The repeated failure of Agitator in the Phosphoric acid Reactor in MPC was a major incident causing high downtime and production loss. While doing the root cause analysis of this “Class A” incident many causes not considered in normal agitator design were considered and analyzed. This paper lists such special cases and the proposed solutions and calculations to be incorporated in design of critical systems with varying process fluid parameters for different applications. Agitators constitute almost 20% of rotating equipment in a fertilizer and similar plants but are given less priority compared to others until a severe failure happens. There are no standard analytical design criteria for agitator design due to large variations and uncertainties in the process conditions in the reactor or tank. Most designs are left to the EPC companies using preformatted design models based on experimental results, on the combination of few variables. (Like Power Number, Pumping Number, Geometrical ratios etc.) However, none these models considers the fluid flow conditions which changes inside the reactor which affects the agitator design in many ways like Localized flow, non-homogenous fluid, solid contents, Liquid additives or recycling etc. which can cause much higher alternating forces and bending stresses at the joints holding the blades causing fatigue and other failures. This paper gives more quantitative design calculations to determine the forces acting on the agitator and blades as listed above which can be used in similar application even with different fluids.

The numerical analysis of heat transfer by finite element method (FEM) has been used widely. It is usually assumed that the parameters relevant to the heat transfer process are accurately known. However, many of these parameters may vary in a random way in reality. The reliability of the heat transfer performance is needed to be evaluated. The paper introduces an accurate, efficient sensitivity analysis method to compute the FEM response with respect to input parameters. Combining this sensitivity analysis, first order reliability method (FORM) algorithm based stochastic finite element method (SFEM) method is used to evaluate the reliability of the limit state for heat conduction of a benchmark plate with input uncertainties.

The study concerns the coating process of metal substrates in an electrostatic fluidized bed (EFB). This eco-friendly process is profitably used to coat components of particularly complex shapes. Although this technology is widely spread in several industrial domains, the implementation of appropriate process control procedures is still object of investigation. A model was generated from experimental data with the aim of predicting, for any set of process parameters, the resulting coating thickness of the sample. With a design of experiment (DOE) approach, the experimental investigation, that is the base for the model, quantifies the coating thickness as a function of the main process parameters namely coating time, applied voltage, and gas flow rate fed into the fluidized bed. This study addresses the effect of the inherent uncertainties on the predicted coating thickness caused by the approximation in the model parameters. In particular, a fuzzy-logic based approach is used to describe the model uncertainties and the transformation method is used to propagate their effect on the thickness. The fuzzy results are then compared with the data produced by the experimentation leading to the evaluation of the membership level of the dataset to the uncertain model.

A Piezoelectric Energy Harvester (PEH) of cantilever beam type is developed to optimize the generated power by means of active control of moment of inertia of the beam. Distributed parameter equations of vibration of the beam are developed. Then the electromechanical response of the piezoelectric actuator is discussed. The harvester configuration is then described and it is shown that such a configuration can avoid the drastic power drop in presence of uncertainty around resonance frequency by applying voltage to the piezoelectric actuator. Finally the proposed harvester output power working frequency span is compared to conventional methods to show that the significant performance optimization in proposed method is achieved.

Two new Sliding Mode Control (SMC) design methods for nonlinear systems are presented in order to eliminate the reaching phase in the SMC. The sliding surface design approaches are based on optimal sliding surface selection methods for Linear Time Invariant (LTI) and Linear Time Varying (LTV) systems. The reaching phase is eliminated by confining the LTI/LTV system on a predefined linear level surface that moves to the designed optimal sliding hyperplane exponentially. The methodology is extended to nonlinear systems by using two approaches; the “State Dependent Riccati Equation” (SDRE) and “Approximating Sequence of Riccati equations” (ASRE) methods. Systematic ways are defined to eliminate the reaching phase and to design optimal sliding surface for the nonlinear system. The proposed methods are then applied to a spacecraft model with flexible solar panels in order to control the attitude and to suppress some of the vibration modes of the flexible panels. Numerical simulations are used to illustrate the application of proposed methods which are also compared with each other to reveal the effectiveness in coping with uncertainty and vibration suppression and minimization of the energy cost.

This work addresses the problem of the reliability of simulations for realistic nonlinear systems, by using efficient techniques for the analysis of the propagation of the uncertainties of the model parameters through the dynamics of the system. We present the sensitivity analysis of the critical speed of a railway vehicle with respect to its suspension design. The variance that stems from parameter tolerances of the suspension is taken into account and its propagation through the dynamics of a full car with a couple of two-axle Cooperrider bogies running on curved track is studied. Modern Uncertainty Quantification methods, such as Stochastic Collocation and Latin Hypercube, are employed in order to assess the global uncertainty in the computation of the critical speed. The sensitivity analysis of the critical speed to each parameter and combination of parameters is then carried out in order to quantify the importance of different suspension components. This is achieved using combined approaches of sampling methods, ANOVA expansions, Total Sensitivity Indices and Low-dimensional Cubature Rules.

This paper proposes a method that dynamically improves a statistical model of system degradation by incorporating uncertainty. The method is illustrated by a case example of fouling, or degradation, in a heat exchanger in a cogeneration desalination plant. The goal of the proposed method is to select the best model from several representative condenser fouling models including linear, falling rate, and asymptotic fouling, and to validate and improve model parameters over the duration of operation. Maximum likelihood estimation (MLE) was applied to obtain a stochastic distribution of condenser fouling. Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) were then computed at time intervals to assess the accuracy of the MLE results. The degradation model was further evaluated by estimating future prognoses and then cross-validating with real world fouling data. The results show the accuracy of a prognosis can be improved substantially by continuously updating fouling model parameters. The proposed method is a step toward facilitating prognosis of engineering systems in the early design stages by improving the prediction of future component degradation.

For Multi-Objective Robust Optimization Problem (MOROP), it is important to obtain design solutions that are both optimal and robust. To find these solutions, usually, the designer need to set a threshold of the variation of Performance Functions (PFs) before optimization, or add the effects of uncertainties on the original PFs to generate a new Pareto robust front. In this paper, we divide a MOROP into two Multi-Objective Optimization Problems (MOOPs). One is the original MOOP, another one is that we take the Robustness Functions (RFs), robust counterparts of the original PFs, as optimization objectives. After solving these two MOOPs separately, two sets of solutions come out, namely the Pareto Performance Solutions ( P P ) and the Pareto Robustness Solutions ( P R ). Make a further development on these two sets, we can get two types of solutions, namely the Pareto Robustness Solutions among the Pareto Performance Solutions ( P R ( P P ) ), and the Pareto Performance Solutions among the Pareto Robustness Solutions ( P P ( P R ) ). Further more, the intersection of P R ( P P ) and P P ( P R ) can represent the intersection of P R and P P well. Then the designer can choose good solutions by comparing the results of P R ( P P ) and P P ( P R ) . Thanks to this method, we can find out the optimal and robust solutions without setting the threshold of the variation of PFs nor losing the initial Pareto front. Finally, an illustrative example highlights the contributions of the paper.

In this paper the results of an experimental activity carried out with the aim to investigate on the frictional behaviour of visco-elastic materials in sliding contact with road asperities is presented. Experiments are carried out using a prototype of pin on disk machine whose pin is constituted by a specimen of rubber coming from a commercial tyre while the disk may be in glass, marble or abrasive paper. Tests are performed both in dry and wet conditions. Roughness of the disk materials is evaluated by a tester and by a laser scan device. Temperature in proximity of the contact patch is measured by pyrometer pointed on the disk surface in the pin trailing edge, while room temperature is measured by a thermocouple. Sliding velocity is imposed by an inverter controlled motor driving the disk and measured by an incremental encoder. Vertical load is imposed applying calibrated weights on the pin and friction coefficients are measured acquiring the longitudinal forces signal by means of a load cell. As regards to the road roughness, the experimental results show a marked dependence with road R a index. Dry and wet tests performed on different micro-roughness profiles (i.e. glass and marble) highlighted that friction coefficient in dry conditions is greater on smoother surfaces, while an opposite tendency is shown in wet conditions. Although affected by uncertainties the results confirm the dependence of friction on temperature, vertical load and track conditions.

The numerical optimization of the connecting rod big-end lubrication involves several main steps. The first, which can be considered as the most important one, is the identification of the main input factors and their varying range. In the same time, the meaningful resulting values have to be identified because the optimization will be performed on the basis of this choice. The computing time for a TEHD solution prevents from performing a huge amount of calculi to draw the Pareto-Front of the solutions. Thus, the next step is the creation of a metamodel, based on polynomials, with a good predictability property and a low computing cost. In the third step, a fast Multi Objective Optimization is performed on the metamodel. The Pareto-Front, which represents the best trade-offs of solutions, is identified: one can now easily choose the input parameters which will give a particular desired solution. In the last step, the robustness of the solutions has to be checked: if a given solution is chosen, the corresponding input parameters have to enclose a minimal uncertainty gap to be realistic. Otherwise, this wanted solution will never be reached, because in a real-life problem, the parameter values are not deterministic.

Verification of dimensional compliance is becoming a crucial aspect in every kind of production, even when the size of the product to be checked is in the order of several meters. To this purpose, several tools based on different technologies, working principles, functionalities and architectures have been recently designed. Among these, a distributed flexible system based on a network of low cost infrared (IR) cameras — the Mobile Spatial coordinate Measuring System (MScMS) — has been developed. This paper proposes a model for the real time assessment of the system uncertainty referring to the measured point coordinates in the 3D space. The paper focuses on the sources of measurement uncertainty and, basing on the multivariate law of propagation of uncertainty, suggests a model for relating them to the uncertainty of a measured point.

In industrial plants some parameters can not be evaluated properly or they are varying with time. These parametric uncertainties has to be taken into account during the design process of industrial systems. In this work, the developped optimization approach is applied on an industrial roll-to-roll sytem. Such systems are commonly used to handle materials as polymer, metal, paper and textile. The key challenge is to move the web at the expected speed while maintaining the web tension in an acceptable range around its reference. Moreover, the Young’s modulus of the web is difficult to evaluate and it is varying with time due to temperature and moisture variations. This paper deals with the web tension controller synthesis on a large-scale roll-to-roll system with uncertain Young’s modulus. To synthesize web tension controllers, an H∞ approach is applied and adapted to the system with parametric uncertainties using multi-objective robust design optimization.

The presence of numerous localized sources of uncertainties in stochastic models leads to high dimensional and multiscale problems. A numerical strategy is here proposed to propagate the uncertainties through such models. It is based on a multiscale domain decomposition method that exploits the localized side of uncertainties. The separation of scales has the double benefit of improving the conditioning of the problem as well as the convergence of tensor based methods (namely Proper Generalized Decomposition methods) used within the strategy for the separated representation of high dimensional stochastic parametric solutions.

The paper takes on the issue of uncertainty in statistical methods of cracks propagation. The goal of the paper was to develop a method, which would enable use of diagnostic information in assessment of fatigue damage process. Particular attention was paid to the possibility of forecasting the occurrence of damage due to fatigue while relying on the analysis of the structure of a vibroacoustic signal. The difficulty in this case is that the set of parameters containing diagnostic information may change as defects develop. This fact confirms the necessity of examining the evolution of probability distribution and defining the periods of an object’s operation, carried out while taking into account the actual technical condition as well as the associated identification of defect development phases. The study presents the following issue: developing the method of diagnosing the early stages of defect development while analyzing energy of vibroacoustics signal as parameter of logistics model of cracks development.

This paper presents an application of adaptive 2 nd order sliding mode control. This control is based on twisting algorithm and ensures a finite time convergence to the sliding manifold σ = σ̇ = 0, σ being the sliding variable and defined from the control objectives. The control solution required a limited information about the uncertainties and the disturbances acting on the system. This control strategy is applied to an electropneumatic set-up. This bench consists of two rod coupled pneumatic cylinders: one cylinder is controlled on position and perturbed by the second cylinder which is force-controlled. The efficacy of this strategy is evaluated through some simulations.

This work presents an approach to solve stochastic optimal control problems in the application of flow quality management in reservoir systems. These applications are challenging because they require real-time decision-making in the presence of uncertainties such as wind velocity. These uncertainties must be accounted for as stochastic variables in the mathematical model. In addition, computational costs and storage requirements increase rapidly due to the stochastic nature of the simulations and optimisation formulations. To overcome these challenges, an approach is developed that uses the combination of a reduced-order model and an adjoint-based method to compute the optimal solution rapidly. The system is modelled by a system of stochastic partial differential equations. The finite element method together with collocation in the stochastic space provide an approximate numerical solution—the “full model”, which cannot be solved in real-time. The proper orthogonal decomposition and Galerkin projection technique are applied to obtain a reduced-order model that approximates the full model. The conjugate-gradient method with Armijo line-search is then employed to find the solution of the optimal control problem under the uncertainty of input parameters. Numerical results show that the stochastic control yields solutions that are above the bound of the set solutions of the deterministic control. Applying the reduced model to the stochastic optimal control problem yields a speed-up in computational time by a factor of about 80 with acceptable accuracy in comparison with the full model. Application of the optimal control strategy shows the potential effectiveness of this computational modeling approach for managing flow quality.

The multihead weigher is a complex machine which has to be properly configured and managed by taking into account the uncertainty of the load cells. Specifically, this paper focuses on the configuration problem of the multihead weigher First an objective function is proposed. This function considers both the costs of “non conforming” packages (i.e. packages that have to be scrapped or reworked because their weight is below the law lower limit) and the cost of extra product (i.e. cost of material that exceeds the target weight). Secondly, the paper presents an approach to select the average weight to be set for each hopper by combining a RSM (Response Surface Methodology) and a multihead weighing machine simulator. The performance of the proposed approach is presented and discussed.

This paper aims at handling high dimensional uncertainty propagation problems by proposing a tensor product approximation method based on regression techniques. The underlying assumption is that the model output functional can be well represented in a separated form, as a sum of elementary tensors in the stochastic tensor product space. The proposed method consists in constructing a tensor basis with a greedy algorithm and then in computing an approximation in the generated approximation space using regression with sparse regularization. Using appropriate regularization techniques, the regression problems are well posed for only few sample evaluations and they provide accurate approximations of model outputs.

Often a designer has the problem to apply a suitable system of geometrical and dimensional tolerances to an assembly. The right solution is not unique, in fact it depends on the chosen parameters. If the tolerances have to be optimized, some important parameters have to be taken into account, e.g. the efficiency of each prescription, or if this last is reachable, or it can be verified and how much the realization costs. The authors opinion is that a statistical approach based on the Monte Carlo Method is very useful when the tolerances chains are complex. This paper shows an application of this method in order to verify the functional alignment between two assemblies and a critical analysis of the uncertainty in phase both of the component design and test. This study has been developed thanks to the strict requirements imposed by ESA (European Space Agency) on the components that Thales Alenia Space has to realize within the LISA Pathfinder experiment. The very critical aspect of this work is to reciprocally align two cylindrical elements of two different assemblies. The specifications require 100 μm as maximum linear displacement and 300 μrad as maximum angular displacement. Moreover this prescriptions have to be verified also when the two elements are independently moving. To be able to reach such strict accuracy level the components have been assembled in an ISO 100 class cleanroom and the work space was a 3D Coordinate-Measuring Machine (CMM). The cylindrical elements have a 10 mm diameter, so the value of the measurement uncertainty associated with the alignment check is fundamental. Starting from the different uncertainty sources, the measurability and verifiability of the alignment have been considered and evaluated. The overall uncertainty has been assessed by numerical simulations which have taken into account the dimensional, geometrical and form tolerances as well as the instrumental uncertainty of the 3D CMM. This estimation has been positively validated by a session of repeated measurements. Numerical simulations have also allowed performing a sensitivity analysis, in order to give information about which sources more contribute to the overall uncertainty.

Depleting oil reserves in shallow water are opening the avenues of new ventures in deep sea conditions. India is no exception; deep sea explorations are highly recommended and exercised. As part of the design process, there are requirements of structural strength based on criteria referring to failure modes, such as rupture by over loading, fatigue failures, buckling or an unstable fracture. 3D Nonlinear dynamic analysis of riser is obtained in the time domain using finite element solver ABAQUS/Aqua. The response histories so obtained are employed for the study of fatigue reliability analysis of riser. It is based on a bi-linear relationship to model fatigue crack growth and incorporates a failure criterion to describe the interaction between fracture and plastic collapse. Uncertainty modeling, especially on fatigue crack growth parameters, is undertaken with the aid of recently published data in support of the bi-linear crack growth relationship. Results pertaining to fatigue reliability and fatigue crack size evolution are presented using Monte Carlo Simulation. The bi-linear S-N curve and crack growth models are found to lead to higher fatigue life estimation. Sensitivity behavior pertinent to limit state adopted has been thoroughly investigated. These findings implicate inspection schemes for components of the marine structures to ensure minimization of the surprises due to wide scatter of the fatigue phenomenon in marine environment.