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**Space Research Institute**

Space whether affects on power systems: prediction, risk analysis and modeling Vitaliy Yatsenko Panos Pardalos Nikita Boiko Steffen Rebbenack Space Research Institute NASU & NSAU University of Florida ІКД

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Problem Modeling natural space ionizing radiation effects on devices and materials Space whether prediction Risk analysis space nuclear power systems electrons damage satellites nano-engineered super-capacitors micro-solar power systems optical devices and lasers 2

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What is space weather? Space weather describes the physical processes induced by solar activity that have impact on our terrestrial and space environment, on ground based and space technological systems, and on human activities and health.

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Early views

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**Manifestations of space weather**

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**Space weather affects on electrical power system**

Space weather storm can cause electricity to flow in Earth’s atmosphere Space weather storm mess up the flow of electricity to homes Transformers work fine with AC (alternating current) electricity, but can damage if too much DC (direct current) electricity flows into them.

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**Electrons damage satellites**

In January 1994, three geostationary satellites suffered total failures of their momentum wheel control circuitry. Services were affected for hours, and one satellite never fully recovered. At the time it was well known that satellites could suffer damage when high energy particles were emitted from the sun during an explosive Solar Particle Event (SPE). Protons and electrons travelling at relativistic speeds (a significant fraction of the speed of light such as 0.3c) could impact with orbiting satellites causing damage in a number of different ways. In this case, however, no SPE had been observed. 7

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**Main goals of space weather**

establishing the scientific basis to understand physical phenomena and processes in near space; developing operational tools to predict and forecast them. Space weather measurements Space weather on the Earth is measured by geomagnetic indices. There are lots of them, but the most widely used are 3: storm-time disturbance Dst, planetary index Kp and auroral index AE.

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**Number of traumas due to traffic accidents in Kyiv correlates with solar activity**

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Introduction The most straightforward approach in understanding the dynamics of the magnetosphere is to study the whole complex chain of physical processes involved in its dynamics and to conjugate them in a global model of the evolution of the magnetosphere under the influence of the solar wind.

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**Problem Problem Problem Problem**

Space radiation comes in many forms and affects electronic components in diverse ways. Aerospace investigations of how energetic particles interact with integrated circuits and other electronics have been helping spacecraft designers and mission planners minimize the risk of component failure or performance degradation. 11

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**Problem Problem Problem Problem**

Explosions on the Sun create storms of radiation, fluctuating magnetic fields, and swarms of energetic particles. These phenomena travel outward through the Solar System with the solar wind. Upon arrival at Earth, they interact in complex ways with Earth's magnetic field, creating Earth's radiation belts and the Aurora. Some space weather storms can damage satellites, disable electric power grids, and disrupt cell phone communications systems. 12

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**Solar wind parameters solar wind speed density positive ions protons**

magnetic field electric field 13

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**Problem y(k+1) y(k+m) u(k) z=f(v,u) μ(v)=Ef(v,u) v(k) Black Box**

Prediction Device Risk Analysis Black Box Prediction Device Risk Analysis u(k) Solar wind parameters z=f(v,u) μ(v)=Ef(v,u) v(k) Fig. 1 Prediction and Risk Analysis 14

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Problem B E V Burton, R. K., R. L. McPherron, and C. T. Russell, The terrestrial magnetosphere: A half-wave rectifier of the interplanetary electric field, Science, 189, 717, 1975. Burton, R. K., R. L. McPherron, and C. T. Russell, An empirical relationship between interplanetary conditions and Dst, J. Geophys. Res., 80, , 1975. Kan, J. R., and L. C. Lee, Energy coupling function and solar wind-magnetosphere dynamo, Geophys. Res. Lett, 6, , 1979. Boyle, C. B., P. H. Reiff, and M. R. Hairston, Empirical polar cap potentials, J. Geophys. Res., 102, , 1997.

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Experimental data The SPDF hosts the S3C Active Archive, which consists of web-based services for survey and high resolution data, trajectories, and modeling software. The Facility delivers value-added services and leads in the definition, development, operation, and promotion of collaborative projects.

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**Dynamic-information forecasting of Dst index**

Magnetosphere is considered as a nonlinear complex dynamical system Dst index Dst is sought for as an output of a nonlinear dynamical “black-box” Solar wind parameters Data are from OMNI2 database: and Kyoto WDC for Geomagnetism:

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**“Black-box model” approach**

Discrete recursive (nonlinear autoregressive moving average model with exogenous inputs) models are considered. This is a so-called ‘black box’ or ‘input-output’ model, which seeks only to reproduce the behaviour of the system’s output in response to changes in its setpoint or inputs. One of the most important features of models is that model terms are physically interpretable. For example, discrete and continuous time models of the evolution of Dst can be derived using NARMAX methodology.

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**Dynamical-information approach**

Dynamical-information approach is based on the “black-box” model and Lyapunov exponents to describe magnetospheric dynamics. Reconstruction of the dynamical model is based upon the application of multiobjective learning algorithms to identification of model’s structure and parameters. A forecasting algorithm based on Lyapunov exponents is also proposed.

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**Dynamical-information approach**

Time domain techniques are used to identify a dynamical model for the evolution of the Dst index under the influence of the solar wind. Frequency domain analysis of this model is used to study spectral properties of the Dst index dynamics.

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**Nonlinear AutoRegressive Moving Average model with eXogenous input.**

F[.]

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Mathematical models y(k) = F[y(k - 1),…,y(k - n), u(k - 1), …, u(k - n), ξ(k - 1),…,ξ(k - n)+ξ(k)]

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**Optimization problem y (k) = ψ(k - 1)T θ + ξ (k) (1) min J(θ)**

subject to (2)

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Numerical algorithms For structure and parameter identification we use two numerical methods: Genetic optimization Nonlinear optimization with constraints

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**Results (genetic optimization)**

A comparison of the model predicted values of Dst (red) with real measurements of the Dst (blue) for the test interval.

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**Results (Nonlinear optimization)**

Dst, nT N, hours

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Numerical results yi = 1.36 yi−1 − 4.99 ui−1 − 0.18 yi−2 ui−1 − 0.57 yi−4 − −1.43 ui−4 ui−6 − 0.75 yi− yi− yi−3 ui−1 + +0.36 yi− ui−6 ui− ui− yi−3 ui−2 + +0.78 ui−2 ui−5 − 0.91 ui− ui−7 ui−12

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**Identification of linear perturbations**

Local maxima correspond to magnetospheric eigenmodes (Cheremnykh & Yatsenko, 2007) (Balikhin et al., 2001) phase magnitude Frequency, h-1

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**Neural network prediction of interplanetary shocks**

Neural network prediction method based on the data from 5 data channels of ACE spacecraft (EPAM) Preliminary experimental research showing promising capabilities of the method

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**Risk Analysis of Laser Elements for Complex Characterization of Damages by Space Radiation**

Dynamic probabilistic risk analysis of optical elements for complex characterization of damages using physical model of solid state lasers and predictable level of ionizing radiation and space weather. The following models and software have been studied: solid-state laser model mathematical models for dynamic probabilistic risk assessment software for modeling and prediction of ionizing radiation

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**Risk Analysis of Laser Elements for Complex Characterization of Damages by Space Radiation**

Probabilistic risk assessment is a comprehensive, structured, and logical analysis method aimed at identifying and assessing risks in solid-state lasers for the purpose of cost-effectively improving their safety and performance. This method based on the Conditional Value-at-Risk measure (CVaR) and the expected loss exceeding Value-at-Risk (VaR). We propose to use a new dynamical-information approach for radiation damage risk assessment of laser elements by cosmic radiation.

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**Optimization problem with constraints on risk**

Let z=f(v,u) be a loss function of a device depending upon the control vector v and a random vector u. The control vector v belongs to a feasible set V, satisfying imposed requirements. We assume that the random vector u has a probability density p(u). We can define a function Optimization model

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Papers O. Cheremnykh, V. Yatsenko, O. Semeniv, Iu. Shatokhina. Nonlinear dynamical model for space weather prediction. Ukr. Phys. J , N 5. - P P. Pardalos, V. Yatsenko. Optimization approach to the estimation and control of Lyapunov exponents. Optimization Theory and its Applications, 2006, 128(1).-P

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Conclusion The following models have been proposed: (a) solar wind influences on devices; (b) forecasting of ionizing radiation; and (c) risk assessment in safety analysis. An application of the multicriterion optimization method to the prediction of the Dst index was proposed. Two novel algorithms of the identification of discrete input-output models have been developed. The simulation results shown that the proposed technique provides an efficient method to get the optimum difference equation model of the Dst index.

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