Domestic hot water consumption vs. solar thermal energy storage: the optimum size of the storage tank

Many efforts have been made in order to adequate the production of a solar thermal collector field to the consumption of domestic hot water of the inhabitants of a building. In that sense, much has been achieved in different domains: research agencies, government policies and manufacturers. However, most of the design rules of the solar plants are based on steady state models, whereas solar irradiance, consumption and thermal accumulation are inherently transient processes. As a result of this lack of physical accuracy, thermal storage tanks are sometimes left to be as large as the designer decides without any aforementioned precise recommendation. This can be a problem if solar thermal systems are meant to be implemented in nowadays buildings, where there is a shortage of space. In addition to that, an excessive storage volume could not result more efficient in many residential applications, but costly, extreme in space consumption and in some cases too heavy. A proprietary transient simulation program has been developed and validated with a detailed measurement campaign in an experimental facility. In situ environmental data have been obtained through a whole year of operation. They have been gathered at intervals of 10 min for a solar plant of 50 m2 with a storage tank of 3 m3, including the equipment for domestic hot water production of a typical apartment building. This program has been used to obtain the design and dimensioning criteria of DHW solar plants under daily transient conditions throughout a year and more specifically the size of the storage tank for a multi storey apartment building. Comparison of the simulation results with the current Spanish regulation applicable, “Código Técnico de la Edificación” (CTE 2006), offers fruitful details and establishes solar facilities dimensioning criteria.

Maximum likelihood estimation of new state space models for operational modal analysis

The modal analysis of a structural system consists on computing its vibrational modes. The experimental way to estimate these modes requires to excite the system with a measured or known input and then to measure the system output at different points using sensors. Finally, system inputs and outputs are used to compute the modes of vibration. When the system refers to large structures like buildings or bridges, the tests have to be performed in situ, so it is not possible to measure system inputs such as wind, traffic, . . .Even if a known input is applied, the procedure is usually difficult and expensive, and there are still uncontrolled disturbances acting at the time of the test. These facts led to the idea of computing the modes of vibration using only the measured vibrations and regardless of the inputs that originated them, whether they are ambient vibrations (wind, earthquakes, . . . ) or operational loads (traffic, human loading, . . . ). This procedure is usually called Operational Modal Analysis (OMA), and in general consists on to fit a mathematical model to the measured data assuming the unobserved excitations are realizations of a stationary stochastic process (usually white noise processes). Then, the modes of vibration are computed from the estimated model. The first issue investigated in this thesis is the performance of the Expectation- Maximization (EM) algorithm for the maximum likelihood estimation of the state space model in the field of OMA. The algorithm is described in detail and it is analysed how to apply it to vibration data. After that, it is compared to another well known method, the Stochastic Subspace Identification algorithm. The maximum likelihood estimate enjoys some optimal properties from a statistical point of view what makes it very attractive in practice, but the most remarkable property of the EM algorithm is that it can be used to address a wide range of situations in OMA. In this work, three additional state space models are proposed and estimated using the EM algorithm: • The first model is proposed to estimate the modes of vibration when several tests are performed in the same structural system. Instead of analyse record by record and then compute averages, the EM algorithm is extended for the joint estimation of the proposed state space model using all the available data. • The second state space model is used to estimate the modes of vibration when the number of available sensors is lower than the number of points to be tested. In these cases it is usual to perform several tests changing the position of the sensors from one test to the following (multiple setups of sensors). Here, the proposed state space model and the EM algorithm are used to estimate the modal parameters taking into account the data of all setups. • And last, a state space model is proposed to estimate the modes of vibration in the presence of unmeasured inputs that cannot be modelled as white noise processes. In these cases, the frequency components of the inputs cannot be separated from the eigenfrequencies of the system, and spurious modes are obtained in the identification process. The idea is to measure the response of the structure corresponding to different inputs; then, it is assumed that the parameters common to all the data correspond to the structure (modes of vibration), and the parameters found in a specific test correspond to the input in that test. The problem is solved using the proposed state space model and the EM algorithm. Resumen El análisis modal de un sistema estructural consiste en calcular sus modos de vibración. Para estimar estos modos experimentalmente es preciso excitar el sistema con entradas conocidas y registrar las salidas del sistema en diferentes puntos por medio de sensores. Finalmente, los modos de vibración se calculan utilizando las entradas y salidas registradas. Cuando el sistema es una gran estructura como un puente o un edificio, los experimentos tienen que realizarse in situ, por lo que no es posible registrar entradas al sistema tales como viento, tráfico, . . . Incluso si se aplica una entrada conocida, el procedimiento suele ser complicado y caro, y todavía están presentes perturbaciones no controladas que excitan el sistema durante el test. Estos hechos han llevado a la idea de calcular los modos de vibración utilizando sólo las vibraciones registradas en la estructura y sin tener en cuenta las cargas que las originan, ya sean cargas ambientales (viento, terremotos, . . . ) o cargas de explotación (tráfico, cargas humanas, . . . ). Este procedimiento se conoce en la literatura especializada como Análisis Modal Operacional, y en general consiste en ajustar un modelo matemático a los datos registrados adoptando la hipótesis de que las excitaciones no conocidas son realizaciones de un proceso estocástico estacionario (generalmente ruido blanco). Posteriormente, los modos de vibración se calculan a partir del modelo estimado. El primer problema que se ha investigado en esta tesis es la utilización de máxima verosimilitud y el algoritmo EM (Expectation-Maximization) para la estimación del modelo espacio de los estados en el ámbito del Análisis Modal Operacional. El algoritmo se describe en detalle y también se analiza como aplicarlo cuando se dispone de datos de vibraciones de una estructura. A continuación se compara con otro método muy conocido, el método de los Subespacios. Los estimadores máximo verosímiles presentan una serie de propiedades que los hacen óptimos desde un punto de vista estadístico, pero la propiedad más destacable del algoritmo EM es que puede utilizarse para resolver un amplio abanico de situaciones que se presentan en el Análisis Modal Operacional. En este trabajo se proponen y estiman tres modelos en el espacio de los estados: • El primer modelo se utiliza para estimar los modos de vibración cuando se dispone de datos correspondientes a varios experimentos realizados en la misma estructura. En lugar de analizar registro a registro y calcular promedios, se utiliza algoritmo EM para la estimación conjunta del modelo propuesto utilizando todos los datos disponibles. • El segundo modelo en el espacio de los estados propuesto se utiliza para estimar los modos de vibración cuando el número de sensores disponibles es menor que vi Resumen el número de puntos que se quieren analizar en la estructura. En estos casos es usual realizar varios ensayos cambiando la posición de los sensores de un ensayo a otro (múltiples configuraciones de sensores). En este trabajo se utiliza el algoritmo EM para estimar los parámetros modales teniendo en cuenta los datos de todas las configuraciones. • Por último, se propone otro modelo en el espacio de los estados para estimar los modos de vibración en la presencia de entradas al sistema que no pueden modelarse como procesos estocásticos de ruido blanco. En estos casos, las frecuencias de las entradas no se pueden separar de las frecuencias del sistema y se obtienen modos espurios en la fase de identificación. La idea es registrar la respuesta de la estructura correspondiente a diferentes entradas; entonces se adopta la hipótesis de que los parámetros comunes a todos los registros corresponden a la estructura (modos de vibración), y los parámetros encontrados en un registro específico corresponden a la entrada en dicho ensayo. El problema se resuelve utilizando el modelo propuesto y el algoritmo EM.

State of the Art and Future Trends in Grid Codes Applicable to Isolated Electrical Systems

Electrical power systems are changing their traditional structure, which was based on a little number of large generating power plants placed at great distances from loads by new models that tend to split the big production nodes in many smaller ones. The set of small groups which are located close to consumers and provide safe and quality energy is called distributed generation (DG). The proximity of the sources to the loads reduces losses associated with transportation and increases overall system efficiency. DG also favors the inclusion of renewable energy sources in isolated electrical systems or remote microgrids, because they can be installed where the natural resource is located. In both cases, as weak grids unable to get help from other nearby networks, it is essential to ensure appropriate behavior of DG sources to guarantee power system safety and stability. The grid codes sets out the technical requirements to be fulfilled for the sources connected in these electrical networks. In technical literature it is rather easy to find and compare grid codes for interconnected electrical systems. However, the existing literature is incomplete and sparse regarding isolated electrical systems and this happens due to the difficulties inherent in the pursuit of codes. Some countries have developed their own legislation only for their island territory (as Spain or France), others apply the same set of rules as in mainland, another group of island countries have elaborated a complete grid code for all generating sources and some others lack specific regulation. This paper aims to make a complete review of the state of the art in grid codes applicable to isolated systems, setting the comparison between them and defining the guidelines predictably followed by the upcoming regulations in these particular systems.

Seven challenges for RESTful transaction models

The REpresentational State Transfer (REST) architectural style describes the design principles that made the World Wide Web scalable and the same principles can be applied in enterprise context to do loosely coupled and scalable application integration. In recent years, RESTful services are gaining traction in the industry and are commonly used as a simpler alternative to SOAP Web Services. However, one of the main drawbacks of RESTful services is the lack of standard mechanisms to support advanced quality-ofservice requirements that are common to enterprises. Transaction processing is one of the essential features of enterprise information systems and several transaction models have been proposed in the past years to fulfill the gap of transaction processing in RESTful services. The goal of this paper is to analyze the state-of-the-art RESTful transaction models and identify the current challenges.

State space models for multi-setup operational modal analysis

Operational Modal Analysis consists on estimate the modal parameters of a structure (natural frequencies, damping ratios and modal vectors) from output-only vibration measurements. The modal vectors can be only estimated where a sensor is placed, so when the number of available sensors is lower than the number of tested points, it is usual to perform several tests changing the position of the sensors from one test to the following (multiple setups of sensors): some sensors stay at the same position from setup to setup, and the other sensors change the position until all the tested points are covered. The permanent sensors are then used to merge the mode shape estimated at each setup (or partial modal vectors) into global modal vectors. Traditionally, the partial modal vectors are estimated independently setup by setup, and the global modal vectors are obtained in a postprocess phase. In this work we present two state space models that can be used to process all the recorded setups at the same time, and we also present how these models can be estimated using the maximum likelihood method. The result is that the global mode shape of each mode is obtained automatically, and subsequently, a single value for the natural frequency and damping ratio of the mode is computed. Finally, both models are compared using real measured data.

On nonlinearity in neural encoding models applied to the primary visual cortex

Within the regression framework, we show how different levels of nonlinearity influence the instantaneous firing rate prediction of single neurons. Nonlinearity can be achieved in several ways. In particular, we can enrich the predictor set with basis expansions of the input variables (enlarging the number of inputs) or train a simple but different model for each area of the data domain. Spline-based models are popular within the first category. Kernel smoothing methods fall into the second category. Whereas the first choice is useful for globally characterizing complex functions, the second is very handy for temporal data and is able to include inner-state subject variations. Also, interactions among stimuli are considered. We compare state-of-the-art firing rate prediction methods with some more sophisticated spline-based nonlinear methods: multivariate adaptive regression splines and sparse additive models. We also study the impact of kernel smoothing. Finally, we explore the combination of various local models in an incremental learning procedure. Our goal is to demonstrate that appropriate nonlinearity treatment can greatly improve the results. We test our hypothesis on both synthetic data and real neuronal recordings in cat primary visual cortex, giving a plausible explanation of the results from a biological perspective.

Using ecological niche models to support tree species selection for forest restoration planning in largely deforested regions

Species selection for forest restoration is often supported by expert knowledge on local distribution patterns of native tree species. This approach is not applicable to largely deforested regions unless enough data on pre-human tree species distribution is available. In such regions, ecological niche models may provide essential information to support species selection in the framework of forest restoration planning. In this study we used ecological niche models to predict habitat suitability for native tree species in "Tierra de Campos" region, an almost totally deforested area of the Duero Basin (Spain). Previously available models provide habitat suitability predictions for dominant native tree species, but including non-dominant tree species in the forest restoration planning may be desirable to promote biodiversity, specially in largely deforested areas were near seed sources are not expected. We used the Forest Map of Spain as species occurrence data source to maximize the number of modeled tree species. Penalized logistic regression was used to train models using climate and lithological predictors. Using model predictions a set of tools were developed to support species selection in forest restoration planning. Model predictions were used to build ordered lists of suitable species for each cell of the study area. The suitable species lists were summarized drawing maps that showed the two most suitable species for each cell. Additionally, potential distribution maps of the suitable species for the study area were drawn. For a scenario with two dominant species, the models predicted a mixed forest (Quercus ilex and a coniferous tree species) for almost one half of the study area. According to the models, 22 non-dominant native tree species are suitable for the study area, with up to six suitable species per cell. The model predictions pointed to Crataegus monogyna, Juniperus communis, J.oxycedrus and J.phoenicea as the most suitable non-dominant native tree species in the study area. Our results encourage further use of ecological niche models for forest restoration planning in largely deforested regions.

W-singularities in cosmological models

Recently a new type of cosmological singularity has been postulated for infinite barotropic index w in the equation of state p = wρ of the cosmological fluid, but vanishing pressure and density at the singular event. Apparently the barotropic index w would be the only physical quantity to blow up at the singularity. In this talk we would like to discuss the strength of such singularities and compare them with other types. We show that they are weak singularities

Equation of state for hot dense matter using a relativistic screened hydrogenic model

The study of matter under conditions of high density, pressure, and temperature is a valuable subject for inertial confinement fusion (ICF), astrophysical phenomena, high-power laser interaction with matter, etc. In all these cases, matter is heated and compressed by strong shocks to high pressures and temperatures, becomes partially or completely ionized via thermal or pressure ionization, and is in the form of dense plasma. The thermodynamics and the hydrodynamics of hot dense plasmas cannot be predicted without the knowledge of the equation of state (EOS) that describes how a material reacts to pressure and how much energy is involved. Therefore, the equation of state often takes the form of pressure and energy as functions of density and temperature. Furthermore, EOS data must be obtained in a timely manner in order to be useful as input in hydrodynamic codes. By this reason, the use of fast, robust and reasonably accurate atomic models, is necessary for computing the EOS of a material.

Mathematical models for the arrangement and the cleaning of the river basin and surroundings of the river sandy grounds to its passage by the city of Salta (Argentina)

The province of Salta is located the Northwest of Argentina in the border with Bolivia, Chile and Paraguay. Its Capital is the city of Salta that concentrates half of the inhabitants of the province and has grown to 600000 hab., from a small active Spanish town well founded in 1583. The city is crossed by the Arenales River descending from close mountains at North, source of water and end of sewers. But with actual growing it has become a focus of infection and of remarkable unhealthiness. It is necessary to undertake a plan for the recovery of the river, directed to the attainment of the well-being and to improve the life?s quality of the Community. The fundamental idea of the plan is to obtain an ordering of the river basin and an integral management of the channel and its surroundings, including the cleaning out. The improvement of the water?s quality, the healthiness of the surroundings and the improvement of the environment, must go hand by hand with the development of sport activities, of relaxation, tourism, establishment of breeding grounds, kitchen gardens, micro enterprises with clean production and other actions that contribute to their benefit by the society, that being a basic factor for their care and sustainable use. The present pollution is organic, chemical, industrial, domestic, due to the disposition of sweepings and sewer effluents that affects not only the flora and small fauna, destroying the biodiversity, but also to the health of people living in their margins. Within the plan it will be necessary to consider, besides hydric and environmental cleaning and the prevention of floods, the planning of the extraction of aggregates, the infrastructure and consolidation of margins works and the arrangement of all the river basin. It will be necessary to consider the public intervention at state, provincial and local level, and the private intervention. In the model it has been necessary to include the sub-model corresponding to the election of the entity to be the optimal instrument to reach the proposed objectives, giving an answer to the social, environmental and economic requirements. For that the authors have used multi-criteria decision methods to qualify and select alternatives, and for the programming of their implementation. In the model the authors have contemplated the short, average and long term actions. They conform a Paretooptimal alternative which secures the ordering, integral and suitable management of the basin of the Arenales River, focusing on its passage by the city of Salta.

Service needs forecasting: an approach for the automotive industry using analogies with medical ER management models.

During the past years, the industry has shifted position and moved towards “the luxury universe” whose customers are demanding, treating individuals as unique and valued customer for the business, offering vehicles produced with the state of the art technologies and implementing the highest finishing standards. Due to the competitive level in the market, car makers enable processes which equalizes customer services to E.R. management, being dealt with the maximum urgency that allows the comparison between both, car workshops and emergency rooms, where workshop bays or ramps will be equal to emergency boxes and skilled technicians are equivalent to the health care specialist, who will carry out tests and checks prior to afford any final operation, keeping the “patient” under control before it is back to normal utilization. This paper establishes a valid model for the automotive industry to estimate customer service demand forecasting under variable demand conditions using analogies with patient demand models used for the medical ER.

SERVICE NEEDS FORECASTING: An Approach for the Motor Industry Using Analogies with Medical ER Management Models.

During the past years, the industry has shifted position and moved towards “the luxury universe” whose customers are demanding, treating individuals as unique and valued customer for the business, offering vehicles produced with the state of the art technologies and implementing the highest finishing standards. Due to the competitive level in the market, motor makers enable processes which equalizes customer services to E.R. management, being dealt with the maximum urgency that allows the comparison between both, car workshops and emergency rooms, where workshop bays or ramps will be equal to emergency boxes and skilled technicians are equivalent to the health care specialist, who will carry out tests and checks prior to afford any final operation, keeping the “patient” under control before it is back to normal utilization. This paper ratify a valid model for the automotive industry to estimate customer service demand forecasting under variable demand conditions using analogies with patient demand models used for the medical ER

The Analysis of Airline Business Models in the Development of Possible Future Business Options

Innovations in the current interconnected world of organizations have lead to a focus on business models as a fundamental statement of direction and identity. Although industry transformations generally emanate from technological changes, recent examples suggest they may also be due to the introduction of new business models. In the past, different types of airline business models could be clearly separated from each other. However, this has changed in recent years partly due to the concentration process and partly to reaction caused by competitive pressure. At least it can be concluded that in future the distinction of different business models will remain less clear. To advance the use of business models as a concept, it is essential to be able to compare and perform analyses to identify the business models that may have the highest potential. This can essentially contribute to understanding the synergies and incompatibilities in the case of two airlines that are going in for a merger. This is illustrated by the example of Swiss Air-Lufthansa merger analysis. The idea is to develop quantitative methods and tools for comparing and analyzing Aeronautical/Airline business models. The paper identifies available methods of comparing airline business models and lays the ground work for a quantitative model of comparing airline business models. This can be a useful tool for business model analysis when two airlines are merged

Propuesta metodológica de aplicación sectorial de Análisis de Ciclo de Vida (ACV) para la evaluación ambiental de la edificación en España

La aplicación de criterios de sostenibilidad ha de entenderse como el procedimiento esencial para la necesaria reconversión del sector de la construcción, que movilizando el 10% de la economía mundial, representa más de la tercera parte del consumo mundial de recursos, en torno al 30-40% del consumo energético y emisiones de gases de efecto invernadero, 30-40% de la generación de residuos y el 12% de todo el gasto en agua dulce del planeta. La presente investigación se enmarca en una estrategia general de promover la evaluación de la sostenibilidad en la edificación en el contexto español, dando un primer paso centrado en la evaluación del comportamiento ambiental. El hilo conductor de la investigación parte de la necesidad de establecer un marco teórico de sostenibilidad, que permita clarificar conceptos y definir criterios de valoración adecuados. Como siguiente paso, la investigación se dirige a la revisión del panorama internacional de normativa e instrumentos voluntarios, con el objetivo de clarificar el difuso panorama que caracteriza a la sostenibilidad en el sector de la edificación en la actualidad y enmarcar la investigación en un contexto de políticas y programaciones ya existentes. El objetivo principal reside en el planteamiento de una metodología de evaluación de los aspectos o impactos ambientales asociados al ciclo de vida de la edificación, aplicable al contexto español, como una de las tres dimensiones que constituyen los pilares básicos de la sostenibilidad. Los ámbitos de evaluación de los aspectos sociales y económicos, para los que no existe actualmente un grado de definición metodológico suficientemente congruente, son adicionalmente examinados, de cara a ofrecer una visión holística de la evaluación. Previo al desarrollo de la propuesta, se aborda, en primer lugar, la descripción de las características básicas y limitaciones de la metodología de Análisis de Ciclo de Vida (ACV), para posteriormente proceder a profundizar en el estado del arte de aplicación de ACV a la edificación, realizando una revisión crítica de los trabajos de investigación que han sido desarrollados en los últimos años. Esta revisión permite extraer conclusiones sobre su grado de coherencia con el futuro entorno normativo e identificar dos necesidades prioritarias de actuación: -La necesidad de armonización, dadas las fuertes inconsistencias metodológicas detectadas, que imposibilitan la comparación de los resultados obtenidos en los trabajos de evaluación. -La necesidad de simplificación, dada la complejidad inherente a la evaluación, de modo que, manteniendo el máximo rigor, sea viable su aplicación práctica en el contexto español. A raíz de la participación en los trabajos de desarrollo normativo a nivel europeo, se ha adquirido una visión crítica sobre las implicaciones metodológicas de la normativa en definición, que permite identificar la hoja de ruta que marcará el escenario europeo en los próximos años. La definición de la propuesta metodológica integra los principios generales de aplicación de ACV con el protocolo metodológico establecido en la norma europea, considerando adicionalmente las referencias normativas de las prácticas constructivas en el contexto español. En el planteamiento de la propuesta se han analizado las posibles simplificaciones aplicables, con el objetivo de hacer viable su implementación, centrando los esfuerzos en la sistematización del concepto de equivalente funcional, el establecimiento de recomendaciones sobre el tipo de datos en función de su disponibilidad y la revisión crítica de los modelos de cálculo de los impactos ambientales. Las implicaciones metodológicas de la propuesta se describen a través de una serie de casos de estudio, que ilustran su viabilidad y las características básicas de aplicación. Finalmente, se realiza un recorrido por los aspectos que han sido identificados como prioritarios en la conformación del escenario de perspectivas futuras, líneas de investigación y líneas de acción. Abstract Sustainability criteria application must be understood as the essential procedure for the necessary restructuring of the construction sector, which mobilizes 10% of the world economy, accounting for more than one third of the consumption of the world's resources, around 30 - 40% of energy consumption and emissions of greenhouse gases, 30-40% of waste generation and 12% of all the fresh water use in the world. This research is in line with an overall strategy to promote the sustainability assessment of building in the Spanish context, taking a first step focused on the environmental performance assessment. The thread of the present research sets out from the need to establish a theoretical framework of sustainability which clarifies concepts and defines appropriate endpoints. As a next step, the research focuses on the review of the international panorama regulations and voluntary instruments, with the aim of clarifying the fuzzy picture that characterizes sustainability in the building sector at present while framing the research in the context of existing policies and programming. The main objective lies in the approach of a methodology for the assessment of the environmental impacts associated with the life cycle of building, applicable to the Spanish context, as one of the three dimensions that constitute the pillars of sustainability. The areas of assessment of social and economic issues, for which there is currently a degree of methodological definition consistent enough, are further examined, in order to provide a holistic view of the assessment. The description of the basic features and limitations of the methodology of Life Cycle Assessment (LCA) are previously addressed, later proceeding to deepen the state of the art of LCA applied to the building sector, conducting a critical review of the research works that have been developed in recent years. This review allows to establish conclusions about the degree of consistency with the future regulatory environment and to identify two priority needs for action: - The need for harmonization, given the strong methodological inconsistencies detected that prevent the comparison of results obtained in assessment works. - The need for simplification, given the inherent complexity of the assessment, so that, while maintaining the utmost rigor, make the practical application feasible in the Spanish context. The participation in the work of policy development at European level has helped to achieve a critical view of the methodological implications of the rules under debate, identifying the roadmap that will mark the European scene in the coming years. The definition of the proposed methodology integrates the general principles of LCA methodology with the protocol established in the European standard, also considering the regulatory standards to construction practices in the Spanish context. In the proposed approach, possible simplifications applicable have been analyzed, in order to make its implementation possible, focusing efforts in systematizing the functional equivalent concept, establishing recommendations on the type of data based on their availability and critical review of the calculation models of environmental impacts. The methodological implications of the proposal are described through a series of case studies, which illustrate the feasibility and the basic characteristics of its application. Finally, the main aspects related to future prospects, research lines and lines of action that have been identified as priorities are outlined.

Modal contribution and state space order selection in operational modal analysis

The estimation of modal parameters of a structure from ambient measurements has attracted the attention of many researchers in the last years. The procedure is now well established and the use of state space models, stochastic system identification methods and stabilization diagrams allows to identify the modes of the structure. In this paper the contribution of each identified mode to the measured vibration is discussed. This modal contribution is computed using the Kalman filter and it is an indicator of the importance of the modes. Also the variation of the modal contribution with the order of the model is studied. This analysis suggests selecting the order for the state space model as the order that includes the modes with higher contribution. The order obtained using this method is compared to those obtained using other well known methods, like Akaike criteria for time series or the singular values of the weighted projection matrix in the Stochastic Subspace Identification method. Finally, both simulated and measured vibration data are used to show the practicability of the derived technique. Finally, it is important to remark that the method can be used with any identification method working in the state space model.