Modelizado y optimización de problemas biomecánicos mediante la combinación del método de los elementos finitos (mef) y técnicas avanzadas de optimización

Los problemas biomecánicos generalmente presentan comportamientos no lineales producidos por contactos mecánicos, grandes deformaciones, grandes desplazamientos, hiperelasticidad, etc. Este tipo de comportamiento no lineal es muy difícil de modelizar y optimizar mediante métodos ampliamente utilizados como es el Método de los Elementos Finitos (MEF). En primer lugar, el coste computacional que requiere el MEF cuando es aplicado de manera individual para modelizar y optimizar problemas biomecánicos es muy elevado. Además, por motivos éticos, resolver este tipo de problemas biomecánicos de modo experimental (mediante prueba-error) resulta hoy en día inviable. Esta tesis presenta una metodología que combina el MEF con técnicas avanzadas de análisis de datos como es el Método de Superficie de Respuesta Múltiple (MSR) y el Machine Learning (ML) para modelizar y optimizar problemas biomecánicos presentes en humanos y en animales. La aplicación de la metodología que se presenta en esta tesis se desarrolla en tres fases principales. La primera fase se centra en la creación de modelos de EF, en la segunda fase se obtienen los modelos de predicción mediante técnicas de regresión, árboles de decisión, redes neuronales, etc. y finalmente, en una tercera fase, se realiza la optimización utilizando la metodología de superficie de respuesta múltiple o algoritmos genéticos. La metodología propuesta puede ser aplicada a cualquier problema biomecánico, si bien en esta tesis se ha validado mediante su implementación en cuatro casos reales encontrados en seres humanos y en animales. En animales, se aplica al modelizado del comportamiento biomecánico de una pelvis canina con dos tipos diferentes de placas de fijación (ventral y DPO), utilizadas para el tratamiento de la osteotomía pélvica canina. En este caso, se aplica de manera individual el MEF con el fin de estudiar y comparar la rigidez entre las placas de fijación. De esta manera, se reduce el coste experimental y se evita el problema ético. En el caso de los seres humanos, se aplica la metodología que combina el MEF y el MSR con funciones de deseabilidad para el modelizado y optimización del comportamiento biomecánico de discos intervertebrales (DIV) en unidades vertebrales funcionales (UVF) lumbares, con el objetivo de obtener los parámetros más adecuados que definan el comportamiento biomecánico de los modelos de EF. La ventaja del uso combinado del MEF y MSR, tal como se propone en esta tesis, es que permite ajustar y optimizar los parámetros que definen el comportamiento biomecánico de los modelos de EF de estructuras complejas de un modo más eficiente, evitando así, el arduo ajuste de los parámetros para obtener el modelo de EF óptimo mediante el método prueba-error. Finalmente, la metodología propuesta se aplica en el diseño de un disco artificial o prótesis lumbar mediante la combinación de MEF y técnicas de ML. En este caso, los modelos de regresión generados se basan en redes neuronales y árboles de regresión, mientras que la optimización de la geometría del disco artificial se realiza mediante la aplicación de algoritmos genéticos. De este modo, también es posible obtener, de una manera eficiente, los parámetros que mejor definen la geometría planteada para el disco artificial lumbar para los diferentes pesos y estaturas de los pacientes, con lo que se considera que proporciona una herramienta importante para el diseño y la optimización de prótesis de disco artificial (diseño de prótesis a medida). En definitiva, la metodología que se propone en esta tesis, la cual combina varias técnicas (MEF, MSR y ML) que generan modelos matemáticos o metamodelos, se muestra como una metodología muy valiosa que permite de una manera eficiente modelizar y optimizar problemas biomecánicos complejos. Las ventajas fundamentales de esta metodología, son las siguientes: Reduce significativamente el coste experimental y se elimina el problema ético asociado al uso de cadáveres. Permite obtener modelos de predicción lo suficientemente precisos, fáciles de interpretar y mucho más eficientes computacionalmente que los modelos obtenidos mediante el MEF para el modelizado de problemas biomecánicos. Permite optimizar problemas biomecánicos complejos, de una manera más eficiente, reduciendo de forma significativa el coste computacional que ocasionaría el uso exclusivo del MEF aplicando el método prueba-error.Usually, biomechanical problems present non-linear behaviours produced by mechanical contacts, large deformations, large displacements, hyperelasticity, etc. This type of nonlinear behaviour is difficult to model and optimise by widely used methods such as the Finite Element Method (FEM). First, there is a very high computational cost when only FEM is applied to model and optimise biomechanical problems. In addition, solving this type of biomechanical problems experimentally (through trial-error tests) is nowadays unfeasible for ethical reasons. This thesis presents a methodology that combines FEM with advanced data analysis techniques, such as the Multiple Response Surface Method (MRS) or Machine Learning (ML) algorithms, to model and optimise the biomechanical problems that are present in humans and animals. The application of the proposed methodology in this thesis is carried out in three main phases. The first phase focuses on the creation of FE models, while the second phase is devoted to the generation of prediction models by means of regression techniques, decision trees, neural networks, etc. Finally, in the third phase, an optimisation is performed using either the MRS or genetic algorithms. The proposed methodology can be applied to any biomechanical problem. In this thesis, it has been validated through its implementation in four actual problems that are found in humans and animals. In animals, it is applied to model the biomechanical behaviour of a canine pelvis with two different types of fixation plates (ventral and DPO), used for the treatment of canine pelvic osteotomy. In this case, the FEM is solely applied to analyse and compare the stiffness difference between ventral and DPO fixation plates. In this manner, the experimental cost is reduced and the ethical problem is avoided. In the case of human problems, the methodology that combines the FEM and the MRS with desirability functions is applied for the modelling and optimisation of the biomechanical behaviour of intervertebral discs (DIV) in lumbar functional spinal units (FSU), with the aim of obtaining the most appropriate parameters that define the biomechanical behaviour of the FE models. The advantage of the combined use of FEM and MRS, as proposed in this thesis, is that it allows adjusting and optimising the parameters that define the biomechanical behavior of FE models of complex structures in a more efficient way. Thus, avoiding the arduous adjustment of the parameters to obtain the optimal FE model through the trial-error method. Finally, the proposed methodology is applied to the design of an artificial disc or lumbar prosthesis by combining FEM and ML techniques. In this case, the regression models generated are based on neural networks and regression trees, while the optimisation of the geometry of the artificial disc is carried out through the application of genetic algorithms. This way, it is also possible to obtain, the parameters that best define the geometry proposed for the artificial lumbar disc for different patients weights and statures in an efficient manner. Therefore, this methodology is considered to provide an important tool for the design and optimisation of artificial disc prostheses (custom-made prostheses). In short, it has been proven that the methodology proposed in this thesis, which combines several techniques (FEM, MSR MRS and ML) to generate mathematical models or metamodels, is very useful to efficiently model and optimise complex biomechanical problems. The main advantages of the methodology are the following: It significantly reduces the experimental cost and eliminates the ethical problem associated with the use of cadavers. It allows to obtain prediction models that are accurate enough, easy to interpret and much more computationally efficient than the models obtained through the FEM to model biomechanical problems. It allows to optimise complex biomechanical problems, in a more efficient way. That is, it substantially reduces the computational cost as compared to the solely use of the FEM by applying the trial-error method

Adsorptive of Nickel in Wastewater by Olive Stone Waste: Optimization through Multi-Response Surface Methodology Using Desirability Functions

Pollution from industrial wastewater has the greatest impact on the environment due to the wide variety of wastes and materials that water can contain. These include heavy metals. Some of the technologies that are used to remove heavy metals from industrial effluents are inadequate, because they cannot reduce their concentration of the former to below the discharge limits. Biosorption technology has demonstrated its potential in recent years as an alternative for this type of application. This paper examines the biosorption process for the removal of nickel ions that are present in wastewater using olive stone waste as the biosorbent. Kinetic studies were conducted to investigate the biosorbent dosage, pH of the solution, and stirring speed. These are input variables that are frequently used to determine the efficiency of the adsorption process. This paper describes an effort to identify regression models, in which the biosorption process variables are related to the process output (i.e., the removal efficiency). It uses the Response Surface Method (RSM) and it is based on Box Benken Design experiments (BBD), in which olive stones serves as the biosorbent. Several scenarios of biosorption were proposed and demonstrated by use of the Multi-Response Surface (MRS) and desirability functions. The optimum conditions that were necessary to remove nickel when the dosage of biosorbent was the minimum (0.553 g/L) were determined to be a stirring speed of 199.234 rpm and a pH of 6.369. The maximum removal of nickel under optimized conditions was 61.73%. Therefore, the olive stone waste that was investigated has the potential to provide an inexpensive biosorbent material for use in recovering the water that the nickel has contaminated. The experimental results agree closely with what the regression models have provided. This confirms the use of MRS since this technique and enables satisfactory predictions with use of the least possible amount of experimental data

Effecting Partial Elimination of Isocyanuric Acid from Swimming Pool Water Systems

It is essential to disinfect the water in swimming pools in order to deactivate pathogenic microorganisms. Chlorination of swimming pool water provides rapid and long-lasting disinfection, but leads to the formation of potentially toxic compounds, including isocyanuric acid, that are used to stabilize chlorine in pool water. Hygiene and health guidelines require an isocyanuric acid concentration in swimming pools of 25 to 75 ppm and that there be no level in excess of 100 ppm. This paper provides a new method to partially remove isocyanuric acid from the water of swimming pool systems with the use of melamine-based reagents. A melamine-photometry process stabilizes the isocyanuric acid. The melamine-based reagent that is added to the raw water reacts with the isocyanuric acid and forms a precipitated salt. The reaction also creates turbidity that is proportional to the isocyanuric acid concentration in the water. It was noted in this study that the optimum functioning range of melamine doses in the raw water was 0.04 to 0.06 g/L and that the reduction of isocyanuric acid in raw water increased as the dose of melamine was increased. Thus, it is necessary to obtain an estimate of the dose of melamine that is necessary to reduce the isocyanuric acid in the water without needing to add fresh water from the network to dilute it. Finally, it can be stated that eliminating isocyanuric acid that has accumulated in a pool’s water by treatment with melamine provides an efficient process, as it eliminates the amount of isocyanuric acid that is necessary to conform to the human health criteria of the European Union Directive 2006/7/EC. Treatment with melamine also reduces water network consumption and sewer discharge by successive purges that eventually will become unnecessary. Therefore, this proposed method is environmentally and economically beneficial

Coagulation: Determination of Key Operating Parameters by Multi-Response Surface Methodology Using Desirability Functions

The clarification process removes colloidal particles that are suspended in waste water. The efficiency of this process is influenced by a series of inputs or parameters of the coagulation process, of which the most commonly used are initial turbidity, natural coagulant dosage, temperature, mixing speed and mixing time. The estimation of the natural coagulant dosage that is required to effectively remove these total suspended solids is usually determined by a jar test. This test seeks to achieve the highest efficiency of removal of the total suspended solids while reducing the final turbidity of waste water. This is often configured in iterative fashion, and requires significant experimentation and coagulant. This paper seeks to identify regression models that relate the clarification process parameters to the process outputs (final turbidity and total suspend solid) by the Response Surface Methodology (RSM) based on experiments of Central Composite Design (CCD) of experiments that involve three emerging natural coagulants. Several clarification process scenarios also were proposed and demonstrated using the Multi-Response Surface (MRS) with desirability functions. The experimental results were found to be in close agreement to what are provided by the regression models. This validates the use of the MRS-based methodology to achieve satisfactory predictions after minimal experimentation

Optimizing biodiesel production fromwaste cooking oil using genetic algorithm-based support vector machines

The ever increasing fuel demands and the limitations of oil reserves have motivated research of renewable and sustainable energy resources to replace, even partially, fossil fuels, which are having a serious environmental impact on global warming and climate change, excessive greenhouse emissions and deforestation. For this reason, an alternative, renewable and biodegradable combustible like biodiesel is necessary. For this purpose, waste cooking oil is a potential replacement for vegetable oils in the production of biodiesel. Direct transesterification of vegetable oils was undertaken to synthesize the biodiesel. Several variables controlled the process. The alkaline catalyst that is used, typically sodium hydroxide (NaOH) or potassium hydroxide (KOH), increases the solubility and speeds up the reaction. Therefore, the methodology that this study suggests for improving the biodiesel production is based on computing techniques for prediction and optimization of these process dimensions. The method builds and selects a group of regression models that predict several properties of biodiesel samples (viscosity turbidity, density, high heating value and yield) based on various attributes of the transesterification process (dosage of catalyst, molar ratio, mixing speed, mixing time, temperature, humidity and impurities). In order to develop it, a Box-Behnken type of Design of Experiment (DoE) was designed that considered the variables that were previously mentioned. Then, using this DoE, biodiesel production features were decided by conducting lab experiments to complete a dataset with real production properties. Subsequently, using this dataset, a group of regression models—linear regression and support vector machines (using linear kernel, polynomial kernel and radial basic function kernel)—were constructed to predict the studied properties of biodiesel and to obtain a better understanding of the process. Finally, several biodiesel optimization scenarios were reached through the application of genetic algorithms to the regression models obtained with greater precision. In this way, it was possible to identify the best combinations of variables, both independent and dependent. These scenarios were based mainly on a desire to improve the biodiesel yield by obtaining a higher heating value, while decreasing the viscosity, density and turbidity. These conditions were achieved when the dosage of catalyst was approximately 1 wt %