THE EXTENDED TRANSFORMATION METHOD FOR THE SIMULATION AND ANALYSIS OF FUZZY-PARAMETERIZED MODELS

The importance of design robustness and reliability is a well-established notion and practice in today’s industry. Manufacturing companies strive to achieve Six-Sigma quality measures. While Virtual Prototyping is a key-factor in accelerating the product development process while reducing development costs; it has not contributed in the quest for improved product reliability and robustness performance since it is based on deterministic approaches. This paper provides a systematic approach to design for sixsigma simultaneously addressing variability and uncertainty present in real life on most design parameters. The first step is the ability to flexibly integrate and federate best-of-class virtual prototyping simulation software programs -most based on Finite Element Modeling techniques- thus, capturing existing engineering processes. These engineering processes provide the deterministic calculation engines for assessing design performance outputs of interest, such as -but not limited to- stress, structural impact, eigenfrequencies, forced response functions, fatigue life. Second is the assessment of design parameter variability on the design performance outputs. Analytical methods for the efficient calculation of dynamic response variability examined in this work include reliability-based methods such as First and Second Order Reliability methods, the Importance Sampling Monte Carlo (ISMC) method and the Transformed Importance Latin Hypercube Sampling (TILHS) method. They have been assessed for their ability to accurately predict the failure probability in a reasonable amount of time. The latter criterion is paramount for successful application to large industrial FE models, where the computation time is the main bottleneck. The accuracy has been examined with the comparison of the aforementioned methods with classical and advanced Monte-Carlo methodologies. Uncertainty is treated with the use of Transformation Method based on Fuzzy arithmetic concepts. Fuzzy arithmetic is an attractive mathematical concept to solve problems with uncertain parameters. The Transformation Method (TM) follows a fuzzy approach based on the concept of α-cuts, i.e. discretization of the parameter’s magnitude into a number of intervals. Uncertainty is then assessed by solving the problem in a systematic way: for each combination of the values attained by the uncertain parameters a deterministic computation of the response is performed. In this paper, the TM is demonstrated on an airplane FE model, to assess the effect of material stiffness uncertainty on the FRF from wing tip to pilot seat. A second demonstration example on this model aims to ensure a certain frequency difference between two free-free modes that may result in flutter at certain air speed; several reliability methods are applied for this purpose, namely Monte Carlo simulations, FORM and Importance Sampling.

To localize damages in engineering structures, such as power lines, ultrasonic wave-based techniques are widely used for Structural Health Monitoring applications. In a cylindrical waveguide, longitudinal, flexural and torsional modes may propagate. Additionally, the wave propagation is generally of dispersive nature. Since cable structures usually consist of several smaller wires, coupling in between individual wires must also be considered. Friction contact causes energy transfer and dissipation as well as mode conversion of propagating waves. Precise transient simulation of wave propagation in multi-wire cables with common FE software results in tremendous computational costs. Therefore, recent research follows a different strategy: only power flows due to propagating waves are considered. Since these models incorporate significant simplifications, a model assessment strategy through advanced fuzzy arithmetic is applied. Uncertainty in model parameters, especially due to simplification and idealization during the modeling process, is considered as epistemic uncertainty. Therefore, the effects of uncertain model parameters represented as fuzzy numbers are investigated by simulations with the use of the Transformation Method. Different models are simulated and an inverse fuzzy arithmetical technique is used to identify parameter uncertainty based on experimentally derived data. Finally, the models' validity is verified.

This paper develops Mean and Range control charts in fuzzy environment using different transformation methods. It is assumed that the observations of each sample are fuzzy random variables, which have triangular membership functions. After calculating fuzzy mean and fuzzy range of each sample using fuzzy arithmetic, their representative values are calculated exploiting the transformation methods. Then, using statistical properties of the obtained representative values and basic structure of Shewhart control charts, new Mean and Range control charts are constructed to monitor the process mean and variation. After that, the power of control charts constructed based on different transformation methods are examined applying average run length ARL criterion. According to this criterion, it is concluded that, contrary to the previous claim, these different transformation methods lead to mean and rang control charts with various performances. Moreover, it is represented that the value of α --level has significant influence on the performance of obtained control charts. Finally, it is derived that incorporating fuzziness into observations results in less powerful control charts.

The steam turbine and a boiler are important components of a power generation plant. Improved effciency of a power plant leads to increase of energy production and less waste. In this paper, a model of the power plant as a multivariable system using fuzzy arithmetic which is based on the Transformation Method (TM) is presented. The analytical solution is used to evaluate the state space model. The TM is then used to quantify the in uence of each parameter and their gain factors are calculated to allow estimation of relative measures of uncertainty. The method is applied to a boiler and a steam turbine systems for simulation, analysis and indication of TM's efficiency. The efficiency of TM is presented in this paper.

Groundwater is a crucial resource for water supply and irrigation in many parts of the world, especially in the Middle East. The Eocene aquifer, located in the northern part of the West Bank, Palestine, is threatened by unsustainable groundwater abstractions and on-ground pollution. Analysis and management of this aquifer are challenging because of limited data availability. This research contributes to the long-term sustainability of the aquifer by model-based design of future abstraction strategies considered within an uncertainty analysis framework. The methodology employed started with development of a single-layer steady-state MODFLOW groundwater model of the area, followed by uncertainty analysis of model parameters using Monte Carlo simulations. The same model was afterwards coupled with a Successive Linear Programming (SLP) optimization algorithm, implemented in the Groundwater Management tool (GWM) of the United States Geological Survey (USGS). The purpose of optimization was deriving five optimal abstraction strategies, each aiming to maximize groundwater abstraction, subject to different constraints regarding groundwater depletion. Given the uncertainty of model parameters, the sensitivity and reliability of these optimal strategies were then tested. Sensitivity was checked for two optimal strategies by performing re-optimization with different values of uncertain model parameters (one at a time). Reliability of the five strategies was tested by analyzing the extent of constraints’ violation for each strategy when varying the uncertain parameters using Monte Carlo simulations. Finally, the model was used for determining capture zones of wells for the five optimal abstraction strategies, land-use in these capture zones, and the associated estimates of on-ground nitrogen loading. The developed strategies were then deployed in a web-based decision support application (named Groundwater Decision Support System—GDSS), together with other relevant information. Users can analyze results of different optimal strategies in terms of groundwater level variations and total water balance results, and test consequences of uncertain parameters. Capture zones of wells for different abstraction strategies, together with land-use and on-ground nitrogen loading in these capture zones, are also presented. Results show that critical uncertain parameters are recharge, hydraulic conductivity, and conductance at key boundary condition locations. Optimal abstraction strategies results indicate that an increase in total abstractions could be between 5% and 20% from the current level (estimated at about 56 × 106 m3/year, which is about 74% of estimated annual recharge). The uncertain parameters, however, are impacting the sensitivity and the reliability of the optimal strategies to variable degrees. Recharge and hydraulic conductivity are the most critical uncertain parameters regarding sensitivity of the optimal strategies, while reliability is also impacted by the level of abstraction proposed in a given strategy (number, locations, and abstraction rates of new wells). The main novelty and contribution of this research is in combining modelling, uncertainty analysis, and optimization techniques in a comprehensive decision support system for the area of the Eocene aquifer, characterized with limited data availability.

Exact analytic solutions of the Schrodinger equation are obtained for classes of newly constructed potentials which are generated from the trigonometric Rosen-Morse potential as the input reference potential via extended transformation method. A set of quantized energy spectra of the bound states and the corresponding wave functions of the generated potentials are obtained. We also focus on to the Romanovski Polynomials which is a family of the real orthogonal polynomials and is required to present exact real analytic solutions of the generated potentials.

Exact analytic solutions of the Schrödinger equation are obtained for the classes of newly constructed hyperbolic type of potentials which are generated from the Eckart and trigonometric Rosen–Morse (tRM) potentials as input reference potentials via the extended transformation method. A set of quantized energy spectra of the bound states and the corresponding wavefunctions of the constructed potentials are obtained. We also focus on the Romanovski polynomial, which is a family of real orthogonal polynomials and is required to present exact solutions of tRM potential.

A new technique is presented for generating linear fractional transformation-based uncertainty models for use in the robustness analysis of flight control systems using the structured singular value p. The proposed approach can be almost fully automated and does not require closed-form linear expressions for how the aircraft dynamics vary as a function of the uncertain aircraft parameters. Only a nonlinear software model of the closed-loop aircraft, which can be efficiently trimmed and linearized numerically, is required. In the proposed technique, linear dependencies of the aircraft dynamics on the uncertain parameters are modeled by a multidimensional regression plane. Additional nonlinear dependencies are modeled using a band structure defined by nonlinearity compensation parameters. The capability of the proposed approach to identify worst-case uncertain parameter combinations is demonstrated through the robustness analysis of a lateral-axis control law for a generic civil transport aircraft. The approach is compared with classical analysis methods via the robustness analysis of a multivariable glide-slope coupler control law for a Boeing 747 transport aircraft.

Data assimilation is predominantly used for state estimation, combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts, we need good estimates of both the current system state and the model parameters. This article presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three‐dimensional variational (3D‐Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from synthetic aperture radar (SAR) satellite imagery and a ship‐borne survey is shown to significantly improve the predictive capability of the model over a 2‐year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this article considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D‐Var data assimilation algorithm for joint state‐parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation‐based state‐parameter estimation in coastal morphodynamic modelling. Copyright © 2012 Royal Meteorological Society

Many advanced methods proposed for control of robot manipulators are based on the dynamic models of the robot systems. Model-based control design needs a correct dynamic model and precise parameters of the system. Practically speaking, however, every dynamic model has some degrees of incorrectness and every parameter associates with some degrees of identification error. The incorrectness and errors eventually result positioning or trajectory tracking errors, and even cause the system to be unstable. In the past two decades, intensive research activities have been devoted on the design of robust control systems and adaptive control systems for the robot in order to overcome the control system drawback caused by the model errors and uncertain parameters, and a great number of research results have been reported, for example, (Hsia, 1989), (Kou, and Wang, 1989), (Slotine and Li, 1989), ( Spong, 1992), and (Cheah, Liu and Slotine, 2006). However, almost parts of results associate with complicated control system design approaches and difficulties in the control system implementation for industrial robot manipulators. Recently, neural network technology attracts many attentions in the design of robot controllers. It has been pointed out that multi-layered neural network can be used for the approximation of any nonlinear function. Other advantages of the neural networks often cited are parallel distributed structure, and learning ability. They make such the artificial intelligent technology attractive not only in the application areas such as pattern recognition, information and graphics processing, but also in intelligent control of nonlinear and complicated systems such as robot manipulators (Sanger, 1994), (Kim and Lewis, 1999), (Kwan and Lewis, 2000), (Jung and Yim, 2001) (Yu and Wang, 2001). A new field in robot control using neural network technology is beginning to emerge to deal with the issues related to the dynamics in the robot control design. A neural network based dynamics compensation method has been proposed for trajectory control of a robot system (Jung and Hsia, 1996). A combined approach of neural network and sliding mode technology for both feedback linearization and control error compensation has been presented (Barambones and Etxebarria, 2002). Sensitivity of a neural network performance to learning rate in robot control has been investigated (Clark and Mills, 2000). In the following, we present a simple control system consisting of a traditional controller and a neural network controller with parallel structure for trajectory tracking control of 16

Rheological models of tested rubber blend samples, with different ratios of smut/recycled material, were developed, analyzed and discussed according to experimental data. The experimental measurements show the dynamical behavior of these samples after a short-term axial load. The rheological model of samples was assumed as a viscoelastic Voigt-Maxwell and hyperelastic Mooney-Rivlin model. Real coded genetic algorithms were implemented for optimal model parameters identification in order to minimize the difference between the real sample behavior and dynamical model output. Numerical results obtained for analyzed mixture were compared with the original sample to verify the presented method. In purpose of predicting the dynamical characteristics for desirable rubber blends, an interrelation was formed based on the concentration of recycled material in sample blends and dynamical model parameters dependence.

This article investigates the effect of three uncertain parameters on a model of conjugated polymer actuators. These uncertain parameters are the diffusion coefficient (D), the resistance (R), and the double-layer thickness (δ). The model sensitivity to these parameters is analyzed and a parameter estimation study is performed using artificially generated data as well as laboratory yielded experimental measurements. The parameter estimation method used in this article is based on a Bayesian cost function, and gives us an insight on how much the estimation can be trusted, which is useful information for the design of controllers. Results indicate that for stochastic controllers to be designed effectively using this model, the resistance is the best known parameter and should therefore be designed for with greater confidence in its value, while the controller should be more robust with respect to the diffusion coefficient and the double-layer thickness. However, significant discrepancies between the model and its reduced form used for control purposes seem to indicate that a better suited model would be needed to start developing stochastic controllers.

<div class="htmlview paragraph">The purpose of dynamic modeling and simulation of Advanced Life Support (ALS) systems is to help design them. Static steady state systems analysis provides basic information and is necessary to guide dynamic modeling, but static analysis is not sufficient to design and compare systems. ALS systems must respond to external input variations and internal off-nominal behavior. Buffer sizing, resupply scheduling, failure response, and control system design are aspects of dynamic system design. We develop two dynamic mass flow models and use them in simulations to evaluate systems issues, optimize designs, and make system design trades. One model is of nitrogen leakage in the space station, the other is of a waste processor failure in a regenerative life support system.</div> <div class="htmlview paragraph">Most systems analyses are concerned with optimizing the cost/benefit of a system at its nominal steady-state operating point. ALS analysis must go beyond the static steady state to include dynamic system design. All life support systems exhibit behavior that varies over time. ALS systems must respond to equipment operating cycles, repair schedules, and occasional off-nominal behavior or malfunctions. Biological components, such as bioreactors, composters, and food plant growth chambers, usually have operating cycles or other complex time behavior. Buffer sizes, material stocks, and resupply rates determine dynamic system behavior and directly affect system mass and cost. Dynamic simulation is needed to avoid the extremes of costly over-design of buffers and material reserves or system failure due to insufficient buffers and lack of stored material.</div>

This paper proposes a comprehensive model to predict the dynamical coupling behaviors of a rotating rigid manipulator mounted on a rectangular plate, which represents real applications such as on-orbit array installation of solar panels. The three-dimensional relationship of displacement field between the end-effector, with arbitrary installation position and azimuth, and the rectangular plate is first established based on spatial descriptions and transformations method. Galerkin’s method is employed and extended to treat the spatial partial derivatives. Then, the governing equation of motion is derived using the Hamilton principle. The dynamic behavior of the system with respect to torque input, the variation of structural parameters as well as installation position and azimuth of the manipulator, is analyzed by simulation, which may provide some principles to control the vibration amplitude of plate and oscillating value of end-effector. Simulation results show that the presented three-dimensional dynamic model is more proper and accurate to describe the dynamic behaviors of system through comparison with two conventional dynamic models, and especially the large structure parameter manipulator is mounted on a rectangular plate.

In this paper, an equivalent multi‐body dynamics model of high‐speed train with uncertain parameter is established. Based on this detailed model and neural network minimum parameter learning algorithm, an adaptive sliding mode control method is designed for speed and position tracking control of high‐speed train, and the stability of the proposed control method is proved strictly. Then an adaptive fuzzy sliding mode control method (AFSMC) is presented to avoid chattering caused by excessive robust switching gain. Finally, numerical tests are carried out on the proposed AFSMC under different scenarios and operation strategies, and model reference adaptive control (MRAC), PID control and sliding mode control are also tested under the same condition for performance comparison. The results show that the proposed control method is superior to the currently used method. More specifically, compared with MRAC and PID, the average speed tracking accuracy of AFSMC is improved by 0.25 km/h and 0.18 km/h, and the average position tracking accuracy is improved by 0.68 m and 0.7 m, respectively.