Watershed segmentation of the same group of subjects on two different templates. Against this backdrop, Hurlin (2004) and Dumitrescu and Hurlin (2012) proposed the following procedure: Run the N individual regressions implicitly enclosed in Eq. 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 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. 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. 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. In this chapter, we have discussed different possibilities to study stability, robustness, and the ability to recover from large perturbations that can be used to study gaits in robotics and biomechanics. The sample size is decided from a trade-off between the expected run time of each numerical model and the acceptable statistical error. Let (X; ) be the probability space of instances and f be the underlying ground-truth. The earlier results of control engineering referred only for the statement that the quality of the control cannot be improved, only at the expense of the robustness, so this result, which connects the quality of the identification and the robustness of the control, can be considered, by all mean, novel. Figure 6-11. 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. For each experiment, a sample is planned for robust design evaluation (e.g., the Monte Carlo simulation). Under this category, the robustness measures can be defined either with or without probability distributions. In Figure 9.5.4 δID = δ and σID = σ, and thus the minimization of δM directly maximizes ρm. 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. 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. The simplest case to investigate (9.5.15) is when ℓ=0, since then, This equation gives a new uncertainty relationship, according to which, The product of the modeling accuracy and the robustness measure of the control must not be greater than one, when the optimality condition ℓ=0 is reached. 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). Under the assumption that the host signal is distributed uniformly in each quantization interval (σC2≫Δ), the extracted signal W⌢ null is iid uniformly distributed in [−Δ4,Δ4] and uncorrelated with any of the watermark signals. 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. As in Granger (1969) and Holtz-Eakin et al. However, the analytical results indicate that, as in Eqs. As indicated in Fan et al. A structure designed and constructed to be robust should not suffer from disproportionate collapse under accidental loading. Section III introduces the new measure in detail. Our two statistics depend on a parameter , which captures the idea that we only care about robustness below a certain threshold—we disregard adversarial examples x whose L 1distance to x is greater than . To make use of these measures, the structural robustness design strategy is idealized. For large N but relatively small T data sets, Z˜ should be favored. The worst case can be chosen either from a finite number of scenarios, for example, historical data, or continuous, convex uncertainty sets, such as polyhedrons or ellipsoids. for the relative quadratic identification error. Thus for each subject, its feature representation from all K templates consists of M × K features, which will be further selected for classification. Fig. N1 is strictly smaller than N, otherwise there is no causality for all individuals, and H1 reduces to H0. The robustness measure discussed in Section II can be considered as a “worst-case analysis”: a component is con-sidered non-robust as soon as there is a single testpattern that shows faulty behavior of this component at least at one primary output. Section 9.4 discussed the dialectics of the quality and robustness for some special cases, especially for dead-time systems. measures, worst-case analysis and usage of all input stimuli, can be embedded into the new measure. The new procedure by Hurlin (2004) and Dumitrescu and Hurlin (2012) also followed a standard Granger causality where the variables entering into the system need to be covariance-stationary. (9.15) and (9.16) is finally based on Z¯ and Z˜. In Figure 9.5.3, there is no clear relation between δID and δ, or σID and σ, and therefore there is no guarantee that minimizing δM increases ρm. However, this approach may result in several problems. What is the best method to measure robustness? Changes in the parameters should be realistic in the context of normal use of the method. The well-known empirical, heuristics formula is. 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. The test assumes that there might be causality for some individuals but not necessarily for all. In the subprocess A1, an NLA simulation is carried out for each sample design, which is controlled by a numerical incrementation algorithm and a ply progressive failure (PFA) scheme. In this paper, we study the problem of measuring robustness. 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. Each member of the set is generated by splitting the sample into two subsamples based on covariate values, constructing separate parameter estimates for … On the other hand, the probability of error for single codebook hiding also decreases with the increasing signal size N. Consequently, fewer codebooks are required to further improve the performance. 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. 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. Here Δz and Δp are the alterations of the canonical coordinate and the impulse variables, respectively, and thus their inverse corresponds to the generalized accuracy and “rigidity” which are known as performance and robustness in control engineering. In the subprocess A2, the load-shortening curves are assessed, their characteristic points are identified (cf. Figure 6-13. (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. Measuring robustness. With the advent of using panel data for econometric analysis, some authors attempted to extend the model (9.11) to its panel data counterpart. Figure 6-16. Figure 9.5.1. A Measure of Robustness to Misspecification by Susan Athey and Guido Imbens. vht-online.de. In the subprocess A1, a nonlinear finite element analysis (NLA) is carried out for each design, so that the shortening displacement for each load increment, the ply failure sequence, and the structural mass is obtained. 6 shows the solutions of the classical GA (the stars) against the robustness GGA solutions (the full triangles) in terms of robustness. So it can be clearly seen that when the modeling error decreases, the robustness of the control increases. In robust optimization problems, the random parameters may be either continuous or discrete. Similarly to the notations σM(Cˆ) and σ⌣M applied above, the notations σm(ℓ)=minℓ[σ(ℓ,Cˆ)] and σmo=σm(ℓ=0) can also be introduced. Consider the following example. First, it is well known that the fixed effects estimator is biased and inconsistent in the dynamic panel data model when the data used is micropanel, for example, there are a large number of cross-sectional units observed over relatively short time periods (Nickell, 1981). 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.) Such efforts could be supported by simple parameter studies, but also by extensive model-based simulations and optimization to evaluate all choices. when the regulator is properly set, and the Nyquist stability limit (i.e., Designing FDI Observers by Improved Evolutionary Multi-Objective Optimization, Zdzisław Kowalczuk, Tomasz Białaszewski, in, Fault Detection, Supervision and Safety of Technical Processes 2006, Uncertainty Issues in Biomass-Based Production Chains, Decision-Making for Biomass-Based Production Chains, In robust optimization problems, the random parameters may be either continuous or discrete. For each design of the sample, an FEM is established. Measures of robustness The basic tools used to describe and measure robustness are, the breakdown point, the influence function and the sensitivity curve. 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. Before starting the investigation of robustness it is crucial to find out what are the most important performance characteristics of the method. The homo-M refers to the regions that are simultaneously identified from different templates, whereas the hetero-M refers to the regions identified in a certain template but not in other templates. In the subprocess A0, a numerical DOE is also planned. When jointly considering all identified regions from different templates in the classification, the integration of homo-M features is helpful to improve both robustness and generalization of feature extraction for the unseen subjects, while the combination of hetero-M features can provide complementary information for distinguishing subjects during the classification. These intervals are also known as interval-uncertainties and this approach is called interval-uncertainty modeling. (9.12) by using the following linear panel data model: where i captures the individual specific effects across i. The other factor, however, can be considered as the relative correctness of the applied model. 9.5. Before starting the investigation of robustness it is crucial to find out what are the most important performance characteristics of the method. 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. 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. As a result, the selection of the P-optimal individuals is less effective. Thus if during the iterative identification the condition ‖ℓk‖∞=k→∞0 is guaranteed then, at the same time, the convergences δ⌣Mk=k→∞δ⌣Mo and ρ⌢mk=k→∞ρ⌢mo are ensured. 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. Here |Tˆ(jω)| (although it is usually called a design factor) can be considered as the quality factor of the control. In this thesis, a new Robustness measurement technique; the Robustness Grid, is introduced. and influential environmental factors (room temperature, air humidity, etc.) I like robustness checks that act as a sort of internal replication (i.e. While separately either of these two changes can still lead to insignificant loss of resolution, their occurrence together may lead to peak overlap. The robustness is an important functionality of networks because it manifests the ability of networks to resist failures or attacks. In this paper, we study the problem of measuring robustness. However, for healthy adult gait, steady-state walking is typically very close to a limit cycle. 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. To plan changes to the usage of mathematic models as Weibull or Arrhenius hypothesis is formulated as: i. 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