Search results for: Probabilistic models

Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed

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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

Keywords: Equivalent Martingale Measure, European Put Option, Girsanov Theorem, Martingales, Monte Carlo method, option price valuation, option price valuation formula.

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Authors: Moulay A. Akhloufi, Abdelhakim Bendada

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Face recognition in the infrared spectrum has attracted a lot of interest in recent years. Many of the techniques used in infrared are based on their visible counterpart, especially linear techniques like PCA and LDA. In this work, we introduce a probabilistic Bayesian framework for face recognition in the infrared spectrum. In the infrared spectrum, variations can occur between face images of the same individual due to pose, metabolic, time changes, etc. Bayesian approaches permit to reduce intrapersonal variation, thus making them very interesting for infrared face recognition. This framework is compared with classical linear techniques. Non linear techniques we developed recently for infrared face recognition are also presented and compared to the Bayesian face recognition framework. A new approach for infrared face extraction based on SVM is introduced. Experimental results show that the Bayesian technique is promising and lead to interesting results in the infrared spectrum when a sufficient number of face images is used in an intrapersonal learning process.

Keywords: Face recognition, biometrics, probabilistic imageprocessing, infrared imaging.

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Authors: A.M. Al-Fahed Nuseirat, R. Abu-Zitar

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In this paper the design of maximally flat linear phase finite impulse response (FIR) filters is considered. The problem is handled with totally two different approaches. The first one is completely deterministic numerical approach where the problem is formulated as a Linear Complementarity Problem (LCP). The other one is based on a combination of Markov Random Fields (MRF's) approach with messy genetic algorithm (MGA). Markov Random Fields (MRFs) are a class of probabilistic models that have been applied for many years to the analysis of visual patterns or textures. Our objective is to establish MRFs as an interesting approach to modeling messy genetic algorithms. We establish a theoretical result that every genetic algorithm problem can be characterized in terms of a MRF model. This allows us to construct an explicit probabilistic model of the MGA fitness function and introduce the Ising MGA. Experimentations done with Ising MGA are less costly than those done with standard MGA since much less computations are involved. The least computations of all is for the LCP. Results of the LCP, random search, random seeded search, MGA, and Ising MGA are discussed.

Keywords: Filter design, FIR digital filters, LCP, Ising model, MGA, Ising MGA.

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Authors: Selvam M, Natarajan. A M, Thangarajan R

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Parsing is important in Linguistics and Natural Language Processing to understand the syntax and semantics of a natural language grammar. Parsing natural language text is challenging because of the problems like ambiguity and inefficiency. Also the interpretation of natural language text depends on context based techniques. A probabilistic component is essential to resolve ambiguity in both syntax and semantics thereby increasing accuracy and efficiency of the parser. Tamil language has some inherent features which are more challenging. In order to obtain the solutions, lexicalized and statistical approach is to be applied in the parsing with the aid of a language model. Statistical models mainly focus on semantics of the language which are suitable for large vocabulary tasks where as structural methods focus on syntax which models small vocabulary tasks. A statistical language model based on Trigram for Tamil language with medium vocabulary of 5000 words has been built. Though statistical parsing gives better performance through tri-gram probabilities and large vocabulary size, it has some disadvantages like focus on semantics rather than syntax, lack of support in free ordering of words and long term relationship. To overcome the disadvantages a structural component is to be incorporated in statistical language models which leads to the implementation of hybrid language models. This paper has attempted to build phrase structured hybrid language model which resolves above mentioned disadvantages. In the development of hybrid language model, new part of speech tag set for Tamil language has been developed with more than 500 tags which have the wider coverage. A phrase structured Treebank has been developed with 326 Tamil sentences which covers more than 5000 words. A hybrid language model has been trained with the phrase structured Treebank using immediate head parsing technique. Lexicalized and statistical parser which employs this hybrid language model and immediate head parsing technique gives better results than pure grammar and trigram based model.

Keywords: Hybrid Language Model, Immediate Head Parsing, Lexicalized and Statistical Parsing, Natural Language Processing, Parts of Speech, Probabilistic Context Free Grammar, Tamil Language, Tree Bank.

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Authors: Seon Soon Choi

Abstract:

The principal purpose of this paper is to find the influence of maximum fatigue load on the probabilistic aspect of fatigue crack propagation life at a specified grown crack in magnesium alloys. The experiments of fatigue crack propagation are carried out in laboratory air under different conditions of the maximum fatigue loads to obtain the fatigue crack propagation data for the statistical analysis. In order to analyze the probabilistic aspect of fatigue crack propagation life, the goodness-of fit test for probability distribution of the fatigue crack propagation life at a specified grown crack is implemented through Anderson-Darling test. The good probability distribution of the fatigue crack propagation life is also verified under the conditions of the maximum fatigue loads.

Keywords: Fatigue crack propagation life, magnesium alloys, maximum fatigue load, probability.

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Authors: Marina Gorunescu, Florin Gorunescu, Kenneth Revett

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Hepatocellular carcinoma, also called hepatoma, most commonly appears in a patient with chronic viral hepatitis. In patients with a higher suspicion of HCC, such as small or subtle rising of serum enzymes levels, the best method of diagnosis involves a CT scan of the abdomen, but only at high cost. The aim of this study was to increase the ability of the physician to early detect HCC, using a probabilistic neural network-based approach, in order to save time and hospital resources.

Keywords: Early HCC diagnosis, probabilistic neural network.

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Authors: S. Z. Moussavi, A. Badri, F. Rastegar Kashkooli

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Wind farms (WFs) with high level of penetration are being established in power systems worldwide more rapidly than other renewable resources. The Independent System Operator (ISO), as a policy maker, should propose appropriate places for WF installation in order to maximize the benefits for the investors. There is also a possibility of congestion relief using the new installation of WFs which should be taken into account by the ISO when proposing the locations for WF installation. In this context, efficient wind farm (WF) placement method is proposed in order to reduce burdens on congested lines. Since the wind speed is a random variable and load forecasts also contain uncertainties, probabilistic approaches are used for this type of study. AC probabilistic optimal power flow (P-OPF) is formulated and solved using Monte Carlo Simulations (MCS). In order to reduce computation time, point estimate methods (PEM) are introduced as efficient alternative for time-demanding MCS. Subsequently, WF optimal placement is determined using generation shift distribution factors (GSDF) considering a new parameter entitled, wind availability factor (WAF). In order to obtain more realistic results, N-1 contingency analysis is employed to find the optimal size of WF, by means of line outage distribution factors (LODF). The IEEE 30-bus test system is used to show and compare the accuracy of proposed methodology.

Keywords: Probabilistic optimal power flow, Wind power, Pointestimate methods, Congestion management

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Authors: Milad Eghtedari Naeini, Gholamreza Heravi

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In this paper, based on the past project cost and time performance, a model for forecasting project cost performance is developed. This study presents a probabilistic project control concept to assure an acceptable forecast of project cost performance. In this concept project activities are classified into sub-groups entitled control accounts. Then obtain the Stochastic S-Curve (SS-Curve), for each sub-group and the project SS-Curve is obtained by summing sub-groups- SS-Curves. In this model, project cost uncertainties are considered through Beta distribution functions of the project activities costs required to complete the project at every selected time sections through project accomplishment, which are extracted from a variety of sources. Based on this model, after a percentage of the project progress, the project performance is measured via Earned Value Management to adjust the primary cost probability distribution functions. Then, accordingly the future project cost performance is predicted by using the Monte-Carlo simulation method.

Keywords: Monte Carlo method, Probabilistic model, Project forecasting, Stochastic S-curve

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Authors: K. Jayakumar, S. Thangavel

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In this paper proposed the effective fault detection of industrial drives by using Biorthogonal Posterior Vibration Signal-Data Probabilistic Wavelet Neural Network (BPPVS-WNN) system. This system was focused to reducing the current flow and to identify faults with lesser execution time with harmonic values obtained through fifth derivative. Initially, the construction of Biorthogonal vibration signal-data based wavelet transform in BPPVS-WNN system localizes the time and frequency domain. The Biorthogonal wavelet approximates the broken bearing using double scaling and factor, identifies the transient disturbance due to fault on induction motor through approximate coefficients and detailed coefficient. Posterior Probabilistic Neural Network detects the final level of faults using the detailed coefficient till fifth derivative and the results obtained through it at a faster rate at constant frequency signal on the industrial drive. Experiment through the Simulink tool detects the healthy and unhealthy motor on measuring parametric factors such as fault detection rate based on time, current flow rate, and execution time.

Keywords: Biorthogonal Wavelet Transform, Posterior Probabilistic Neural Network, Induction Motor.

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Authors: Wenbin Zhang, Hantian Wu, Jian Tang

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An artificial neural network is a mathematical model inspired by biological neural networks. There are several kinds of neural networks and they are widely used in many areas, such as: prediction, detection, and classification. Meanwhile, in day to day life, people always have to make many difficult decisions. For example, the coach of a soccer club has to decide which offensive player to be selected to play in a certain game. This work describes a novel Neural Network using a combination of the General Regression Neural Network and the Probabilistic Neural Networks to help a soccer coach make an informed decision.

Keywords: General Regression Neural Network, Probabilistic Neural Networks, Neural function.

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Authors: Yanqi Yang, Chongshan Liao, Cheuk Hin Ho, Susan Bridges

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Aim: To investigate students’ perceptions of using e-models in an inquiry-based curriculum. Approach: 52 second-year dental students completed a pre- and post-test questionnaire relating to their perceptions of e-models and their use in inquiry-based learning. The pre-test occurred prior to any learning with e-models. The follow-up survey was conducted after one year's experience of using e-models. Results: There was no significant difference between the two sets of questionnaires regarding students’ perceptions of the usefulness of e-models and their willingness to use e-models in future inquiry-based learning. Most students preferred using both plaster models and e-models in tandem. Conclusion: Students did not change their attitude towards e-models and most of them agreed or were neutral that e-models are useful in inquiry-based learning. Whilst recognizing the utility of 3D models for learning, students' preference for combining these with solid models has implications for the development of haptic sensibility in an operative discipline.

Keywords: E-models, inquiry-based curriculum, education.

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Authors: Sergei Yendiyarov, Sergei Petrushenko

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In this article we present a change point detection algorithm based on the continuous wavelet transform. At the beginning of the article we describe a necessary transformation of a signal which has to be made for the purpose of change detection. Then case study related to iron ore sinter production which can be solved using our proposed technique is discussed. After that we describe a probabilistic algorithm which can be used to find changes using our transformed signal. It is shown that our algorithm works well with the presence of some noise and abnormal random bursts.

Keywords: Change detection, sinter production, wavelet transform.

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Authors: M. Glomski, M. Lopes

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Seemingly simple probabilities in the m-player game bingo have never been calculated. These probabilities include expected game length and the expected number of winners on a given turn. The difficulty in probabilistic analysis lies in the subtle interdependence among the m-many bingo game cards in play. In this paper, the game i got it!, a bingo variant, is considered. This variation provides enough weakening of the inter-player dependence to allow probabilistic analysis not possible for traditional bingo. The probability of winning in exactly k turns is calculated for a one-player game. Given a game of m-many players, the expected game length and tie probability are calculated. With these calculations, the game-s interesting payout scheme is considered.

Keywords: Conditional probability, games of chance, npersongames, probability theory.

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Authors: Ali Y Al-Attraqchi, P. Rajeev, M. Javad Hashemi, Riadh Al-Mahaidi

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This paper presents a probabilistic incremental dynamic analysis (IDA) of a full reinforced concrete building subjected to column loss scenario for the assessment of progressive collapse. The IDA is chosen to explicitly account for uncertainties in loads and system capacity. Fragility curves are developed to predict the probability of progressive collapse given the loss of one or more columns. At a broader scale, it will also provide critical information needed to support the development of a new generation of design codes that attempt to explicitly quantify structural robustness.

Keywords: Incremental dynamic analysis, progressive collapse, structural engineering, pushdown analysis.

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Authors: W.S. Lim, M.V.C. Rao

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In this paper, the processing of sonar signals has been carried out using Minimal Resource Allocation Network (MRAN) and a Probabilistic Neural Network (PNN) in differentiation of commonly encountered features in indoor environments. The stability-plasticity behaviors of both networks have been investigated. The experimental result shows that MRAN possesses lower network complexity but experiences higher plasticity than PNN. An enhanced version called parallel MRAN (pMRAN) is proposed to solve this problem and is proven to be stable in prediction and also outperformed the original MRAN.

Keywords: Ultrasonic sensing, target classification, minimalresource allocation network (MRAN), probabilistic neural network(PNN), stability-plasticity dilemma.

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Authors: Chaw Su Mon

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Abstract— The paper presents a preliminary study on modeling and estimation of basic wind speed ( extreme wind gusts ) for the consideration of vulnerability and design of building in Ayeyarwady Region. The establishment of appropriate design wind speeds is a critical step towards the calculation of design wind loads for structures. In this paper the extreme value analysis of this prediction work is based on the anemometer data (1970-2009) maintained by the department of meteorology and hydrology of Pathein. Statistical and probabilistic approaches are used to derive formulas for estimating 3-second gusts from recorded data (10-minute sustained mean wind speeds).

Keywords: Basic Wind Speed, Building, Gusts, Statistical and probabilistic approaches

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Authors: Tomoaki Hashimoto

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Recently, feedback control systems using random dither quantizers have been proposed for linear discrete-time systems. However, the constraints imposed on state and control variables have not yet been taken into account for the design of feedback control systems with random dither quantization. Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. An important advantage of model predictive control is its ability to handle constraints imposed on state and control variables. Based on the model predictive control approach, the objective of this paper is to present a control method that satisfies probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization. In other words, this paper provides a method for solving the optimal control problems subject to probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization.

Keywords: Optimal control, stochastic systems, discrete-time systems, probabilistic constraints, random dither quantization.

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Authors: Hossam Shalabi, George Hadjisophocleous

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The Canadian Nuclear Power Plants (NPPs) use some portions of NUREG/CR-6850 in carrying out Fire Probabilistic Risk Assessment (PRA). An assessment for the applicability of NUREG/CR-6850 to CANDU reactors was performed and a CANDU Fire PRA was introduced. There are 19 operating CANDU reactors in Canada at five sites (Bruce A, Bruce B, Darlington, Pickering and Point Lepreau). A fire load density survey was done for all Fire Safe Shutdown Analysis (FSSA) fire zones in all CANDU sites in Canada. National Fire Protection Association (NFPA) Standard 557 proposes that a fire load survey must be conducted by either the weighing method or the inventory method or a combination of both. The combination method results in the most accurate values for fire loads. An updated CANDU Fire PRA model is demonstrated in this paper that includes the fuel survey in all Canadian CANDU stations. A qualitative screening step for the CANDU fire PRA is illustrated in this paper to include any fire events that can damage any part of the emergency power supply in addition to FSSA cables.

Keywords: Fire safety, CANDU, nuclear, fuel densities, FDS, qualitative analysis, fire probabilistic risk assessment.

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Authors: Ali Jahanfar, Brajesh Dubey, Bahram Gharabaghi, Saber Bayat Movahed

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Ever increasing population growth of major urban centers and environmental challenges in siting new landfills have resulted in a growing trend in design of mega-landfills some with extraordinary heights and dangerously steep slopes. Landfill failure mobility risk analysis is one of the most uncertain types of dynamic rheology models due to very large inherent variabilities in the heterogeneous solid waste material shear strength properties. The waste flow of three historic dumpsite and two landfill failures were back-analyzed using run-out modeling with DAN-W model. The travel distances of the waste flow during landfill failures were calculated approach by taking into account variability in material shear strength properties. The probability distribution function for shear strength properties of the waste material were grouped into four major classed based on waste material compaction (landfills versus dumpsites) and composition (high versus low quantity) of high shear strength waste materials such as wood, metal, plastic, paper and cardboard in the waste. This paper presents a probabilistic method for estimation of the spatial extent of waste avalanches, after a potential landfill failure, to create maps of vulnerability scores to inform property owners and residents of the level of the risk.

Keywords: Landfill failure, waste flow, Voellmy rheology, friction coefficient, waste compaction and type.

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Authors: J. R. Wang, W. Y. Cheng, J. S. Yeh, S. W. Chen, Y. M. Ferng, J. H. Yang, W. S. Hsu, C. Shih

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To understand the risk for dry storage concrete casks in the cask loading, transfer, and storage phase, the purpose of this research is to establish the probabilistic risk assessment (PRA) analysis methodology for dry storage concrete casks by using SAPHIRE 8 code. This analysis methodology is used to perform the study of Taiwan nuclear power plants (NPPs) dry storage system. The process of research has three steps. First, the data of the concrete casks and Taiwan NPPs are collected. Second, the PRA analysis methodology is developed by using SAPHIRE 8. Third, the PRA analysis is performed by using this methodology. According to the analysis results, the maximum risk is the multipurpose canister (MPC) drop case.

Keywords: PRA, Dry storage, concrete cask, SAPHIRE.

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Authors: Mohamed H. S. Mohamed, Yang Xiao-zong, Liu Hong-wei, Wu Zhi-bo

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The reliability of distributed systems and computer networks have been modeled by a probabilistic network or a graph G. Computing the residual connectedness reliability (RCR), denoted by R(G), under the node fault model is very useful, but is an NP-hard problem. Since it may need exponential time of the network size to compute the exact value of R(G), it is important to calculate its tight approximate value, especially its lower bound, at a moderate calculation time. In this paper, we propose an efficient algorithm for reliability lower bound of distributed systems with unreliable nodes. We also applied our algorithm to several typical classes of networks to evaluate the lower bounds and show the effectiveness of our algorithm.

Keywords: Distributed systems, probabilistic network, residual connectedness reliability, lower bound.

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Authors: Taiki Baba, Tomoaki Hashimoto

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The random dither quantization method enables us to achieve much better performance than the simple uniform quantization method for the design of quantized control systems. Motivated by this fact, the stochastic model predictive control method in which a performance index is minimized subject to probabilistic constraints imposed on the state variables of systems has been proposed for linear feedback control systems with random dither quantization. In other words, a method for solving optimal control problems subject to probabilistic state constraints for linear discrete-time control systems with random dither quantization has been already established. To our best knowledge, however, the feasibility of such a kind of optimal control problems has not yet been studied. Our objective in this paper is to investigate the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization. To this end, we provide the results of numerical simulations that verify the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization.

Keywords: Model predictive control, stochastic systems, probabilistic constraints, random dither quantization.

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Authors: S. Jarernprasert, E. Bazan-Zurita, P. C. Rizzo

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Currently, seismic probabilistic risk assessments (SPRA) for nuclear facilities use In-Structure Response Spectra (ISRS) in the calculation of fragilities for systems and components. ISRS are calculated via dynamic analyses of the host building subjected to two orthogonal components of horizontal ground motion. Each component is defined as the median motion in any horizontal direction. Structural engineers applied the components along selected X and Y Cartesian axes. The ISRS at different locations in the building are also calculated in the X and Y directions. The choice of the directions of X and Y are not specified by the ground motion model with respect to geographic coordinates, and are rather arbitrarily selected by the structural engineer. Normally, X and Y coincide with the “principal” axes of the building, in the understanding that this practice is generally conservative. For SPRA purposes, however, it is desirable to remove any conservatism in the estimates of median ISRS. This paper examines the effects of the direction of horizontal seismic motion on the ISRS on typical nuclear structure. We also evaluate the variability of ISRS calculated along different horizontal directions. Our results indicate that some central measures of the ISRS provide robust estimates that are practically independent of the selection of the directions of the horizontal Cartesian axes.

Keywords: Seismic, Directionality, In-Structure Response Spectra, Probabilistic Risk Assessment.

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Authors: Hadi Firouzi, Majid Nili Ahmadabadi, Babak N. Araabi

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Conceptualization strengthens intelligent systems in generalization skill, effective knowledge representation, real-time inference, and managing uncertain and indefinite situations in addition to facilitating knowledge communication for learning agents situated in real world. Concept learning introduces a way of abstraction by which the continuous state is formed as entities called concepts which are connected to the action space and thus, they illustrate somehow the complex action space. Of computational concept learning approaches, action-based conceptualization is favored because of its simplicity and mirror neuron foundations in neuroscience. In this paper, a new biologically inspired concept learning approach based on the probabilistic framework is proposed. This approach exploits and extends the mirror neuron-s role in conceptualization for a reinforcement learning agent in nondeterministic environments. In the proposed method, instead of building a huge numerical knowledge, the concepts are learnt gradually from rewards through interaction with the environment. Moreover the probabilistic formation of the concepts is employed to deal with uncertain and dynamic nature of real problems in addition to the ability of generalization. These characteristics as a whole distinguish the proposed learning algorithm from both a pure classification algorithm and typical reinforcement learning. Simulation results show advantages of the proposed framework in terms of convergence speed as well as generalization and asymptotic behavior because of utilizing both success and failures attempts through received rewards. Experimental results, on the other hand, show the applicability and effectiveness of the proposed method in continuous and noisy environments for a real robotic task such as maze as well as the benefits of implementing an incremental learning scenario in artificial agents.

Keywords: Concept learning, probabilistic decision making, reinforcement learning.

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Authors: Zviad Ghadua, Biswa Bhattacharya

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The Flash Flood Guidance (FFG) provides the rainfall amount of a given duration necessary to cause flooding. The approach is based on the development of rainfall-runoff curves, which helps us to find out the rainfall amount that would cause flooding. An alternative approach, mostly experimented with Italian Alpine catchments, is based on determining threshold discharges from past events and on finding whether or not an oncoming flood has its magnitude more than some critical discharge thresholds found beforehand. Both approaches suffer from large uncertainties in forecasting flash floods as, due to the simplistic approach followed, the same rainfall amount may or may not cause flooding. This uncertainty leads to the question whether a probabilistic model is preferable over a deterministic one in forecasting flash floods. We propose the use of a Bayesian probabilistic approach in flash flood forecasting. A prior probability of flooding is derived based on historical data. Additional information, such as antecedent moisture condition (AMC) and rainfall amount over any rainfall thresholds are used in computing the likelihood of observing these conditions given a flash flood has occurred. Finally, the posterior probability of flooding is computed using the prior probability and the likelihood. The variation of the computed posterior probability with rainfall amount and AMC presents the suitability of the approach in decision making in an uncertain environment. The methodology has been applied to the Posina basin in Italy. From the promising results obtained, we can conclude that the Bayesian approach in flash flood forecasting provides more realistic forecasting over the FFG.

Keywords: Flash flood, Bayesian, flash flood guidance, FFG, forecasting, Posina.

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Authors: Zhifeng Kong

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Over-parameterized neural networks have attracted a great deal of attention in recent deep learning theory research, as they challenge the classic perspective of over-fitting when the model has excessive parameters and have gained empirical success in various settings. While a number of theoretical works have been presented to demystify properties of such models, the convergence properties of such models are still far from being thoroughly understood. In this work, we study the convergence properties of training two-hidden-layer partially over-parameterized fully connected networks with the Rectified Linear Unit activation via gradient descent. To our knowledge, this is the first theoretical work to understand convergence properties of deep over-parameterized networks without the equally-wide-hidden-layer assumption and other unrealistic assumptions. We provide a probabilistic lower bound of the widths of hidden layers and proved linear convergence rate of gradient descent. We also conducted experiments on synthetic and real-world datasets to validate our theory.

Keywords: Over-parameterization, Rectified Linear Units (ReLU), convergence, gradient descent, neural networks.

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Authors: Eva Eggeling, Dieter W. Fellner, Torsten Ullrich

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The objective of global optimization is to find the globally best solution of a model. Nonlinear models are ubiquitous in many applications and their solution often requires a global search approach; i.e. for a function f from a set A ⊂ Rn to the real numbers, an element x0 ∈ A is sought-after, such that ∀ x ∈ A : f(x0) ≤ f(x). Depending on the field of application, the question whether a found solution x0 is not only a local minimum but a global one is very important. This article presents a probabilistic approach to determine the probability of a solution being a global minimum. The approach is independent of the used global search method and only requires a limited, convex parameter domain A as well as a Lipschitz continuous function f whose Lipschitz constant is not needed to be known.

Keywords: global optimization, probability theory, probability of globality

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Authors: Vladimir K. Mukhomorov

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Within the framework of a method of the information theory it is offered statistics and probabilistic model for definition of cause-and-effect relations in the coupled multicomponent subsystems. The quantitative parameter which is defined through conditional and unconditional entropy functions is introduced. The method is applied to the analysis of the experimental data on dynamics of change of the chemical elements composition of plants organs (roots, reproductive organs, leafs and stems). Experiment is directed on studying of temporal processes of primary soil formation and their connection with redistribution dynamics of chemical elements in plant organs. This statistics and probabilistic model allows also quantitatively and unambiguously to specify the directions of the information streams on plant organs.

Keywords: Chemical elements, entropy function, information, plants.

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Authors: D. De-León-Escobedo, D. J. Delgado-Hernández, S. Pérez

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A probabilistic formulation to assess the slopes safety under the hazard of strong storms is presented and illustrated through a slope in Mexico. The formulation is based on the classical safety factor (SF) used in practice to appraise the slope stability, but it is introduced the treatment of uncertainties, and the slope failure probability is calculated as the probability that SF<1. As the main hazard is the rainfall on the area, statistics of rainfall intensity and duration are considered and modeled with an exponential distribution. The expected life-cycle cost is assessed by considering a monetary value on the slope failure consequences. Alternative mitigation measures are simulated, and the formulation is used to get the measures driving to the optimal one (minimum life-cycle costs). For the example, the optimal mitigation measure is the reduction on the slope inclination angle.

Keywords: Expected life-cycle cost, failure probability, slopes failure, storms.

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Authors: Hyun-Woo Cho

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Detection of incipient abnormal events is important to improve safety and reliability of machine operations and reduce losses caused by failures. Improper set-ups or aligning of parts often leads to severe problems in many machines. The construction of prediction models for predicting faulty conditions is quite essential in making decisions on when to perform machine maintenance. This paper presents a multivariate calibration monitoring approach based on the statistical analysis of machine measurement data. The calibration model is used to predict two faulty conditions from historical reference data. This approach utilizes genetic algorithms (GA) based variable selection, and we evaluate the predictive performance of several prediction methods using real data. The results shows that the calibration model based on supervised probabilistic principal component analysis (SPPCA) yielded best performance in this work. By adopting a proper variable selection scheme in calibration models, the prediction performance can be improved by excluding non-informative variables from their model building steps.

Keywords: Prediction, operation monitoring, on-line data, nonlinear statistical methods, empirical model.

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