Virtual Sensor Modeling for Nonlinear Dynamic Processes Based on Local Weighted PSFA
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Modern industrial processes are featured with complex dynamic, nonlinear, and noisy characteristics. It is of great significance to apply the probabilistic latent variable models (LVMs) to mine the pivotal features of the industrial processes. A probabilistic slow feature analysis (PSFA) can extract slowly varying features in rapidly changing data sequences as a dynamic LVM. However, the performance of PSFA is limited because of its linear assumption. In this article, a locally weighted PSFA (LWPSFA) is proposed for nonlinear dynamic modeling of industrial data with random noises. Two different kinds of weighting techniques are designed to approximate the nonlinear slow feature transition and emission functions. After that, the expectation maximum (EM) algorithm is adopted to estimate the parameters of LWPSFA with a weighted log-likelihood function (W-LLF). Eventually, a debutanizer column and a hydrocracking process are used to validate the effectiveness of LWPSFA.Keywords:
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Index weighting is an important issue in multiple attribute decision making. The application of combination weighting approach can overcome the limitations of using subjective weighting or objective weighting method only. It will help to reflect the essential characteristics of the evaluated object better. The paper discusses the combination weighting approach which based on ldquoimproved AHP-entropyrdquo. The method is used in the process of ldquoresearch project evaluationrdquo decision making. The result of application shows that the combination weighting method can correct the weights obtained by subjective weighting and objective weighting method respectively.
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Quality variables, which are usually measured offline, play important roles in describing process behaviors. However, online data obtained from soft sensors are significant as they provide accurate and immediate information. The reliability of online soft sensors is questionable due to changes in sensors, equipment, raw material availability, and operation conditions. In addition, chemical plants have dynamic properties and complex correlations amidst a large number of process variables. This causes most of the predictions obtained from steady-state soft sensors to be inaccurate in representing the particular chemical process. In this paper, the latent dynamic variational autoencoder is proposed to provide an estimation model and supervise soft-sensors. The input data are encoded in the latent space to remove underlying noises and disturbances in the data. Afterward, the dynamical properties are learned in the latent space through the bi-directional recurrent neural network, whose output (latent variable) is used to reconstruct back the input data. A simulation case study is conducted to show the effectiveness of the proposed method.
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The algorithm for dynamic weighing presented in this paper is a method used in research studies based on samples when due to the large number of weighting parameters it is not possible to establish a fixed set of sample weights without nonacceptable dispersion of weights.
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Several extensions to implied weighting, recently implemented in TNT, allow a better treatment of data sets combining morphological and molecular data sets, as well as those comprising large numbers of missing entries (e.g. palaeontological matrices, or combined matrices with some genes sequenced for few taxa). As there have been recent suggestions that molecular matrices may be better analysed using equal weights (rather than implied weighting), a simple way to apply implied weighting to only some characters (e.g. morphology), leaving other characters with a constant weight (e.g. molecules), is proposed. The new methods also allow weighting entire partitions according to their average homoplasy, giving each of the characters in the partition the same weight (this can be used for dynamically weighting, e.g. entire genes, or first, second, and third positions collectively). Such an approach is easily implemented in schemes like successive weighting, but in the case of implied weighting poses some particular problems. The approach has the peculiar implication that the inclusion of uninformative characters influences the results (by influencing the implied weights for the partitions). Last, the concern that characters with many missing entries may receive artificially inflated weights (because they necessarily display less homoplasy) can be solved by allowing the use of different weighting functions for different characters, in such a way that the cost of additional transformations decreases more rapidly for characters with more missing entries (thus effectively assuming that the unobserved entries are likely to also display some unobserved homoplasy). The conceptual and practical aspects of all these problems, as well as details of the implementation in TNT, are discussed.
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Modeling of complex systems can be greatly facilitated by the inclusion of empirical data directly into the solution of the model. Data can then be used to provide information about the fidelity of the model (goal) to the real system and/or act as a temporary model component for a subsystem not yet well-defined (probe).This method utilizes existing, highly-developed statistical packages to reduce development effort as well as obtain valuable statistical information useful in model validation. An example of the method applied to a molecular model of hemoglobin is provided.
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In this manuscript we investigate on the statistical modeling of hyperspectral data. Accurately modeling real data is of paramount importance in the design of optimal classification or detection strategies and in evaluating their performances. In the work three nonGaussian models are considered and their capability in characterizing the statistical behavior of real data is discussed with reference to a data set acquired by the multispectral infrared and visible imaging spectrometer (MIVIS) sensor.
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Abstract The article deals with the weighting step in Life Cycle Assessment (LCA). Different weighting methods are briefly described, and four operational such methods (Ecoscarcity 97, EDIP, Ecoindicator 99, and EPS 2000d) are applied to a simplified case to illustrate how they can contribute with additional information to the environmental assessment and decision making process. It is argued that the use of weighting can contribute to the relevance and acceptability of LCA results, but that the weighting step should be seen as a test of the compatibility between environmental impact profiles and different value profiles rather than as a procedure leading to a true measure of the aggregated impact. The authors also discuss some issues of controversy connected to weighting, as well as the practical implications of the ISO standard for weighting in LCA.
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