Adaptive Gaussian Mixture Model for Uncertainty Propagation Using Virtual Sample Generation

Identification, Segmentation, and Image Property Study of Acute Infarcts in Diffusion-Weighted Images by Using a Probabilistic Neural Network and Adaptive Gaussian Mixture Model

In the complex industrial processes, the process data have the characteristics of imbalance and are incomplete due to the difficult-to-measure key variables, leading to the performance degradation of soft sensors. In order to deal with this problem, a novel noise injection virtual sample generation approach based on target-relevant autoencoder (NITAE-VSG) is proposed in this article. Different from the conventional VSG methods, the presented NITAE-VSG model can generate useful input and output virtual samples directly. To increase the diversity of virtual samples, the Gaussian noise (G_noise) is added into the features extracted from the target-relevant autoencoder (TAE) hidden layer. The generated virtual samples are combined with the original small samples to enhance the soft sensor model performance. To verify the reliable feasibility and superior effectiveness of the presented NITAE-VSG, two actual industrial cases: an industrial process of purified terephthalic acid shortened as PTA and a production system of ethylene are carried out. The results of simulations demonstrate that the presented NITAE-VSG can generate superior virtual samples to some other virtual sample generation (VSG) methods and can effectively improve the soft sensor modeling accuracy.

The application of support vector regression and virtual sample generation technique in the optimization design of transonic compressor

Chloride diffusivity of concrete is essentially determined by its microstructural parameters. Establishing a reliable and accurate prediction model for chloride diffusion has become a research hotspot. In this study, a database containing 144 sets of macro–micro property parameters of concrete is established to train a Multilayer Perceptron (MLP) model. Taking the original collected data as a benchmark, data are randomly missing to simulate data incompleteness, and the models are trained using data filled by the Lagrange, K-Nearest Neighbor (KNN), and Miceforest methods. Moreover, the original data is expanded by the virtual sample generation (VSG) algorithm, based on a Gaussian mixture model (GMM) that fits the joint probability distribution of the original data to generate virtual samples preserving statistical (mean, standard deviation) and physical (e.g., porosity range, pore size ratio) consistency, thus mitigating the randomness caused by small sample sizes. Results indicate that the MLP model demonstrates excellent predictive performance: among schemes handling missing data, the model preprocessed by normalization with KNN imputation yields the best results with testing R2 of 0.78; the baseline model (without missing value filling, normalized) achieves testing R2 of 0.83, MAE of 0.572, and MSE of 0.424. VSG-expanded data significantly enhances the MLP model’s prediction accuracy. When expanding to 3000 groups, the testing R2 reaches 0.85, a 2.4% increase compared to 1000 groups, with further improvements as the dataset expands, confirming the feasibility of the VSG algorithm for small-sample scenarios.

In this paper, an image stabilization method based on the adaptive Gaussian mixture model (GMM) is presented in order to smooth down the airborne image vibration. Firstly, the projection algorithm is adopted for the motion estimation; secondly, GMM parameter is obtained after analyzing characteristics of the first n images; finally, a stable image sequence is achieved after GMM motion filter operates on the motion parameter. The experimental results show that the method has the advantage of fast speed and effectively smooth unwanted vibration of image sequences.

Municipal solid waste incineration (MSWI) becomes the most popular technique to enhance environment protection. This process produces one of the most toxic chemicals in the world, i.e., polychlorinated dibenzo-p-dioxins and polychlorinated dibenzofurans (PCDD/Fs). The dioxin (DXN) production should be restricted rigidly by using operation optimization and control of MSWI process based on present industrial devices. However, it is difficult to realize the on-line real-time continuous measuring of DXN duo to the complexity formation mechanism and high-cost long-time off-line detection approach. In this paper, a soft measuring method based on virtual sample generation (VSG) is used to address this problem at the first time. A few numbers of true training samples are used to produce virtual training samples based on feasibility-based programming (FBP) model using selective ensemble kernel partial least squares (SENKPLS) and prior knowledge. Simulation result based on dataset in reference [31] for a HL MSWI process shows effectiveness of the proposed method.

In order to accurately predict key variables of complex industrial processes, it is necessary to establish reliable data-driven soft sensing models. The accuracy of soft sensors can be compromised when we meet limited process data or a high sample repetition rate with insufficient valuable information. Generally, virtual sample generation (VSG) methods such as variational autoencoder (VAE) prove to be effective strategies for addressing the small data problem. However, it is unavoidable to generate similar samples by traditional VSG methods. Moreover, the time-relevant features are usually ignored since individual samples are generated according to the original data distribution. To improve the data augmentation performance of complex processes with limited time-series data, this article introduces a novel VSG method based on time conditional VAE (TimeCVAE). By incorporating labeled data into the VSG process, the generator ensures that the generated virtual samples are closer to the distribution of real samples. Besides, time-related modules are designed as an important part of TimeCVAE model. These developments enhance the quality of the generated data and assist to improve the prediction accuracy of the soft sensor with small data. The effectiveness of the proposed method is validated through two industrial applications.

Virtual sample generation for soft-sensing in small sample scenarios using glow-embedded variational autoencoder

The prediction of the ablation rate of silicone rubber-based composites is of great significance to accelerate the development of flexible thermal protection materials. Herein, a method which combines uniform design experimentation, active learning, and virtual sample generation was proposed to establish a prediction model of the mass ablation rate based on a small dataset. Briefly, a small number of sample points were collected using uniform design experimentation, which were marked to construct the initial dataset and primitive model. Then, data points were acquired from the sample pool and iterated using various integrated algorithms through active learning to update the above dataset and model. Finally, a large number of virtual samples were generated based on the optimal model, and a further optimized prediction model was achieved. The results showed that after introducing 300 virtual samples, the average percentage error of the gradient boosting decision tree (GBDT) prediction model on the test set decreased to 3.1%, which demonstrates the effectiveness of the proposed method in building prediction models based on a small dataset.

A small dataset that contains very few samples, a maximum of thirty as defined in traditional normal distribution statistics, often makes it difficult for learning algorithms to make precise predictions. In past studies, many virtual sample generation (VSG) approaches have been shown to be effective in overcoming this issue by adding virtual samples to training sets, with some methods creating samples based on their estimated sample distributions and directly treating the distributions as unimodal without considering that small data may actually present multimodal distributions. Accordingly, before estimating sample distributions, this paper employs density-based spatial clustering of applications with noise to cluster small data and applies the AICc (the corrected version of the Akaike information criterion for small datasets) to assess clustering results as an essential procedure in data pre-processing. Once the AICc shows that the clusters are appropriate to present the data dispersion of small datasets, each of their sample distributions is estimated by using the maximal p value (MPV) method to present multimodal distributions; otherwise, all of the data is inferred as having unimodal distributions. We call the proposed method multimodal MPV (MMPV). Based on the estimated distributions, virtual samples are created with a mechanism to evaluate suitable sample sizes. In the experiments, one real and two public datasets are examined, and the bagging (bootstrap aggregating) procedure is employed to build the models, where the models are support vector regressions with three kernel functions: linear, polynomial, and radial basis. The results show that the forecasting accuracies of the MMPV are significantly better than those of MPV, a VSG method developed based on fuzzy C-means, and REAL (using original training sets), based on most of the statistical results of the paired t test.

Since the product life cycles are getting shorter and shorter, the issue of small data set learning has drawn more and more attentions in both academics and enterprises. Many methods have been proposed to improve the learning performance of small data set. In these methods, the virtual sample generation approach is the most popular technique for improving small data learning. In the process of virtual sample generation, the attribute independence in small data is the key part to determine the learning performance, because it is the necessary assumption before generating virtual samples. However, in the real world, attributes in the data set usually are not mutual independent. Therefore, this paper proposes a new process to generate independent virtual samples based on the box-and-whisker plot domain estimation. In order to validate the effectiveness of the proposed method, one data set is used to calculate the classification accuracy average and standard deviation based on the support vector machine. The results of the experiment show that the presented method has a superior classification performance than other methods.

Collision Probability with Gaussian Mixture Orbit Uncertainty

For the detection of moving objects, background subtraction methods are widely used. In case the background changes, we need to update the background in real-time for the reliable detection of foreground objects. An adaptive Gaussian mixture model (GMM) combined with probabilistic learning is one of the most popular methods for the real-time update of the complex and dynamic background. However, the probabilistic learning approach does not work well in high traffic regions. In this paper, we classify each pixel into four different types: still background, dynamic background, moving object, and still object, and update the background model based on the classification. For the classification, we analyze a sequence of frame differences at each pixel and its neighborhood. We experimentally show that the proposed method learn complex and dynamic backgrounds in high traffic regions more reliably, compared with traditional methods.

Multilayer perceptrons have been shown to approximate any continuous functions with a desired precision. With insufficient training samples, however, the network can not learn the function properly and popular model selection methods such as cross validation can not be used. We propose a scheme to generate virtual samples using a population of networks. They are applied to regression problems and are shown to improve generalization and to solve the model selection problem at the same time.

Intelligent modeling is an effective method to build prediction model of the plant medicine with ultrasonic extraction. However, there are obstacles when obtaining lots of data by the plant medicine extraction experiments, and small dataset will result in a model with low accuracy and poor generalization ability, which has a great influence on it. This paper proposes a novel virtual sample generation (VSG) approach based on Response Surface Methodology (RSM) and Extreme Learning Machine (ELM) algorithm, selecting through Cuckoo Search (CS) algorithm. The new prediction model is constructed based on ELM with the virtual sample dataset generated by this method and the original small sample dataset. The performance of the model is verified via the case of extracting the active ingredients, liquiritin, from liquorice by dual-frequency ultrasound. The experiment results show that the model established by the method proposed in this paper can significantly reduce the prediction error and improve the accuracy of the model, which provides a certain theoretical basis and reference for the industrialization of the active ingredients extraction of plant medicine.