Solving some special cases of monomial ratio equations appearing frequently in physical and engineering problems

We first show that monomial ratio equations are not only very common in Physics and Engineering, but the natural type of equations in many practical problems. More precisely, in the case of models involving scale variables if the used formulas are not of this type they are not physically valid. The consequence is that when estimating the model parameters we are faced with systems of monomial ratio equations that are nonlinear and difficult to solve. In this paper, we provide an original algorithm to obtain the unique solutions of systems of equations made of linear combinations of monomial ratios whose coefficient matrix has a proper null space with low dimension that permits solving the problem in a simple way. Finally, we illustrate the proposed methods by their application to two practical problems from the hydraulic and structural fields.Peer ReviewedPostprint (published version

Analysis of measurement and simulation errors in structural system identification by observability techniques

This is the peer reviewed version of the following article: [Lei, J., Lozano-Galant, J. A., Nogal, M., Xu, D., and Turmo, J. (2017) Analysis of measurement and simulation errors in structural system identification by observability techniques. Struct. Control Health Monit., 24: . doi: 10.1002/stc.1923.], which has been published in final form at http://onlinelibrary.wiley.com/wol1/doi/10.1002/stc.1923/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.During the process of structural system identification, errors are unavoidable. This paper analyzes the effects of measurement and simulation errors in structural system identification based on observability techniques. To illustrate the symbolic approach of this method a simply supported beam is analyzed step-by-step. This analysis provides, for the very first time in the literature, the parametric equations of the estimated parameters. The effects of several factors, such as errors in a particular measurement or in the whole measurement set, load location, measurement location or sign of the errors, on the accuracy of the identification results are also investigated. It is found that error in a particular measurement increases the errors of individual estimations, and this effect can be significantly mitigated by introducing random errors in the whole measurement set. The propagation of simulation errors when using observability techniques is illustrated by two structures with different measurement sets and loading cases. A fluctuation of the observed parameters around the real values is proved to be a characteristic of this method. Also, it is suggested that a sufficient combination of different load cases should be utilized to avoid the inaccurate estimation at the location of low curvature zones.Peer ReviewedPostprint (author's final draft

Distribution planning in a weather-dependent scenario with stochastic travel times: a simheuristics approach

In real-life logistics, distribution plans might be affected by weather conditions (rain, snow, and fog), since they might have a significant effect on traveling times and, therefore, on total distribution costs. In this paper, the distribution problem is modeled as a multi-depot vehicle routing problem with stochastic traveling times. These traveling times are not only stochastic in nature but the specific probability distribution used to model them depends on the particular weather conditions on the delivery day. In order to solve the aforementioned problem, a simheuristic approach combining simulation within a biased-randomized heuristic framework is proposed. As the computational experiments will show, our simulation-optimization algorithm is able to provide high-quality solutions to this NP-hard problem in short computing times even for large-scale instances. From a managerial perspective, such a tool can be very useful in practical applications since it helps to increase the efficiency of the logistics and transportation operations.Peer ReviewedPostprint (published version

Distribution planning in a weather-dependent scenario with stochastic travel times: a simheuristics approach

In real-life logistics, distribution plans might be affected by weather conditions (rain, snow, and fog), since they might have a significant effect on traveling times and, therefore, on total distribution costs. In this paper, the distribution problem is modeled as a multi-depot vehicle routing problem with stochastic traveling times. These traveling times are not only stochastic in nature but the specific probability distribution used to model them depends on the particular weather conditions on the delivery day. In order to solve the aforementioned problem, a simheuristic approach combining simulation within a biased-randomized heuristic framework is proposed. As the computational experiments will show, our simulation-optimization algorithm is able to provide high-quality solutions to this NP-hard problem in short computing times even for large-scale instances. From a managerial perspective, such a tool can be very useful in practical applications since it helps to increase the efficiency of the logistics and transportation operations.Peer ReviewedPostprint (published version

Constrained observability method in static structural system identification

This is the peer reviewed version of the following article: [Lei J, Nogal M, Lozano-Galant JA, Xu D, Turmo J. Constrained observability method in static structural system identification. Struct Control Health Monit. 2018;25:e2040. https://doi.org/10.1002/stc.2040], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/stc.2040/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.Identifiability of parameters in structural system identification (SSI) is of primary importance in any SSI method. It depends on the number and the location of the measurements, which is linked with sensor configuration. In this paper, under the framework of SSI by observability method (OM), the number of necessary measurements to identify all parameters of structural system was clarified first. Then, an example was solved step by step to show the lacking constraints among unknowns in SSI by OM. In a frame example, it was found that no measurement set having as many measurements as the number of unknowns was able to identify all parameters. To further understand this phenomenon, the observability of a simply supported beam was analyzed in an exhaustive way using 252 possible measurement sets. Three quarters of these sets were not able to identify all the parameters. In order to solve this issue, for the very first time, SSI by constrained observability method (COM), which appends the nonlinear constraints to SSI by OM, was proposed. With SSI by COM applied, the observability of the structural parameters with respect to the 252 sets was greatly improved. Finally, the efficacy of SSI by COM was verified by a 13-story frame building.Peer ReviewedPostprint (author's final draft

ProFatigue: a software program for probabilistic assessment of experimental fatigue data sets

In this work, the software program ProFatigue is presented as a practical tool for derivation of probabilistic S-N and ε-N fields from experimental fatigue data. The program provides an estimation of the parameters involved in the regression probabilistic Weibull fatigue model developed by the authors, allowing an advantageous application of both fields to the stress or strain based approaches in the fatigue design of structures and mechanical components. An extension to the analysis of more complex and varied lifetime problems as thermomechanical, multiaxial and fretting fatigue is possible by adopting suitable damage parameters proposed in the literature as driving force. Application to probabilistic assessment of cumulative damage and further program enhancement are now envisaged

Simulation-based education involving online and on-campus models in different European universities

Simulation-based education (SE) refers to the use of simulation software, tools, and serious games to enrich the teaching and learning processes. Advances in both computer hardware and software allow for employing innovative methodologies that make use of SE tools to enhance the learning experience. Moreover, thanks to the globalisation of e-learning practices, these educational experiences can be made available to students from different geographical regions and universities, which promotes the development of international and inter-university cooperation in education. This paper provides a review of recent works in the SE subject, with a focus on the areas of engineering, science, and management. It also discusses some experiences in SE involving different European universities and learning models. Finally, it also points out open challenges as well as noticeable trends

Métodos matemáticos para la predicción de tráfico

RESUMEN: Esta tesis desarrolla los siguientes modelos matemáticos originales: - Un modelo bayesiano conjugado para la reconstrucción y estimación de los flujos de tráfico a partir de la lectura de las matrículas, que permite calcular los diferentes flujos de tráfico, tales como los de rutas, origen-destino, arcos escaneados o arcos aforados. - Un modelo dinámico de recarga, continuo en el tiempo, consistente con la regla FIFO, que evalúa el efecto de la congestión teniendo en cuenta la interacción de los flujos de todas las rutas y su coincidencia en diferentes momentos y lugares. Se supone que el tiempo de recorrido del arco es función no lineal de los volúmenes de tráfico del mismo y, además, se tiene en cuenta el efecto derivado de la congestión en los arcos aguas abajo de la ruta. - Un modelo de tráfico dinámico con demanda estocástica para la predicción de algunas variables de tráfico, tales como los tiempos de recorrido, flujos o densidad de los arcos y su evolución en el tiempo. Todos los modelos propuestos se han ensayado en redes de tráfico reales como son Cuenca y Ciudad Real (España) y el estado de Vermont (EE.UU.), con el fin de analizar sus características, validez de los resultados y los correspondientes requisitos computacionales. Además, se incluye una revisión de la literatura existente acerca de los modelos de tráfico estáticos y dinámicos.ABSTRACT: In this thesis we present the following mathematical models: - A conjugate Bayesian model for traffic flow reconstruction and estimation based on plate scanning, which permits us to identify the path, origin-destination and link flows. - A continuous dynamic traffic loading model. This FIFO rule consistent model evaluates the congestion effect taking into account the interaction of flows of all paths and their coincidence at different times and locations. It is assumed a non-linear link travel time function of the link volumes and considered the effect of a link congestion on the upstream route links. - A dynamic traffic model with stochastic demand for predicting some traffic variables such as link travel times, link flows or link densities and their time evolution in real networks. These three models have been tested with real traffic networks such as the Cuenca and Ciudad Real (Spain) networks and the Vermont-State (US) example, in order to analyze their characteristics and computational costs and validate results. Moreover, a literature revision about static and dynamic traffic models is included

Comparison among different structural system identification methods

The observability techniques have been proposed to deal with structural system identification under static loading tests. Up to now, this method has only been analyzed from a symbolical point of view. Despite the elegance of this approach, this mathematic analysis is far from being applicable in actual structures. To fill this gap, this paper presents a new observability procedure that combines both a symbolical and a numerical approach. To illustrate the potential of the proposed method, the observability technique is compared with two alternative methods presented in the literature. This comparison shows that, unlike to other analyzed methods, no information from the undamaged structure is required. Furthermore, the number of measurements required to be measured for damage detection is significantly reduced.Postprint (published version

Comparison among different structural system identification methods

The observability techniques have been proposed to deal with structural system identification under static loading tests. Up to now, this method has only been analyzed from a symbolical point of view. Despite the elegance of this approach, this mathematic analysis is far from being applicable in actual structures. To fill this gap, this paper presents a new observability procedure that combines both a symbolical and a numerical approach. To illustrate the potential of the proposed method, the observability technique is compared with two alternative methods presented in the literature. This comparison shows that, unlike to other analyzed methods, no information from the undamaged structure is required. Furthermore, the number of measurements required to be measured for damage detection is significantly reduced