In Fig. Thus in each cycle of our evolutionary multioptimization process all individuals are iteratively assigned one of these three definite gender variants (performance, insensitivity, and robustness), and, next, the corresponding GG sets are suitably applied in the inter-gender crossover mating process. A “good” regulator minimizes the internal signal changes in the closed loop and therefore most of the identification methods, which use these inner signals provide worse modeling error, if the regulator is better. Figure 6-20. Supply Chain robustness can be measured in quantitative terms by following metrics : Amount of inventory across the whole supply chain (minimize) Total lead time to procure the raw materials, convert it and ship it to the end customer (minimize) Speed of information flow in both directions between both end points of the supply chain (minimize) (1988) imposes a homogeneous alternative hypothesis, which is a very strong hypothesis (Granger, 2003). Probability of error performance for multiple codebook hiding based on minimum distance criterion and distortion-compensation type of processing for M = 1000 and N = 500. Introduce the following coefficient for the excitation caused by the reference signal, which represents a signal/noise ratio. The basic idea is that if past values of x are significant predictors of the current value of y even when past values of y have been included in the model, then x exerts a causal influence on y. The exciting signal of KB-parameterized identification is an outer signal and therefore the phenomenon does not exist. It is worth noting that each template will yield its own unique ROI partition, since different tissue density maps (of same subject) are generated in different template spaces. Watershed segmentation of the same group of subjects on two different templates. Linearity of signal, linear range, sensitivity, 6. Changes in the parameters should be realistic in the context of normal use of the method. In our experiments, we always have two evaluation settings: the “standard” test set, and the test set with distribution shift. What is the best method to measure robustness? (9.11) to a panel of 88 countries to detect the causality between income and emission. Upper row: image registered to template 1. Using Monte Carlo simulations, Dumitrescu and Hurlin (2012) proved that the test exhibits very good finite sample properties. Published in volume 105, issue 5, pages 476-80 of American Economic Review, May 2015, Abstract: Researchers often report estimates and standard errors for the object of interest (such as a … To overcome the drawbacks of the panel Granger causality test proposed by Holtz-Eakin et al. The underlying circuit model as well as the approach of robustness computation based on [8] are described. Even though this is a crucial topic for robot locomotion as well as for physiological and pathological human locomotion, no uniquely accepted and generally applicable criteria for stability and robustness exist. The key benefits of defining intervals are in protecting the optimization problems against deviations in uncertain parameters, which may lead to generation of unfeasible solutions and maintain computational tractability. The other factor, however, can be considered as the relative correctness of the applied model. Commonly, they suggest the use of surrogate measures for the resource constrained project scheduling problem. Fig. (9.12) does not follow standard distribution (Hurlin & Venet, 2001). It can be simply derived that, where σo=σ(ℓ=0). Because of its features, the Dumitrescu-Hurlin procedure is commonly adopted by the studies searching for the growth-emission nexus in a bivariate setting. The robustness is an important functionality of networks because it manifests the ability of networks to resist failures or attacks. In all cases, as the number of codebooks increases, the bound on the probability of error decreases exponentially. As a reminder, there was a list of LC parameters, sample and sample preparation parameters and mass spectrometry parameters. In most cases experiments with one-by-one variations (One Variable At a Time approach) of the most important parameters are carried out. Notice that the coefficients βk and γk in Eq. Probability of error performance for multiple codebook hiding based on maximum correlation criterion and distortion-compensation type of processing for M = 200 and N =100. Figure 6-15. Figure 6-12. For large N but relatively small T data sets, Z˜ should be favored. In summary, the structural robustness design strategy makes use of the innovative structural robustness measures both deterministically and probabilistically. Note that, before applying watershed segmentation, we use a Gaussian kernel to smooth each map DRMk, to avoid any possible oversegmentation, as also suggested in Fan et al. 4 on the performance line (one-dimensional plane). Consequently, all codebooks become almost equally favorable. With the advent of using panel data for econometric analysis, some authors attempted to extend the model (9.11) to its panel data counterpart. An interesting analysis is presented in Fig. Figure 6-14. Many robustness measures have been proposed from different aspects, which provide us various ways to evaluate the network robustness. Since clustering will be performed on each template space separately, the complementary information from different templates can be preserved for the same subject image. 9.5). "Do not stop there!" Mulvey et al. In the subprocess A0, a numerical design of experiment (DOE) is planned and a finite element model (FEM) for each design is generated. We study the robustness of empirical efficiency valuations of production processes in an extended Farrell model. Section 9.4 discussed the dialectics of the quality and robustness for some special cases, especially for dead-time systems. The obtained uncertainty relation can be written in another form, since. Robustness can be however achieved by tackling the problem from a different perspective. The product in this case is a website. For each experiment, a sample is planned for robust design evaluation (e.g., the Monte Carlo simulation). For example, if the method’s LoQ is very close to the LoQ required by legislation, then the changes in the LoQ value have to be monitored against small changes in the method parameters. Obviously, δρ = 1 for all frequencies (here ρ=|1+L˜|). Color indicates the discriminative power of the identified region (with the hotter color denoting more discriminative region). Because of the very large number of potentially variable parameters it is reasonable to divide assessment of ruggedness into separate parts. 2 Measuring robustness We first discuss how to measure robustness as a quantity distinct from accuracy. In the subprocess A2, the load-shortening curve of each numerical model is assessed with appropriate postprocessing methods, so that its characteristic points (LB, GB, OD, and collapse) are identified. So if it is an experiment, the result should be robust to different ways of measuring the same thing (i.e. So it seems that variability is not useful as a basis for controller decisions. Husrev T. Sencar, ... Ali N. Akansu, in Data Hiding Fundamentals and Applications, 2004. Since the maximization of the structural robustness could lead to an increase in the structural mass, it is suggested that this parameter should be used as a design constraint. Second, for panel data with finite time period, the Wald-type statistic with respect to Eq. This is the main reason why it is difficult to elaborate a method which guarantees, or at least forces, similar behavior by the two errors, though some results can be found in the literature [4,50][4][50]. The well-known empirical, heuristics formula is. This process is extended in a probabilistic framework to deal with inherent uncertainties, as illustrated in Fig. The most influential method parameters impacting the LoQ could be MS parameters, mobile phase pH and sample preparation parameters. Robust optimization provides a feasible solution for any realization of the uncertainty in a given set for decision-making environments with incomplete or unknown information about the probability knowledge of uncertain phenomena. The representation is now expressed as follows: where βik and γik are various coefficients of yi,t−k and xi,t−k for individual i, respectively. The development of good and reliable stability and robustness measures for fast dynamic locomotion will be an important research topic for the next years. For robust feature extraction, it is important to group voxel-wise morphometric features into regional features. Unfortunately, it's nearly impossible to measure the robustness of an arbitrary program because in order to do that you need to know what that program is supposed to do. Then the following bivariate model: can be used to test whether x causes y. 7, where the numbers of Pareto fronts found by both the classical and the gender P-optimizing procedures are given. The axial, sagittal, and coronal views of the original MR image of the subject after warping to each of the two different templates are displayed. Lin-Sea Lau, ... Chee-Keong Choong, in Environmental Kuznets Curve (EKC), 2019. As the result of the evolutionary Pareto-optimization search procedure using the gender recognition, one performance individual, four insensitive individuals and two robust individuals have been obtained. Illustration of uncertainty relationships (9.5.11). In the end, however, this approach to multi-model inference is haphazard and idiosyncratic, with limited transparency. (9.13) are implicitly assumed to be fixed for all i. In the subprocess A0, a numerical DOE is also planned. (6.37) and (6.61) at different WNRs and for various numbers of codebooks and codebook sizes M × N. Corresponding results for the distortion-compensation type of postprocessing are similarly displayed in Figs. (6.61) is valid for the minimum distance criterion due to the improvement in distance properties from ddep to dmin. To solve the optimization problem, multiple robust counterparts, which are deterministic equivalents of robust programs, can be formulated based on the structure of uncertain parameters. Robustness measurement is the value that reflects the Robustness Degree of the program. How to Measure Lifetime for Robustness Validation – Step by Step A key point of Robustness Validation is the statistical interpretation of failures generated in accelerated Stress Tests. Specifically, one first selects a most relevant voxel, according to the PC calculated between this voxel’s tissue density values and class labels from all N training subjects. (9.14), perform F-tests of the K linear hypotheses γi1 = … = γiK = 0 to retrieve Wi, and finally compute W¯ as the average of the N individual Wald statistics: where Wi is the standard adjusted Wald statistic for individual i observed during T period. To achieve these tasks, the measure must be expressive, objective, simple, calculable, and generally applicable. Self-stabilizing mechanical elements might also be used on humanoid robots. for the relative quadratic identification error. Figure 9.5.1. (2014), can be referred to for more detailed information on robust optimization. The alternative hypothesis is formulated as: where N1 ∈ [0,N − 1] is unknown. Respectively, using minimum distance criterion, the threshold is determined based on the statistics of ddep. Inspired by the work in passive dynamic walking robots, the mechanics and inherent stability of typical motions to be executed should already be taken into account in the design phase. Whether this is the case, can often be determined by educated inspection of the effects of the changes (without additional experiments) and noting potential problems. Fig. In human movement, there always is some variability from step to step, and the assumption of a perfect limit cycle as it was used for some of the criteria does, of course, not hold precisely. This paper describes a method to measure the robustness of schedules for aircraft fleet scheduling within KLM Airlines. Thus for each subject, its feature representation from all K templates consists of M × K features, which will be further selected for classification. Most empirical papers use a single econometric method to demonstrate a relationship between two variables. The terms robustness and ruggedness refer to the ability of an analytical method to remain unaffected by small variations in the method parameters (mobile phase composition, column age, column temperature, etc.) (1988), Hurlin and Venet (2001), Hurlin (2004), and later Dumitrescu and Hurlin (2012) proposed testing the homogeneous noncausality (HNC) null hypothesis against the heterogeneous noncausality hypothesis (HENC) to complement the homogeneous causality (HC) hypothesis as in Holtz-Eakin et al. Al-Fawzan and Haouari (2005)use the sum of free slacks as a surrogate metric for measuring the robustness of a schedule. The pioneering work of Holtz-Eakin, Newey, and Rosen (1988) involved testing the hypothesis in Eq. Note that this iterative voxel selection process will finally lead to a voxel set (called the optimal subregion) r~lk with Ũlk voxels, which are selected from the region rlk. However, this approach may result in several problems. While separately either of these two changes can still lead to insignificant loss of resolution, their occurrence together may lead to peak overlap. Measuring robustness. Consider the following example. This notion will now be made precise. Probability of error performance for multiple codebook hiding based on minimum distance criterion and distortion-compensation type of processing for M = 200 and N =100. It is not possible to use the expected value criterion or other criteria based on probability knowledge in the case where the probability distributions of uncertain factors are not known. In the lecture 10.1 Robustness and ruggedness relation to LC-MS method development we saw different LC-MS parameters that influence robustness and ruggedness, as well as what the influence of these parameters. Such efforts could be supported by simple parameter studies, but also by extensive model-based simulations and optimization to evaluate all choices. For large N and T panel data sets, Z¯ can be reasonably considered. Among them, El Ghaoui and Lebret (1997), and Ben-Tal and Nemirovski (1998, 1999), developed approaches to generate less conservative solutions through nonlinear convex formulations, which are more difficult to solve and require more complex solution algorithms in comparison with Soyster’s method. Then the neighboring voxels are iteratively included to increase the discriminative power of all selected voxels, until no increase is found when adding new voxels. 4-6 present the solutions obtained by the classical, total P-optimization (GA) and the results achieved with the use of the genetic gender (GGA). The ROI partition for the kth template is based on the combined discrimination and robustness measure, DRMk(u), computed from all N training subjects, which takes into account both feature relevance and spatial consistency as defined below: where Pk(u) is the voxel-wise Pearson correlation (PC) between tissue density set {Iik(u),i∈[1,N]} and label set {yi ∈ [−1, 1], i ∈ [1, N]} (1 for AD and −1 for NC) from all N training subjects, and Ck(u) denotes the spatial consistency among all features in the spatial neighborhood (Fan et al., 2007). (1988). For treating continuous uncertain parameters, these parameters are assumed to vary within some predefined intervals, in other words, uncertain data bounds. Probability of error performance for multiple codebook hiding based on minimum distance criterion and distortion-compensation type of processing for M =100 and N = 50. The main purpose of robust optimization approach is for optimizing the worst case performance of the production chain, which is the most undesired realization of the uncertainty, and thus increasing the robustness of the production chain, which is treated as only a side effect in stochastic programming approaches. In this course we will give an overview of both – One Variable At a Time approach and the Experimental Design approach. Probability of error performance for multiple codebook hiding based on maximum correlation criterion and thresholding type of processing for M = 200 and N =100. Instead of using all Ulk voxels in each region rlk for total regional volumetric measurement, only a subregion r~lk in each region rlk is aggregated to further optimize the discriminative power of the obtained regional feature, by employing an iterative voxel selection algorithm. Investigate the product σρ (which is called the uncertainty product) in an iterative procedure where the relative error ℓ of the model is improved gradually. For this reason, rare disruptions in supply chains can be modeled more effectively by using robust optimization. The above results are not surprising. 5 in terms of insensitivity. Under the assumption that Wald statistics Wi are independently and identically distributed across individuals, it can be showed that the standardized statistic Z¯ when T → ∞ first and then N → ∞ (sometimes interpreted as “T should be large relative to N”) follows a standard normal distribution: In addition, for a fixed T dimension with T > 5 + 3K, the approximated standardized statistic Z˜ follows a standard normal distribution: The testing procedure of the null hypothesis in Eqs. In Figure 9.5.4 δID = δ and σID = σ, and thus the minimization of δM directly maximizes ρm. With reference to the ‘dimensionality curse’, in the full scope P-optimization case (as opposed to GGA), the number of Pareto fronts is very small (only 2 fronts on average). These intervals are also known as interval-uncertainties and this approach is called interval-uncertainty modeling. As a result, the selection of the P-optimal individuals is less effective. Each regional feature is then normalized to have zero mean and unit variance, across all N training subjects. However, the analytical results indicate that, as in Eqs. The procedure can be integrated in an optimization process with the objective of maximizing the failure load and minimizing the structural mass but keeping the energy-based structural robustness in a desirable level. The fact that they are valid even for the modeling error in the case of KB-parameterized identification methods makes them special. Figure 6-18. Fig. Similar relationships can be obtained if the H2 norm of the “joint” modeling and control error is used instead of the absolute values. The sample size is decided from a trade-off between the expected run time of each numerical model and the acceptable statistical error. A complete comparison of multiple codebook hiding and single codebook hiding schemes would involve calculating the actual probability of errors (not the union bound), which would be extremely difficult. 6 shows the solutions of the classical GA (the stars) against the robustness GGA solutions (the full triangles) in terms of robustness. The main criteria for choosing parameters are (a) how much a given method parameter can influence the critical characteristic and (b) how likely it is that this parameter will change uncontrollably. Finally, in the subprocess A3, a statistical assessment is carried out using standard statistical methods to obtain basic statistical parameters (average, standard deviation, coefficient of variance) and to compute the reliability for the strength criterion and the probabilistic structural robustness measures. It also should be noted that in general one tries to link variability to the general walking performance and the global risk of falling, and not to the imminent risk of falling. Design and management problems can be optimized efficiently by optimization with a measure of robustness against the negative influences of uncertainties that are specified by a deterministic or set-based variability in the value of problem parameters or parameters of its solution. Using maximum correlation criterion, the threshold is set based on the statistics of ρdep, which is the normalized correlation between an embedded watermark signal and its extracted version, so that the embedded message can be distinguished from the rest at a constant false-alarm rate. Intuitively, this is due to increasing confidence in the detection with the increasing N. With reference to the analyses in Sections 6.2.3 and 6.2.5, as mρdep increases and σρdep2 decreases, the maximum of the ensemble of random variables ρ˜m,m1,…,ρ˜m,mL is less likely to differ from the rest. N1 is strictly smaller than N, otherwise there is no causality for all individuals, and H1 reduces to H0. The definition for robustness/ruggedness applied is "The robustness/ruggedness of an analytical procedure is a measure of its capacity to remain unaffected by small, but deliberate variations in method parameters and provides an indication of its reliability during normal usage" [1]. This phenomenon can arguably be considered as the Heisenberg uncertainty relation of control engineering, according to which. Coefficients are now allowed to differ across individuals but are assumed time-invariant. If N1 = 0, there is causality for all individuals in the panel. Figure 6-13. Discrete uncertain parameters may be specified by scenario-based robust optimization programs, that is, discrete scenarios. The methodology allows the evaluation of alternative designs based on a trade-off between strength, energy-based structural robustness, and weight requirements. 2 Robustness and Concentration of Measure In this paper, we work with the following definition of adversarial risk: Definition 2.1 (Adversarial Risk). Here the maximum of the robustness measure is ρ⌢mo=ρ⌢m,ISo=0.9 according to (9.1.25). Buildings of … P-optimization in terms of insensitivity, Fig 6. For example, look at the Acid2 browser test. The minimax regret measure obtains a solution minimizing the maximum relative or absolute regret, which is defined as the difference between the cost of a solution and the cost of the optimal solution for a scenario, whereas minimax cost is determined by minimizing the maximum cost for all scenarios. The most common measures in this class are minimax regret and minimax cost. measures, worst-case analysis and usage of all input stimuli, can be embedded into the new measure. The fact that the quality of the identification (which is the inverse of the model correctness) can have a certain relationship with the robustness of the control is not very trivial. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. URL:, URL:, URL:, URL:, URL:, URL:, URL:, URL:, Data Hiding Fundamentals and Applications, Stability of composite stringer-stiffened panels, Richard Degenhardt, ... Adrian Orifici, in, Stability and Vibrations of Thin Walled Composite Structures, Energy-based structural robustness measures. A very logical division would be to test ruggedness separately for the sample preparation and for the LC-MS analytical part. The x and y variables can of course be interchanged to test for causality in the other direction, and it is possible to observe bidirectional causality (or feedback relationship) between the time series. The second gender (33) embraces the three insensitivity criteria (the influence of disturbances and noise). While in elderly people there is a high variability and also a higher risk of falling, there are many children who also walk in a variable way, yet are very stable at the same time. Our proposed robustness measure is the standard deviation of the point estimates over the set of models. In this paper, we study the problem of measuring robustness. Voxel-wise morphometric features (such as the Jacobian determinants, voxel-wise displacement fields, and tissue density maps) usually have very high feature dimensionality, which includes a large amount of redundant/irrelevant information as well as noises that are due to registration errors. This can be observed only in a special case, namely in the identification technique based on Keviczky–Bányász (KB) parameterization, as described in Section 10.3, when εID=−e˜. Richard Degenhardt, ... Adrian Orifici, in Stability and Vibrations of Thin Walled Composite Structures, 2017. Figure 6-21. each different template). Another case in practical supply chain design and management problems, is that the distribution of uncertain parameters may be subject to uncertainty, and the moment that the information about this uncertainty of the distribution is available instead of the exact distributions itself.
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