Search results for: Differential speed rolling

Authors: Zdenek Bohuslavek

Abstract:

Development of microprocessor controlled sensor for measurement of wind speed and direction is the aim of this study. Electrical circuits and software were developed to the existing electromechanical part of the sensor TM-W2 becoming the properties of so-called smart sensor. The measured data about wind speed (sensitivity 0.01 m/s) and direction (0-360° by step 10°) are transmitted as 16-bit information. The connection between sensor and control unit is realized by radio communication (FM 433 MHz). Transition range is 220 m if used Quad type antenna. This concept provides substitution of actual cable systems by wireless ones.

Keywords: smart wind sensor, anemometer, wind speed, wireless communication

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Authors: Juan David Arango, Alejandro Restrepo-Martinez

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The Rolling Element Bearing (REB) vibration diagnosis is worth of special interest by the variety of REB and the wide necessity of those elements in industrial applications. The presence of a localized fault in a REB gives rise to a vibrational response, characterized by the modulation of a carrier signal. Frequency content of carrier signal (Spectral Frequency –f) is mainly related to resonance frequencies of the REB. This carrier signal is modulated by another signal, governed by the periodicity of the fault impact (Cyclic Frequency –α). In this sense, REB fault vibration response gives rise to a second-order cyclostationary signal. Second order cyclostationary signals could be represented in a bi-spectral map, where Spectral Coherence –SCoh are plotted against f and α. The Improved Envelope Spectrum –IES, is a useful approach to execute REB fault diagnosis. IES could be applied by the integration of SCoh over a predefined bandwidth on the f axis. Approaches to select f-bandwidth have been recently exposed by the definition of a metric which intends to evaluate the magnitude of the IES at the fault characteristics frequencies. This metric is represented in a 1/3-binary tree as a function of the frequency bandwidth and centre. Based on this binary tree the optimal frequency band is selected. However, some advantages have been seen if the metric is changed, which in fact tends to dictate different optimal f-bandwidth and so improve the IES representation. This paper evaluates the behaviour of the IES from a different metric optimization. This metric is based on the sample correlation coefficient, detecting high peaks in the selected frequencies while penalizing high peaks in the neighbours of the selected frequencies. Prior results indicate an improvement on the signal-noise ratio (SNR) on around 86% of samples analysed, which belong to IMS database.

Keywords: Sample Correlation IESFOgram, cyclostationary analysis, improved envelope spectrum, IES, rolling element bearing diagnosis, spectral coherence.

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Authors: Manish Pal, Rumi Sutradhar

Abstract:

Pavement surface unevenness plays a pivotal role on roughness index of road which affects on riding comfort ability. Comfort ability refers to the degree of protection offered to vehicle occupants from uneven elements in the road surface. So, it is preferable to have a lower roughness index value for a better riding quality of road users. Roughness is generally defined as an expression of irregularities in the pavement surface which can be measured using different equipments like MERLIN, Bump integrator, Profilometer etc. Among them Bump Integrator is quite simple and less time consuming in case of long road sections. A case study is conducted on low volume roads in West District in Tripura to determine roughness index (RI) using Bump Integrator at the standard speed of 32 km/h. But it becomes too tough to maintain the requisite standard speed throughout the road section. The speed of Bump Integrator (BI) has to lower or higher in some distinctive situations. So, it becomes necessary to convert these roughness index values of other speeds to the standard speed of 32 km/h. This paper highlights on that roughness index conversional model. Using SPSS (Statistical Package of Social Sciences) software a generalized equation is derived among the RI value at standard speed of 32 km/h and RI value at other speed conditions.

Keywords: Bump Integrator, Pavement Distresses, Roughness Index, SPSS.

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Authors: Rudolf Csikja, Janos Toth

Abstract:

Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.

Keywords: blow up, finite escape time, polynomial ODE, singularity, Lotka–Volterra equation, Painleve analysis, Ψ-series, global existence

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Authors: Cheng-Ying Lo

Abstract:

This paper adopted the hybrid differential transform approach for studying heat transfer problems in a gold/chromium thin film with an ultra-short-pulsed laser beam projecting on the gold side. The physical system, formulated based on the hyperbolic two-step heat transfer model, covers three characteristics: (i) coupling effects between the electron/lattice systems, (ii) thermal wave propagation in metals, and (iii) radiation effects along the interface. The differential transform method is used to transfer the governing equations in the time domain into the spectrum equations, which is further discretized in the space domain by the finite difference method. The results, obtained through a recursive process, show that the electron temperature in the gold film can rise up to several thousand degrees before its electron/lattice systems reach equilibrium at only several hundred degrees. The electron and lattice temperatures in the chromium film are much lower than those in the gold film.

Keywords: Differential transform, hyperbolic heat transfer, thin film, ultrashort-pulsed laser.

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Authors: Patrick Nwabueze Okechukwu, Ima Nirwana Soelaiman, Gabriele Anisah Ruth Froemming, Mohd Yusri Idorus, Norazlina Mohamed

Abstract:

Supplementation of palm vitamin E has been reported to prevent loss of bone density in ovariectomised female rats. The mechanism by which palm vitamin E exerts these effects is still unknown. We hypothesized that palm vitamin E may act by preventing the protein expression changes. Two dimensional poly acyrilamide gel electrophoresis (2-D PAGE) and PD Quest software genomic solutions Investigator (proteomics) was used to analyze the differential protein expression profile in femoral and humeri bones harvested from three groups of rats; sham-operated rats (SO), ovariectomised rats (Ovx) and ovariectomised rats supplemented for 2 months with palm vitamin E. The results showed that there were over 300 valued spot on each of the groups PVE and OVX as compared to about 200 in SO. Comparison between the differential protein expression between OVX and PVE groups showed that ten spots were down –regulated in OVX but up-regulated in PVE. The ten differential spots were separately named P1-P10. The identification and understanding of the pathway of the differential protein expression among the groups is ongoing and may account for the molecular mechanism through which palm vitamin E exert its anti-osteoporotic effect.

Keywords: Palm vitamin E, ovariectomised, osteoporosis protein expression, 2-d-page.

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Authors: Ben Hamed M., Sbita L

Abstract:

This paper presents a new method for the implementation of a direct rotor flux control (DRFOC) of induction motor (IM) drives. It is based on the rotor flux components regulation. The d and q axis rotor flux components feed proportional integral (PI) controllers. The outputs of which are the target stator voltages (vdsref and vqsref). While, the synchronous speed is depicted at the output of rotor speed controller. In order to accomplish variable speed operation, conventional PI like controller is commonly used. These controllers provide limited good performances over a wide range of operations even under ideal field oriented conditions. An alternate approach is to use the so called fuzzy logic controller. The overall investigated system is implemented using dSpace system based on digital signal processor (DSP). Simulation and experimental results have been presented for a one kw IM drives to confirm the validity of the proposed algorithms.

Keywords: DRFOC, fuzzy logic, variable speed drives, control, IM and real time.

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Authors: M. O. Ale, S. I. Manuwa, O. J. Olukunle, T. Ewetumo

Abstract:

Five varying speeds of 1.5, 1.8, 2.1, 2.3 and 2.6 km/h were used at a constant soil depth of 100 mm to determine the effects of forward speed on the draught requirement of a semi-automatic cassava planter under pneumatic wheel and rigid wheel usage on a well-prepared sandy clay loam soil. The soil draught was electronically measured using an on-the-go soil draught measuring instrumentation system developed for the purpose of this research. The results showed an exponential relationship between forward speed and draught in which draught ranging between 24.91 and 744.44 N increased with an increase in forward speed in the rigid wheel experiment. This is contrary to the polynomial relationship observed in the pneumatic wheel experiment in which the draught varied between 96.09 and 343.53 N. It was observed in the experiments that the optimum speed of 1.5 km/h had the least values of draught in both the pneumatic wheel and rigid wheel experiments with higher values in the pneumatic experiment. It was generally noted that the rigid wheel planter with the less value of draught requires less energy requirement for operation. It is therefore concluded that operating the semi-automatic cassava planter with rigid wheels will be more economical for cassava farmers than operating the planter with pneumatic wheels.

Keywords: Cassava planter, planting, forward speed, draught, wheel type.

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Option price valuation, Partial Differential Equations, Black-Scholes PDEs, Ito process.

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Authors: V. Chitra, R. S. Prabhakar

Abstract:

Because of the low maintenance and robustness induction motors have many applications in the industries. The speed control of induction motor is more important to achieve maximum torque and efficiency. Various speed control techniques like, Direct Torque Control, Sensorless Vector Control and Field Oriented Control are discussed in this paper. Soft computing technique – Fuzzy logic is applied in this paper for the speed control of induction motor to achieve maximum torque with minimum loss. The fuzzy logic controller is implemented using the Field Oriented Control technique as it provides better control of motor torque with high dynamic performance. The motor model is designed and membership functions are chosen according to the parameters of the motor model. The simulated design is tested using various tool boxes in MATLAB. The result concludes that the efficiency and reliability of the proposed speed controller is good.

Keywords: Induction motor, Field Oriented Control, Fuzzy logic controller, Maximum torque, Membership function.

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Authors: M. Zerikat, S. Chekroun

Abstract:

This paper proposes an effective adaptation learning algorithm based on artificial neural networks for speed control of an induction motor assumed to operate in a high-performance drives environment. The structure scheme consists of a neural network controller and an algorithm for changing the NN weights in order that the motor speed can accurately track of the reference command. This paper also makes uses a very realistic and practical scheme to estimate and adaptively learn the noise content in the speed load torque characteristic of the motor. The availability of the proposed controller is verified by through a laboratory implementation and under computation simulations with Matlab-software. The process is also tested for the tracking property using different types of reference signals. The performance and robustness of the proposed control scheme have evaluated under a variety of operating conditions of the induction motor drives. The obtained results demonstrate the effectiveness of the proposed control scheme system performances, both in steady state error in speed and dynamic conditions, was found to be excellent and those is not overshoot.

Keywords: Electric drive, Induction motor, speed control, Adaptive control, neural network, High Performance.

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Authors: Rajesh Kumar, Roopali Dogra, Puneet Aggarwal

Abstract:

Based on a survey conducted for second and third year students of the electrical engineering department at Maharishi Markandeshwar University, India, it was found that around 92% of students felt that it would be better to introduce a virtual environment for laboratory experiments. Hence, a need was felt to perform modern pedagogy techniques for students which consist of a virtual environment using MATLAB/Simulink. In this paper, a virtual environment for the speed control of a DC motor is performed using MATLAB/Simulink. The various speed control methods for the DC motor include the field resistance control method and armature voltage control method. The performance analysis of the DC motor is hence analyzed.

Keywords: Pedagogy techniques, speed control, virtual environment, DC motor, field control, voltage control.

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Authors: Fuziyah Ishak, Mohamed B. Suleiman, Zanariah A. Majid, Khairil I. Othman

Abstract:

This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is evident that the block method performs very well. Stability regions of the block method are also investigated.

Keywords: block method, delay differential equations, predictor-corrector, stability region, variable stepsize variable order.

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Authors: I. U. Wickramasinghe, D. J. Hargreaves, D. V. De Pellegrin

Abstract:

This paper presents a strategy to predict the lifetime of rails subjected to large rolling contact loads that induce ratchetting strains in the rail head. A critical element concept is used to calculate the number of loading cycles needed for crack initiation to occur in the rail head surface. In this technique the finite element method (FEM) is used to determine the maximum equivalent ratchetting strain per load cycle, which is calculated by combining longitudinal and shear stains in the critical element. This technique builds on a previously developed critical plane concept that has been used to calculate the number of cycles to crack initiation in rolling contact fatigue under ratchetting failure conditions. The critical element concept simplifies the analytical difficulties of critical plane analysis. Finite element analysis (FEA) is used to identify the critical element in the mesh, and then the strain values of the critical element are used to calculate the ratchetting rate analytically. Finally, a ratchetting criterion is used to calculate the number of cycles to crack initiation from the ratchetting rate calculated.

Keywords: Critical element analysis, finite element modeling (FEM), wheel/rail contact.

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Authors: Zhang Tianci, Ding Meng, Zuo Hongfu, Zeng Lina, Sun Zejun

Abstract:

Automation of airport operations can greatly improve ground movement efficiency. In this paper, we study the speed profile design problem for advanced airport ground movement control and guidance. The problem is constrained by the surface four-dimensional trajectory generated in taxi planning. A decomposed approach of two stages is presented to solve this problem efficiently. In the first stage, speeds are allocated at control points, which ensure smooth speed profiles can be found later. In the second stage, detailed speed profiles of each taxi interval are generated according to the allocated control point speeds with the objective of minimizing the overall fuel consumption. We present a swarm intelligence based algorithm for the first-stage problem and a discrete variable driven enumeration method for the second-stage problem, since it only has a small set of discrete variables. Experimental results demonstrate the presented methodology performs well on real world speed profile design problems.

Keywords: Airport ground movement, fuel consumption, particle swarm optimization, smoothness, speed profile design.

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Authors: N. A. Samat, D. F. Percy

Abstract:

The main aim of this study is to describe and introduce a method of numerical analysis in obtaining approximate solutions for the SIR-SI differential equations (susceptible-infectiverecovered for human populations; susceptible-infective for vector populations) that represent a model for dengue disease transmission. Firstly, we describe the ordinary differential equations for the SIR-SI disease transmission models. Then, we introduce the numerical analysis of solutions of this continuous time, discrete space SIR-SI model by simplifying the continuous time scale to a densely populated, discrete time scale. This is followed by the application of this numerical analysis of solutions of the SIR-SI differential equations to the estimation of relative risk using continuous time, discrete space dengue data of Kuala Lumpur, Malaysia. Finally, we present the results of the analysis, comparing and displaying the results in graphs, table and maps. Results of the numerical analysis of solutions that we implemented offers a useful and potentially superior model for estimating relative risks based on continuous time, discrete space data for vector borne infectious diseases specifically for dengue disease. 

Keywords: Dengue disease, disease mapping, numerical analysis, SIR-SI differential equations.

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Authors: Yuan L. Lai, Jian H. Chen, Jui P. Hung

Abstract:

Owning to the high-speed feed rate and ultra spindle speed have been used in modern machine tools, the tool-path generation plays a key role in the successful application of a High-Speed Machining (HSM) system. Because of its importance in both high-speed machining and tool-path generation, approximating a contour by NURBS format is a potential function in CAD/CAM/CNC systems. It is much more convenient to represent an ellipse by parametric form than to connect points laboriously determined in a CNC system. A new approximating method based on optimum processes and NURBS curves of any degree to the ellipses is presented in this study. Such operations can be the foundation of tool-radius compensation interpolator of NURBS curves in CNC system. All operating processes for a CAD tool is presented and demonstrated by practical models.

Keywords: Ellipse, Approximation, NURBS, Optimum.

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Authors: P. Karimi, A. H. Khedmati Bazkiaei

Abstract:

The main goal of this study is to test differential neural network as a controller of smart structure and is to enumerate its advantages and disadvantages in comparison with other controllers. In this study, the smart structure has been considered as a Euler Bernoulli cantilever beam and it has been tried that it be under control with the use of vibration neural network resulting from movement. Also, a linear observer has been considered as a reference controller and has been compared its results. The considered vibration charts and the controlled state have been recounted in the final part of this text. The obtained result show that neural observer has better performance in comparison to the implemented linear observer.

Keywords: Smart material, on-line differential artificial neural network, active control, finite element method.

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Authors: Mohd Sazli Saad, Hishamuddin Jamaluddin, Intan Zaurah Mat Darus

Abstract:

This paper presents the development of an active vibration control using direct adaptive controller to suppress the vibration of a flexible beam system. The controller is realized based on linear parametric form. Differential evolution optimisation algorithm is used to optimize the controller using single objective function by minimizing the mean square error of the observed vibration signal. Furthermore, an alternative approach is developed to systematically search for the best controller model structure together with it parameter values. The performance of the control scheme is presented and analysed in both time and frequency domain. Simulation results demonstrate that the proposed scheme is able to suppress the unwanted vibration effectively.

Keywords: flexible beam, finite difference method, active vibration control, differential evolution, direct adaptive controller

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular equation.

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Authors: Gu Wei, Gao Wei

Abstract:

In this report, an OTA which is used in fully differential pipelined ADC was described. Using gain-boost architecture with difference-ended amplifier, this OTA achieve high-gain and high-speed. Besides, the CMFB circuit is also used, and some methods are concerned to improve the performance. Then, by optimization the layout design, OTA-s mismatch was reduced. This design was using TSMC 0.18um CMOS process and simulation both schematic and layout in Cadence. The result of the simulation shows that the OTA has a gain up to 80dB,a unity gain bandwidth of about 1.437GHz for a 2pF load, a slew rate is about 428V/μs, a output swing is 0.2V~1.35V, with the power supply of 1.8V, the power consumption is 88mW. This amplifier was used in a 10bit 150MHz pipelined ADC.

Keywords: OTA, common drain, CMFB, pipelined ADC

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Authors: Adeosun S. Oluropo, Sekunowo O. Israel, Talabi S. Isaac

Abstract:

This study investigated the combined effect of cold rolling and heat treatment on the mechanical properties of Al-Ti alloy. Samples of the alloy are cast in metal mould to obtain 0.94-2.19wt% mixes of titanium. These samples are grouped into untreated (as-cast) and those that are cold rolled to fifty percent reduction, homogenized at 500⁰C and soaked for one hour. The cold rolled and heat treated samples are normalized (RT_n) and quench-tempered (RT_q-t) at 100⁰C. All these samples are subjected to tensile, micro-hardness and microstructural evaluation. Results show remarkable improvement in the mechanical properties of the cold rolled and heat treated samples compared to the as-cast. In particular, the RT_q-t samples containing titanium in the range of 1.7-2.2% demonstrates improve tensile strength by 24.7%, yield strength, 28%, elastic modulus, 38.3% and micro-hardness, 20.5%. The Al₃Ti phase being the most stable precipitate in the α-Al matrix appears to have been responsible for the significant improvement in the alloy’s mechanical properties. It is concluded that quench and temper heat treatment is an effective method of improving the strength-strain ratio of cold rolled Al-.0.9-2.2%Ti alloy.

Keywords: Aluminum-titanium alloy, heat treatment, mechanical properties, precipitate.

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Authors: F. Pourhasanzade, S. H. Sabzpoushan

Abstract:

The heart tissue is an excitable media. A Cellular Automata is a type of model that can be used to model cardiac action potential propagation. One of the advantages of this approach against the methods based on differential equations is its high speed in large scale simulations. Recent cellular automata models are not able to avoid flat edges in the result patterns or have large neighborhoods. In this paper, we present a new model to eliminate flat edges by minimum number of neighbors.

Keywords: Cellular Automata, Action Potential Simulation, Isotropic Pattern.

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Authors: H. Ghanbari, H. Nikbakht, A. Zahedi, M. Ghanbari

Abstract:

This paper is focusing on designing a control system for wind turbine which can control the speed and output power according to arbitrary algorithm. Reference Tracking Method is used to control the turbine spinning speed in order to increase its output energy.

Keywords: Wind Turbine, Simulink, Reference Tracking Method.

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Authors: A. M. Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different four discrete schemes, each of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: Kholod M. Abu-Alnaja

Abstract:

In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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Authors: Faranak Rabiei, Fudziah Ismail, S. Norazak, Saeid Emadi

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In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.

Keywords: Improved Runge-Kutta Nystrom method, Two step method, Second-order ordinary differential equations, Order conditions

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Authors: Banaja Mohanty, Prakash Kumar Hota

Abstract:

This paper demonstrates dynamic performance evaluation of load frequency control (LFC) with different intelligent techniques. All non-linearities and physical constraints have been considered in simulation studies such as governor dead band (GDB), generation rate constraint (GRC) and boiler dynamics. The conventional integral time absolute error has been considered as objective function. The design problem is formulated as an optimisation problem and particle swarm optimisation (PSO), bacterial foraging optimisation algorithm (BFOA) and differential evolution (DE) are employed to search optimal controller parameters. The superiority of the proposed approach has been shown by comparing the results with published fuzzy logic control (FLC) for the same interconnected power system. The comparison is done using various performance measures like overshoot, undershoot, settling time and standard error criteria of frequency and tie-line power deviation following a step load perturbation (SLP). It is noticed that, the dynamic performance of proposed controller is better than FLC. Further, robustness analysis is carried out by varying the time constants of speed governor, turbine, tie-line power in the range of +40% to -40% to demonstrate the robustness of the proposed DE optimized PID controller.

Keywords: Automatic generation control, governor dead band, generation rate constraint, differential evolution.

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Authors: Dileep Malkhede, Bhartendu Seth

Abstract:

In this paper, the full state feedback controllers capable of regulating and tracking the speed trajectory are presented. A fourth order nonlinear mean value model of a 448 kW turbocharged diesel engine published earlier is used for the purpose. For designing controllers, the nonlinear model is linearized and represented in state-space form. Full state feedback controllers capable of meeting varying speed demands of drivers are presented. Main focus here is to investigate sensitivity of the controller to the perturbations in the parameters of the original nonlinear model. Suggested controller is shown to be highly insensitive to the parameter variations. This indicates that the controller is likely perform with same accuracy even after significant wear and tear of engine due to its use for years.

Keywords: Diesel engine model, Engine speed control, State feedback controller, Controller robustness.

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

Keywords: Eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Itô chaos expansion.

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