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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
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Novel manifold learning based virtual sample generation for optimizing soft sensor with small data.

Xiao-Han Zhang1, Yuan Xu1, Yan-Lin He1

  • 1College of Information Science & Technology, Beijing University of Chemical Technology, Beijing, 100029, China; Engineering Research Center of Intelligent PSE, Ministry of Education of China, Beijing 100029, China.

ISA Transactions
|October 19, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces Isomap-VSG, a new method to create virtual samples for industrial processes. This approach effectively addresses the small sample problem, improving the accuracy of data-driven soft sensor models.

Keywords:
Industrial processesManifold learningSmall dataSoft sensorVirtual sample generation

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Area of Science:

  • Process Engineering
  • Data Science
  • Machine Learning

Background:

  • Industrial processes exhibit complex mechanisms and non-linear dynamics, necessitating intelligent measurement solutions.
  • Data-driven soft sensor technologies are crucial for real-time monitoring but are hindered by limited and unreliable data in steady states, leading to the small sample problem.
  • Accurate soft sensor model development is challenging with insufficient data, impacting process understanding and control.

Purpose of the Study:

  • To propose a novel manifold learning-based virtual sample generation method (Isomap-VSG) to address the small sample problem in industrial soft sensor modeling.
  • To generate feasible virtual samples in information gaps to supplement limited original process data.
  • To enhance the accuracy and reliability of data-driven soft sensor models developed from small sample spaces.

Main Methods:

  • Utilizing Isomap, a manifold learning technique, to visualize high-dimensional process data and identify data-sparse regions.
  • Generating virtual samples through interpolation methods combined with the extreme learning machine algorithm.
  • Supplementing the original small sample space with generated virtual samples to create a more comprehensive dataset.

Main Results:

  • The proposed Isomap-VSG method demonstrated superior performance in generating feasible virtual samples compared to existing advanced techniques.
  • Soft sensor models built using the augmented dataset (original + virtual samples) showed significant improvements in accuracy.
  • Validation on a standard dataset and a real-world industrial application confirmed the effectiveness of the Isomap-VSG approach.

Conclusions:

  • The Isomap-VSG method offers an effective solution for the small sample problem in data-driven soft sensor development.
  • Manifold learning, specifically Isomap, is a valuable tool for identifying data gaps and guiding virtual sample generation.
  • The proposed approach enhances the practical applicability of soft sensors in complex industrial environments with limited data.