspensions, the laser reflectance measurement (FBRM) technique has gained significant attention for its measurements can detect particles from 1 μm up to several millimetres and performs re- liably in a wide range of concentrations (0.1 to 40% vol.) [9]. The main drawback of the FBRM is its tendency to downsize the size of the par- ticles measured. Concerning the shape of microalgal flocs, particulate flocs induced by flocculation have been recognised as having a fractal nature [10], which geometry can be characterised through their fractal dimension (D f ). The concept fractal dimension can be expressed by the following scaling power-law: ⎜ ⎟ ∝ ⎛ ⎝ ⎞ ⎠ N R a , g D f (1) https://doi.org/10.1016/j.algal.2018.12.007 Received 27 April 2018; Received in revised form 3 December 2018; Accepted 3 December 2018 Abbreviations: CCA, cluster-cluster aggregation; CLD, chord length distribution; CLSM, Confocal laser scanning microscopy; D 2 , two-dimensional fractal dimension; D f , three-dimensional fractal dimension; MFD, maximum Feret diameter; FBRM, laser beam reflectance measurement; RFR, random forest regression E-mail address: plopezex@ucm.es (P. Lopez-Exposito). Algal Research 37 (2019) 240–247 2211-9264/ © 2018 Elsevier B.V. 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