# PDF Stochastic Systems, Modeling Identification and Optimization, I

Then, these modal parameters were applied to determine machine dynamic stability lobes. Ebrahimi et al. They modeled the blade using finite element method by Ansys software and calculate the dynamic behavior of the cutting blade platform in a harvest combine, and updated the model by natural frequencies obtained from FDD method. Then, by using mass change strategy and finite element model, a modification technique was introduced to reduce the vibration of cutting blade platform. Van Overschee and De Moor introduced the stochastic subspace identification SSI method which has been proposed as an alternative to classical methods.

In this stochastic method, the state space model is calculated from system output measurements. The key step in the SSI method is to calculate projection of future outputs matrix on past outputs matrix. To verify their method, they calculated modal parameters of a 5 degree of freedom system with two nonlinear parts. They pointed out that, to obtain modal parameters of a large structure, a large number of sensors should be used to record vibration signals, which incurs higher costs. To solve this problem, they developed a sensor-integrating method which could extract modal parameters of a large structure using few sensors.

Goursat et al. The analysis was performed using SSI algorithm, the direct data utilization and covariance functions calculation methods. It was found that natural frequencies of the structure show small changes during the mission; however, mode shapes were more stable before and after its operation. Kompalka et al. They demonstrated that SSI algorithm can predict the presence and location of damage with an appropriate accuracy. Moreover, they confirmed their approach by performing experiments on damaged beam. Updating the finite element model is considered as an inverse method which involves reducing the difference between finite element model and empirical data.

Methods based on gradient are extensively used in finite element model updating. Collins et al. Failing to find global optimum point of the system is one of the fundamental problems of these methods. In addition, existence of optimum points in system boundaries results in reduction in efficiency of these methods. To cope with these problems, evolutionary intelligent optimization methods such as genetic, bees and particle swarm optimization algorithms were introduced, which inspired from natural evolution.

These methods are not relying on the initial guess and do not need complicated mathematical concepts. Consequently, considering these characteristics, they can be used in finite element model updating. Dunn et al. Moradi et al. Then, they compared their results with those obtained by genetic and PSO algorithms. Malekzehtab and Golafshani applied genetic algorithm for finite element model updating and damage detection of a jacket offshore platform. Their objective function was defined based on the natural frequencies and mode shapes of offshore platform.

Chouksey et al. They modeled the supports with linear and rotational springs and dampers. Moradi and Jamshidi moghadam used bees algorithm to find location and depth of crack in post-buckled beam-type structures. Bussetta et al. Altunisik and Bayraktar updated model of Birecik Highway Bridge using operational modal analysis and finite element analysis. They changed some prominent parameters such as boundary conditions, material properties and section properties manually in order to reduce the difference between finite element and real models.

In this study, the modal parameters of a system are calculated empirically using SSI method. Then, the effective parameters in model updating are obtained by performing a sensitivity analysis. Next, the sum of the squared errors between the natural frequencies obtained by the OMA and FEM is defined as the objective function, and will be minimized by the bees algorithm.

In order to verify the integrity and the effectiveness of the proposed updating algorithm, the finite element model of a three-story frame is updated. Dynamic model of a linear system can be defined by a set of linear second-order differential equations with constant coefficients such as Goursat et al. Also, y t is the vector of displacement and f t denotes vector of structure input forces. Equation 1 can be rewritten as a system of first order differential equations using various methods.

A is state matrix and C is output matrix which is illustrated as a link between output and state variables. Moreover, v possesses noise due to modeling inaccuracy and w is the measurement noise related to data gathering system. Processing noise and data gathering noise are non-measurable signals and cannot be calculated by mathematical equations or signal processing, however, they are assumed as zero mean white noise signals between which the below relation exists Goursat et al.

Unscaled natural frequencies and mode shapes of system are obtained by eigenvalue and eigenvector analysis of matrix A and matrix C as:.

## Stochastic Systems: Modeling, Identification and Optimization I

Moreover, by using Equations 5 - 6 , scaled natural frequencies and damping ratios are estimated by the following relations:. Therefore, vibration equation is converted to a system identification problem by solving which the desired modal parameters can be obtained. For obtaining modal parameters in time domain strategies, there is no need to transfer data to frequency domain, thus, eliminate any leakage error. Stochastic subspace identification method is one of the strong methods for estimating modal parameters in time domain. Making covariance functions of output data is regarded as the first step in SSI method Equation 7.

Also, y k is the output signals in time k which is defined in Equation 8. Since, output data are discrete in time domain, the expected value operator of them is stated as Equation 9.

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Next, the Henkel matrix is decomposed into controllable and observable matrices using singular value decomposition factorization. Matrix C , that plays an important role in modal identification, equals to the first row block of observable matrix Equation In addition, the state transfer matrix A is calculated by shift invariance property of the observable matrix o and least square solution which is presented in Equation By identifying state matrix A and according to Equations 5 - 6 , the natural frequencies and damping ratios can be obtained.

Furthermore, the mode shapes of the system can be computed using the C matrix. In order to calculate correct natural frequencies, order selection is regarded as a prominent factor in SSI method. If user underestimates order of SSI method, the method will not be able to obtain all of the natural frequencies. In contrast, spurious natural frequencies can be calculated if order is overestimated. Therefore, to solve this problem stabilization diagram is applied to distinct real natural frequencies from spurious ones.

In stabilization diagram, different selected orders versus the natural frequencies obtained at each order is plotted. Real natural frequencies show a consistent behavior at different system orders whilst superior natural frequencies do not have stable attitude. For identification and omitting spurious natural frequencies in stabilization diagram, three criteria must be implemented Cara et al. As a result, by observing these conditions in SSI algorithm, spurious modes can be omitted. These limiting criteria are chosen by trial and error and in this research they are considered as 0.

In order to transfer the excitation energy to all degrees of freedom a system, the excitation points should not be located close to the nodes of the mode shapes of the system. By using ODP parameter given in Equation 17 , the distance of the degrees of freedom to the modal nodes can be estimated. The points of which ODP values are zero or close to zero are not suitable to be used for stimulation of the system, since they are on the mode shape nodes or near them. By contrast, points with maximal ODP values are appropriate for excitation and mounting the accelerometers. While exciting a structure by a shaker, the possibility of interference between the shaker and structure establishes that should be minimized.

Each shaker is composed of a system of mass, spring and damper and any interference between it and the structure causes changes in signal generated by the shaker. To reduce this effect, shaker should be installed in locations where average acceleration is of minimum value. Various mathematical models have been implemented for estimation of complex phenomena in different areas such as engineering, economy and physics. Identification of effective parameters in these mathematical models is the major challenge which users often deal with.

Sensitivity analysis is one of the most important methods capable of identifying the parameters that have the most impact on results. In other words, any small changes in sensitive parameters would result in significant changes in output. Once at a time index OAT is considered as one of the most applicable criteria for determination of sensitive parameters. Equation 19 states OAT index for identification of sensitive parameters. According to Equation 19 , a dimensionless index is considered in order to remove effects of various units of parameters Hamby Global sensitivity index GSI is defined by Equation 20 in which overall sensitivity can be estimated Hamby In this equation, Y min and Y max are the minimum and maximum output of the model using upper and lower limit bounds of the input parameters.

According to Equations 19 - 20 , parameters that play significant role in output can be identified. In this research, input parameters are physical properties of the structure, whereas the natural frequencies are considered as outputs. By using sensitivity analysis, physical parameters which are suitable for optimization algorithm can be determined.

Bees optimization algorithm is classified in evolutionary algorithms. There is an organized social behavior among bees which can be used for solving complex optimization problems. There are scout bees in each swarm whose main task is to find food sources for their hives. As scout bees find new food sources, they return to their hives and evaluate various discovered gardens based on specific parameters. Then, by performing a toggle dance, they provide the information of the direction, distance and amount of nectar in these gardens for worker bees.

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Next, the worker bees fly to the detected locations. The number of worker bees sent to these locations is proportional to the available nectar amount in the detected gardens. In other words, more worker bees are sent to gardens which have more nectars and shorter distance to the hive. Therefore, this strategy enables bees swarm to obtain food sources in an efficient manner. Figure 1 shows the flowchart of the bees algorithm. From N t random solutions, N t1 solutions which have the highest fitness values are selected as the best solutions.

Then, among the best solutions N t2 solutions are selected as the elite ones. In order to find better solutions, the best solution neighborhoods are searched.

Next, the remaining solutions are chosen randomly in the search space to find other solutions. Equation 21 indicates formation of a new generation in bees algorithm. Additionally, the number of population in each generation is fixed.

These steps continue until the convergence criteria have been reached. In this research, an objective function is defined to update the finite element model and bring it closer to the experimental model. It is expressed as the summation of the errors between the natural frequencies obtained by the operational modal analysis and the finite element method as represented by the following equation.

Moreover, vector Z includes design parameters which are identified by the sensitivity analysis section By minimization of the objective function Equation 22 using bees optimization algorithm, design parameters are obtained and a precise finite element model based on real structure is designed.

The main objective of this research is to optimize the finite element model of structures by using a combination of SSI, sensitivity analysis and finite element methods. The algorithm of the proposed method is described in Figure 2. To verify the proposed algorithm, a three-story structure is built numerically and experimentally, the updating algorithm is applied on it, and the results are presented in the following sections.

Figure 3 shows sketch of the three-story structure. It is built by steel bars with all connections welded. Bars are cut carefully and welded together using templates. Moreover, anchor bolts are used to connect the structure to the ground. The dimensions of the three-story structure are presented in Table 1. Solid element is used for building this model. Additionally, in this model, welds are taken into account as a change in Young's modulus in connections. Next, an eigenvalue analysis was performed on the model to obtain the natural frequencies and the results for the first six natural frequencies are tabulated in Table 2.

Also, the corresponding mode shapes are displayed in Figure 5. Acquiring modal parameters requires an accurate planning for conducting experiments. Appropriate locations of accelerometers and shaker can lead to more precise modal parameters. Figure 6 displays these points for installation of accelerometers and shaker in y direction.

The points are also tabulated in Table 3. Figure 7 shows the best places for the installation of accelerometers and shaker in x direction and Table 4 presents their corresponding coordinates. In order to determine effective parameters for finite element model updating, a sensitivity analysis is performed on the three-story frame according to section Table 5 presents the lower and upper limits of design parameters for sensitivity analysis see section Figures 8 - 9 present the local and global sensitivity results for the three-story structure, respectively.

Figure 8 shows that the maximum local sensitivity belongs to design parameters related to length of the members, and physical characteristics of the structure such as Young's modulus and density. However, the minimum values are related to Young's modulus of welded connections and the cross-section of the members. Moreover, in global sensitivity, approximately the same parameters that considered in local sensitivity can have direct impact on the obtained natural frequencies Figure 9. Operational modal analysis is regarded as a subset of modal analysis that only depends on output responses.

In this research, SSI method is applied to identify dynamic parameters of the three-story frame. Random inputs are the main assumption of SSI method. Therefore, for random excitation of the three-story structure, an electro-dynamic shaker is used. This electro-dynamic shaker can produce random, burst random, pseudo random, sweep random and periodic random signals.

Then, by using accelerometers attached on the structure, the output signals are captured and send to the time recorder software. Figure 10 shows equipment used in data acquisition of the structure. Figure 11 demonstrates the time response obtained from the three-story structure under random excitation.

These data were recorded using a sampling rate of samples per second. Table 6 presents the natural frequencies obtained by SSI method under different excitations, plus those frequencies obtained by classical modal analysis. Figure 12 shows the relative error of natural frequencies of the structure obtained from operational modal analysis and classical modal analysis hammer test. According to this figure, natural frequencies calculated by pusedo random signals are more consistent with those obtained from classic modal analysis, therefore, only this signal will be used in the following sections of this research.

Stability diagram of SSI method for pusedo random excitation signal in y direction is depicted in Figure As stated in section , points deployed next to each other in rows are an approximation of natural frequencies and can be seen in the figure clearly. As can be seen from Figure 13 , system order varies between 40 and Table 7 compares the natural frequencies obtained by SSI method and those computed by the finite elements method.

As can be seen from the table the relative error between the two methods is comparable. According to Table 7 , the relative error between the natural frequencies obtained by SSI and FE methods is high and therefore the finite element model needs to be updated. In order to update the finite element method and reduced the discrepancy between the computed and measured natural frequencies, an objective function is defined and minimized by the bees algorithm.

Three different sets of design parameters are defined for bees algorithm. The first set includes parameters obtained from sensitivity analysis, second set includes parameters not important for sensitivity analysis and material properties, and the third set consists of all design parameters. Table 8 summarizes all the design parameter sets in this study. As shown in the table, these sets consist of 14, 59 and 71 design variables, respectively.

Figure 14 shows the convergence of bees algorithm for different sets of design parameters. As it is clear from this figure the convergence of the first and third sets are faster and the results are more precise than the second set. However, the convergence occurred with 14 design parameters by set 1 and 71 design parameters by set 3. Additionally, the run time of the optimization process in set 1 is lower than that in set 3.

This shows that optimization using set 1 could achieve optimal response in minimum time. Moreover, since all of design parameters in set 1 were obtained by sensitivity analysis, it is clear that sensitivity analysis is able to identify effective parameters in optimization process. Second, QEs decreased vix Volatility index , so that investors would like to take risks in stock market trading. Third, QEs raise longer term interest rates via the income, price-level, and Fisher effects.

These results suggest that the unconventional monetary policy in USA has been effective as a means to ease the economic slump. Yoji Morita, Shigeyoshi Miyagawa. The paper confirms that the monetary policy has contributed to the recovery of the prolonged deflation. Next we decompose money stock into transaction money and precautionary money to evaluate the transmission mechanism of the effect of reserves on the real economy by taking into account the financial anxiety.

We have found a quantitative easing shock firstly increase transaction money and then raise output and price, which dispel the anxiety. We also confirm that a liquidity trap did not exist during the period of quantitative easing monetary policy. Effects of information and estimations in portfolio maximization problems of expected utility with respect to terminal wealth are considered. In this paper, assuming several strategies whose differences come from information of markets and estimations of a parameter, we theoretically and numerically study their effects to expected utility and distributions of wealth at the maturity, and characters of paths where the strategy works well or bad.

Arbitrage Opportunity on Nonlinear Wealth Processes.

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In this paper, we mainly concern about nonlinear BSDE which is often used to describe the case of constraint on the wealth of an investor. Unlike the linear case, we can show that under a certain situation, both buyer and seller can create arbitrage opportunities in the derivative market. As a result, we succeeded in establishing a sufficient condition which guarantees the existence of arbitrage opportunities in the market as well as the limitation of an arbitrage. Optimal execution problem: a combined stochastic optimal control approach. We propose the optimal execution strategy including the limit order.

The arrival of the counterpart market order of our limit order is modelled by the Poisson process reduced from the Cox process. We formulate the limit order and market order by the regular stochastic control and impulse control respectively. The performance criterion consists of the terminal wealth and the inventory penalty function which copes with the uncertainty of the limit order.

We solve the corresponding Hamilton-Jacobi-Bellman quasi variational inequality numerically using the implicit method. The result of the numerical simulation with the obtained optimal strategy gives a quantitative evaluation of the advantage to include the limit order into the execution strategy. Then we price a certain type of lookback options in the discrete Black Sholes Model and find the discrete hedging strategy of these exotic options.

We note that these results are concrete example of discrete Kennedy martingales. Tanaka-Yamawaki, X. A new tool to measure the degree of randomness of a given sequence, named as the RMT-test, is introduced and applied on machine-generated random numbers as well as real-world data sequences. The tool consists of two parts: the qualitative evaluation that is aimed to visualize the degree of randomness, and the quantitative evaluation that is aimed to distinguish subtle differences of randomness among highly random sequences based on moment analysis, in which the moments of the actual eigenvalue distributions of the correlation matrix to the corresponding theoretical expression derived by the random matrix theory.

The RMT-test is applied to solve practical problems by comparing the randomness of real data, such as the output of cryptographic hash functions MD5 and SHA-1, and high-frequency time series of stock prices. It is found that the stock of higher randomness tends to perform better than the stock of lower randomness in the following time period. A generalized Cauchy process has been extensively studied since it gives one of the three universal distributions in Beck-Cohen superstatistics. There are many stochastic processes which give Cauchy type distributions in non-equilibrium open systems.

However, their different features of intermittency and associated nonlinear structures are not elucidated completely. This paper exhibits a class of generalized Cauchy processes with their temporal features in the first, second and third order systems. A theoretical method for discriminating their various stochastic models is also discussed. In this paper, for the purpose of evaluating the degradation level of the performance in application with the estimated parametric model in which the estimated parameters have the disturbance, we consider the relation between the robustness of parameter estimation and the model order.

In this paper, the robustness of the estimated parameter is defined as the degradation level of the performance. After the application performance cost function is derived, the gradient at the estimated parameter is focused to evaluate the disturbance level of the performance in the application. As a result, when identifying the model with the true structure by maximum-likelihood method, the disturbance level is simply given as the function of the model order. And it is shown that the larger the model order is, the more the estimated parameter lacks the robustness in the application.

In addition, the relation between the robustness and a information criterion is introduced.

## Piecewise parameter estimation for stochastic models in COPASI | Bioinformatics | Oxford Academic

Akio Tanikawa, Yuichi Sawada. We consider partially observed discrete-time linear stochastic systems and assume that some entries of the system matrices are unknown. We propose a new method which identifies those unknown entries and the state vectors of those systems simultaneously. The key idea of the proposed method is utilization of the pseudomeasurement which is a fictitious and additional observation process on the unknown entries and will be modified so as to work for the partially observed systems.

Augmenting the pseudomeasurement with the original observation process, we derive the new identification method by applying the extended Kalman filter. The proposed method is consistent with the conventional method without pseudomeasurement and so they can easily be unified to be a single iterative process for simultaneous identification and state estimation by switching the coefficient matrix of the augmented observation process.

Grey-box modeling for mechanical systems in frequency domain. Hideyuki Tanaka, Yoshito Ohta. This paper studies grey-box modeling for mechanical systems in the frequency domain. A two-step grey-box modeling algorithm is developed: The state of the grey-box model is estimated by an initial model, and an improved model is then computed from the state. The effectiveness of the proposed algorithm is shown by a rotary type pendulum system. A signal for online whiteness testing generated by recursive subspace model identification from closed-loop data. In this paper, we will develop an online statistical change detection method, which is used for detection of changes in a system under surveillance in closed-loop.

A recursive algorithm of closed loop subspace model identification is presented, which is based on the matrix inversion lemma. The relation between the proposed recursive algorithm and the predictor-based subspace identification method PBSID is clarified from the viewpoint of a matrix-valued least squares problem.

A test signal generated sequentially by the recursive algorithm is studied and its asymptotic whiteness is proved explicitly. The proposed online change detection method is based on a likelihood ratio test to examine the change in the covariance of the aforementioned test signal.

Ionospheric anomaly is one of the major error sources that affect the performance of the GPS Global Positioning System. In order to improve the tracking performance of GPS receivers under scintillation conditions, a tracking loop aided by INS Inertial Navigation System has been developed and flight tests to evaluate it were conducted around the island of Ishigaki where ionosphere scintillation frequently occurs.

Evaluation of phase tracking performance was carried out off-line using a software-defined GPS receiver which processes stored IF Intermediate Frequency data. As a result, the INS-aided tracking loop achieved continuous phase tracking even under strong scintillation conditions. Several techniques to improve PPP quality are also integrated into a PPP algorithm which is available in case that there are few only two or three visible satellites from automobiles moving on the street in urban canyons.

Therefore, this paper verifies the usefulness to integrate barometric pressure information into these methods. In this paper we present a carrier-phase-based RTK-PPP algorithm with multiple antennas which are disposed with solid geometrical distances and with the common receivers' clock errors, based on GR models. We present GR equations for multiple antennas, and derive the Kalman filtering formula of very precise point positioning in urban cayons. Ohashi, K. Nishimoto, Y. Kubo, S.

In our previous research, Least Squares method has been applied. In this paper, we propose the method by applying Kalman Filter. In the experiments, the ionospheric VTEC is modeled by the previous and proposed methods. Nishimoto, M. Ohashi, Y. For single frequency system, it is very important to effectively correct the ionospheric delay and the so-called Klobuchar model has been widely used due to its well known properties such as computational simplicity.

On the other hand, there are some models that can achieve better accuracy than the Klobuchar model, the SCHA Spherical Cap Harmonics Analysis model is one of such models. By the SCHA model, it has been reported that the ionospheric delays can be well modeled in the regional area such as the sky over Japan[2, 3]. In this paper, we investigate the parameter which is assumed to be constant in the Klobuchar model as well as Klobuchar like models in [4, 5, 6], and try to improve the model accuracy by assuming the parameter as a function of the geomagnetic latitude.

Also, the positioning results based on the Klobuchar like models are compared by experiments using long term half year observation data. Randomized Algorithms for Optimal Power Flow. Randomized algorithms for optimal power flow problems are presented. A standard optimal power flow problem is to minimize a fuel cost satisfying power flow equations and some inequalities consisting of the limits on control variables and the operating limits of a power system.

Then, the robust optimal power flow problem is considered when uncertain active and reactive power is injected into the power system. Although both problems are highly nonconvex, the proposed algorithms always stop within the finite number of iterations and find a suboptimal solution which is a feasible in a probabilistic sense.

It is shown that the maximum number of random samples is a polynomial of the size of the problems. The integration of renewable energy into an electric grid introduces new challenges to achieve optimal operating point for the power flow problem, because of randomness in generation and the distance between generation and consumption.

These challenges can be overcome by using storage with appropriate capacity and efficient strategy to charge and discharge. In this work, we introduce a model of the power flow problem with storage so that it can be used to inject active and reactive power into the grid. We formulate an optimal power flow problem for a distribution grid with storage as a multi-period control problem based on the deterministic and stochastic nature of load and generation.

We propose a multi-objective optimization function, in which the operating objectives are as follows: i injecting reactive power into the power system for decreasing distribution loss and voltage deviation; and ii maximizing renewable energy integration with minimum curtailment.

In car-navigation systems, car position measurement estimates the car's position and heading angle from the out-puts of a GPS receiver and sensors, and calculates the position on a link that represents a road and is recorded in a digital road map. We focus on the latter process, which is map matching. If there are large errors in the car's estimated position and heading angle as well as in link position and direction angle, map matching selects an incorrect link.

We previously proposed a map-matching method that calculates the criterion from the error variances of the positions and direction angles of the links, too. However, this method must in advance measure the error variances of the positions and direction angles of the links, which are different from one area to another. This paper proposes a map-matching method with a function to calculate the error variances of the position and direction angle of the links in a digital road map and that can remove the previous measurement work.

The performance of this function was evaluated, and the performance of this map-matching method was compared with that of the conventional method by using numerical computation. Shigeki Matsumoto, Katsutoshi Yoshida. In this paper, we experimentally investigate the cooperative balancing task on a virtual coupled inverted pendula CIP model, performed by a pair of an invisible artificial controller and a human subject, where experimental participants were not allowed to watch the movement of the artificial partner during experiments.

The experimental result on Lyapunov exponents implies that the human subjects who never have experienced the balancing tasks with visible controller, seems to try to make the artificial controller neutrally stable as well as the subjects who have already experienced.

Therefore, the result implies that at least as to the human subjects in the present study, there are no influence of learning with the visible controller on the stabilities of the task with invisible controller. This research investigates the deterioration of rotating equipment with misalignment via actual experimental data. Data to use the analysis of the deterioration are obtained from an acceleration sensor.

Not only the deterioration prediction but also the residual life prediction is conducted by using on-line estimation through weighted least square method. In this research, to evaluate the prediction method, the deterioration is analyzed via multiple experimental data obtained from rotating equipment with misalignment. The aim of this research is to evaluate the behavior of small scaled wind turbine system against strong wind input using electromagnetic stall control system.

In general, the wind turbine system is generating energy from the revolution of blades. The revolution of blades is depended on the velocity of wind. Therefore, if there is strong wind then the revolution of blade is increased and consequently more energy will be generated. Therefore, generally the wind turbine systems are located in the gale area in order to generate energy efficiency. However, there are some limitations of the revolution of blades or the angular velocity of blades, especially in small-scaled turbine.

If the angular velocity exceeds the limit of revolution, then wind turbine system may breakdown. Thus in this paper, in order to avoid the malfunction of small-scaled wind turbine system, electromagnetic stall control ESC is suggested. ESC can control the angular velocity without having any connection with shaft.

Thus, we would control angular velocity much efficiently than the conventional stall control method such friction stall control. As a consequence, we could verify the reliability of ESC system. The results of experiments on balancing a virtual inverted pendulum with over-damped dynamics are reported. Three types of pendulum, namely, an inverted stick, a triangle pendulum, and a vibrating spring were used in experiments and subjects of different age, gender, and skill of balancing participated in these experiments.

It is demonstrated that the main characteristics of human balancing under the analyzed conditions, in particular, the phase portraits and the distribution functions of the pendulum angle and the angular velocity are universal in form. Only the characteristic scales depend on the subject features and the difficulty of balancing. Arkady Zgonnikov, Ihor Lubashevsky.

Understanding how humans control unstable systems is central to many research problems, with applications ranging from quiet standing to aircraft landing. Increasingly much evidence appears in favor of event-driven control hypothesis: human operators are passive by default and only start actively controlling the system when the discrepancy between the current and desired system states becomes large.

The present study proposes a stochastic model describing the transitions between the passive and the active phase of control behavior, which is based on the concept of random walk in double-well potential. Unlike the conventionally used model of fixed threshold, the proposed model is intrinsically stochastic and thus conforms to the physiological interpretation of the threshold as a probabilistic rather than deterministic notion. The model is studied numerically and is confronted to the experimental data on virtual stick balancing. The results confirm the validity of the model and suggest that the double-well potential can be used in modeling human control behavior in a diverse range of applications.

Synchronization over stochastically switching networks with imperfect prior information. This paper is concerned with output synchronization of nonlinear agents over a switching communication network. Under the assumption that the topology of the network is an i. However, such an expected value may not be available in practical situations, we attempt to extend the above synchronization condition to the case where the expected Laplacian belongs to a prescribed polytopic set.

Simulation results are also included. In this paper, we propose visual support ways for articulation in pronunciation correction and investigate the effect through some experiences. The way which we have proposed is realized by display of formants and shapes of mouth and tongue, which are derived based on the formants of speaker's voice. These displays can lead supported ones to recognize their pronunciation different from correct pronunciation. This paper discusses human brain activities of frontal lobe under glucose tolerance test. The results of the test are treated and evaluated numerically using oxidized hemoglobin densities which are measured by near infrared spectroscopy.

We apply multivariable estimated models of auto-regressive form with upper triangular estimates. They are given by hierarchical decomposition analysis, which show properties of each stage. Estimation of the pulmonary elastance and setting of the ventilation condition using fuzzy logic.

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Artificial respirators are widely used for patients with little or no autonomous breathing ability. Doctors are required to pay scrupulous attention for the use of the artificial respirators. And doctors must set the artificial respirator in consideration of each patient's pulmonary characteristic. However, we do not understand the pulmonary characteristic of the patient by the measurement of data. Therefore, the setting of the artificial respirator is decided by the experience and the intuition of the doctor now. In our previous work, we have presented an estimation technique of the pulmonary elastance by fuzzy logic.

Parameters of the pulmonary elastance f E V are different in each fuzzy rules. Then, it is said that other parameters do not change in a short time one cycle breath. Nevertheless, in the previous study, these parameters were estimated to be different values in parameters estimation of each fuzzy rule.