Robust failure compensation for a morphing aircraft model using a probabilistic approach

An adaptive compensation control scheme is developed for a morphing aircraft model with actuator failures. Morphing actuators are special in the sense that they operate only at two states: on or off, and that they are used in large numbers to fulfill certain actuation function. We derive a failure model for morphing actuators and develop an adaptive scheme to estimate the actuation effectiveness and to update the number of actuators to be activated. A feedback control scheme is redesigned for adaptive actuator failure compensation, which ensures desired closed-loop stability and tracking properties. A simulation study with a linearized lateral dynamics model of the ICE aircraft is presented to demonstrate the system performance in the presence of uncertain actuator failures.

SUMMARYThis paper presents an adaptive actuator failure compensation method, which compensates for uncertainties due to unknown actuator failures for redundant manipulator systems. The method is first developed for manipulators whose joints are concurrently actuated. While physical realization of concurrently actuated manipulators and the advantages of their use have been understood before, in this paper failure modeling, controller structure, and adaptive update rules for handling uncertainties from the actuator failures are studied. The adaptive actuator failure compensation method is then expanded for a cooperating multiple manipulator system with uncertain actuator failures. Dynamic equations of such a multiple manipulator system in the task space are derived and the adaptive actuator failure compensation problem is formulated in the task space, for which a compensation controller structure is proposed with stable adaptive parameter update laws. The adaptive control scheme is able to compensate for the uncertainties of system parameters and actuator failures in a more general sense. For both cases, closed-loop system stability and asymptotic tracking are proved, despite uncertain system failures.

Probabilistic structural design tends to apply higher safety factors to inexpensive or light-weight components, because it is a more efficient way to achieve a desired level of safety. We show that even with limited knowledge about stress probability distributions we can increase the safety of an airplane by following this paradigm. This is accomplished by a small perturbation of the deterministic design that maximizes safety for the same weight. The structural optimization for safety of a representative system composed of a wing, a horizontal tail and a vertical tail is used to demonstrate the paradigm. We find that moving small amount of material from the wing to the tails leads to substantially increased structural safety. Since aircraft companies often apply additional safety factors beyond those mandated by the Federal Aviation Administration (FAA), this opens the door to obtaining probabilistic design that satisfies also the FAA code based rules for deterministic design. We also find that probabilistic design is insensitive to errors committed while assessing the stress probability distribution of the deterministic design, which is the starting point of the probabilistic design. This suggests that using the deterministic design as the basis for the probabilistic design insulates the latter from the extreme sensitivity to statistical data that have been observed in the past. Finally, we find that for independent components subject to the same failure mode, the probabilities of failure at the probabilistic optimum are approximately proportional to the weight. So a component which is ten times lighter than another should be designed to be about 10 times safer.

Compensation of nonlinear MIMO systems for actuator failures is investigated with systematic sufficient conditions which guarantee the existence of stable adaptive compensation control schemes for asymptotic output tracking. As an application, we examine the actuator failure compensation of a twin otter aircraft longitudinal model, verify such sufficient conditions, and develop an adaptive control scheme for the nonlinear aircraft model in the presence of uncertain actuator failures, whose effectiveness is demonstrated by simulation results.

Because of increased requirements on the reliability, maneuverability and survivability of modern highspeed trains, more and more advanced control theory is applied against actuator failures. The control reallocation and adaptive control have long been attracting research interest in the field of fault-tolerant control, which is reflected in the design and development of powerful and complex control systems against actuator failures. In this paper we investigate the velocity tracking control problem of high-speed trains with multiple vehicles connected through couplers in the case of actuator failures. First, the multiple point-mass model is built and the common actuator failures of the train operation control system are divided into two types: stuck in a fixed value and loss of effectiveness. When plant inputs are stuck in a fixed value, a novel approach based on the control reallocation theory is implemented to ensure the system stability and performance. Meanwhile when the loss of the actuator effectiveness occurs, a robust adaptive fault-tolerant control method is applied. Then, the effectiveness of the proposed approach is also confirmed through numerical simulations based on a train similar to China Railways High-speed 5 (CRH5).

This paper presents a probabilistic design approach for the Gerber bending fatigue failure rule using sensitivity-based analysis. The design model parameters are considered as random variables that are characterized by mean values and coefficients of variation (covs). The coefficient of variation of a design parameter is obtained by using first order Taylor series expansion for strength and stress in a stress-based fatigue design. A reliability factor is determined based on the coefficients of variation and a failure probability. The reliability factor is then used for design sizing and analysis. Probabilistic design allows a quantification of risk that is not possible with deterministic design approaches. This risk quantification can help to avoid over- or under-design problems while ensuring that safety and quality levels are economically achieved. Over design requires more resources than necessary and leads to costly products. Avoiding over-design helps to conserve product materials and reduce manufacturing resources, machining accuracy, quality control, and processing. Under-designed products are prone to failures, making the products unsafe and unreliable. This increases the risks of product liability lawsuits, customer dissatisfaction, and even accidents. This study shows a 51% reduction in component size without compromising desired reliability and hence a possible 51% reduction in component mass and cost. Therefore, significant savings in product cost can be obtained through probabilistic design. Probabilistic design seems to be the most practical approach in product design due to the inherent variability associated with service loads, material properties, geometrical attributes, and mathematical design models. It is becoming the preferred design method because over- or under-design can be avoided while still ensuring the safety of a product.

Actuator failure compensation problem for nonlinear systems is formulated and adaptive actuator failure compensation control with state feedback is investigated for feedback linearizable systems. Under different structure conditions which characterize different classes of systems, adaptive state feedback control schemes are developed for systems with uncertain actuator failures. It is proved that the proposed control schemes ensure asymptotic output tracking and closed-loop signal boundedness.

The purpose of robust design optimization is to minimize variations in design performances and therefore to make the design insensitive to uncertainties. Current robust design methods fall into two types — probabilistic robust design and worst-case (interval) robust design. The former method is used when random variables are involved. In this method, robustness is measure by standard deviations of design performances. The later method is used when uncertainties are represented by intervals. The widths of design performances are then used to measure robustness. In many engineering application, both random variables and interval variables may exist simultaneously. In this paper, a general approach to robust design optimization is proposed. The generality comes from the ability to handle both random and interval variables. To alleviate the computational burden, we employ a previously developed general robustness assessment method — semi-second-order Taylor expansion method, to evaluate the maximum and minimum standard deviations of a design performance. An efficient integration strategy of the general robustness assessment and optimization is proposed. With the integration strategy, the number of function calls can be reduced while good accuracy is maintained. A robust shaft design problem is given for demonstration.

Gain-scheduled control for morphing aircraft via switching polytopic linear parameter-varying systems

One of the possible constraint configuration of an annular combustion chamber in a gas turbine is by means of radial pins. Radial pins usually connect the outer turbine casing to the combustor dome and fix combustor axial and circumferential displacements while allowing combustor free radial deformation, under thermal loads. In the typical mounting scheme, radial pins are screwed on the outer casing and then inserted into dedicated housing holes on the dome. Because of this arrangement the force (introduced by mechanical, thermal and dynamic loads) reacted by each pin is inherently not deterministic since it depends on the actual gap between the pin itself and the housing bush on the dome, which, in turn, is not explicitly known, being a function of the overall tolerance stack up. The scope of this study was to develop a method to design the radial pins of NovaLT™16 (*) combustion chamber, applicable since the conceptual phase, using a probabilistic approach [7]. Actual pin-bush gap distribution is calculated from stack up analysis and then used as input for a numerical simulation which computes the distribution of the reaction force on each pin, as a function of number of pins, stiffness of the pin, gap between pin and bush. Two different arrangements have been considered: the classic scheme and the floating pin configuration. The new probabilistic design approach allowed to have a robust understanding of the force distribution within the whole set of pins, to compute the optimal combination of pin number, pin stiffness, and gap and ultimately to select the floating pin configuration as the one to be implemented in NovaLT16 combustor. Test results revealed pin contact distribution was in line with predictions.

This paper presents a case study for a deep-water, HPHT, short flowline evaluated using a probabilistic lateral buckling design approach that aims to predict the pipeline end loads. The lateral buckling assessment of short flowlines, with fixed pipe ends and length of 1000m, may show an acceptable lateral buckling result, not requiring a controlled lateral buckling strategy, i.e., no engineered triggers, to ensure the pipe integrity. Although the integrity of the pipeline is ensured, it is recommended to introduce at least one engineered trigger in the pipeline to reduce the end loads stably by creating a lateral buckle to release the compressive axial force in the pipeline. The end loads, affected by uncertain parameters, are evaluated based on a probabilistic approach to have a robust and demonstrably efficient design. It is expected that short flowlines have small, lateral out-of-straightness features (which are inherent to the pipeline installation process). The uncertainty in the out-of-straightness features along the line can influence the critical buckling force and therefore the end loads due to cyclic thermal loads. The proposed approach is useful for predicting the pipeline end loads for the anchor structures design at early or detailed phase in the presence of uncertain parameters. This probabilistic approach requires more simulation time, compared with the deterministic approach, but it helps to predict a more robust range for the lateral buckling response and lower anchor load, which may result in project cost savings.

<p>Implementation of Bridge weigh-in-motion (B-WIM) measurements and probabilistic approaches in bridge assessment may reveal hidden bridge reserves and changes in reliability levels over their projected service life, providing a key input for optimized bridge management. But, as scientists and engineers and at the same time vendors of our own ideas, we need to be in position to present the results of our sophisticated methods and algorithms, expressed mostly in terms of safety or reliability indexes, probabilities of failures and similar indicators, with expected monetary savings which are decisive for an owner or an investor.</p><p>In previous research, as presented at the COST TU1402 special session in Nantes 2018, in order to define the optimal management bridge strategy, a decision tree encompassing three B-WIM strategies (no B-WIM, short term B-WIM, long term B-WIM), two possible activities (no action, bridge repair/strengthening) and two possible outcomes (bridge is safe, bridge may experience failure) have been formulated.</p><p>In this paper, a further development of the decision and Value of B-WIM Information analysis in the context of assessing road bridges are discussed.</p><p>The focus in the present paper is directed on a detailed assessment and modelling of costs, benefits and associated indicators related to the probability of bridge failure. Costs required for the Value of Information analysis encompass: (i) the initial cost of the new bridge CBV, (ii) direct costs of bridge repair/strengthening<i>C</i>rep, (iii) indirect costs of bridge non-availability due to repair measures<i>C</i>N/A, and costs of B-WIM measurements (iv)<i>C</i>B-WIM,1 and (v)<i>C</i>B-WIM 2, applying short- or long-term monitoring respectively.</p>

This paper compares probabilistic and possibility-based methods for design under uncertainty. It studies the effect of the amount of data about uncertainty on the effectiveness of each method. Only systems whose failure is catastrophic are considered, where catastrophic means that the boundary between success and failure is sharp. First, the paper examines the theoretical foundations of probability and possibility, focusing on the impact of the differences between the two theories on design. Then the paper compares the two theories on design problems. A major difference between probability and possibility is in the axioms about the union of events. Because of this difference, probability and possibility calculi are fundamentally different and one cannot simulate possibility calculus using probabilistic models. Possibility-based methods tend to underestimate the risk of failure of systems with many failure modes. For example, the possibility of failure of a series system of nominally identical components is equal to the possibility of failure of a single component. When designing for safety, the two methods try to maximize safety in radically different ways and consequently may produce significantly different designs. Probability minimizes the system failure probability whereas possibility maximizes the normalized deviation of the uncertain variables from their nominal values that the system can tolerate without failure. In contrast to probabilistic design, which accounts for the cost of reducing the probability of each failure mode in design, possibility tries to equalize the possibilities of failure of the failure modes, regardless of the attendant cost. In many safety assessment problems, one can easily determine the most conservative possibilistic model that is consistent with the available information, whereas this is not the case with probabilistic models. When we have sufficient data to build accurate probabilistic models of the uncertain variables, probabilistic design is better than possibility-based design. However, when designers need to make subjective decisions, both probabilistic and possibility-based designs can be useful. The reason is that large differences in these designs can alert designers to problems with the probabilistic design associated with insufficient data and tell them that they have more flexibility in the design than they may have known.

In a pavement management system (PMS), time to maintenance is generally estimated based on the predicted condition of the pavement. Usually a deterministic approach is applied in the PMS to estimate the time to maintenance by following the deterioration equation of the performance index. However, it is necessary to be aware of the probability of failure to investigate whether the estimated time to maintenance by the deterministic approach is reasonably probable. For this reason, a probabilistic approach is applied in this study to estimate the probability of failure over the estimated time to maintenance. In this approach, the probability of failure is estimated from the distribution of the mean time to maintenance by considering both the overall condition of the pavement and individual instances of distress. These mean times to failure or maintenance are calculated from the overall condition of pavement in relation to the pavement condition index (PCI) when the trigger value becomes 65 or less. A pavement may be expected to fail, however, because of any specific distress before it reaches the PCI trigger value for maintenance. For this reason, the probability of failure of each specific distress is also investigated by using a Monte Carlo simulation. It is found that the survival probability up to the fifth year is approximately 80% to 90% for each category of traffic and material type based on the overall condition, and the probability of failure for individual distress is very low over the performance cycle.

In this paper, a new algorithm for probabilistic design based on empirical distributions is proposed. The proposed algorithm can model a diverse spectrum of observed probabilistic phenomena and is computationally more efficient than several approaches currently in use. Information regarding the variability of a part or loading condition is usually obtained by observation and controlled experiments. This data is usually fitted to one of several common probability distributions like the Normal, Lognormal, Weibull, etc. There are however many phenomenon that cannot be modeled using conventional distributions, and Johnson [1949] proposed a family of four-parameter distributions to overcome this problem. A unique property of the Johnson family of distributions is the ability to transform data from design space to normally distributed space via close form transformation. This property makes it extremely attractive for probabilistic design, as experimental data can be modeled directly using a unified approach that can handle a wide variety of data. In this paper, a new probabilistic design algorithm based on the Johnson family of distributions is proposed. The proposed algorithm appears to have a greater flexibility than current approaches in terms of modeling probabilistic phenomenon. Additionally, test cases have demonstrated that the proposed algorithm significant decreases computational costs with negligible loss of accuracy. Both theoretical derivations as well as numerical results are presented in the paper. Introduction A significant source of error in applied probabilistic design is the inability to model real-life engineering data well. Often, traditional probability density functions like Normal or Lognormal distributions are “forced” to fit the data, and these functions are then used in probabilistic algorithms like the Hazofer-Lind (HL) and Hazofer-LindRackwitz-Fiessler (HLRF) algorithms. The HLRF approach mitigates this error to some extent by making two-parameter equivalent normal approximations to the random variable at the point of interest. For example, if the design variable were assumed to have a Weibull distribution, then normal approximations to this would have to be developed at each checking point. A wide range of distributions have been proposed to model equally wide and diverse spectra of phenomena leaving designers at a loss to decide which distribution represents the best fit. In addition, if the probabilistic design code does not have that assumed distribution built into its menu of functions; there may be significant errors in the final result. Any single unified approach that can take raw, experimental data and convert it directly into equivalent Normal variates within a standard probabilistic design algorithm will solve this problem significantly. One of the lesser-known distributions in statistical theory is a powerful family of empirical distributions proposed by Johnson in 1949. These are rather complicated fourparameter density functions that can model almost all known probability density functions in addition to phenomenon that will not fit any other model. The Johnson approach is an elegant approach that is based on transforming empirical data into standard Normal variates. The only source that the *Graduate Student, **Professor, Fellow AIAA Copyright  2003 by P. Hajela . Published by the American Institute of Aeronautics and Astronautics, Inc. with permission 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Confere 7-10 April 2003, Norfolk, Virginia AIAA 2003-1658 Copyright © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. American Institute of Aeronautics and Astronautics 2 author found which describes this distribution is one by Hahn and Shapiro (1967). Till date, the author is not aware of any published articles in the literature in probabilistic design that uses the Johnson distribution. Most researchers in probabilistic design appear to be unaware of the existence of this powerful function. In this paper, an algorithm is proposed that uses the Johnson family of distributions as a unified approach to probabilistic design. Both theoretical derivations and case studies that support the approach are included in this paper. The proposed hybrid algorithm will select the appropriate Johnson distribution, identify its parameters and transform the engineering variables into equivalent normal variates. Then, the original Hazofer-Lind approach is used to compute the reliability safety index for this problem in reduced space, and the final probability of failure can be calculated Johnson [1949] proposed basing empirical distributions on transformed normal variates. If ‘x’ were a random variable that is fitted by a Johnson distribution, then the general form of the transformation is as shown in (1). = z + γ η ( ) τ , , x e λ (1) Here, is an arbitrary function, z is a standard normal variate and , , and are parameters of the distribution. Johnson proposed three families of functions based on the functional form of , which are described in Eqns. 2-4 = ( ) τ1 , , x e λ       ln − x e λ (2) = ( ) τ2 , , x e λ       ln − x e + − λ e x (3) ( )       − = − λ e λ e τ x x 1 3 sinh , , (4) Based on the functional form of , three families of the Johnson distribution have been identified, referred to as the Johnson SL, SB and SU families. The following notation JSl, J-Sb and J-Su will be subsequently used to denote the Johnson SL, SB and SU families. The J-Sl distribution takes the form shown in (5).