Set Membership Research Articles

A set membership theory based parameter and state of charge co-estimation method for all-climate batteries

State of charge estimation of the battery is one of the core functions in the battery management system. Accurate and reliable state of charge estimation under wide temperature range is critical for the application of all-climate electric vehicles. The main work of this paper is as follows: (1) To achieve accurate closed-loop state estimation, a temperature dependent battery model is proposed; (2) The common model-based state of charge estimation methods using filters like Kalman filter assume that the state perturbations and measurement noise are white and Gaussian noises, which is not realistic in practical application. To solve this problem, set membership method which holds that the noises are unknown but bounded is used for state of charge estimation. Based on the established temperature dependent battery model and the set membership method, battery parameter and state of charge co-estimation algorithm is proposed for all-climate battery state estimation; (3) The proposed method is fully verified at −10 °C–40 °C and the comparison between the proposed method and extended Kalman filter is conducted to illustrate its superiorities. Furthermore, the validity and real time performance of the co-estimation method are verified in a hardware-in-loop test bench. Results show that the proposed co-estimation method has excellent robustness and the state of charge estimation error is bounded to 5% under wide temperature range.

Association between social-emotional strengths and school membership: A cross-cultural comparison

ABSTRACT This study examined associations among a concurrent set of social-emotional strengths and school membership across the United States (N = 1,009) and Chinese (N = 747) students aged 9 to 11 years old. Results identified significant positive relations of school membership with four social-emotional strengths (i.e., gratitude, optimism, zest, and persistence) and a higher-order latent variable (covitality) in both countries, with optimism having the strongest association in both countries. Cross-culturally, U.S. students showed a stronger gratitude association with school membership whereas Chinese students had stronger zest and persistence associations with school membership. Implications for promoting school membership across cultural contexts are discussed.

Fundamental non-qualitative properties

The distinction between qualitative and non-qualitative properties should be familiar from discussions of the principle of the identity of indiscernibles: two otherwise exactly similar individuals, Castor and Pollux, might share all their qualitative properties yet differ with respect to their non-qualitative properties—for while Castor has the property being identical to Castor, Pollux does not. But while this distinction is familiar, there has not been much critical attention devoted to spelling out its precise nature. I argue that the class of non-qualitative properties is broader than it is often taken to be. When properly construed, it will not only include properties such as being identical to Castor, which somehow make reference to particular individuals, it will also include more general properties such as identity, composition, set membership, as well as various peculiarly ontological properties. Given that some of these more general properties help to explain objective similarity, we have reason to believe that there are fundamental non-qualitative properties.

Ellipsoidal Fusion Estimation for Multisensor Dynamic Systems With Bounded Noises

This paper considers the set membership fusion estimation problem for the general multisensor dynamic systems with unknown but bounded noises. In order to achieve the ellipsoidal fusion formulae, we divide the set membership filter problem into two steps: the prediction step and the fusion update step. The proposed method has the following nice properties. First, each step can be converted into a semidefinite programming problem, which can be efficiently computed. Second, part-analytical formulae of the shape matrix and the center of the bounding ellipsoid can be derived by using a decoupled technique, which can significantly reduce the computational complexity. Moreover, the relationship between the fusion center and local sensors can be clearly revealed based on the ellipsoidal fusion formula. Finally, it is interesting that the ellipsoidal fusion formula is similar in form to the classic mean-squared error filter fusion, although they are of the different optimization frameworks. However, the fusion weights of the information matrix provided by the different sensors are different and the optimal fusion weights can be calculated by solving a convex optimization problem. A typical numerical example in target tracking demonstrates the effectiveness of the proposed centralized and distributed fusion formula.

Approximation of real data by fuzzy sets for the classification problem

The article deals with the method of classification of real data using the apparatus of fuzzy sets and fuzzy logic as a flexible tool for learning and recognition of natural objects on the example of oil and gas prospecting sections of the Dnieper-Donetsk basin. The real data in this approach are the values for the membership function that are obtained not through subjective expert judgment but from objective measurements. It is suggested to approximate the fuzzy set membership functions by using training data to use the approximation results obtained during the learning phase at the stage of identifying unknown objects. In the first step of learning, each traditional future of a learning data is matched by a primary traditional one-dimensional set whose membership function can only take values from a binary set — 0 if the learning object does not belong to the set, and 1 if the learning object belongs to the set. In the second step, the primary set is mapped to a fuzzy set, and the parameters of the membership function of this fuzzy set are determined by approximating this function of the traditional set membership. In the third step, the set of one-dimensional fuzzy sets that correspond to a single feature of the object is mapped to a fuzzy set that corresponds to all the features of the object in the training data set. Such a set is the intersection of fuzzy sets of individual features, to which the blurring and concentration operations of fuzzy set theory are applied in the last step. Thus, the function of belonging to a fuzzy set of a class is the operation of choosing a minimum value from the functions of fuzzy sets of individual features of objects, which are reduced to a certain degree corresponding to the operation of blurring or concentration. The task of assigning the object under study to a particular class is to compare the values of the membership functions of a multidimensional fuzzy set and to select the class in which the membership function takes the highest value. Additionally, after the training stage, it is possible to determine the degree of significance of an object future, which is an indistinctness index, to remove non-essential data (object futures) from the analysis.

A task priority approach to cooperative mobile manipulation: Theory and experiments

Cooperative manipulation and transportation by means of multi-robot systems is a subject that has received an increased interest in the last few years. In this work, a task priority approach is first recalled from the authors previous works as framework for the control of a single mobile manipulator, to manage all its control objectives, including set membership ones and a proper coordination between the manipulator and its supporting vehicle. The approach is then extended, through a novel coordination policy, to execute a cooperative transportation of a common load by means of two (or more) mobile manipulators, via an explicit but limited information exchange, without modifying the individual controllers. Experimental results with two YouBot mobile manipulators are shown to demonstrate the effectiveness of the approach.

Adaptive MPC for constrained systems with parameter uncertainty and additive disturbance

In this study, the authors propose an adaptive model predictive control (MPC) algorithm for constrained linear systems in state space subject to uncertain model parameters and disturbances. An iterative set membership identification algorithm is first presented to update the uncertain parameter set at each time step. Based on the shrunken uncertain parameter set, an MPC controller is then designed to robustly stabilise the uncertain systems subject to state and input constraints. The algorithm can efficiently reduce the size of the uncertain parameter set in min-max MPC setting, and therefore improve the control performance. The algorithm is proved to ensure constraint satisfaction, recursive feasibility and input-to-state practical stability of the closed-loop system even in the presence of system uncertainties. A numerical example and a brief comparison with traditional min-max MPC are provided to demonstrate the efficiency of the proposed algorithm.

Identification of optimal wind, solar and hybrid wind-solar farming sites using fuzzy logic modelling

In this paper, an analytical framework is developed using fuzzy logic to evaluate optimal sites for wind, solar and hybrid wind-solar farms; using criterial components for energy optimization through climatological, topographic and human factors. The model is applied through a case study to the island of Mauritius which bears a highly complex topography. Through this computation, fuzzy constraints including wind and solar power, site elevation, settlement areas, and proximity to grid lines are all fitted to different fuzzy membership sets and the individual satisfaction degrees of each were calculated and aggregated into overall satisfaction degrees. Decision maps of highly suitable regions for hybrid wind-solar farming were then highlighted revealing two potential sites on the island for hybrid wind-solar farming; revealing a total generation potential of energy per year of 161.58 GWh at Le Morne and 281.28 GWh at La Laura-Malenga. The findings of this study aim to guide energy and urban planners to better identify optimum sites for wind, solar and hybrid wind-solar farm construction whilst making optimal use of land resources to achieve both sustainable dimensions and energy economic resilience.

Distributed Interpolatory Algorithms for Set Membership Estimation

This work addresses the distributed estimation problem in a set membership framework. The agents of a network collect measurements which are affected by bounded errors, thus implying that the unknown parameters to be estimated belong to a suitable feasible set. Two distributed algorithms are considered, based on projections of the estimate of each agent onto its local feasible set. The main contribution of the paper is to show that such algorithms are asymptotic interpolatory estimators, i.e. they converge to an element of the global feasible set, under the assumption that the feasible set associated to each measurement is convex. The proposed techniques are demonstrated on a distributed linear regression estimation problem.

Two Low Computational Complexity Improved Multiband Structured Subband Adaptive Filter Algorithms

The improved multiband-structured subband adaptive filter (IMSAF) applies the input regressors at each subband to speed up the convergence rate of MSAF. When the projection order is increased, the convergence rate of the IMSAF algorithm improves at the cost of increased complexity. The present research introduces two new IMSAF algorithms with low computational complexity feature. In the first algorithm, the selective partial update approach (SPU) is extended to IMSAF algorithms and SPU-IMSAF is established. In SPU-IMSAF, the filter coefficients are partially updated at each subband for every adaptation. In the second algorithm, the set-membership (SM) strategy is utilized in IMSAF and SM-IMSAF is established. The SM-IMSAF has fast convergence rate, low steady-state error and low computational complexity features at the same time. Also, by combining SM and SPU methods, the SM-SPU-IMSAF is introduced. Simulation results demonstrate the good performance of the proposed algorithms.

Morton filters: fast, compressed sparse cuckoo filters

Approximate set membership data structures (ASMDSs) are ubiquitous in computing. They trade a tunable, often small, error rate ($$\epsilon $$) for large space savings. The canonical ASMDS is the Bloom filter, which supports lookups and insertions but not deletions in its simplest form. Cuckoo filters (CFs), a recently proposed class of ASMDSs, add deletion support and often use fewer bits per item for equal $$\epsilon $$. This work introduces the Morton filter (MF), a novel CF variant that introduces several key improvements to its progenitor. Like CFs, MFs support lookups, insertions, and deletions, and when using an optional batching interface raise their respective throughputs by up to 2.5$$\times $$, 20.8$$\times $$, and 1.3$$\times $$. MFs achieve these improvements by (1) introducing a compressed block format that permits storing a logically sparse filter compactly in memory, (2) leveraging succinct embedded metadata to prune unnecessary memory accesses, and (3) more heavily biasing insertions to use a single hash function. With these optimizations, lookups, insertions, and deletions often only require accessing a single hardware cache line from the filter. MFs and CFs are then extended to support self-resizing, a feature of quotient filters (another ASMDS that uses fingerprints). MFs self-resize up to 13.9$$\times $$ faster than rank-and-select quotient filters (a state-of-the-art self-resizing filter). These improvements are not at a loss in space efficiency, as MFs typically use comparable to slightly less space than CFs for equal $$\epsilon $$.

Monte Carlo and Reconstruction Membership Inference Attacks against Generative Models

Abstract We present two information leakage attacks that outperform previous work on membership inference against generative models. The first attack allows membership inference without assumptions on the type of the generative model. Contrary to previous evaluation metrics for generative models, like Kernel Density Estimation, it only considers samples of the model which are close to training data records. The second attack specifically targets Variational Autoencoders, achieving high membership inference accuracy. Furthermore, previous work mostly considers membership inference adversaries who perform single record membership inference. We argue for considering regulatory actors who perform set membership inference to identify the use of specific datasets for training. The attacks are evaluated on two generative model architectures, Generative Adversarial Networks (GANs) and Variational Autoen-coders (VAEs), trained on standard image datasets. Our results show that the two attacks yield success rates superior to previous work on most data sets while at the same time having only very mild assumptions. We envision the two attacks in combination with the membership inference attack type formalization as especially useful. For example, to enforce data privacy standards and automatically assessing model quality in machine learning as a service setups. In practice, our work motivates the use of GANs since they prove less vulnerable against information leakage attacks while producing detailed samples.

Unsupervised Learning with Contrastive Latent Variable Models

In unsupervised learning, dimensionality reduction is an important tool for data exploration and visualization. Because these aims are typically open-ended, it can be useful to frame the problem as looking for patterns that are enriched in one dataset relative to another. These pairs of datasets occur commonly, for instance a population of interest vs. control or signal vs. signal free recordings. However, there are few methods that work on sets of data as opposed to data points or sequences. Here, we present a probabilistic model for dimensionality reduction to discover signal that is enriched in the target dataset relative to the background dataset. The data in these sets do not need to be paired or grouped beyond set membership. By using a probabilistic model where some structure is shared amongst the two datasets and some is unique to the target dataset, we are able to recover interesting structure in the latent space of the target dataset. The method also has the advantages of a probabilistic model, namely that it allows for the incorporation of prior information, handles missing data, and can be generalized to different distributional assumptions. We describe several possible variations of the model and demonstrate the application of the technique to de-noising, feature selection, and subgroup discovery settings.

Learning-based predictive control for linear systems: A unitary approach

A comprehensive approach addressing identification and control for learning-based Model Predictive Control (MPC) for linear systems is presented. The design technique yields a data-driven MPC law, based on a dataset collected from the working plant. The method is indirect, i.e. it relies on a model learning phase and a model-based control design one, devised in an integrated manner.In the model learning phase, a twofold outcome is achieved: first, different optimal p-steps ahead prediction models are obtained, to be used in the MPC cost function; secondly, a perturbed state-space model is derived, to be used for robust constraint satisfaction. Resorting to Set Membership techniques, a characterization of the bounded model uncertainties is obtained, which is a key feature for a successful application of the robust control algorithm.In the control design phase, a robust MPC law is proposed, able to track piece-wise constant reference signals, with guaranteed recursive feasibility and convergence properties. The controller embeds multistep predictors in the cost function, it ensures robust constraints satisfaction thanks to the learnt uncertainty model, and it can deal with possibly unfeasible reference values. The proposed approach is finally tested in a numerical example.

The iterated extended set membership filter applied to relative localization between autonomous vehicles based on GNSS and UWB ranging

AbstractThis paper presents a novel Iterated Extended Set Membership Filter (IESMF) with an application to relative localization. For safe operation of formations of automatic vehicles, consistent uncertainty estimates are of crucial importance. Here, a localization filter that provides ellipsoidal regions that are guaranteed to contain another vehicles position is presented. The proposed iterative update step can appreciably reduce the size of the a posteriori state ellipsoid. The idea of using SIVIA as a baseline to quantify conservativeness is introduced. Another novelty is that we take into account parametric uncertainty of the observation equation.The proposed filter is applied to a two unmanned aircraft systems (UAS) localization problem in simulation with observation noise obtained from real sensors. Simulation results illustrate the effective reduction of filter conservativeness by a small number of iterative updates.

Research on Evaluation of Linux in Aerospace Based on Improved FAHP

The evaluation and selection of embedded operating system are very important for manned spaceflight engineering. Considering the fuzziness and hierarchy of the evaluation process, a fuzzy analytic hierarchy process (FAHP) based on variation coefficient method and Criteria Importance Though Intercrieria Correlation (CRITIC) method is proposed to be applied to comprehensive evaluation of real-time Linux in space embedded system. The evaluation system, evaluation set and Gaussian distribution membership function are constructed, and the weight values of each criterion and index are determined by variation coefficient method and CRITIC method. The measured data are used for quantitative indexes such as real-time performance, and the expert scoring method is used for qualitative indexes such as reliability and compatibility, and verifies the validity of the model through simulation. The results show that the improved FAHP can quickly and intuitively judge the performance characteristics of Linux system and its derivatives, and provide a method for scientific and effective evaluation of space embedded operating system.

Adaptive model predictive control for linear time varying MIMO systems

A robust, adaptive Model Predictive Control (MPC) approach for asymptotically stable, constrained linear time-varying (LTV) systems with multiple inputs and outputs is proposed. The approach consists of two-steps, carried out on-line with a receding horizon strategy. In the first one, a real-time Set Membership identification algorithm exploits the measured input–output data and the available prior knowledge to build and refine a set of admissible models of the plant (Feasible Parameter Set, FPS). This set is guaranteed to contain also the true system dynamics under the considered working assumptions. In the second step, a robust finite-horizon optimal control problem is formulated and solved. The variation of system dynamics is taken into account by inflating the FPS over the prediction horizon, according to worst-case bounds, assumed a priori, on the parameters’ rate of change. The resulting optimal control sequence guarantees that the outputs of all possible plants inside the FPS satisfy the operational constraints, also considering all possible future parameter changes. The main theoretical properties of the proposed approach are demonstrated and the method is showcased in numerical simulations, highlighting the fundamental improvement over previous approaches not designed for LTV systems.

Graph MBO on Star Graphs and Regular Trees. With Corrections to DOI 10.1007/s00032-014-0216-8

The graph Merriman–Bence–Osher scheme produces, starting from an initial node subset, a sequence of node sets obtained by iteratively applying graph diffusion and thresholding to the characteristic (or indicator) function of the node subsets. One result in [14] gives sufficient conditions on the diffusion time to ensure that the set membership of a given node changes in one iteration of the scheme. In particular, these conditions only depend on local information at the node (information about neighbors and neighbors of neighbors of the node in question). In this paper we show that there does not exist any graph which satisfies these conditions. To make up for this negative result, this paper also presents positive results regarding the Merriman–Bence–Osher dynamics on star graphs and regular trees. In particular, we present sufficient (and in some cases necessary) results for the set membership of a given node to change in one iteration.

Evaluating generalization through interval-based neural network inversion

Typically, measuring the generalization ability of a neural network relies on the well-known method of cross-validation which statistically estimates the classification error of a network architecture thus assessing its generalization ability. However, for a number of reasons, cross-validation does not constitute an efficient and unbiased estimator of generalization and cannot be used to assess generalization of neural network after training. In this paper, we introduce a new method for evaluating generalization based on a deterministic approach revealing and exploiting the network’s domain of validity. This is the area of the input space containing all the points for which a class-specific network output provides values higher than a certainty threshold. The proposed approach is a set membership technique which defines the network’s domain of validity by inverting its output activity on the input space. For a trained neural network, the result of this inversion is a set of hyper-boxes which constitute a reliable and \(\varepsilon\)-accurate computation of the domain of validity. Suitably defined metrics on the volume of the domain of validity provide a deterministic estimation of the generalization ability of the trained network not affected by random test set selection as with cross-validation. The effectiveness of the proposed generalization measures is demonstrated on illustrative examples using artificial and real datasets using swallow feed-forward neural networks such as Multi-layer perceptrons.

Extended Tsukamoto's inference method for solving multi-objective linguistic optimization problems

Multi-objective linguistic optimization problems (MOLOPs) are quite useful in modeling a number of real life problems. The decision variables used to define the problem constraints and the objective functions take linguistic values in MOLOPs. In those MOLOPs, where the values of objective functions are unknown at all the points of the variable space, the link between the values of decision variables and objective functions is defined using if-then rules. MOLOPs formulated in this way were often solved using the Tsukamoto's inference method. However, the Tsukamoto's method can solve MOLOPs if the consequents in the if-then rules are defined as monotonic functions. Also, the solution obtained from Tsukamoto's method is a precise number. So in the present work, we propose a novel extension of Tsukamoto's inference method. The extended Tsukamoto's inference method can overcome both the above limitations. That is, it can solve MOLOPs where the consequents are defined as non-monotonic functions as well as monotonic functions. Also the extended Tsukamoto's method generates intervals instead of unique numbers, in the solution. From these intervals, we then generate type-1 fuzzy set membership functions and compare them using two of their fuzzy set uncertainty measures viz. centroid and fuzziness. Furthermore, we generate linguistic recommendations for these generated type-1 fuzzy set membership functions, as humans understand linguistic information naturally. We have also demonstrated the applicability of the proposed extended Tsukamoto's inference method to the case study for student's performance evaluation. We strongly believe that our proposed method is a novel one and will provide directions to future research.