WO2014194482A1 - 基于压缩感知理论的气体识别方法 - Google Patents

基于压缩感知理论的气体识别方法 Download PDF

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WO2014194482A1
WO2014194482A1 PCT/CN2013/076759 CN2013076759W WO2014194482A1 WO 2014194482 A1 WO2014194482 A1 WO 2014194482A1 CN 2013076759 W CN2013076759 W CN 2013076759W WO 2014194482 A1 WO2014194482 A1 WO 2014194482A1
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data
neural network
sparse matrix
matrix
method based
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李冬梅
张�浩
梁圣法
罗庆
李小静
谢常青
刘明
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Institute of Microelectronics of CAS
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/0004—Gaseous mixtures, e.g. polluted air
    • G01N33/0009—General constructional details of gas analysers, e.g. portable test equipment
    • G01N33/0027—General constructional details of gas analysers, e.g. portable test equipment concerning the detector
    • G01N33/0031—General constructional details of gas analysers, e.g. portable test equipment concerning the detector comprising two or more sensors, e.g. a sensor array
    • G01N33/0034—General constructional details of gas analysers, e.g. portable test equipment concerning the detector comprising two or more sensors, e.g. a sensor array comprising neural networks or related mathematical techniques
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/084—Backpropagation, e.g. using gradient descent

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  • the present invention relates to the field of sensor array signal processing technologies, and in particular, to a gas recognition method based on compression sensing theory.
  • Gas sensors are generally sensitive to cross-sensitivity, and their output signals are affected by factors such as temperature, humidity, and environmental conditions, and their stability and selectivity are poor, so that their applications are limited to low detection accuracy or simple gas composition. Occasionally, such as a hazardous gas leak alarm.
  • the traditional solution is to eliminate the above-mentioned adverse effects by finding new sensitive materials, device structures and compensation circuits. However, this solution not only complicates the device structure, but also increases the manufacturing cost of the device.
  • Compressed sensing theory is a new signal acquisition and codec theory that has taken advantage of signal sparsity or compressibility in recent years.
  • the basic idea of the theory is to extract as much information as possible from as little data as possible.
  • the theory states that as long as the signal is sparse in a certain domain, it can be projected with an uncorrelated matrix, and then use these small projection values to solve an optimization problem, and finally reconstruct the original signal with a high probability. That is to say, a compressible signal can be sampled at a much lower rate than the Nyquist sampling rate, and then the small amount of data can be used to accurately reconstruct the original data.
  • neural networks With its nonlinear mapping, parallel processing and highly self-learning, self-organizing and self-adaptive capabilities, neural networks can effectively solve the nonlinear problems caused by the cross-sensitivity of gas sensors and suppress the drift or noise of the sensors to some extent. , which contributes to the improvement of gas detection accuracy. Therefore, the combination of high-performance, low-cost gas sensors and intelligent identification technology represented by neural networks has become a popular trend in gas detection.
  • Back Propagation (BP) neural networks are multi-layer feedforward networks trained according to the error back propagation algorithm. They are generally composed of multiple network layers, including an input layer, one or several Hidden layer, one output layer, full layer between layers Interconnected, there is no interconnection between the same layer of neurons.
  • the hidden layer neurons usually use the Sigmoid type transfer function, and the output layer uses the purelin type transfer function.
  • the learning process of BP neural network consists of forward propagation and back propagation. In the forward propagation process, the input mode is processed layer by layer through the input layer and hidden layer, and transmitted to the output layer. If the desired output cannot be obtained at the output layer, the process proceeds to the backpropagation process, and the error value is transmitted layer by layer along the connection path, and the connection weights of the layers are corrected until the expected training error is reached.
  • the present invention provides a gas recognition method based on the compressed sensing theory, which solves the problem that the amount of data stored and stored in the gas detection is large and the identification is inaccurate, and reaches a problem with a small amount of data.
  • the purpose of precise deterministic identification is a gas recognition method based on the compressed sensing theory, which solves the problem that the amount of data stored and stored in the gas detection is large and the identification is inaccurate, and reaches a problem with a small amount of data.
  • the present invention provides a gas recognition method based on a compressed sensing theory, the method comprising: Step 1: collecting compressed data in an undersampling manner; Step 2: collecting the compressed data The data is reconstructed to obtain reconstructed data; Step 3: Using the reconstructed data to train the backpropagation neural network and save the trained backpropagation neural network; Step 4: Enter the data to be tested into training Backpropagation neural network, the trained back-propagation neural network identifies the measured data to achieve qualitative identification of the gas.
  • the compressed data is collected in an undersampling manner as described in the first step, and the method includes: collecting, by the array node of the sensor network, compressable original data; performing sparse decomposition on the original data to obtain a first sparse matrix, The first sparse matrix is a sparse matrix associated with the original data; performing nonlinear projection processing on the first sparse matrix to obtain a second sparse matrix, the elements in the second sparse matrix being elements of the first sparse matrix Random combination; low-speed undersampling of data having a larger coefficient in the second sparse matrix at a frequency less than the Nyquist sampling frequency.
  • the sparse decomposition of the original data is performed to obtain a first sparse matrix.
  • the method includes: constructing a sparse matrix of a random Gaussian distribution, and multiplying the collected raw data by a sparse matrix of the constructed random Gaussian distribution to obtain a first sparse matrix.
  • the constructing a sparse matrix of a random Gaussian distribution comprises: selecting a Gaussian matrix of dimension w, each element of the Gaussian matrix obeying a Gaussian distribution, and then normalizing each column of the Gaussian matrix to obtain a sparse matrix ⁇
  • the multiplying the collected raw data by the sparse matrix of the constructed random Gaussian distribution to obtain the first sparse matrix comprises: thinning the collected compressible original data X with the constructed random Gaussian distribution Multiplying the matrix ⁇ to obtain a first sparse matrix, which is the most sparse representation of the compressible original data X, if the number ⁇ of non-zero elements in the first sparse matrix is smaller than the non-compressible original data X The number of zero elements, then the first sparse matrix is compressible.
  • reconstructing the collected compressed data to obtain reconstructed data includes: selecting an observation matrix, the observation matrix is not related to the first sparse matrix; The data is multiplied by the observation matrix to obtain observation data; the observation data is inversely transformed to obtain reconstructed data.
  • the selected observation matrix is an observation matrix MX of the MXN dimension, and the observation matrix ⁇ is not related to the first sparse matrix; and the collected compressed data X is multiplied by the observation matrix , to obtain observation data; , ; is the linear combination of the non-zero vectors in the first sparse matrix corresponding to the column vectors in the observation matrix ⁇ .
  • the backpropagation neural network is trained by using the reconstructed data in step 3, and the trained backpropagation neural network is saved, which specifically includes: inputting the reconstructed data as an input sample to the reverse Propagating the neural network, the back-propagating neural network iteratively processes the reconstructed data, and each iteration error is compared with the previous iterative error. When the iterative error reaches the initial set threshold, the training ends and the back-propagating nerve is saved.
  • the internet specifically includes: inputting the reconstructed data as an input sample to the reverse Propagating the neural network, the back-propagating neural network iteratively processes the reconstructed data, and each iteration error is compared with the previous iterative error.
  • the training ends and the back-propagating nerve is saved.
  • the trained back-propagation neural network described in step 4 identifies the measured data, and the trained back-propagation neural network compares the weights of each connection during training.
  • the binary quantized number is output with the most similar weights, and the binary quantized number of the output represents different kinds of gases, thereby achieving qualitative identification of the gas.
  • the present invention has the following beneficial effects:
  • the gas recognition method based on the compressed sensing theory provided by the invention applies the compressed sensing technology to the transmission process of the array signal in the sensor network, and uses the BP neural network to train and identify at the receiving end, and the computational complexity is detected from the online. Transfer to off-line network training, which can greatly improve the real-time and accuracy of the online detection of the detection system, and solve the problem of large amount of transmission and storage data and inaccurate identification in the current gas detection, reaching a small amount of data. The purpose of precise deterministic identification.
  • the gas recognition method based on the compressed sensing theory provided by the present invention combines the compressed sensing theory with the neural network, compresses and transmits the data at the same time, and then trains the BP neural network at the back end. Identifying the compressed and reconstructed signal can effectively improve the data storage capacity and bandwidth utilization, and can accurately identify and improve the accuracy of gas detection.
  • FIGS. 2 to 4 illustrate a gas recognition method based on a compressed sensing theory according to an embodiment of the present invention, wherein:
  • Figure 2 is a comparison diagram of the original signal and the reconstructed signal
  • Figure 3 is a training state diagram of the BP neural network
  • Figure 4 is a training error map for qualitative identification. DETAILED DESCRIPTION OF THE INVENTION
  • the invention provides a gas recognition method based on compressed sensing theory, applies compressed sensing technology to the transmission process of array signals in a sensor network, and uses BP neural network to train and recognize, and transfers computational complexity from online detection to offline network training, thereby It can greatly improve the real-time and accuracy of the online detection of the detection system.
  • FIG. 1 is a flowchart of a gas recognition method based on a compressed sensing theory provided by the present invention.
  • the method first collects compressed data in an undersampling manner, and reconstructs the compressed data to obtain reconstructed data. Then, the BP network is trained by using the reconstructed data, and the trained network is saved. Finally, the data to be tested is input into the trained neural network, and the trained neural network identifies the measured data, and the output represents binary quantization of different gases. Number, to achieve qualitative identification of the gas, the method specifically includes the following steps:
  • Step 1 collecting compressed data in an undersampling manner
  • Step 2 reconstructing the acquired compressed data to obtain reconstructed data
  • Step 3 training the back propagation neural network with the reconstructed data, and saving the trained back propagation neural network
  • Step 4 Input the data to be tested into the trained back-propagation neural network, and the trained back-propagation neural network identifies the measured data to achieve qualitative identification of the gas.
  • the compressed data is collected in an undersampling manner as described in the first step, and the method includes: collecting, by the array node of the sensor network, compressable original data; performing sparse decomposition on the original data to obtain a first sparse matrix, the first A sparse matrix is a sparse matrix associated with the original data; performing nonlinear projection processing on the first sparse matrix to obtain a second sparse matrix, the elements in the second sparse matrix being random combinations of elements in the first sparse matrix Data with a larger coefficient in the second sparse matrix is subjected to low-speed undersampling at a frequency less than the Nyquist sampling frequency.
  • Performing sparse decomposition on the original data to obtain a first sparse matrix comprising: constructing a sparse matrix of a random Gaussian distribution, multiplying the collected raw data by a sparse matrix of the constructed random Gaussian distribution, to obtain a first sparse matrix .
  • the constructing a sparse matrix of a random Gaussian distribution comprises: selecting a Gaussian matrix of dimension M, each element of the Gaussian matrix obeying a Gaussian distribution, and then normalizing each column of the Gaussian matrix to obtain a sparse matrix ⁇
  • Multiplying the collected raw data by the sparse matrix of the constructed random Gaussian distribution to obtain a first sparse matrix comprising: multiplying the collected compressible original data X by a sparse matrix ⁇ of the constructed random Gaussian distribution Obtaining a first sparse matrix, wherein the first sparse matrix is the most sparse representation of the compressible original data X, if the number of non-zero elements in the first sparse matrix is smaller than the non-zero elements in the compressible original data X
  • the first sparse matrix is compressible.
  • Reconstructing the collected compressed data to obtain reconstructed data comprising: selecting an observation matrix, the observation matrix is not related to the first sparse matrix; and collecting the compressed data and the The observation matrix is multiplied to obtain observation data; the observation data is inversely transformed to obtain reconstructed data.
  • the selected observation matrix is an observation matrix ⁇ of ⁇ X ⁇ dimension, and the observation matrix ⁇ is not related to the first sparse matrix; the acquired compressed data X is multiplied by the observation matrix , to obtain observation data ⁇ , ⁇ That is, the non-zero vector in the first sparse matrix corresponds to the linear combination of the column vectors in the observation matrix ⁇ .
  • the back propagation neural network is trained by using the reconstructed data in step 3, and the trained back propagation neural network is saved, which specifically includes: inputting the reconstructed data as an input sample to the back propagation neural network,
  • the backpropagation neural network iteratively processes the reconstructed data, and each iteration error is compared with the previous iteration error. When the iterative error reaches the initial set threshold, the training ends and the backpropagation neural network is saved.
  • the trained back-propagation neural network described in step 4 identifies the measured data, and the trained back-propagation neural network compares each connection weight in the training, and outputs the binary quantized number with the most similar weight.
  • the binary quantized number of the output represents a different type of gas, which in turn enables qualitative identification of the gas.
  • FIG. 2 to FIG. 4 illustrate a gas recognition method based on the compressed sensing theory according to an embodiment of the present invention, which specifically includes the following steps:
  • Step 1 Collect compressed data in an undersampling manner
  • a discrete Fourier transform is performed on the compressible original data X to obtain a sparse representation result of the original data, and then a pseudo-random Gaussian matrix is used as the observation matrix, and a non-linear projection operation is performed on the sparse representation result, that is, the two matrices are multiplied
  • the specific algorithm uses the orthogonal matching pursuit algorithm (OMP) to reconstruct the original signal.
  • Figure 2 is a comparison of the data acquired by the sensor array with the compressed data and the original data. The approximation error is 0.87031.
  • Step 3 Using the reconstructed data to train the back propagation neural network and save the trained back propagation neural network;
  • the reconstructed data is restored to a 6x30 vector matrix as an input to the BP neural network, and the target vector is also defined as a three-dimensional matrix.
  • Each target vector contains 3 elements.
  • the vector represents a gas.
  • the value of the element at its corresponding position is 1, and the value of the element at the other position is 0.
  • the vector corresponding to CO has an element value of 1 in the first position and an element value of 0 in the other two positions, gp[l, 0, 0] o
  • the BP neural network used in the design of the present invention has a structure of 6:7:3, that is, the input layer has 6 inputs (the number of sensors of the node), the number of intermediate single hidden layer nodes is 7, and the output layer needs 3 Neurons (dimensions of the target vector).
  • the neural network with single hidden layer and the neural network with multiple hidden layers can complete the task of qualitative detection. The only difference is that the training time of multi-hidden layer neural network is significantly higher than that of single hidden layer neural network.
  • a single hidden layer BP network is used to train the reconstructed signals with different sparsity.
  • a single hidden layer BP network is used, that is, an input layer, a hidden layer, and an output layer.
  • the sample data is divided into two groups.
  • the odd array data is the training sample
  • the even array data is used to test the actual performance of the trained network.
  • trainbr the training function of the network. This function uses the Bayesian framework structure, assuming that the weight and threshold of the network are special distributed random variables, and then use statistical methods. Get an estimate.
  • the training samples are divided into three parts: training, verification and testing.
  • the mean square error is used to evaluate the training results of the network.
  • the training state is shown in Figure 3.
  • Figure 4 is the error curve of the training process. It can be seen from the figure. The number of iterations is 24, the training purpose is achieved, the error index converges to the expected index, the training stops, and the trained network is saved, which is reserved for later prediction.
  • Step 4 Input the data to be tested into the trained back-propagation neural network, and the trained back-propagation neural network identifies the measured data to achieve qualitative identification of the gas.
  • Input the data sample to be tested into the trained network, and ensure that the input format is the same as the training format.
  • the trained network compares each connection weight during training, and outputs the binary quantization number with the most similar weight.
  • the binary quantization of the output The numbers represent different kinds of gases, and the accuracy of the network prediction output is 100%, and the average output error is only 6.0206e- 6 .
  • ⁇ represents the sparse matrix for sparse representation
  • M and N represent the dimensions of the sparse matrix
  • ⁇ is the sparse representation of the original data
  • ⁇ represents the non-zero element in the sparse result.
  • the number also called the sparsity of X, indicates the degree of compressibility of the original data
  • P represents the observation matrix for nonlinear projection, and the observation of the original data.
  • the compressed sensing is different from the traditional method of compressing the redundant information after sampling, the information is directly “acquired", so that the amount of data to be sampled is reduced, and the compression step is eliminated, and the combination is single.
  • the simple structure of the hidden layer neural network considering the data transmission storage capacity and the recognition accuracy, the gas recognition method based on the compressed sensing theory proposed by the invention has the best performance.

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Abstract

一种基于压缩感知理论的气体识别方法，该方法包括：以欠采样的方式采集压缩后的数据；对采集的该压缩后的数据进行重构得到重构数据；利用该重构数据对反向传播神经网络进行训练，并保存训练好的反向传播神经网络；将待测数据输入训练好的反向传播神经网络，该训练好的反向传播神经网络对待测数据进行识别，实现对气体的定性识别。该方法解决了目前气体检测中传输存储数据量大，识别不精确的问题，达到了以较少的数据量达到精确定性识别的目的。

Description

基于压缩感知理论的气体识别方法
技术领域 本发明涉及传感器阵列信号处理技术领域， 特别是涉及一种基于压 缩感知理论的气体识别方法。
背景技术 气体传感器由于普遍存在交叉敏感性， 其输出信号受到温度、 湿度 以及环境条件等因素的影响， 稳定性和选择性较差， 使得它的应用局限 于检测精度不高或气体成份较简单的场合， 如有害气体泄漏报警等。 传 统的解决方案是通过寻找新的敏感材料、 器件结构和补偿电路来消除上 述各种不利影响， 然而这种解决方案不仅使器件结构复杂化， 而且使器 件制造成本提高。
压缩感知理论是近年来出现的一个充分利用信号稀疏性或可压缩 性的全新信号采集、 编解码理论。 该理论的基本思路是从尽量少的数据 中提取尽量多的信息。 该理论指出， 只要信号在某个域是稀疏的， 那么 就可以利用一个不相关的矩阵对其进行投影， 再利用这些少量的投影值 求解一个优化问题， 最终以一个高概率重构原始信号， 也就是说一个可 压缩的信号能够以一个比奈奎斯特采样速率低得多的速率进行无失真 的采样， 然后利用这些少量的数据能够精确重构原始数据。
神经网络以其非线性映射、 并行处理和高度自学习、 自组织、 自适 应的能力， 能有效地解决气体传感器交叉敏感性所产生的非线性问题， 并在一定程度上抑制传感器的漂移或噪声， 有助于气体检测精度的提高。 因此， 高性能、 低成本的气体传感器与以神经网络为代表的智能识别技 术相结合的检测技术已成为时下气体检测的流行趋势。
在神经网络中， 反向传播（Back Propagation, BP)神经网络是一种 按照误差逆传播算法训练的多层前馈网络， 一般由多个网络层构成， 其 中包括一个输入层、 一个或几个隐层、 一个输出层， 层与层之间采用全 互连接，同层神经元之间不存在相互连接。隐层神经元通常采用 Sigmoid 型传递函数， 输出层采用 purelin型传递函数。 BP神经网络的学习过程 由前向传播和反向传播组成， 在前向传播过程中， 输入模式经输入层、 隐层逐层处理， 并传向输出层。 如果在输出层不能得到期望的输出， 则 转入反向传播过程， 将误差值沿连接通路逐层反向传送， 并修正各层连 接权值， 直到达到预期的训练误差。
发明内容
(一） 要解决的技术问题
为了克服上述现有技术的不足， 本发明提供了一种基于压缩感知理 论的气体识别方法， 以解决目前气体检测中传输存储数据量大， 识别不 精确的问题， 达到以较少的数据量达到精确定性识别的目的。
(二） 技术方案
为达到上述目的， 本发明提供了一种基于压缩感知理论的气体识别 方法， 该方法包括： 歩骤 1 : 以欠采样的方式采集压缩后的数据； 歩骤 2： 对采集的该压缩后的数据进行重构得到重构数据； 歩骤 3 : 利用该重 构数据对反向传播神经网络进行训练， 并保存训练好的反向传播神经网 络； 歩骤 4: 将待测数据输入训练好的反向传播神经网络， 该训练好的 反向传播神经网络对待测数据进行识别， 实现对气体的定性识别。
上述方案中， 歩骤 1中所述以欠采样的方式采集压缩后的数据， 具 体包括： 传感器网络的阵列节点采集可压缩的原始数据； 对该原始数据 进行稀疏分解， 得到第一稀疏矩阵， 该第一稀疏矩阵是一个与原始数据 相关的稀疏矩阵； 对该第一稀疏矩阵进行非线性投影处理， 得到第二稀 疏矩阵， 该第二稀疏矩阵中的元素是该第一稀疏矩阵中元素的随机组合; 对该第二稀疏矩阵中系数较大的数据以小于奈奎斯特采样频率的频率 进行低速欠采样。
上述方案中，所述对该原始数据进行稀疏分解，得到第一稀疏矩阵， 包括： 构造一个随机高斯分布的稀疏矩阵， 将采集的原始数据与该构造 的随机高斯分布的稀疏矩阵相乘， 得到第一稀疏矩阵。 所述构造一个随 机高斯分布的稀疏矩阵， 包括： 选择一个维度为 w的高斯矩阵， 该 高斯矩阵的每一个元素都服从高斯分布， 然后对该高斯矩阵的每一列进 行归一化处理得到稀疏矩阵 Ψο
上述方案中， 所述将采集的原始数据与该构造的随机高斯分布的稀 疏矩阵相乘， 得到第一稀疏矩阵， 包括： 将采集的可压缩的原始数据 X 与该构造的随机高斯分布的稀疏矩阵 ^相乘， 得到第一稀疏矩阵， 该第 一稀疏矩阵是可压缩的原始数据 X最稀疏表示， 若第一稀疏矩阵中非零 元素的个数 κ小于可压缩的原始数据 X中的非零元素的个数，则第一稀 疏矩阵是可压缩的。
上述方案中， 歩骤 2中所述对采集的该压缩后的数据进行重构得到 重构数据， 包括： 选择一个观测矩阵， 该观测矩阵与第一稀疏矩阵不相 关； 将采集的该压缩后的数据与该观测矩阵相乘， 得到观测数据； 对该 观测数据进行反变换得到重构数据。
上述方案中， 所述选择的观测矩阵为 M X N维的观测矩阵 Ρ， 该观 测矩阵 Ρ与第一稀疏矩阵不相关；将采集的该压缩后的数据 X与观测矩 阵 Ρ相乘， 得到观测数据； , ； 就是第一稀疏矩阵中非零向量对应观测 矩阵 Ρ中列向量的线性组合。 所述对该观测数据进行反变换， 是求解方 程 P I = F中的 X， 其中 β = ΨΙ， 由于这个方程未知数的个数多于方 程组的个数， 所以 X的解并不唯一， 在此采用最小 1范数逼近求解， 求 得的结果就是重构后的数据。
上述方案中， 歩骤 3中所述利用该重构数据对反向传播神经网络进 行训练， 并保存训练好的反向传播神经网络， 具体包括： 将该重构数据 作为输入样本输入到反向传播神经网络， 该反向传播神经网络对该重构 数据进行迭代处理， 每一歩迭代误差与上一歩迭代误差进行对比， 当迭 代误差达到初始设定阈值时， 训练结束， 保存该反向传播神经网络。
上述方案中， 歩骤 4中所述该训练好的反向传播神经网络对待测数 据进行识别， 是该训练好的反向传播神经网络对比训练时各个连接权值， 以最多相近权值输出二进制量化数， 该输出的二进制量化数代表不同种 类的气体， 进而实现对气体的定性识别。
(三） 有益效果
从上述技术方案可以看出， 本发明具有以下有益效果：
1、 本发明提供的这种基于压缩感知理论的气体识别方法， 将压缩 感知技术应用于传感器网络中阵列信号的传输过程， 并在接收端用 BP 神经网络训练识别， 将计算复杂度从在线检测转移到离线的网络训练， 从而可大幅提高检测系统的在线检测的实时性和准确性， 解决了目前气 体检测中传输存储数据量大， 识别不精确的问题， 达到了以较少的数据 量达到精确定性识别的目的。
2、 本发明提供的这种基于压缩感知理论的气体识别方法， 与现有 技术相比， 将压缩感知理论和神经网络结合， 同时对数据进行压缩和传 输， 然后在后端利用 BP神经网络训练识别压缩重构的信号， 可以有效 提高数据存储能力和带宽利用率， 并且能够做到准确识别， 有助于提高 气体检测的精度。
附图说明 为了更进一歩说明本发明的内容， 以下结合附图及实施例子， 对本 发明做详细描述， 其中：
图 1是本发明提供的基于压缩感知理论的气体识别方法流程图； 图 2至图 4示出了依照本发明实施例的基于压缩感知理论的气体识 别方法， 其中：
图 2为原始信号和重构信号对比图；
图 3为 BP神经网络的训练状态图；
图 4为定性识别的训练误差图。 具体实施方式 为使本发明的目的、 技术方案和优点更加清楚明白， 以下结合具体 实施例， 并参照附图， 对本发明进一歩详细说明。
本发明提供的基于压缩感知理论的气体识别方法， 将压缩感知技术 应用于传感器网络中阵列信号的传输过程，并用 BP神经网络训练识别， 将计算复杂度从在线检测转移到离线的网络训练， 从而可大幅提高检测 系统的在线检测的实时性和准确性。
如图 1所示， 图 1是本发明提供的基于压缩感知理论的气体识别方 法流程图， 该方法首先以欠采样的方式采集压缩后的数据， 对压缩后的 数据进行重构得到重构数据，然后利用该重构数据对 BP网络进行训练， 并保存训练好的网络， 最后将待测数据输入训练好的神经网络， 训练好 的神经网络对待测数据进行识别， 输出代表不同气体的二进制量化数， 实现对气体的定性识别， 该方法具体包括以下歩骤：
歩骤 1 : 以欠采样的方式采集压缩后的数据；
歩骤 2: 对采集的该压缩后的数据进行重构得到重构数据； 歩骤 3: 利用该重构数据对反向传播神经网络进行训练， 并保存训 练好的反向传播神经网络；
歩骤 4: 将待测数据输入训练好的反向传播神经网络， 该训练好的 反向传播神经网络对待测数据进行识别， 实现对气体的定性识别。
其中，歩骤 1中所述以欠采样的方式采集压缩后的数据，具体包括： 传感器网络的阵列节点采集可压缩的原始数据； 对该原始数据进行稀疏 分解， 得到第一稀疏矩阵， 该第一稀疏矩阵是一个与原始数据相关的稀 疏矩阵； 对该第一稀疏矩阵进行非线性投影处理， 得到第二稀疏矩阵， 该第二稀疏矩阵中的元素是该第一稀疏矩阵中元素的随机组合； 对该第 二稀疏矩阵中系数较大的数据以小于奈奎斯特采样频率的频率进行低 速欠采样。
所述对该原始数据进行稀疏分解， 得到第一稀疏矩阵， 包括： 构造 一个随机高斯分布的稀疏矩阵， 将采集的原始数据与该构造的随机高斯 分布的稀疏矩阵相乘， 得到第一稀疏矩阵。 所述构造一个随机高斯分布的稀疏矩阵， 包括： 选择一个维度为 M 的高斯矩阵， 该高斯矩阵的每一个元素都服从高斯分布， 然后对该 高斯矩阵的每一列进行归一化处理得到稀疏矩阵 Ψο
所述将采集的原始数据与该构造的随机高斯分布的稀疏矩阵相乘， 得到第一稀疏矩阵， 包括： 将采集的可压缩的原始数据 X与该构造的随 机高斯分布的稀疏矩阵 ^相乘， 得到第一稀疏矩阵， 该第一稀疏矩阵是 可压缩的原始数据 X最稀疏表示， 若第一稀疏矩阵中非零元素的个数 ^ 小于可压缩的原始数据 X中的非零元素的个数， 则第一稀疏矩阵是可压 缩的。
歩骤 2中所述对采集的该压缩后的数据进行重构得到重构数据， 包 括： 选择一个观测矩阵， 该观测矩阵与第一稀疏矩阵不相关； 将采集的 该压缩后的数据与该观测矩阵相乘， 得到观测数据； 对该观测数据进行 反变换得到重构数据。 所述选择的观测矩阵为 Μ X Ν维的观测矩阵 Ρ, 该观测矩阵 Ρ与第一稀疏矩阵不相关；将采集的该压缩后的数据 X与观 测矩阵 Ρ相乘， 得到观测数据 Υ， Υ就是第一稀疏矩阵中非零向量对应 观测矩阵 Ρ中列向量的线性组合。 所述对该观测数据进行反变换， 是求 解方程 P = F中的 X， 屮 0 = ΨΧ, 由于这个方程未知数的个数多 于方程组的个数，所以 X的解并不唯一，在此采用最小 1范数逼近求解， 求得的结果就是重构后的数据。
歩骤 3中所述利用该重构数据对反向传播神经网络进行训练， 并保 存训练好的反向传播神经网络， 具体包括： 将该重构数据作为输入样本 输入到反向传播神经网络， 该反向传播神经网络对该重构数据进行迭代 处理， 每一歩迭代误差与上一歩迭代误差进行对比， 当迭代误差达到初 始设定阈值时， 训练结束， 保存该反向传播神经网络。
歩骤 4 中所述该训练好的反向传播神经网络对待测数据进行识别， 是该训练好的反向传播神经网络对比训练时各个连接权值， 以最多相近 权值输出二进制量化数， 该输出的二进制量化数代表不同种类的气体， 进而实现对气体的定性识别。
基于图 1所示的本发明提供的基于压缩感知理论的气体识别方法流 程图， 图 2至图 4示出了依照本发明实施例的基于压缩感知理论的气体 识别方法， 具体包括以下歩骤：
歩骤 1、 以欠采样的方式采集压缩后的数据；
以传感器阵列作为传感器网络的一个节点， 节点测得的输出电压为 X[n] , n=l、 2、 3...180， 即得到我们所需的可压缩的原始数据 Λ：。 对该 可压缩的原始数据 X进行离散傅里叶变换得到原始数据的稀疏表示结果 Θ, 然后以伪随机高斯矩阵作为观测矩阵 Ρ对稀疏表示结果进行非线性 投影操作， 即两个矩阵相乘得到经稀疏压缩后的观测数据 F[ 】， m=l、 2、 3...30, 可以看到经过处理后的数据量不到原始数据量的 20%。
歩骤 2: 对采集的该压缩后的数据进行重构得到重构数据； 利用压缩后的 30个数据重建原始信号， 即求解方程 = F (其中 = 1：)中的 ， 由于未知数的个数小于方程组的个数， 所以 的解并 不唯一， 需要采用非线性逼近， 在此本发明采用采用最小 1范数逼近求 解， 具体算法是采用正交匹配追踪算法 （OMP)重构原始信号。 图 2是 传感器阵列采集到的数据利用压缩感知重构后数据与原始数据的对比， 逼近误差为 0.87031。
歩骤 3: 利用该重构数据对反向传播神经网络进行训练， 并保存训 练好的反向传播神经网络；
将重构后的数据还原成为一个 6x30的向量矩阵作为 BP神经网络的 输入， 同时目标向量也被定义成一个三维矩阵。 每个目标向量都含有 3 个元素， 向量代表着某种气体， 与其对应位置的元素值即为 1， 而其他 位置的元素值为 0。例如， CO对应的向量，其第一个位置的元素值为 1， 另外两个位置的元素值为 0， gp[l， 0， 0] o
基于上述考虑， 本发明设计采用的 BP神经网络的结构为 6:7:3， 即 输入层有 6个输入 (节点的传感器数目）， 中间单隐层节点数目是 7个， 输出层则需要 3个神经元 (目标向量的维数)。 采用单隐层的神经网络和 多隐层的神经网络都可以完成定性检测的任务， 不同点仅在于： 多隐层 神经网络的训练时间明显高于单隐层神经网络的训练时间。 根据本文的 实际问题，采用单隐含层 BP网络，对不同稀疏度的重构信号进行训练。 本实施例中， 采用单隐层的 BP网络， 即一个输入层， 一个隐层， 一个 输出层。
进行训练时， 先把样本数据均分成两组， 其中奇数组数据为训练样 本， 偶数组数据用来检验训练好的网络的实际性能。 使用快速 BP算法 来训练网络， 将网络的隐层神经元数选为 7。 为了使网络对新的输入有 良好的泛化能力，将网络的训练函数选为 trainbr,该函数使用了 Bayesian 框架结构， 假设网络的权值和阈值是特殊分布的随机变量， 然后用统计 学方法得到估计值。针对网络的训练部分，把训练样本分成训练、验证、 测试三部分， 使用均方误差来评估网络的训练结果， 训练状态如图 3所 图 4是训练过程的误差曲线， 由图中可以看出迭代次数是 24次， 训练目的达到， 误差指数收敛于预期指标， 训练停止， 保存训练好的网 络， 留待后面预测使用。
歩骤 4、 将待测数据输入训练好的反向传播神经网络， 该训练好的 反向传播神经网络对待测数据进行识别， 实现对气体的定性识别。
将待测数据样本输入到训练好的网络中， 确保输入格式跟训练时格 式相同， 该训练好的网络对比训练时的各个连接权值， 以最多相近权值 输出二进制量化数， 输出的二进制量化数则代表不同种类的气体， 网络 预测输出的识别的精确率达到 100%,而其输出平均误差仅为 6.0206e— 6。
上述实施例中， 代表采集到的可压缩的原始数据， ^表示稀疏表 示用的稀疏矩阵， M 、 N表示稀疏矩阵的维度， Θ是原始数据的稀疏表 示结果， ^代表稀疏结果中非零元素的个数， 也叫做 X的稀疏度， 表示 的是原始数据的可压缩程度， P表示非线性投影用的观测矩阵， ； 表示 原始数据的观测结果。
由于压缩感知不同于传统方法先采样后压缩掉其中的冗余信息的 方法， 而是直接"采集"压缩后的信息， 使得采样的数据量减少， 同时省 去了压缩的歩骤， 同时结合单隐层神经网络结构简单的优势， 综合考虑 数据传输存储量和识别精度， 本发明提出的基于压缩感知理论的气体识 别方法性能最优。 以上所述的具体实施例， 对本发明的目的、 技术方案和有益效果进 行了进一歩详细说明， 所应理解的是， 以上所述仅为本发明的具体实施 例而已， 并不用于限制本发明， 凡在本发明的精神和原则之内， 所做的 任何修改、 等同替换、 改进等， 均应包含在本发明的保护范围之内。

Claims

权利要求
1、 一种基于压缩感知理论的气体识别方法， 其特征在于， 该方法 包括：
歩骤 1 : 以欠采样的方式采集压缩后的数据；
歩骤 2: 对采集的该压缩后的数据进行重构得到重构数据； 歩骤 3 : 利用该重构数据对反向传播神经网络进行训练， 并保存训 练好的反向传播神经网络；
歩骤 4: 将待测数据输入训练好的反向传播神经网络， 该训练好的 反向传播神经网络对待测数据进行识别， 实现对气体的定性识别。
2、 根据权利要求 1 所述的基于压缩感知理论的气体识别方法， 其 特征在于，歩骤 1中所述以欠采样的方式采集压缩后的数据，具体包括： 传感器网络的阵列节点采集可压缩的原始数据；
对该原始数据进行稀疏分解， 得到第一稀疏矩阵， 该第一稀疏矩阵 是一个与原始数据相关的稀疏矩阵；
对该第一稀疏矩阵进行非线性投影处理， 得到第二稀疏矩阵， 该第 二稀疏矩阵中的元素是该第一稀疏矩阵中元素的随机组合；
对该第二稀疏矩阵中系数较大的数据以小于奈奎斯特采样频率的 频率进行低速欠采样。
3、 根据权利要求 2所述的基于压缩感知理论的气体识别方法， 其 特征在于，所述对该原始数据进行稀疏分解，得到第一稀疏矩阵，包括： 构造一个随机高斯分布的稀疏矩阵， 将采集的原始数据与该构造的 随机高斯分布的稀疏矩阵相乘， 得到第一稀疏矩阵。
4、 根据权利要求 3 所述的基于压缩感知理论的气体识别方法， 其 特征在于， 所述构造一个随机高斯分布的稀疏矩阵， 包括：
选择一个维度为 M X N的高斯矩阵， 该高斯矩阵的每一个元素都服 从高斯分布， 然后对该高斯矩阵的每一列进行归一化处理得到稀疏矩阵
5、 根据权利要求 4所述的基于压缩感知理论的气体识别方法， 其 特征在于， 所述将采集的原始数据与该构造的随机高斯分布的稀疏矩阵 相乘， 得到第一稀疏矩阵， 包括：
将采集的可压缩的原始数据 X与该构造的随机高斯分布的稀疏矩阵 ^相乘， 得到第一稀疏矩阵， 该第一稀疏矩阵是可压缩的原始数据 最 稀疏表示，若第一稀疏矩阵中非零元素的个数 κ小于可压缩的原始数据
X中的非零元素的个数， 则第一稀疏矩阵是可压缩的。
6、 根据权利要求 1 所述的基于压缩感知理论的气体识别方法， 其 特征在于， 歩骤 2中所述对采集的该压缩后的数据进行重构得到重构数 据， 包括：
选择一个观测矩阵， 该观测矩阵与第一稀疏矩阵不相关；
将采集的该压缩后的数据与该观测矩阵相乘， 得到观测数据； 对该观测数据进行反变换得到重构数据。
7、 根据权利要求 6所述的基于压缩感知理论的气体识别方法， 其 特征在于， 所述选择的观测矩阵为 M X N维的观测矩阵 P, 该观测矩阵 P与第一稀疏矩阵不相关； 将采集的该压缩后的数据 X与观测矩阵 P相 乘， 得到观测数据； , ； 就是第一稀疏矩阵中非零向量对应观测矩阵 P 中列向量的线性组合。
8、 根据权利要求 7 所述的基于压缩感知理论的气体识别方法， 其 特征在于，所述对该观测数据进行反变换，是求解方程 P = F中的 ΛΓ, 其中 β = ϊ¾， 由于这个方程未知数的个数多于方程组的个数， 所以 的解并不唯一， 在此采用最小 1范数逼近求解， 求得的结果就是重构后 的数据。
9、 根据权利要求 1 所述的基于压缩感知理论的气体识别方法， 其 特征在于，歩骤 3中所述利用该重构数据对反向传播神经网络进行训练， 并保存训练好的反向传播神经网络， 具体包括：
将该重构数据作为输入样本输入到反向传播神经网络， 该反向传播 神经网络对该重构数据进行迭代处理， 每一歩迭代误差与上一歩迭代误 差进行对比， 当迭代误差达到初始设定阈值时， 训练结束， 保存该反向 传播神经网络。
10、 根据权利要求 1所述的基于压缩感知理论的气体识别方法， 其 特征在于， 歩骤 4中所述该训练好的反向传播神经网络对待测数据进行 识别， 是该训练好的反向传播神经网络对比训练时各个连接权值， 以最 多相近权值输出二进制量化数， 该输出的二进制量化数代表不同种类的 气体， 进而实现对气体的定性识别。
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