Optimum adhesive thickness in structural adhesives joints using statistical techniques base on Weibull distribution

The geometrical factors defining an adhesive joint are of great importance as its design greatly conditions the performance of the bonding. One of the most relevant geometrical factors is the thickness of the adhesive as it decisively influences the mechanical properties of the bonding and has a clear economic impact on the manufacturing processes or long runs. The traditional mechanical joints (riveting, welding, etc.) are characterised by a predictable performance, and are very reliable in service conditions. Thus, structural adhesive joints will only be selected in industrial applications demanding mechanical requirements and adverse environmental conditions if the suitable reliability (the same or higher than the mechanical joints) is guaranteed. For this purpose, the objective of this paper is to analyse the influence of the adhesive thickness on the mechanical behaviour of the joint and, by means of a statistical analysis based on Weibull distribution, propose the optimum thickness for the adhesive combining the best mechanical performance and high reliability. This procedure, which is applicable without a great deal of difficulty to other joints and adhesives, provides a general use for a more reliable use of adhesive bondings and, therefore, for a better and wider use in the industrial manufacturing processes.

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability p in inverse binomial sampling is considered in this paper. For any estimator pˆ , its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters a and b for pˆ

p , respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as p→0, and which guarantee that, for any p∈(0,1), the risk is lower than its asymptotic value. This allows selecting the required number of successes, r, to meet a prescribed quality irrespective of the unknown p. In addition, the proposed estimators are shown to be approximately minimax when a/b does not deviate too much from 1, and asymptotically minimax as r→∞ when a=b.

Improved estimation of Weibull Parameters considering unreliability uncertainties

We propose a linear regression method for estimating Weibull parameters from life tests. The method uses stochastic models of the unreliability at each failure instant. As a result, a heteroscedastic regression problem arises that is solved by weighted least squares minimization. The main feature of our method is an innovative s-normalization of the failure data models, to obtain analytic expressions of centers and weights for the regression. The method has been Monte Carlo contrasted with Benard?s approximation, and Maximum Likelihood Estimation; and it has the highest global scores for its robustness, and performance.

Fracture strength of drilled wafers: study of the stress concentration factor and determination of the weibull distribution of the fracture stress

In the photovoltaic field, the back contact solar cells technology has appeared as an alternative to the traditional silicon modules. This new type of cells places both positive and negative contacts on the back side of the cells maximizing the exposed surface to the light and making easier the interconnection of the cells in the module. The Emitter Wrap-Through solar cell structure presents thousands of tiny holes to wrap the emitter from the front surface to the rear surface. These holes are made in a first step over the silicon wafers by means of a laser drilling process. This step is quite harmful from a mechanical point of view since holes act as stress concentrators leading to a reduction in the strength of these wafers. This paper presents the results of the strength characterization of drilled wafers. The study is carried out testing the samples with the ring on ring device. Finite Element models are developed to simulate the tests. The stress concentration factor of the drilled wafers under this load conditions is determined from the FE analysis. Moreover, the material strength is characterized fitting the fracture stress of the samples to a three-parameter Weibull cumulative distribution function. The parameters obtained are compared with the ones obtained in the analysis of a set of samples without holes to validate the method employed for the study of the strength of silicon drilled wafers.

Intermittency reinjection probability density function with and without noise effects.

Intermittency phenomenon is a continuous route from regular to chaotic behaviour. Intermittency is an occurrence of a signal that alternates chaotic bursts between quasi-regular periods called laminar phases, driven by the so called reinjection probability density function (RPD). In this paper is introduced a new technique to obtain the RPD for type-II and III intermittency. The new RPD is more general than the classical one and includes the classical RPD as a particular case. The probabilities of the laminar length, the average laminar lengths and the characteristic relations are determined with and without lower bound of the reinjection in agreement with numerical simulations. Finally, it is analyzed the noise effect in intermittency. A method to obtain the noisy RPD is developed extending the procedure used in the noiseless case. The analytical results show a good agreement with numerical simulations.

Tree height integrated into pantropical forest biomass estimates

Aboveground tropical tree biomass and carbon storage estimates commonly ignore tree height (H). We estimate the effect of incorporating H on tropics-wide forest biomass estimates in 327 plots across four continents using 42 656 H and diameter measurements and harvested trees from 20 sites to answer the following questions: 1. What is the best H-model form and geographic unit to include in biomass models to minimise site-level uncertainty in estimates of destructive biomass? 2. To what extent does including H estimates derived in (1) reduce uncertainty in biomass estimates across all 327 plots? 3. What effect does accounting for H have on plot- and continental-scale forest biomass estimates? The mean relative error in biomass estimates of destructively harvested trees when including H (mean 0.06), was half that when excluding H (mean 0.13). Power- andWeibull-H models provided the greatest reduction in uncertainty, with regional Weibull-H models preferred because they reduce uncertainty in smaller-diameter classes (?40 cm D) that store about one-third of biomass per hectare in most forests. Propagating the relationships from destructively harvested tree biomass to each of the 327 plots from across the tropics shows that including H reduces errors from 41.8Mgha?1 (range 6.6 to 112.4) to 8.0Mgha?1 (?2.5 to 23.0). For all plots, aboveground live biomass was ?52.2 Mgha?1 (?82.0 to ?20.3 bootstrapped 95%CI), or 13%, lower when including H estimates, with the greatest relative reductions in estimated biomass in forests of the Brazilian Shield, east Africa, and Australia, and relatively little change in the Guiana Shield, central Africa and southeast Asia. Appreciably different stand structure was observed among regions across the tropical continents, with some storing significantly more biomass in small diameter stems, which affects selection of the best height models to reduce uncertainty and biomass reductions due to H. After accounting for variation in H, total biomass per hectare is greatest in Australia, the Guiana Shield, Asia, central and east Africa, and lowest in eastcentral Amazonia, W. Africa, W. Amazonia, and the Brazilian Shield (descending order). Thus, if tropical forests span 1668 million km2 and store 285 Pg C (estimate including H), then applying our regional relationships implies that carbon storage is overestimated by 35 PgC (31?39 bootstrapped 95%CI) if H is ignored, assuming that the sampled plots are an unbiased statistical representation of all tropical forest in terms of biomass and height factors. Our results show that tree H is an important allometric factor that needs to be included in future forest biomass estimates to reduce error in estimates of tropical carbon stocks and emissions due to deforestation.

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hatvap$, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters $a$ and $b$ for $\hatvap < p$ and $\hatvap > p$ respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as $p \rightarrow 0$, and which guarantee that, for any $p \in (0,1)$, the risk is lower than its asymptotic value. This allows selecting the required number of successes, $\nnum$, to meet a prescribed quality irrespective of the unknown $p$. In addition, the proposed estimators are shown to be approximately minimax when $a/b$ does not deviate too much from $1$, and asymptotically minimax as $\nnum \rightarrow \infty$ when $a=b$.

An interactive method of fuzzy probability elicitation in risk analysis

Expert knowledge is used to assign probabilities to events in many risk analysis models. However, experts sometimes find it hard to provide specific values for these probabilities, preferring to express vague or imprecise terms that are mapped using a previously defined fuzzy number scale. The rigidity of these scales generates bias in the probability elicitation process and does not allow experts to adequately express their probabilistic judgments. We present an interactive method for extracting a fuzzy number from experts that represents their probabilistic judgments for a given event, along with a quality measure of the probabilistic judgments, useful in a final information filtering and analysis sensitivity process.

Survival probability of round and tape tethers against debris impact

The current space environment, consisting of manmade debris and micrometeoroids, poses a risk to safe operations in space, and the situation is continuously deteriorating due to in-orbit debris collisions and to new satellite launches. Bare electrodynamic tethers can provide an efficient mechanism for rapid deorbiting of satellites from low Earth orbit at end of life. Because of its particular geometry (length very much larger than cross-sectional dimensions), a tether may have a relatively high risk of being severed by the single impact of small debris. The rates of fatal impact of orbital debris on round and tape tethers of equal length and mass, evaluated with an analytical approximation to debris flux modeled by NASA’s ORDEM2000, shows much higher survival probability for tapes. A comparative numerical analysis using debris flux model ORDEM2000 and ESA’s MASTER2005 validates the analytical result and shows that, for a given time in orbit, a tape has a probability of survival of about one and a half orders of magnitude higher than a round tether of equal mass and length. Because deorbiting from a given altitude is much faster for the tape due to its larger perimeter, its probability of survival in a practical sense is quite high.

Analysis of the influence of the different variables involved in a damage progression probability model

Motivated by these difficulties, Castillo et al. (2012) made some suggestions on how to build consistent stochastic models avoiding the selection of easy to use mathematical functions, which were replaced by those resulting from a set of properties to be satisfied by the model.

Estimación y evolución temporal de variables forestales con tecnología LiDAR en el Valle de la Fuenfría (Cercedilla, Madrid)

Este estudio profundiza en la estimación de variables forestales a partir de información LiDAR en el Valle de la Fuenfría (Cercedilla, Madrid). Para ello se dispone de dos vuelos realizados con sensor LiDAR en los años 2002 y 2011 y en el invierno de 2013 se ha realizado un inventario de 60 parcelas de campo. En primer lugar se han estimado seis variables dasométricas (volumen, área basimétrica, biomasa total, altura dominante, densidad y diámetro medio cuadrático) para 2013, tanto a nivel de píxel como a nivel de rodal y monte. Se construyeron modelos de regresión lineal múltiple que permitieron estimar con precisión dichas variables. En segundo lugar, se probaron diferentes métodos para la estimación de la distribución diamétrica. Por un lado, el método de predicción de percentiles y, por otro lado, el método de predicción de parámetros. Este segundo método se probó para una función Weibull simple, una función Weibull doble y una combinación de ambas según la distribución que mejor se ajustaba a cada parcela. Sin embargo, ninguno de los métodos ha resultado suficientemente válido para predecir la distribución diamétrica. Por último se estimaron el crecimiento en volumen y área basimétrica a partir de la comparación de los vuelos del 2002 y 2011. A pesar de que la tecnología LiDAR era diferente y solo se disponía de un inventario completo, realizado en 2013, los modelos construidos presentan buenas bondades de ajuste. Asimismo, el crecimiento a nivel de pixel se ha mostrado estar relacionado de forma estadísticamente significativa con la pendiente, orientación y altitud media del píxel. ABSTRACT This project goes in depth on the estimation of forest attributes by means of LiDAR data in Fuenfria’s Valley (Cercedilla, Madrid). The available information was two LiDAR flights (2002 and 2011) and a forest inventory consisting of 60 plots (2013). First, six different dasometric attributes (volume, basal area, total aboveground biomass, top height, density and quadratic mean diameter) were estimated in 2013 both at a pixel, stand and forest level. The models were developed using multiple linear regression and were good enough to predict these attributes with great accuracy. Second, the measured diameter distribution at each plot was fitted to a simple and a double Weibull distribution and different methods for its estimation were tested. Neither parameter prediction method nor percentile prediction method were able to account for the diameter distribution. Finally, volume and top height growths were estimated comparing 2011 LiDAR flight with 2002 LiDAR flight. Even though the LiDAR technology was not the same and there was just one forest inventory with sample plots, the models properly explain the growth. Besides, growth at each pixel is significantly related to its average slope, orientation and altitude.

Change of extreme rainfall indexes at Ebro River Basin

The purpose of this work is to provide a description of the heavy rainfall phenomenon on statistical tools from a Spanish region. We want to quantify the effect of the climate change to verify the rapidity of its evolution across the variation of the probability distributions. Our conclusions have special interest for the agrarian insurances, which may make estimates of costs more realistically. In this work, the analysis mainly focuses on: The distribution of consecutive days without rain for each gauge stations and season. We estimate density Kernel functions and Generalized Pareto Distribution (GPD) for a network of station from the Ebro River basin until a threshold value u. We can establish a relation between distributional parameters and regional characteristics. Moreover we analyze especially the tail of the probability distribution. These tails are governed by law of power means that the number of events n can be expressed as the power of another quantity x : n(x) = x? . ? can be estimated as the slope of log-log plot the number of events and the size. The most convenient way to analyze n(x) is using the empirical probability distribution. Pr(X mayor que x) ? x-?. The distribution of rainfall over percentile of order 0.95 from wet days at the seasonal scale and in a yearly scale with the same treatment of tails than in the previous section.

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data

Consideration of tip speed limitations in preliminary analysis of minimum COE wind turbines

A relation between Cost Of Energy, COE, maximum allowed tip speed, and rated wind speed, is obtained for wind turbines with a given goal rated power. The wind regime is characterised by the corresponding parameters of the probability density function of wind speed. The non-dimensional characteristics of the rotor: number of blades, the blade radial distributions of local solidity, twist angle, and airfoil type, play the role of parameters in the mentioned relation. The COE is estimated using a cost model commonly used by the designers. This cost model requires basic design data such as the rotor radius and the ratio between the hub height and the rotor radius. Certain design options, DO, related to the technology of the power plant, tower and blades are also required as inputs. The function obtained for the COE can be explored to �nd those values of rotor radius that give rise to minimum cost of energy for a given wind regime as the tip speed limitation changes. The analysis reveals that iso-COE lines evolve parallel to iso-radius lines for large values of limit tip speed but that this is not the case for small values of the tip speed limits. It is concluded that, as the tip speed limit decreases, the optimum decision for keeping minimum COE values can be: a) reducing the rotor radius for places with high weibull scale parameter or b) increasing the rotor radius for places with low weibull scale parameter

Pedestrian wind comfort: feasibility study of criteria homogenisation

One of the aims of COST C14 action is the assessment and evaluation of pedestrian wind comfort. At present there is no general rule available that is applied across Europe. There are several criteria that have been developed and applied in different countries. These criteria are based on the definition of two independent parameters, a threshold effective wind speed and a probability of exceedence of this threshold speed. The difficulty of the criteria comparison arises from the two-dimensional character of the criteria definition. An effort is being made to compare these criteria, trying both to find commonalities and to clearly identify differences, in order to build up the basis for the next step: to try to define common criteria (perhaps with regional and seasonal variations). The first point is to define clearly the threshold effective wind speed (mean velocity definition parameters: averaging interval and reference height) and equivalence between different ways of defining the threshold effective wind speed (mean wind speed, gust equivalent mean, etc.) in comparable terms (as far as possible). It can be shown that if the wind speed at a given location is defined in terms of a probability distribution, e.g. Weibull function, a given criterion is satisfied by an infinite set of wind conditions, that is, of probability distributions. The criterion parameters and the Weibull function parameters are linked to each other, establishing a set called iso-criteria lines (the locus of the Weibull function parameters that fulfil a given criterion). The relative position of iso-criteria lines when displayed in a suitable two-dimensional plane facilitates the comparison of comfort criteria. The comparison of several wind comfort criteria, coming from several institutes is performed, showing the feasibility and limitations of the method.