Worst-case Parameter Research Articles

Robust performance optimization of dual thrust rocket motor

PurposeDuring any design phase, the associated process variations and uncertainties can cause the design to deviate from its expected performance. The purpose of this paper is to propose a robust design optimization (RDO) strategy for the 3D grain design of a dual thrust solid rocket motor (DTRM) under uncertainties in design parameters.Design/methodology/approachThe methodology consists of design of 3D complex grain geometry and hybrid optimization approach through genetic algorithm, globally and simulated annealing, locally considering the uncertainties in design parameters. The robustness of optimized data is measured for a worst case parameter deviation using sensitivity analysis through stochastic Monte Carlo simulation considering variance of design parameters mean.FindingsThe important achievement that can be associated with this methodology is its ability also to evaluate and optimize the propulsion system performance in a complex scenario of intricate 3D geometry under uncertainty. The study shows the objective function to maximize the average thrust in dual levels could be achieved by the proposed optimization technique while satisfying constraints conditions. Also, this technique proved to be a great help in reducing the design space for optimization and increasing the computational quality.Originality/valueThis is the first paper to address the dual thrust solid rocket motor grain design under uncertainties using robust design and hybrid optimization approach.

Minmax optimum design of active control system for earthquake excited structures

► A minmax optimization for structural control considering uncertainties is presented. ► Bimatrix co-evolution algorithm is adopted to solve the minmax problem. ► The optimal controller and the worst-case parameters are searched simultaneously. ► Example design and comparative results of numerical simulation are presented. A minmax optimization method for the vibration control system considering uncertain dynamics is presented in this paper. In the proposed method, structural modeling errors and various excitations, which may cause performance degradation, are treated as plant parameters. The minmax problem considered in this study is not only to find an optimal controller that minimize structural responses but also to search the worst-case plant parameters that maximize structural responses, whereas the conventional optimal design usually deals with a minimization problem for a certain performance index. In order to solve the proposed minmax problem, the bimatrix co-evolution algorithm is adopted. It approximates the minmax problem as the bimatrix game between two fitness measures and finds the optimal solution effectively through the co-evolutionary process, as a result, the optimal controller and the worst-case plant parameters are searched simultaneously. Example design of an earthquake-excited building structure with active tendon control system is performed and comparative results of numerical simulation are presented to validate the proposed method.

Robust consumption-investment problems with random market coefficients

We consider consumption-investment problems in a financial market with general random coefficients where the market price of risk process is unknown. The investor tries to maximize his expected utility under the worst-case parameter configuration. To solve robust consumption-investment problems, we make use of stochastic Bellman–Isaac equations. These equations can be explicitly solved for power, exponential and logarithmic utility. This enables us to characterize a robust optimal consumption-investment strategy and a worst-case market price of risk process in terms of the solution of a backward stochastic differential equation.

Optimisation-based verification process of obstacle avoidance systems for unicycle-like mobile robots

This paper presents an optimisation-based verification process for obstacle avoidance systems of a unicycle-like mobile robot. It is a novel approach for the collision avoidance verification process. Local and global optimisation based verification processes are developed to find the worst-case parameters and the worst-case distance between the robot and an obstacle. The kinematic and dynamic model of the unicycle-like mobile robot is first introduced with force and torque as the inputs. The design of the control system is split into two parts. One is velocity and rotation using the robot dynamics, and the other is the incremental motion planning for robot kinematics. The artificial potential field method is chosen as a path planning and obstacle avoidance candidate technique for verification study as it is simple and widely used. Different optimisation algorithms are applied and compared for the purpose of verification. It is shown that even for a simple case study where only mass and inertia variations are considered, a local optimization based verification method may fail to identify the worst case. Two global optimisation methods have been investigated: genetic algorithms (GAs) and GLOBAL algorithms. Both of these methods successfully find the worst case. The verification process confirms that the obstacle avoidance algorithm functions correctly in the presence of all the possible parameter variations.

Low-voltage low-power rail-to-rail low- R x wideband second generation current conveyor and a single resistance-controlled oscillator based on it

This study presents a novel rail-to-rail second generation current conveyor (CCII) based on quasi-floating gate transistors. The circuit operates at very low supply voltage (±0.5±V), dissipates ultra-low standby power (27±±W), has very high bandwidth ( f -3-dB of 191 and 181 MHz for Ai and Av , respectively) and low input resistance (1.5 ). Most favourably, its total harmonic distortion is 69 dB at an input voltage of 99 of power supply and frequency of 100 KHz. HSPICE simulation results confirm the feasibility and the robustness of the presented CCII against process variations (worst-case parameters) and temperature variation. Performance of this CCII is verified using a low-power grounded-capacitor single resistance-controlled oscillator.

The minimal model of the hypothalamic–pituitary–adrenal axis

This paper concerns ODE modeling of the hypothalamic-pituitary- adrenal axis (HPA axis) using an analytical and numerical approach, combined with biological knowledge regarding physiological mechanisms and parameters. The three hormones, CRH, ACTH, and cortisol, which interact in the HPA axis are modeled as a system of three coupled, nonlinear differential equations. Experimental data shows the circadian as well as the ultradian rhythm. This paper focuses on the ultradian rhythm. The ultradian rhythm can mathematically be explained by oscillating solutions. Oscillating solutions to an ODE emerges from an unstable fixed point with complex eigenvalues with a positive real parts and a non-zero imaginary parts. The first part of the paper describes the general considerations to be obeyed for a mathematical model of the HPA axis. In this paper we only include the most widely accepted mechanisms that influence the dynamics of the HPA axis, i.e. a negative feedback from cortisol on CRH and ACTH. Therefore we term our model the minimal model. The minimal model, encompasses a wide class of different realizations, obeying only a few physiologically reasonable demands. The results include the existence of a trapping region guaranteeing that concentrations do not become negative or tend to infinity. Furthermore, this treatment guarantees the existence of a unique fixed point. A change in local stability of the fixed point, from stable to unstable, implies a Hopf bifurcation; thereby, oscillating solutions may emerge from the model. Sufficient criteria for local stability of the fixed point, and an easily applicable sufficient criteria guaranteeing global stability of the fixed point, is formulated. If the latter is fulfilled, ultradian rhythm is an impossible outcome of the minimal model and all realizations thereof. The second part of the paper concerns a specific realization of the minimal model in which feedback functions are built explicitly using receptor dynamics. Using physiologically reasonable parameter values, along with the results of the general case, it is demonstrated that un-physiological values of the parameters are needed in order to achieve local instability of the fixed point. Small changes in physiologically relevant parameters cause the system to be globally stable using the analytical criteria. All simulations show a globally stable fixed point, ruling out periodic solutions even when an investigation of the 'worst case parameters' is performed.

Accident scenarios of the TRIGA Mark II reactor in Vienna

The safety report of the TRIGA Mark II reactor in Vienna includes three accident scenarios and their deterministic dose consequences to the environment. The destruction of the cladding of the most activated fuel element, the destruction of all fuel elements and a plane crash were considered scenarios in that report. The calculations were made in 1978 with the software program named STRISK. In this paper, the program package PC Cosyma was applied on the TRIGA Mark II reactor in Vienna and the deterministic consequences of the scenarios to the environment were updated. The fission product inventories of all fuel elements were calculated with ORIGEN2. To get meteorological data of the atmospheric condition around the release area, a weather station was installed. The release parameters were taken from the safety report or were replaced by worst case parameters. This paper focuses on two accident scenarios: the destruction of the cladding of the fuel element with the highest activity content and the case of a large plane crash. The current accident scenarios show good agreement with the calculations from 1978, hence no technical modifications in the safety report of the TRIGA reactor Vienna were necessary. Even in the very worst case scenario – complete destruction of all fuel elements in a large plane crash – the expected doses in the Atominstitut's neighborhood remain moderate.

Development of an objective-oriented groundwater model for conjunctive-use planning of surface water and groundwater

[1] In this paper we construct an objective-oriented model for conjunctive-use planning of surface water and groundwater for the Warren groundwater basin in southern California. The goal of conjunctive-use planning is to decrease high-nitrate concentration while maintaining groundwater levels at desired elevations and meeting water demand. We formulate a management problem that minimizes the total cost over the proper choices of the time-varying pumping and recharge rates at prespecified wells and surface ponds. To make the solution of the management problem reliable, we must have an accurate simulation model to predict groundwater level and nitrate concentration distributions under different management alternatives. The objective-oriented model construction approach seeks a representative parameter that has the simplest structure and requires the minimum data for identification but can produce reliable results for a given model application. With the data from the Warren groundwater basin, we show how to incorporate management objectives into the construction of an objective-oriented model, identify the parameter structure and its corresponding parameter values, solve the generalized inverse problem effectively by finding the worst-case parameter (WCP), evaluate the sufficiency of existing data, and find a robust experiment design when the existing data are insufficient. Results of this case study show that the presented methodology is useful in practice because (1) data sufficiency can be judged before conducting actual field experiments and (2) the identified WCP drastically reduces the computation time for constructing an objective-oriented model.

A Robust High-Order Mixed L2-Linfty Estimation for Linear-in-the-Parameters Models

A new algorithm called Mixed L2-Linfty (ML2) estimation is proposed in this paper; it combines both the weighted least squares and the worst-case parameter estimations together as the cost function and strikes the right balance between them. A robust ML2 algorithm and a practical approximate robust ML2 algorithm are also developed under disturbance signals. The properties of the new robust ML2 algorithm are analyzed and the simulation results are given to show the convergence and the validity.

Mad Cows and Computer Models: The U.S. Response to BSE

The proportion of slaughtered cattle tested for BSE is much smaller in the U.S. than in Europe and Japan, leaving the U.S. heavily dependent on statistical models to estimate both the current prevalence and the spread of BSE. We examine the models relied on by USDA, finding that the prevalence model provides only a rough estimate, due to limited data availability. Reassuring forecasts from the model of the spread of BSE depend on the arbitrary constraint that worst-case values are assumed by only one of 17 key parameters at a time. In three of the six published scenarios with multiple worst-case parameter values, there is at least a 25% probability that BSE will spread rapidly. In public policy terms, reliance on potentially flawed models can be seen as a gamble that no serious BSE outbreak will occur. Statistical modeling at this level of abstraction, with its myriad, compound uncertainties, is no substitute for precautionary policies to protect public health against the threat of epidemics such as BSE.

Robust Control Design for Resonance Damping of a Directional Microphone

Abstract This work applies µ analysis and synthesis techniques to develop a robust strategy for damping resonant modes in micromachined directional microphones of the parallel capacitive type. By properly selecting a weighting function, a robust controller is successfully designed via the D-K algorithm. Linear simulations show that the resonant mode of a directional microphone can be flattened out, and pushed to a frequency beyond the sensitivity of the human ear. The closed loop responses are free of ringing effects observed in open loop even for the worst-case parameter values.

Accounting for uncertainty in pedotransfer functions in vulnerability assessments of pesticide leaching to groundwater

A simulation tool for site-specific vulnerability assessments of pesticide leaching to groundwater was developed, based on the pesticide fate and transport model MACRO, parameterized using pedotransfer functions and reasonable worst-case parameter values. The effects of uncertainty in the pedotransfer functions on simulation results were examined for 48 combinations of soils, pesticides and application timings, by sampling pedotransfer function regression errors and propagating them through the simulation model in a Monte Carlo analysis. An uncertainty factor, f(u), was derived, defined as the ratio between the concentration simulated with no errors, c(sim), and the 80th percentile concentration for the scenario. The pedotransfer function errors caused a large variation in simulation results, with f(u) ranging from 1.14 to 1440, with a median of 2.8. A non-linear relationship was found between f(u) and c(sim), which can be used to account for parameter uncertainty by correcting the simulated concentration, c(sim), to an estimated 80th percentile value. For fine-textured soils, the predictions were most sensitive to errors in the pedotransfer functions for two parameters regulating macropore flow (the saturated matrix hydraulic conductivity, K(b), and the effective diffusion pathlength, d) and two water retention function parameters (van Genuchten's N and alpha parameters). For coarse-textured soils, the model was also sensitive to errors in the exponent in the degradation water response function and the dispersivity, in addition to K(b), but showed little sensitivity to d. To reduce uncertainty in model predictions, improved pedotransfer functions for K(b), d, N and alpha would therefore be most useful.

Development of objective‐oriented groundwater models: 1. Robust parameter identification

When the structure of an aquifer is complex and unknown, determining the complexity of model structure and identifying its spatially distributed parameters become very difficult. This two‐paper series describes an approach for objective‐oriented model construction that can identify a model with simplified structure and assure its reliability for predetermined model applications. The theoretical basis of the methodology includes the definition of structure error, the conditions of structure reducibility, the calculation of the worst‐case parameter (WCP), and the solution of a generalized inverse problem. In the first paper of the series we extend the basic theory established in our previous works from zonation parameterization to any kind of parameterization. The extension makes the methodology more general and complete. We present an effective direct search algorithm that can form a nonnested structure series with an optimized pattern for solving the generalized inverse problem. We use numerical examples to show how the WCP depends on the structure complexity, prior information, boundary conditions, and the objectives of model application. Generally speaking, with more prior information, simpler boundary conditions, fewer objectives, and lower accuracy requirement, the WCP will have a simpler shape. As a result, a reliable model can be identified with less observation data. In part 2 of this series we will give the conditions of structure reducibility and the method for robust experimental design. A robust experimental design is independent of the true parameter and can provide sufficient information for identifying an objective‐oriented model.

MOS current mode circuits: analysis, design, and variability

The interest in MOS current-mode logic (MCML) is increasing because of its ability to dissipate less power than conventional CMOS circuits at high frequencies, while providing an analog friendly environment. Moreover, automated design methodologies are gaining attention by circuit designers to provide shorter design cycles and faster time to market. This paper provides designers with an insight to the different tradeoffs involved in the design of MCML circuits to efficiently and systematically design MCML circuits. A comprehensive analytical formulation for the design parameters of MCML circuits using the BSIM3v3 model is introduced. In addition, a closed-form expression for the noise margin of two-level MCML circuits is derived. In order to verify the validity of the analytical formulations, an automated design methodology for MCML circuits is proposed to overcome the complexities of the design process. The effectiveness of the design methodology and the accuracy of the analytical formulations are tested by designing several MCML benchmarks built in a 0.18-/spl mu/m CMOS technology. The error in the required performance in the designed circuits is within 11% when compared to HSPICE simulations. A worst case parameter variations modeling is presented to investigate the impact of variations on MCML circuits as well as designing MCML circuits for variability. Finally, the impact of variations on MCML circuits is investigated with technology scaling and different circuit architectures.

Structure reduction and robust experimental design for distributed parameter identification

Designing an experiment for identifying a distributed parameter is a very challenging problem when the spatial variability of the parameter is unknown. First, we need to determine an appropriate structure complexity for the unknown parameter. A more complicated structure needs more data for identification. Second, we need to evaluate the sufficiency of an experiment design before it is actually conducted. In this paper, the complexity of parameter structure is determined by the accuracy requirement of model application, and the sufficiency of data is evaluated by solving a generalized inverse problem. The worst-case parameter (WCP) defined in this paper is the one that causes the maximum deviation in model application when its structure is simplified. The WCP of a structure can be found by solving a discrete optimization problem with the genetic algorithm. Quantitative relationships between structure complexity, parameter identifiability, data sufficiency and model reliability are derived. For example, it has been proven that if an experimental design is sufficient for identifying the WCP then it must be sufficient for identifying all other parameters with the same structure or simplified structures in the admissible region, and thus, it is a robust design. Based on the theoretical results and algorithms presented in this paper, we may develop a cost-effective methodology for constructing reliable distributed parameter models.

Optimal worst case estimation for LPV–FIR models with bounded errors

In this paper discrete time linear parameter varying (LPV) models with finite impulse response (FIR) dynamic structure are considered. Measurement errors are assumed to be bounded. In such condition optimal input sequences minimizing the worst case parameter uncertainties are derived. The main result of this paper consists in finding optimal worst case input sequences for LPV–FIR models. These are obtained suitably combining the optimal design results for standing alone invariant FIR models and standing alone nonlinear memoryless blocks. The quite relevant improvement obtained using optimal input sequences instead of random sequences is shown by simulation.

Millimeter-wave over fiber systems using hybrid OCDM/WDM transmission

In this paper, we propose and simulate 2 OCDM × 4 WDM transmission system for a millimeter-wave (60 GHz) over fiber system to be used in broadband wireless access networks (BWANs). The general system setup is devised and the necessary building blocks identified. Results gathered (for a 155 Mbit/s per user system) under worst case parameter specifications and settings suggest indicate that system performance is severely limited by optical multiuser interference (OMUI) penalties. Several methods to reduce the OMUI limitations are described. These methods should ensure that this transmission scheme possible wavelength-reuse option for future MMW BWANs.

Digital redesign of uncertain systems with state and input delays using evolutionary programming

This paper presents two novel issues: (i) digital modeling of the analog uncertain system in the presence of state and input delays and unstructured large parametric uncertainties; and (ii) digital redesign of the analog robust output tracking controller for the parametric uncertain system with state and input delays. The Newton's forward formula together with the evolutionary programming (EP) is utilized to find an equivalent discrete-time time-delayed parametric uncertain model of the continuous-time parametric uncertain system with multiple delays in both the state and input. Also, based on the EP global optima-search technique, the integration of the available analog robust controller and a parameter tuning algorithm is established to find a practically implementable "best" digital controller for the analog time-delayed uncertain system. The worst-case parameter set obtained from the analog time-delayed uncertain system with respect to the implemented "best" digital controller is searched to show the capability of the proposed robust digital controller.

Aeronautical channel modeling

A class of aeronautical wide-band channel models is proposed, featuring parking and taxi environments, takeoff and landing situations, and en-route scenarios for ground-air and air-air links. Typical and worst case parameter sets are suggested, based on published measurement results and empirical data. The models are suitable for channel emulators that can be easily implemented on digital computers or in hardware and thus are useful for the validation of digital aeronautical links. A time-domain and frequency-domain implementation of such a channel emulator are derived, and results for a typical multicarrier system are presented. It is shown that the scenarios have distinguishable performance results depending on the underlying maximum ranges and shapes of the Doppler and delay spectra and the presence of a line-of-sight path. Finally, the degrading effects of intersymbol interference and intersubcarrier interference on the multicarrier signal are explained.

Optimal experiment design for regression polynomial models identification

In this paper the problem of optimal experimental design for parameter identification of static non-linear blocks is addressed. Non-linearities are assumed to be polynomial and represented according to the Vandermonde base. The optimality problem is formulated in a set membership context and the cost functions to be minimized are the worst case parameter uncertainties. Closed form optimal input sequences are derived when the input u is allowed to vary on a given interval [ u a, u b ]. Since optimal input sequences are, in general, not invariant to base changes, results and criteria for representing polymomials with different bases, still preserving the optimal set of input levels derived from the Vandermonde parameterization, are introduced as well. Finally numerical results are reported showing the effectiveness of using optimal input sequences especially when identifying some block described dynamic models that include in their structure static non-linearities (such as Hammerstein and LPV models). In such cases the improvement achieved in the confidence of the estimates can add up to a factor of several hundreds with respect to the case of random generated inputs.