KR20190105429A - Apparatus and method for release modeling of toxic gases - Google Patents

Abstract

Provided are a modeling apparatus and a modeling method for toxic gas release with high reliability. The modeling apparatus for toxic gas release may comprise: a conversion module converting toxic gas distribution data; and a generation module connected to the conversion module and generating a prediction model by mapping the converted data with a constant variable.

Description

Toxic gas release modeling device and modeling method {APPARATUS AND METHOD FOR RELEASE MODELING OF TOXIC GASES}

The present invention relates to a toxic gas release modeling device and modeling method.

As the chemical industry continues to grow, concerns about fatal accidents caused by chemicals are growing. Toxic gas leaks during various types of accidents in chemical processes are particularly dangerous because of the wide range of leaks. If the concentration of toxic gases is above a certain level, the local population is at serious risk, and if an accident occurs in a densely populated area, the danger is greater in urban areas. Therefore, a method of predicting toxic gas dispersion is needed.

Computer simulations such as ALOHA and PHAST have been developed to model toxic gas dispersion, but are difficult to use due to their low accuracy in real-world situations with three-dimensional obstacles. Computational Fluid Dynamics (CFD) is widely used in view of geographic information and the nature of toxic chemicals, but it is time-consuming to calculate and is not suitable for emergency situations and real-time alarm systems. As such, toxic gas dispersion predictions are difficult to implement due to cost, risk and technical requirements.

In order to solve the above problems, the present invention provides a highly reliable toxic gas release modeling device.

The present invention provides a method for modeling toxic gas release using the device.

Other objects of the present invention will become apparent from the following detailed description and the accompanying drawings.

The toxic gas release modeling apparatus according to the embodiments of the present invention may include a conversion module for converting toxic gas dispersion data and a generation module connected to the conversion module to generate a prediction model by mapping the converted data to a predetermined variable. Can be.

The transformation module and the generation module may repeatedly learn based on an artificial neural network.

The toxic gas dispersion data includes data simulated by numerically analyzing the behavior of the toxic gas before the toxic gas is dispersed, and the simulation data is sampled using the variable and preprocessed to be input to the conversion module. Can be.

(a, b, 및 n은 상기 독성 가스 종류에 따른 상수, c는 상기 독성 가스의 부피별 농도)이고, 상기 사망 확률은

일 수 있다.The simulation data includes P _death data calculated by a Probit function, and the Probit function is

(a, b, and n is a constant according to the type of the toxic gas, c is the concentration by volume of the toxic gas), the probability of death

Can be.

The conversion module may include an autoencoder for compressing and converting the toxic gas dispersion data, and the auto encoder may include a convolutional layer for detecting and extracting a feature of the toxic gas dispersion data. have.

The autoencoder may use a variable inference that is calculated by parameterizing the extracted feature of the toxic gas dispersion data and approximating it to a normal distribution using the average value and the logarithmic value of the variable data as parameters.

The autoencoder may further include a variational layer for comparing and evaluating the toxic gas dispersion data and the data converted by the autoencoder using a loss function.

The generation module may include a fully connected layer that maps and converts the converted data into the variable.

The generation module may normalize the distribution of the converted data between the fully connected layer and the fully connected layer.

The variable may include one or more of wind speed, wind direction, release rate of the toxic gas, emission duration, emission point, emission material and temperature.

The toxic gas release modeling method according to the embodiments of the present invention includes the steps of inputting toxic gas dispersion data, converting the input data, and mapping the converted data into a constant variable to generate a prediction model. can do.

The transforming step and the generating step may be repeatedly learned based on an artificial neural network.

The modeling method may include numerically analyzing and simulating the behavior of the toxic gas before the data input step and dispersing the toxic gas, sampling the simulation data using the variable, and performing the input step. The method may further include preprocessing the simulation data.

(a, b, 및 n은 상기 독성 가스 종류에 따른 상수, c는 상기 독성 가스의 부피별 농도)이고, 상기 사망 확률은

일 수 있다.The simulation step includes performing P _death data calculation by a probit function, wherein the probit function

(a, b, and n is a constant according to the type of the toxic gas, c is the concentration by volume of the toxic gas), the probability of death

Can be.

The converting step may include detecting and extracting a feature of the input data.

The converting step may further include parameterizing the extracted feature of the input data, converting and restoring the variable data, and comparing the input data with the restored data using a loss function, Variable inference can be performed by approximating a normal distribution using the average value of the variable data and the logarithm of the variance as parameters.

The generating may include mapping and converting the converted data into the variable.

The generating step may further include performing batch normalization to normalize the distribution of the transformed data.

The variable may include one or more of wind speed, wind direction, release rate of the toxic gas, emission duration, emission point, emission material and temperature.

According to embodiments of the present invention, it is possible to provide a toxic gas release modeling device having a short calculation time and high reliability.

According to embodiments of the present invention, it is possible to provide a toxic gas release modeling method using the apparatus.

Figure 1 shows the shape of the Ulsan Mipo complex according to an embodiment of the present invention.
2 shows a flow diagram of data sampling and preprocessing according to one embodiment of the invention.
3 illustrates a structure of a variational auto encoder (VAEDC) having a deep convolutional layer of a surrogate model according to an embodiment of the present invention.
4 illustrates a detailed deep neural network (DNN) configuration for mapping latent space and variable space from a variational autoencoder (VAEDC) having a deep convolutional layer in accordance with an embodiment of the present invention.
5 shows a comparison between the performance of a surrogate model and another type of surrogate model according to an embodiment of the present invention.
6 shows a comparison of loss function graphs of various surrogate models for epochs.
7 illustrates the mean squared error of the extracted test data set according to an embodiment of the present invention.
8 illustrates P _death images according to various models according to an exemplary embodiment of the present invention.
9 shows the results of walking in the variable space of a deep neural network using a variational autoencoder with a deep convolutional layer.

Hereinafter, the present invention will be described in detail through examples. The objects, features and advantages of the present invention will be readily understood through the following examples. The invention is not limited to the embodiments described herein, but may be embodied in other forms. The embodiments introduced herein are provided so that the disclosure may be made thorough and complete, and the spirit of the present invention may be sufficiently delivered to those skilled in the art. Therefore, the present invention should not be limited by the following examples.

The toxic gas release modeling apparatus according to embodiments of the present invention may include a conversion module and a generation module. The transformation module and the generation module may repeatedly learn based on an artificial neural network. The artificial neural network (ANN) is a statistical learning algorithm for implementing a biological neural network such as a brain. An artificial neural network (ANN) includes an input layer for receiving data and an output layer for processing the data and outputting a final result. layer) and one or more hidden layers disposed between the input layer and the output layer. The artificial neural network may include a deep neural network (DNN) including two or more hidden layers.

The conversion module can convert toxic gas dispersion data. The toxic gas dispersion data may include data simulated by numerically analyzing the behavior of the toxic gas before the toxic gas is dispersed due to a leakage accident, for example, data obtained by computational fluid dynamics (CFD). Can be. The simulation data may be sampled by the number of data required for modeling using a constant variable. In addition, the simulation data may be preprocessed using various utilities to be input to the conversion module.

이고, 상기 사망 확률은

으로 나타날 수 있다. 상기 프로빗 함수에서 a, b, 및 n은 상기 독성 가스 종류에 따른 상수, c는 상기 독성 가스의 부피별 농도이다. 상기 변수는 풍속, 풍향, 상기 독성 가스의 방출률, 방출 지속 시간, 방출 지점, 방출 물질 및 온도 중 하나 이상을 포함할 수 있다. The simulated data may include _death probability ( P _death ) data calculated by a probit function, wherein the probit function is

And the probability of death is

May appear. In the probit function, a, b, and n are constants according to the type of the toxic gas, and c is the volumetric concentration of the toxic gas. The variable may include one or more of wind speed, wind direction, release rate of the toxic gas, emission duration, emission point, emission material and temperature.

The conversion module may include an autoencoder. The autoencoder may include an encoder for encoding the toxic gas dispersion data and a decoder for reconstructing the encoded data similarly to the input toxic gas dispersion data. The autoencoder may compress and convert the data, thereby allowing the input data and the restored data to have different dimensions. For example, the dimension of the restored data may be reduced than the dimension of the input data. That is, the autoencoder may have the effect of compression that the restored data can be restored similarly to the input data with a smaller number of values. Since the autoencoder can be operated in various combinations, it is possible to achieve a sufficient dimensional reduction even for nonlinear data, for example, image data of the probability of death.

The autoencoder may further include a convolutional layer that detects and extracts features of the toxic gas dispersion data. The convolutional layer is a layer that detects and computes a characteristic of the toxic gas dispersion data, and may include one or two or more. A pooling layer may be included between the convolutional layers. The pooling layer may receive output data of the convolutional layer as an input and may reduce the size of the output map or emphasize specific data. Processing methods of the pooling layer include Max Pooling, Average Pooling, and Min Pooling.

The autoencoder is variable using a variational inference (Variational Inference) that is calculated by parameterizing the extracted characteristics of the toxic gas dispersion data and approximating the average value of the parameterized data and the log value of the variance as a normal distribution. You can use a null autoencoder (VAE). The autoencoder may further include a variational layer for comparing and evaluating the toxic gas dispersion data and the data converted by the autoencoder using a loss function. The variational autoencoder with the convolutional layer is further improved in performance to detect and extract clear features even in complex image data.

The generation module may be connected to the transformation module to generate a prediction model by mapping the transformed data into the variable. The generation module may include a fully connected layer that maps and converts the converted data into the variable.

The generation module may normalize the distribution of the converted data between the fully connected layer and the fully connected layer. This is called batch normalization. The batch normalization can be used to solve problems such as gradient vanishing. In addition, the active function can be replaced with sigmoid to rectified linear unit (ReLU). The batch normalization may be performed after passing the layer between the fully connected layers, so that the batch normalization may be implemented as a kind of layer.

In the toxic gas release modeling method using the toxic gas release modeling apparatus according to embodiments of the present invention, the method includes: inputting toxic gas dispersion data, converting the input data, and mapping the converted data to a predetermined variable; Generating a predictive model. The transforming step and the generating step may be repeatedly learned based on an artificial neural network.

The modeling method may include numerically analyzing and simulating the behavior of the toxic gas before dispersing the toxic gas due to leakage of the toxic gas or the like before the data input step, and sampling the simulation data using the variable. And preprocessing the simulation data so that the input step can be performed.

이고, 상기 사망 확률은

으로 나타날 수 있다. 상기 프로빗 함수에서 a, b, 및 n은 상기 독성 가스 종류에 따른 상수, c는 상기 독성 가스의 부피별 농도이다. 상기 변수는 풍속, 풍향, 상기 독성 가스의 방출률, 방출 지속 시간, 방출 지점, 방출 물질 및 온도 중 하나 이상을 포함할 수 있다.In the simulation step, P _death data may be calculated by a probit function, and the probit function may be calculated.

And the probability of death is

May appear. In the probit function, a, b, and n are constants according to the type of the toxic gas, and c is the volumetric concentration of the toxic gas. The variable may include one or more of wind speed, wind direction, release rate of the toxic gas, emission duration, emission point, emission material and temperature.

The converting step may include detecting and extracting a feature of the input data. The converting step may further include parameterizing an extracted feature of the input data, restoring the variable data, and comparing the input data with the restored data using a loss function. In addition, variable inference may be performed by approximating a normal distribution using the average value of the variable data and the log value of the variance as parameters.

The loss function is an index for comparing the input data with a prediction value through the modeling apparatus. If the value of the loss function is small, it may be determined that the prediction value is accurate. The loss function may include a mean squared error, a cross entropy error, and the like.

The generating may include mapping and reconstructing the transformed data into the variable based on an artificial neural network having several layers, that is, a deep neural network, and performing batch normalization to normalize the distribution of the converted data. It may further comprise a step. The batch normalization is a normalization is performed in batch units, and each dimension is independently viewed, and normalization proceeds separately for each dimension, and thus the calculation is easy.

EXAMPLE

[Toxic Gas Release Model Using FLACS (CFD)]

In one embodiment of the present invention, the Flame Acceleration Simulator (FLACS) was used as a gas dispersion computational fluid dynamics (CFD) tool. The version of the flame acceleration simulator used was version 10.4, released on July 27, 2015, and was developed by Gexcon. The flame acceleration simulator was developed for explosion simulation but can also simulate gas dispersion and fire models.

Figure 1 shows the shape of the Ulsan Mipo complex according to an embodiment of the present invention. Ulsan Mipo Complex in Korea has many industrial factories as well as residences nearby. Thus, this area has a high potential to cause significant damage as well as gas leakage incidents. Therefore, it was selected as the site of the virtual gas leak accident.

Referring to FIG. 1, (a) is a geometric figure of Ulsan Mipo complex, and (b) and (c) are plan and 3D views of CAD images in a flame acceleration simulator, respectively. (a) assumes a flat terrain with thousands of buildings. The size of the whole area is about 4,000 m in the x direction, 3,000 m in the y direction, and about 80 m on the ground in the z direction. Since more than 500 simulation data points were required, a uniform grid resolution of 20m × 20m × 20m was used to reduce the computational cost.

Since large quantities of liquefied chlorine are used in this area for industrial purposes, the chlorine was chosen as the material for the hypothetical release scenario. Three key variables were randomly selected within certain boundaries to generate distinct simulation samples. Wind direction was selected from 0 to 2π, wind speed from 0.5 to 5m / s and emission rate from 10 to 100kg / s. All other variables were fixed, including the duration of release (60 seconds), the point of release, the release material and the temperature (20 ° C.). The total simulation time in all cases was set to 1000 seconds. Simulation conditions are summarized in Table 1.

Variable Unit Value Ambient temperature ℃ 20 Ambient pressure Bar One Wind direction rad 0-2π Wind speed m / s 0.5-5 Discharge rate kg / s 10-100 Discharge direction - + Y Release duration s 60 Total simulation time s 1000 Pasquill class - None

The flame acceleration simulator can calculate compressive fluid flow using conservation equations for mass, energy and momentum. The flame acceleration simulator solves the three-dimensional Reynolds mean Naver-Stokes (3D RANS) equation widely used in computational fluid dynamics, based on a k-ε turbulence model in a non-uniform Cartesian mesh. Can be. The k-ε model is an eddy viscosity model with turbulent kinetic energy transfer and dissipation of the turbulent kinetic energy equation. In particular, the flame acceleration simulator can use a distributed porosity concept to efficiently calculate smaller obstacle effects than sub-grids in fluid flow. This approach not only considers small hurdles but also reduces computational costs. In one embodiment of the present invention, mass and momentum conservation equations, which are governing equations for the compressible fluid flow, may be used. The mass conservation equation is represented by the following equation (1).

(1)

(One)

Wherein β _v represents volume porosity and β _j represents area porosity in the j direction. j is any direction determined by Cartesian coordinates x, y and z. The momentum conservation equation can be written as

(2)

(2)

Where F _{o, i} is the flow resistance generated by the subgrid obstacle, and F _{w, i} Is the flow resistance produced by the wall, and σ _ij is the stress tensor. Where F _{o, i} and σ _ij are defined as

(3)

(3)

(4)

(4)

Where μ _eff is the effective viscosity defined as

(5)

(5)

Where k is the turbulent kinetic energy and ε is its dissipation. The second term is turbulent viscosity or vortex viscosity.

Chlorine is a very toxic substance. There are several indicators that can be used to assess the risk of exposure to toxic gases. Among them, acute exposure guidance levels (AEGLs), emergency response plan guidelines (ERPGs), and temporary emergency exposure limits (TEELs) can be used. In addition, a probit function can be used to quantitatively calculate the probability of _death ( P _death ). The equation of the method using the probit function is as follows.

(6)

(6)

(7)

(7)

Where Pr is the probit, c is the volume-specific concentration in ppm, and a, b, and n are constants. In the case of chlorine, a is -0.829, b is 0.92, n is 2. In this example, the probit value is integrated up to 10 minutes after the onset of leakage. In the pre-simulation phase, 10 minutes can be considered golden time because toxic gases have been introduced into the residential area for about 10 minutes.

The flame acceleration simulator can solve the conservation equations for each cell of the 3D Cartesian grid using finite volume method. The numerical time step algorithm used in the flame acceleration simulator is based on the implicit first-order backward Euler method. The time step of the transient simulation can be set so that the solution develops smoothly and reliably in time. The Courant-Friedrich-Levy (CFL) number can provide a solver-specific criterion for the maximum time step that yields a stable solution in the compressible solver of the flame acceleration simulator. Two CFL numbers, CFLV and CFLC, can be used to determine the maximum time step. The CFLV is based on fluid velocity, while the CFLC is based on sound velocity. The computational fluid dynamics solver can select the minimum value between CFLV and CFLC.

(8)

(8)

(9)

(9)

(10)

10

Where Δx _i represents the cell length in the i direction and Δt represents the time step. In the embodiment of the present invention, CFLV is set to 1.0, and CFLC is set to 10, which is a general value in the dispersion simulation. Each simulation is performed by a parallel computer with 12 CPU threads. The computer used in this embodiment has a 24-core Intel Xeon E5-2697v2 (2.7GHz) processor and 256GB DDR3 RAM.

[Modeling Using Neural Networks]

2 shows a flow diagram of data sampling and preprocessing according to one embodiment of the invention. Hundreds of sample data points are required for training to create a surrogate model using Neural Networks (NN). However, collecting large amounts of data manually is expensive, so an automated process can be used to generate the data. This can be done by linking the Flame Acceleration Simulator with Python code. It is also difficult to directly use the results obtained from the flame acceleration simulator in surrogate model training. Therefore, pretreatment is necessary.

Referring to FIG. 2, initially three of the input variables applied to each sample, for example, wind speed, wind direction, and emission rate, are randomly selected within a specific range. Using the selected variable, CS (scenario) and CL (leak) files are created. To start calculating the flame acceleration simulator, you need CS (scenario), CL (leak), CO (geometric), CG (lattice), and CP (porosity) files. Among them, the CO, the CG and the CP file are fixed because the simulation is performed with a single geometry. Only variables of the CS and CL files are changed to generate the file for each sample. When the flame acceleration simulator simulation is completed, the resulting r3 file (binary format) can be converted into an a3 file (ASCII format) using the flame acceleration simulator utility. The result thus obtained is four-dimensional data (x, y, z and time). Then P _death is calculated by integrating up to 10 minutes. Only data at height, z = 2m, which directly affects the population is extracted from the reduced 3D data to be 2D data (150 × 200), which is the P _death value corresponding to the x and y coordinates. Accordingly, 550 samples may be generated.

Principal Component Analysis (PCA) and Deep Autoencoder (DAE) can be used for data reduction and feature extraction in reduced order models for chemical engineering problems such as reactor modeling, gas dispersion modeling, and process data monitoring. Can be. The principal component analysis can effectively reduce linear correlation data in certain cases, and may include several applications such as kernel-PCA for nonlinear dimensional reduction or manifold learning, but the deep autoencoder Compared to the Principal Component Analysis and Shallow autoencoder, it shows better performance in nonlinear data reduction and can be useful when designing surrogate models. Therefore, the data reduction performance can be improved by using the autoencoder while maintaining the advantages of the principal component analysis. In addition, the autoencoder can be applied to a generation model due to a theoretical relationship with the latent variable model. This means that not only deterministic and rigorous data but also abstract and probabilistic data can be understood and its features can be extracted efficiently.

를 잠재 공간

으로 압축하기 위해 도입될 수 있고, 여기서 N_Z 는 잠재 변수의 수이다. 마지막으로, 잠재 공간 z는 v로만 이미지를 재구성하기 위해 가변 공간

에 의해 맵핑될 수 있다.Since the P _death image generated in the computational fluid dynamics gas dispersion model is very nonlinear due to complex geometrical factors such as buildings, mountains, rivers, etc., it is quite difficult to extract features from the model. Thus, a surrogate model based on Variational Autoencoder (VAE) puts Variation Bayes, which puts priorities for latent variables in the central isotropic multivariate Gaussian (N (z; 0,1)). output image data using a stochastic encoder ( q _φ (z | x)) and a stochastic decoder ( p _θ (x | z)) as a generator by variational Bayes

Latent space

Can be introduced, where N _Z is the number of latent variables. Finally, latent space z is a variable space to reconstruct the image with only v

Can be mapped by

, 즉 풍속(m/s), 풍향(rad) 및 가스 방출률(kg/s)로 표현될 수 있다. 상기 모델의 출력은

로 표현되고, 이는 P_death의 등고선 이미지이다. 따라서 이 문제는 고성능, 최소 평균 제곱 오차의, f(v)의 사전 계산된 데이터 세트를 이용한 기존 전산 유체 역학 모델

의 대리 모델

을 개발하는 것으로 정의될 수 있다.In order to develop a surrogate model f ^* (v) of the computational fluid dynamics gas emission model f (v) adopted by the flame acceleration simulator, a Variantional Autoencoder with Deep Convolutional layer, VAEDC) and a fully connected deep neural network (DNN) with a batch normalization (BN) layer may be used. The input of the conventional computational fluid dynamics model and the variational auto-encoder-depth neural network (VAEDC-DNN) surrogate model with the deep convolution layer

, Wind speed (m / s), wind direction (rad) and gas emission rate (kg / s). The output of the model

This is the contour image of P _death . Therefore, this problem can be solved by conventional computational fluid dynamics models using a high-performance, least mean square error, f (v) precomputed data set.

Surrogate model

It can be defined as developing.

의 생성된 이미지 데이터와 x^test의 사이의 최종 메트릭(평균 제곱 오차)을 테스트(v^test, x^test)하기 위해 사용되었다.500 data points can be used as a training set (v ^train , x ^train ) and a validation set (v ^validation , x ^validation ). 400 samples were randomly extracted from 500 samples and used as training sets, and 100 samples were extracted and used as validation sets. 50 data points

It was used to test (v ^test , x ^test ) the final metric (mean squared error) between the generated image data of and x ^test .

A variant auto-encoder-deep neural network (VAEDC-DNN) having a deep convolutional layer, which is a surrogate model according to an embodiment of the present invention, may be composed of two parts. The first part can consist of an encoder and decoder using a variational autoencoder with a deep convolutional layer. The second part uses a deep neural network to map the variable space v to the latent space z. The two step method enables the surrogate model to effectively regress the P _death image (x) for the variable (v).

3 illustrates a structure of a variational auto encoder (VAEDC) having a deep convolutional layer of a surrogate model according to an embodiment of the present invention.

을 사용하여 계산된다.Referring to FIG. 3, three convolutional layers with a kernel size of (3, 3), a stride of 1, a He initialization, a Rectified Linear Unit (ReLU) activation function, and padding of the same dimension are used. After each convolution layer, the (2,2) filter and stride 2's max pooling layer are used for dimensional reduction. As a result, the input layer dimension of 152 × 200 is reduced to 19 × 25, which is 1/8 of the width and height of the image. The 19x25x8 (number of filters) layer is then reformed into a 1x3800 vector to form a 3800-128-64 fully connected density layer with the ReLU activity function. Parallel μ and log (σ ² ) layers represent the mean and variance of the latent variables, respectively. Thus, the dimension of the μ layer, log (σ ² ) layer and z layer is 1 × N _Z , where N _Z is the number of latent variables. After the encoding process is completed, the decoding process, which is the inverse of the encoding process, begins. Finally, the loss function represented by the variation lower bound is x ^train and

Is calculated using

4 illustrates a detailed deep neural network (DNN) configuration for mapping latent space and variable space from a variational autoencoder (VAEDC) having a deep convolutional layer in accordance with an embodiment of the present invention.

는 훈련된 심층 컨볼루션 레이어를 가진 베리에이셔널 오토인코더의 디코더에 의해 생성될 수 있다. 성능은

와 x^test 사이의 평균 제곱 오차를 비교함으로써 평가될 수 있다.Referring to FIG. 4, a five layer fully connected deep neural network with batch normalization, ReLU activation function, and He initialization can be used to map variable space to latent space. In the training phase, the network may be trained using 400 resampling training sets (x ^{train '} , v ^train' ) and 100 validation sets (x ^{validation '} , v ^validation' ). The mean of the latent variables designed as the output can be extracted using the encoder portion of the variational autoencoder with a deep convolutional layer already trained. The variable set v ^{train '} , mapped in a one-to-one correspondence, was used as input. Finally, in the generation phase, the model uses a set of tests that were not used as a training or validation set in both the variational autoencoder with the deep convolutional layer and the deep neural network. x ^test is predicted by v ^test and trained deep neural networks,

May be generated by a decoder of a variational autoencoder having a trained deep convolutional layer. Performance

Can be evaluated by comparing the mean squared error between and x ^test .

The loss function is one of the most important settings for configuring an efficient autoencoder. In one embodiment of the invention, a variation lower bound for marginal likelihood may be used. The lower limit can be given by the following equation.

(11)

(11)

Where D _KL represents the Kullback-Leibler divergence, p _θ (x│z) is a stochastic decoder with generation parameter θ and q _φ (z | x) has variation parameter φ Probabilistic encoder.

로 정의된다. 또한, q _φ (z|x)로부터 샘플을 생성하고 근사 사후의 평균(μ) 및 표준 편차(σ)를 갖는 대각 공분산 구조의 다변량 가우시안으로서 φ를 재매개변수화하기 위해, 다음 식이 샘플링에 적용된다.The training may consist of maximizing the variation lower limit for the peripheral likelihood of the data point i via the variation parameter φ and the generation parameter θ . To use this statistical approach in the neural network framework, the loss function is used to convert from the maximization problem to the minimization problem.

Is defined as In addition, to generate a sample from q _φ (z | x) and to reparameterize φ as a multivariate Gaussian of a diagonal covariance structure with approximate post mean ( μ ) and standard deviation ( σ ), the following equation is applied to the sampling: .

(12)

(12)

This sampling may be performed on the z layer located behind the μ and log (σ ² ) layers of FIG. 3. KL divergence can be calculated and differentiated without estimation, and the second term of the lower variation of Equation (11) can be treated as a binary crossentropy loss function. Finally, a variational autoencoder with a deep convolution layer and data point x ⁽ⁱ⁾ The loss function proposed for

(13)

(13)

와 x^test 사이의 평균 제곱 오차를 이용하고, 이 테스트 세트는 심층 컨볼루션 레이어를 가진 베리에이셔널 오토인코더 및 심층 신경망 모두에서 훈련 또는 유효성 검증 세트로 사용되지 않은 것이다.It is very important to accurately evaluate the performance of the surrogate model. The purpose of the surrogate model is to accurately predict the P _death image using the variable space instead of simply encoding and decoding the image data or mapping the variable space to the latent space. Therefore, it is necessary to determine whether the latent space accurately reflects the features representing the P _death image and whether the variable space and the generated image data correspond one-to-one. That is, it should be ensured that the image data is not simply stored in the latent space or overfitting. Therefore, the performance of the surrogate model is not evaluated by the angular loss function of the variational autoencoder with the deep convolutional layer and the deep neural network.

Using the mean squared error between and x ^test , this test set was not used as a training or validation set in both a variational autoencoder and a deep neural network with deep convolutional layers.

5 shows a comparison between the performance of a surrogate model and another type of surrogate model according to an embodiment of the present invention.

Referring to FIG. 5, in order to compare model performance with other types of surrogate models based on an autoencoder neural network, a neural network (NN) with one hidden layer without an autoencoder, three hidden layers without an autoencoder, and batch normalization are used. Deep Neural Network (DNN), Neural Network with Simple Auto Encoder (AE-NN), Neural Network with Deep Auto Encoder and Deep Neural Network (DAE-NN, DAE-DNN), Neural Network with Deep Convolution Auto Encoder (DCAE) NN, DCAE-DNN), deep neural network (VAE-DNN) using simple variant autoencoder and deep neural network (VAEDC-DNN) using variant autoencoder with deep convolution layer It can be compared using a hyperparameter.

In order to compare the models fairly, the epoch number of autoencoder and neural network was set to 1,500, and the size of latent space (N _Z ) was set to 32 in all models. The size of the variable space N _V was set to 3, ie wind speed (m / s), wind direction (rad) and emission rate (kg / s). Adam optimizer (Adam optimizer) may be used to optimize the loss function. All models were coded using the Python deep learning library Keras with the Tensorflow backend. Training was performed using NVDIA GeForce GTX 1070 with 8GB GDDR5.

[result]

6 shows a comparison of loss function graphs of various surrogate models for epochs.

Referring to FIG. 6, a neural network (NN) having one hidden layer without an autoencoder, three hidden layers without an autoencoder, a deep neural network (DNN) using batch normalization, a neural network using a simple autoencoder (AE-NN), Neural and deep neural networks with deep autoencoder (DAE-NN, DAE-DNN), neural and deep neural networks with deep convolutional autoencoder (DCAE-NN, DCAE-DNN), deep with simple variational autoencoder Various training aspects of the deep neural network (VAEDC-DNN) model using a variational autoencoder with a neural network (VAE-DNN) and a deep convolutional layer can be investigated through the change of each loss function for the epoch. The maximum epoch for all trainings is set to 1500. If this number is not correct, training may be inappropriate or overfitting. This can be determined by comparing the loss function of the validation set with the loss function of the test set. Since 1500 is set by trial and error, the entire training processor can be considered suitable for all models.

In the case of neural networks (NN), a fairly unstable training process is manifested as the epochs are elevated above 70. Higher dimension prediction from significantly lower dimensions in a fully connected high density hidden layer results in an unstable training process because the number of parameters (30,434,400) is excessively large and no additional normalization process is added. However, it can be used for comparison because the process appears to stabilize to some extent until the epoch exceeds 800.

Considering three hidden layers applied after each layer and a deep neural network (DNN) using batch normalization to mitigate the vanishing gradient problem of deep networks, the training processor is more stable and faster without overfitting. Can show convergence

With respect to the neural network (AE-NN) using a simple autoencoder, the autoencoder portion and the neural network or the deep neural network portion may be considered separately. In the auto-encoder training processor, which is indicated by a blue line, there is a slight overfit after epoch 100 only in the case of deep auto-encoders. However, the loss function value at the end of training is appropriate for autoencoder, deep convolution autoencoder, variant autoencoder, and variant autoencoder with deep convolution layer. The neural network, shown in red, shows a very stable training processor, unlike neural networks without autoencoders. In addition, there is no difference between training error and validation error. Thus there is no overfitting.

In the case of deep neural networks, there is some vibration in the second half. Nevertheless, it appears to be well trained because it exhibits a monotonically decreasing training processor, and there is little difference between validation error and test error. However, the lower validation error appears in comparison with the training error because the randomized validation set, x ^{validation '} and v ^validation' contains a predictable subset.

7 illustrates the mean squared error of the extracted test data set according to an embodiment of the present invention.

와 x^test 사이의 평균 제곱 오차가 표시되고, 가우시안 분포 피팅 (Gaussian distribution fitting)을 가진 모든 테스트 데이터 세트의 평균 및 표준 편차도 제공된다. Referring to FIG. 7, for each of the 50 newly extracted test data sets (x ^test , v ^test )

The mean squared error between and x ^test is shown, and the mean and standard deviation of all test data sets with Gaussian distribution fitting are also provided.

The surrogate model constructed using the deep neural network (VAEDC-DNN) using a variational autoencoder with a deep convolution layer showed the highest performance. The mean value was the lowest at 0.00246, with the smallest standard deviation of the 50 test data sets. That is, the deep neural network using the variational autoencoder with the deep convolution layer does not simply store the P _death image information obtained from the training set, but extracts the feature in the most suitable format for the latent space and expresses it explicitly. It has the ability to map to variable spaces.

When the neural network NN is used, it can be seen that performance is significantly reduced regardless of the efficiency of autoencoder compression. It can be seen that the relationship between the latent space and the variable space is not clearly captured. However, when each variable stored in latent space is encoded such that the variable space and nonlinear correlation are clearly shown, performance is improved. The neural network can be confirmed that the performance is improved in the order of the variational auto encoder, the deep convolution auto encoder, the deep auto encoder, and the auto encoder. In conclusion, the best performance can be achieved when a variational autoencoder-based autoencoder and convolutional layer are used. For neural networks without autoencoder, the number of parameters is 30,434,400, whereas the number of parameters in a deep neural network using a variational autoencoder with a deep convolutional layer is 1,007,641, the previous 3.31%. Good performance can be efficiently trained and characterized with fewer parameters.

8 illustrates P _death images according to various models according to an exemplary embodiment of the present invention.

가 등고선 그래프에 직접 그려지면, 오토인코더가 없는 신경망 및 심층 신경망은 심각한 노이즈를 나타내는 것을 볼 수 있다. 화염 가속 시뮬레이터(전산 유체 역학), 신경망(NN), 단순 오토인코더를 이용한 신경망(AE-NN), 심층 오토인코더를 이용한 심층 심경망(DAE-DNN), 심층 컨볼루션 오토인코더를 이용한 심층 신경망(DCAE-DNN) 및 심층 컨볼루션 레이어를 가진 베리에이셔널 오토인코더를 이용한 심층 신경망(VAEDC-DNN)으로부터 생성된

의 임의 선택된 다섯개의 등고선 그래프로 이를 시각화할 수 있다.Referring to FIG. 8, in terms of mean squared error, neural networks and deep neural networks without autoencoder appear to perform better compared to various combinations of autoencoder and neural network,

If drawn directly on the contour plot, it can be seen that neural networks and deep neural networks without autoencoder exhibit severe noise. Flame Acceleration Simulator (Computational Fluid Dynamics), Neural Networks (NN), Neural Networks with Simple Auto Encoder (AE-NN), Deep Deep Networks with Deep Auto Encoder (DAE-DNN), Deep Neural Networks with Deep Convolution Auto Encoder ( DCAE-DNN) and generated from deep neural network (VAEDC-DNN) using variant autoencoder with deep convolution layer

You can visualize this with any of the five contour plots.

If you use a neural network or a deep neural network without an autoencoder, serious noise will appear. This is because it is difficult to efficiently extract only the features of the image from the training processor. Thus, other training data images can be stored and reflected in the results. Moreover, because of the nature of nonlinear images, it is difficult to predict the entire image using only variable space and can be misleading in some cases.

The noise disappears from the prediction after data compression by the autoencoder. However, the feature extraction by the autoencoder and the mapping failure of the variable space into the latent space by the neural network degrades the performance of the surrogate model. This phenomenon can be observed directly in neural networks using simple autoencoder. Loss of noise is important but only a rough trend can be predicted. For example, the prediction is quite inaccurate for the second column data, while the fifth column data is very accurate. Here, it can be seen that the introduction of a deep neural network model using a batch normalization model is necessary for improving overall performance. Feature extraction can be activated through a deep convolutional layer and image compression can be accurately performed in latent space by prediction of post-distribution through a variational autoencoder.

Between two best models, a deep neural network with a variational autoencoder with a deep convolutional layer and a deep neural network with a deep convolutional autoencoder, a variational autoencoder with the deep convolutional layer Deep neural networks can provide better predictions compared to flame acceleration simulators (computational fluid dynamics). In the first column, P _death spreads slightly upward, which cannot be detected by the deep neural network using the deep convolutional autoencoder, but the deep neural network using the variational autoencoder with the deep convolutional layer It can be detected. In the third column, the other models cannot clearly predict the width and size, but the prediction of the deep neural network using the variational autoencoder with the deep convolutional layer is almost identical. The data in the fourth and fifth columns show good feature extraction even if the shape has many cracking properties and is complex. Finally, it can be seen that complex images that are cracked and not convex are also predicted.

9 shows the results of walking in the variable space of a deep neural network using a variational autoencoder with a deep convolutional layer. As can be seen in "walking in the latent space," it is very important to understand the landscape of the latent space because it is possible to sense the memory through walking in the latent space. If there is a sharp image transition that means that the latent space has collapsed, the model does not learn the associated representation. In embodiments of the present invention, since variable space has already been mapped to latent space, “variable space walking” may be suitable for determining whether the manifold is to be learned.

Referring to FIG. 9, since the variable space v is three-dimensional, the toxic gas emission rate (discharge rate) is fixed at 50 kg / s and P _death is visualized as a linear series of 10 points in wind speed and wind direction. Smooth transitions were observed in all directions. P _death widens as wind speed increases, and the direction of P _death spreads smoothly with wind direction, and the terrain and obstacles in this area are reflected by asymmetrical motion. Deep neural networks using variational autoencoders with deep convolutional layers are trained to only interpolate the wind direction and not rotate symmetrically, allowing accurate extraction of P _death features.

Table 2 compares the computation time of CPUs between deep computational networks using computational fluid dynamics models and variant autoencoders with deep convolutional layers, storage space to store models, and use in real-time alert systems.

CPU time Storage Use in real-time alarm systems CFD model ~ 700 s with 16 cores GB scale Thousands of cases are needed to predict all variables
VAEDC-DNN
<1 s with single core
KB scale Hundreds of cases,
The surrogate model
Predictable

For real-time alarm systems, wind speed, wind direction and emission rate are provided to the alarm system from external sensors in the event of a chemical release. The concentration of P _death or toxic chemical is then calculated. Using computational fluid dynamics models for P _death calculations, the CPU time is over 700 seconds using a 16-core E5-2667v3 (3.2GHz) processor from Intel Xeon. Therefore, it is impossible to obtain this information before the Golden Time (10 minutes). In addition, the storage requirement for storing computational fluid dynamics data is the GB scale per case, making it difficult to precalculate all scenarios in advance, and the complexity of the geometry results in nonlinearity through the variable space.

Thus, deep neural networks using variational autoencoder with deep convolutional layers can be particularly useful for developing surrogate models with minimal amounts of precomputed computational fluid dynamics data. After training, up to 1 second of CPU time is required with a single core. As mentioned above, the nonlinear correlation between the P _death distribution and the effect of geometry through variable space can be achieved by a variational autoencoder. Thus, as a result of hundreds of precomputed computational fluid dynamics, a deep neural network using a variational autoencoder with the deep convolutional layer can successfully predict the P _death contour through any variable space.

So far, specific embodiments of the present invention have been described. Those skilled in the art will appreciate that the present invention can be implemented in a modified form without departing from the essential features of the present invention. Therefore, the disclosed embodiments should be considered in descriptive sense only and not for purposes of limitation. The scope of the present invention is shown in the claims rather than the foregoing description, and all differences within the scope will be construed as being included in the present invention.

Claims (19)

A conversion module for converting the toxic gas dispersion data; And
And a generation module connected to the conversion module to generate a prediction model by mapping the converted data into a predetermined variable. The method of claim 1,
The conversion module and the generation module is a toxic gas release modeling apparatus, characterized in that for learning repeatedly based on the artificial neural network. The method of claim 1,
The toxic gas dispersion data,
It includes data simulated by numerically analyzing the behavior of the toxic gas before the toxic gas is dispersed,
And the simulation data is sampled using the variable and preprocessed to be input to the conversion module. The method of claim 3, wherein
The simulation data includes P _death data calculated by a Probit function,
The probit function is

(a, b, and n is a constant according to the type of the toxic gas, c is the concentration by volume of the toxic gas),
The probability of death is

Toxic gas release modeling device, characterized in that. The method of claim 1,
The conversion module,
An autoencoder for compressing and converting the toxic gas dispersion data;
The autoencoder includes a convolutional layer (Convolutional layer) for detecting and extracting the characteristics of the toxic gas dispersion data. The method of claim 5,
The auto encoder,
Parameterize the extracted features of the toxic gas dispersion data,
Toxic gas release modeling apparatus characterized in that it uses the variation inference (Variational Inference) to calculate the approximation to the normal distribution with the average value and the logarithm of the variance of the parameterized data. The method of claim 6,
The auto encoder,
And a variational layer for comparing and evaluating the toxic gas dispersion data and the data converted by the autoencoder using a loss function. The method of claim 1,
The generation module,
And a fully connected layer configured to map and convert the converted data into the variable. The method of claim 8,
The generation module,
Wherein the distribution of the transformed data is normalized between the fully connected layer and the fully connected layer. The method of claim 1,
Wherein said variable includes at least one of wind speed, wind direction, release rate of said toxic gas, duration of release, point of release, release material and temperature. Inputting toxic gas dispersion data;
Converting the input data; And
And generating a predictive model by mapping the converted data into a predetermined variable. The method of claim 11,
The transformation step and the generation step is a toxic gas release modeling method, characterized in that the learning repeatedly based on the artificial neural network. The method of claim 11,
The modeling method,
Before the data entry step,
Numerically analyzing and simulating the behavior of the toxic gas before the toxic gas is dispersed, and sampling the simulation data using the variable, and preprocessing the simulation data to perform the input step. Toxic gas release modeling method, characterized in that. The method of claim 13,
The simulation step includes performing a P _death data calculation by a probit function,
The probit function is

(a, b, and n is a constant according to the type of the toxic gas, c is the concentration by volume of the toxic gas),
The probability of death is

Toxic gas release modeling method, characterized in that. The method of claim 11,
The conversion step,
Toxic gas release modeling method comprising the step of detecting and extracting the characteristics of the input data. The method of claim 15,
The conversion step,
Parameterizing the extracted feature of the input data, converting and restoring the variable data, and comparing the input data with the restored data using a loss function,
Toxic gas release modeling method characterized in that for performing the calculation of the approximation to the normal distribution with the average value and the logarithm of the variance of the parameterized data as a parameter. The method of claim 11,
The generating step,
Mapping the converted data to the variable and reconstructing the toxic gas release model. The method of claim 17,
The generating step,
And performing batch normalization to normalize the distribution of the transformed data. The method of claim 11,
Wherein said variable comprises at least one of wind speed, wind direction, release rate of said toxic gas, duration of release, point of release, release material and temperature.

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