Deterministic Sense Research Articles

Rocking block simulation based on numerical dissipation.

In this paper, a computational approach based on numerical dissipation is proposed to simulate rocking blocks. A rocking block is idealized as a solid body interacting with its foundation through a contact-based formulation. An implicit time integration scheme with numerical dissipation, set to optimally treat dissipation in contact problems, is employed. The numerical dissipation is ruled by the time step and the rocking dissipative phenomenon at impacts is accurately predicted without any damping model. A broad numerical campaign is conducted to define a regression law in analytic form for the setting of the time step, depending on the block size and aspect ratio, the contact stiffness, as well as the coefficient of restitution selected. The so-obtained regression law appears accurate and an a posteriori validation with cases not in the training dataset confirms the effectiveness of the approach. Finally, the comparison with available experimental tests highlights the approach efficacy for free rocking and harmonic loading cases (in a deterministic sense), and for earthquake-like loading cases (in a statistical sense). It is found that rocking blocks with sizes of interest for structural engineering (e.g., cultural heritage structures) can be simulated with time steps within 10-3 ÷ 10-1s, so allowing very fast computations.

Can big data and random forests improve avalanche runout estimation compared to simple linear regression?

Accurate prediction of snow avalanche runout-distances in a deterministic sense remains a challenge due to the complexity of all the physical properties involved. Therefore, in many locations including Norway, it has been common practice to define the runout distance using the angle from the starting point to the end of the runout zone (α-angle). We use a large dataset of avalanche events from Switzerland (N = 18,737) acquired using optical satellites to calculate the α-angle for each avalanche. The α-angles in our dataset are normally distributed with a mean of 33° and a standard deviation of 6.1°, which provides additional understanding and insights into α-angle distribution. Using a feature importance module in the Random Forest framework, we found the most important topographic parameter for predicting α-angles to be the average gradient from the release area to the β-point. Despite the large dataset and a modern machine learning (ML) method, we found the simple linear regression model to yield a higher performance than our ML attempts. This means that it is better to use a simple linear regression in an operational context.

The Effects of Interval Uncertainties on Dynamic Characteristics of a Rotor System Supported by Oil-Film Bearings

Rotating systems equipped with oil-film bearings are critical and common in many industrial machines. There are various non-random uncertainties in such fluid-lubricated dynamic systems. It is important to quantify the effects of uncertainties without adequate statistical information on the dynamics of rotor-bearing systems. In this paper, a rotor system with oil-film bearings at both ends is investigated considering many interval uncertainties. The rotating system is modeled in a deterministic sense. The Chebyshev interval method is used to track the propagation of different uncertainties. Deviations in the steady state responses, time history, and shaft orbits are calculated and comparatively discussed. Influence patterns of different interval parameters and dispersions in various dynamics are presented in detail. It is found that there can be global and local impacts as well as cumulative effects caused by multi-source uncertainties. The findings of the present study could be helpful for a more insightful dynamic analysis of rotor-bearing systems as well as their optimal design and maintenance.

Robust design optimisation under lack-of-knowledge uncertainty

Design optimization is common practice in engineering where the goal is to find the optimal combination of design parameters under prescribed constraints. However, some parameters may be impossible to define in a deterministic sense and may only be known with significant uncertainty. This limitation has led to an alternative definition of design optimality called robustness, where attention is payed to the variation around the optimal performance. Straightforward methods to solve robust optimization problems are usually limited in two ways: (1) the computation burden of the so-called ‘double-loop’ optimization problem hinders application to realistic models, and (2) the formalisms are typically limited to probabilistic descriptions of the uncertainty. This paper presents a formulation of the robust optimization problem under interval uncertainty and proposes a new approach taking advantage of the so-called adaptive Gaussian processes to solve it efficiently. The proposed surrogate approach mitigates the computational burden of the resolution, and a dedicated learning function is proposed to ensure iterative minimization of the surrogate modelling error and convergence towards the robust optimum. The algorithm uses a stopping criterion related to the level of confidence associated with the optimality of the solution. The approach is illustrated on six analytical and engineering benchmark problems.

Interval methods for lack-of-knowledge uncertainty in crash analysis

This paper deals with lack-of-knowledge uncertainty in complex non-linear simulations on a component level, i.e., a crashbox during frontal impact of a vehicle. Specifically, the focus lies on using interval field techniques to model the uncertain boundary conditions during impact simulations. The uncertainty considered in this work is the unknown mechanical response from the adjacent structure. This uncertainty is considered to be epistemic, representing the case where this adjacent structure is unknown at the time the impact analysis is performed. In practice, this refers to the situation where the adjacent structure is still under development, e.g., at a different department or even outsourced. In addition, the safety critical performance of both, the component and the overall structure should be guaranteed under a wide range of circumstances, which are typically encountered in real-life situations. Typically, car manufacturers use multidisciplinary optimisation to identify component designs that perform best on all requirements in a deterministic sense, while minimising the overall weight. Unfortunately, the results of such optimisation schemes are known to converge to an often non-robust optimum. As a result, the response of the structure may be sensitive to small changes in input parameters or boundary conditions.As an answer to these challenges, this paper proposes an interval field approach that accounts for the epistemic, i.e., lack-of-knowledge, uncertainty of the adjacent structures, even in an early design stage. This is accomplished by introducing a spatially varying uncertain mechanical compliance in elements that connect the component to the adjacent structures. These elements have an interval valued stiffness, which is varied along the component following the realisations of an interval field. The bounds on the interval-valued response quantities of interest, i.e., mean force and peak force, are identified using a differential evolution algorithm. This method is demonstrated on four case studies of a full overlap crash analysis of a rectangular crash box, which represents a generic component within the front structure of a vehicle. These case studies demonstrate the applicability and the potential of the proposed method. In addition, in the last case it is shown that the performance of the component can be assessed under an increasing range of uncertainty.

Privatized Distributed Anomaly Detection for Large-Scale Nonlinear Uncertain Systems

In this article two limitations in current distributed model based approaches for anomaly detection in large-scale uncertain nonlinear systems are addressed. The first limitation regards the high conservativeness of deterministic detection thresholds, against which a novel family of set-based thresholds is proposed. Such set-based thresholds are defined in a way to guarantee robustness in a user-defined probabilistic sense, rather than a deterministic sense. They are obtained by solving a chance-constrained optimization problem, thanks to a randomization technique based on the Scenario Approach. The second limitation regards the requirement, in distributed anomaly detection architectures, for different parties to regularly communicate local measurements. In settings where these parties want to preserve their privacy, communication may be undesirable. In order to preserve privacy and still allow for distributed detection to be implemented, a novel privacy-preserving mechanism is proposed and a so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">privatized communication</i> protocol is introduced. Theoretical guarantees on the achievable level of privacy, along with a characterization of the robustness properties of the proposed distributed threshold set design, taking into account the privatized communication scheme, are provided. Finally, simulation studies are included to illustrate our theoretical developments.

Probabilistic seismic analysis of single-layer reticulated shell structures controlled by viscoelastic dampers with an effective placement

In this paper, an effective placement of viscoelastic dampers on single-layer reticulated shell structures is proposed to mitigate seismic response. For comparison, an existing placement of viscoelastic dampers is also investigated. The effectiveness of the proposed placement of viscoelastic dampers is investigated from both deterministic and probabilistic perspectives. The single-layer reticulated shell structure is driven by the stochastic seismic ground motions, which are modeled via the random function based spectral representation method. The probability density evolution method is then implemented for probabilistic response and reliability analyses of the shell structure. A series of deterministic numerical simulations are first implemented under different earthquake excitations, including both actual and artificial seismic ground motions, to compare the control effects in deterministic sense. Then, the control effects of the proposed placement and the existing placement are compared in probabilistic sense, where the probabilistic responses, equivalent extreme value distributions and failure probabilities are extracted. Numerical results demonstrate that the seismic performance of the shell structure can be greatly improved by arranging the viscoelastic dampers with the proposed placement.

Structuring Multidimensional Data in the Study of the Development of Information Society in Russian Regions

In the article, the authors present the results of the analysis of the structure of multidimensional data on the factors of use of information and communication technologies (ICT) for the development of the information society in the Russian Federation. We chose the subjects of the Russian Federation as the objects of observations, and the average annual values of the corresponding factors of monitoring the development of the information society in the Russian Federation for the period from 2010 to 2017 as the factors of each object of observations. The study was carried out to reduce the set of factors of ICT use in the subjects of the Russian Federation and identify their structure. The analysis of the structure of factors is carried out by applying the Principal Component Analysis (PCA) method, implemented by the authors in the integrated development environment Rstudio. Through the use of the PCA method, we identified the structure of the initial factors of ICT use for the development of the information society in the Russian Federation and made their reduction. Then, we showed that the identified factor loads have specific semantic interpretations that consolidate the links of individual factors of ICT use for the development of the information society in the Russian Federation. The factor analysis carried out by us proves the effectiveness of the DCA method in research on the development of digitalisation of the regions of the Russian Federation for structuring the initial data and qualitative interpretation of the results. We have proved that factor loadings revealed employing the application of a method of RSA have the deterministic economic sense.

Deterministic Optimality of the Steady-State Behavior of the Kalman–Bucy Filter

In this letter, we provide a deterministic characterization of optimality of the steady-state behavior of the Kalman–Bucy filter, via an inverse optimal control argument. The result is achieved in two steps, both interesting per se . First, a singular linear-quadratic (LQ) optimal control problem is formulated and solved with respect to the innovation term of a classic Luenberger observer, hence yielding a LQ optimal observer. Then, such a construction is employed to interpret the optimality of the steady-state behavior of the celebrated Kalman–Bucy filter in a purely deterministic sense.

On stability of neutral-type linear stochastic time-delay systems with three different delays

We study in this paper the mean square exponential stability of neutral-type linear stochastic time-delay systems with three different delays by using the Lyapunov–Krasovskii functionals (LKFs) based approach. First, for a specified augmented state vector, a complete augmented LKF is constructed to contain all possible integrals so that its time-derivatives (understood in the deterministic sense) can be written as a linear function of the augmented vector. The redundant variables in the LKF are eliminated so as to reduce the computational burden. Moreover, the absolute value requirement of certain terms in the constructed LKFs are removed by analyzing carefully the complex relationship among these three different time delays. Then, for ten different cases of time delays, sufficient stability conditions in terms of linear matrix inequalities are obtained with the help of the Ito formula and properties of stochastic integrals. The degenerated cases that the delays satisfy some equalities are also discussed. A numerical example is employed to illustrate the effectiveness of the proposed approach.

The Bhattacharyya distance: Enriching the P-box in stochastic sensitivity analysis

Abstract The tendency of uncertainty analysis has promoted the transformation of sensitivity analysis from the deterministic sense to the stochastic sense. This work proposes a stochastic sensitivity analysis framework using the Bhattacharyya distance as a novel uncertainty quantification metric. The Bhattacharyya distance is utilised to provide a quantitative description of the P-box in a two-level procedure for both aleatory and epistemic uncertainties. In the first level, the aleatory uncertainty is quantified by a Monte Carlo process within the probability space of the cumulative distribution function. For each sample of the Monte Carlo simulation, the second level is performed to propagate the epistemic uncertainty by solving an optimisation problem. Subsequently, three sensitivity indices are defined based on the Bhattacharyya distance, making it possible to rank the significance of the parameters according to the reduction and dispersion of the uncertainty space of the system outputs. A tutorial case study is provided in the first part of the example to give a clear understanding of the principle of the approach with reproducible results. The second case study is the NASA Langley challenge problem, which demonstrates the feasibility of the proposed approach, as well as the Bhattacharyya distance metric, in solving such a large-scale, strong-nonlinear, and complex problem.

MANUFACTURING PROCESS MANAGEMENT

Production is aimed at the production of certain products in order to meet the requirements of the consumer, then the company as and society, under certain organizational conditions of the market. In other words, consumption is a constant process, and the process of production must be a continuous process. Repetition of the production process is a complex system consisting of elimination subsystems, that is, practically from four phases that are interconnected in terms of the impact of each other, but the entire production system must be manifested as one harmonious system. Production in this system is the first stage when the products are produced, which are then distributed and exchanged through the free market, so that in the end they are subject to the process of consumption in the appropriate form, but depending on the nature of the product. In such a system, the stages of production and consumption are the most important stages of the production process, while the role of other phases in terms of mediating the mentioned phases in a deterministic sense. As it is produced for consumers-in terms of consumption, then the process of production in society is dictated by the consumption itself. This practically means that consumption is always the basis and goal of production.

A metric on the similarity between two frequency response functions

This paper is focused on the development a new metric that can provide information on similarity between a frequency response function (FRF) from a finite element (FE) model and from an experiment to determine a target level of FE model accuracy in a deterministic sense. Typically, this metric could be used in setting a target level of model updating of an FE model that predicts structural-acoustic responses in high modal density mid-frequency regimes. The FRF similarity metric (FRFSM) is based on the likelihood between two FRFs with an assumed normal distribution of structural-acoustic responses. A normalization process over the frequency range of concern provides a metric value between 0 and 1. A numerical model that consists of two substructures and joint bushings objectively examined the characteristics of the proposed FRFSM with known parameter errors. The numerical study showed that the proposed FRFSM well represented the overall difference between two FRFs over the whole frequency band. Next, subjective evaluations that consist of evaluating the similarity for two pairs of FRFs by an expert group within an automotive company were conducted to assess the performance of the proposed metric. Subjective evaluations were conducted for various FRF sets in automotive noise and vibration responses. After compensating the subjective test results in calculating the correlation with the proposed metric, the performance of the metric was investigated. Additionally, the capability of the proposed metric when it represents the amount of updating in the frequency domain was illustrated by comparing the degree of correlation with the subjective evaluations. Comparisons with the results of the subjective evaluations showed that the FRFSM well represented the experts’ knowledge on the similarity of two FRFs, both in an absolute sense and in relative accuracies of the updated FE models.

PUBLIC ADMINISTRATION FROM THE STANDPOINT OF DETERMINISTIC SOCIAL SENSE (ARCHETYPAL APPROACH)

The features and the role of deterministic social sense in the context of the archetypical approach are considered in the article; the specifics of the existence of the above-mentioned phenomenon in relation to public administration are presented. The nature, principles of the functioning of archetypes as a direct, pragmatic decision-making factor of the personality are represented. It is argued that archetypes are significantly different from those historically established or transformed by human characters, whose senses are not mentally inherited, but transmitted from generation to generation. The emphasis is placed on the relevance of the archetypal approach for research in the management sector in general and deterministic social sense — in particular. The author emphasizes that the archetype is a direct pragmatic factor in personal decision-making, acting as a created internal complication that ensures the course of certain socially deter mined processes in the human brain. Attention is focused on the continuity of the concepts of “sense” and “culture”: from the moment of alienation of a person from the surrounding natural world, all thoughts, created things, found and used means and methods of actions are given meanings. Thus, the decision, that is, the choice, appears to be the natural basis for an individual’s being in ontological reality, acting as a necessary precondition for structuring his administrative, legal and so on needs in modern society. Further investigation of the archetypal approach to the study of the phenomenon of deterministic social sense is seen in the study of the features of citizens’ reflection on the images and symbols created by the government in order to achieve some behavioral manifestations in the latter, allowing more deeply and clearly understand the needs of the people, and also to update the relevant role of public administration in his life. At the same time, from the standpoint of social, psychological, culturological pragmatics etc., the archetype is the primary form of sense stratified according to the types described by Jung. This differentiation of this phenomenon is natural, due to its universalism, which allows us to speak about the degree of social adaptability of the latter.

Efficient data-driven reduced-order models for high-dimensional multiscale dynamical systems

We present two data-driven reduced-order models for high-dimensional multiscale dynamical systems. The methodologies proposed assume that the observed high-dimensional dynamic response is generated from some hidden low-dimensional processes. We argue that a single hidden process may not have the representative capability to accurately approximate the dynamical system exhibiting multiple timescales. Hence, the concept of mixture of experts is used where we represent the high-dimensional response as a function of multiple low-dimensional processes. The weight associated with each low-dimensional process is again governed by a separate dynamical process. The primary difference between the two proposed models resides in the procedure adopted for computing the parameters associated with the hidden processes. The first algorithm proposed combines expectation propagation (EP) with expectation maximization (EM) for computing the unknown parameters associated with the latent processes. While some of the parameters are treated in a deterministic sense (point estimates), the others are treated in a Bayesian manner. On the contrary, the second algorithm proposed uses variational Bayes expectation maximization (VBEM) and treats all the parameters in a Bayesian sense. Within VBEM, EP is used as an inference engine. Both the algorithms presented are data-driven. Several numerical examples are presented to certify the accuracy and efficiency of the proposed algorithms.

Online Anomaly Detection With Minimax Optimal Density Estimation in Nonstationary Environments

We introduce a truly online anomaly detection algorithm that sequentially processes data to detect anomalies in time series. In anomaly detection, while the anomalous data are arbitrary, the normal data have similarities and generally conforms to a particular model. However, the particular model that generates the normal data is generally unknown (even nonstationary) and needs to be learned sequentially. Therefore, a two stage approach is needed, where in the first stage, we construct a probability density function to model the normal data in the time series. Then, in the second stage, we threshold the density estimation of the newly observed data to detect anomalies. We approach this problem from an information theoretic perspective and propose minimax optimal schemes for both stages to create an optimal anomaly detection algorithm in a strong deterministic sense. To this end, for the first stage, we introduce a completely online density estimation algorithm that is minimax optimal with respect to the log-loss and achieves Merhav's lower bound for general nonstationary exponential-family of distributions without any assumptions on the observation sequence. For the second stage, we propose a threshold selection scheme that is minimax optimal (with logarithmic performance bounds) against the best threshold chosen in hindsight with respect to the surrogate logistic loss. Apart from the regret bounds, through synthetic and real life experiments, we demonstrate substantial performance gains with respect to the state-of-the-art density estimation based anomaly detection algorithms in the literature.

Some applications of mathematics in golf.

At its core, like many other sports, golf is a game of integers. The minimization of the number of strokes played is generally what determines the winner, whether each of these are associated with the shortest of putts or the longest of drives. The outcomes of these shots are influenced by very slight changes, but hopefully in a deterministic sense. Understanding the mechanics of golf necessitates the development of models and this is coupled more often than not to the use of statistics. In essence, the individual aspects of the sport can be modelled adequately via fairly simplistic models, but the presence of a human at one end of the kinematic chain has a significant impact on the variability of the entire process. In this paper, we will review some of the ways that mathematics has been used to develop the understanding of the physical processes involved in the sport, including some of the analysis which is exploited within the Equipment Rules. We will also discuss some of the future challenges.

Highly efficient hierarchical online nonlinear regression using second order methods

We introduce highly efficient online nonlinear regression algorithms that are suitable for real life applications. We process the data in a truly online manner such that no storage is needed, i.e., the data is discarded after being used. For nonlinear modeling we use a hierarchical piecewise linear approach based on the notion of decision trees where the space of the regressor vectors is adaptively partitioned based on the performance. As the first time in the literature, we learn both the piecewise linear partitioning of the regressor space as well as the linear models in each region using highly effective second order methods, i.e., Newton–Raphson Methods. Hence, we avoid the well known over fitting issues by using piecewise linear models, however, since both the region boundaries as well as the linear models in each region are trained using the second order methods, we achieve substantial performance compared to the state of the art. We demonstrate our gains over the well known benchmark data sets and provide performance results in an individual sequence manner guaranteed to hold without any statistical assumptions. Hence, the introduced algorithms address computational complexity issues widely encountered in real life applications while providing superior guaranteed performance in a strong deterministic sense.

Kalibrisanje konstitutivnih modela korišćenjem instrumentalnog utiskivanja i stohastičke inverzne analize

Indentation test is used with growing popularity for the characterization of various materials on different scales. Developed methods are combining the test with computer simulation and inverse analyses to assess material parameters entering into constitutive models. The outputs of such procedures are expressed as evaluation of sought parameters in deterministic sense, while for engineering practice it is desirable to assess also the uncertainty which affects the final estimates resulting from various sources of errors within the identification procedure. In this paper an experimental-numerical method is presented centered on inverse analysis build upon data collected from the indentation test in the form of force-penetration relationship (so-called 'indentation curve'). Recursive simulations are made computationally economical by an 'a priori' model reduction procedure. Resulting inverse problem is solved in a stochastic context using Monte Carlo simulations and non-sequential Extended Kalman filter. Obtained results are presented comparatively as for accuracy and computational efficiency.

Podemos and the Spanish political crisis

15 May 2011 marked the beginning of a major political and regime crisis in Spain. It has since passed through different stages – the last being the emergence of Podemos, which has become a major player in Spanish politics. The crisis of traditional mechanisms of political representation has become a crisis of hegemony of the ruling class, in the Gramscian sense of the term. The mass support for the ruling class and its traditional form of political representation has been withdrawn. This has led to an open situation with no clear outcome that can be read in terms of Walter Benjamin’s non-linear and deterministic sense of political and historical time.