CN117074913A - Circuit board V-I curve uncertainty measurement method based on multi-objective optimization interval - Google Patents

Circuit board V-I curve uncertainty measurement method based on multi-objective optimization interval Download PDF

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CN117074913A
CN117074913A CN202311045960.5A CN202311045960A CN117074913A CN 117074913 A CN117074913 A CN 117074913A CN 202311045960 A CN202311045960 A CN 202311045960A CN 117074913 A CN117074913 A CN 117074913A
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林鹏
赵岩
赵铮
曹九稳
潘庆国
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Abstract

The invention discloses a circuit board V-I curve uncertainty measurement method based on a multi-objective optimization interval. Aiming at the condition that the V-I curve data of the same measuring point, which is acquired by compensating zero crossing points of the acquisition equipment, have the same shape but are offset up and down, a maximum and minimum normalization method is adopted to eliminate the offset. Aiming at the situation that the deviation of the predicted interval is large due to different data distribution, a loss function containing deviation information is constructed to cover the interval on the low-density data, and fault detection research of the circuit board is further facilitated.

Description

一种基于多目标优化区间的电路板V-I曲线不确定度量方法An uncertainty measurement method for circuit board V-I curve based on multi-objective optimization interval

技术领域Technical field

本发明涉及电路板故障诊断领域,具体涉及电路板电压-电流(V-I)曲线测试中的不确定性,在数据存在偏移和低密度情况,采用区间预测不确定度量方法获取高覆盖率、窄宽度和小偏差多目标的V-I区间。The invention relates to the field of circuit board fault diagnosis, specifically to the uncertainty in circuit board voltage-current (V-I) curve testing. When data has offset and low density, an interval prediction uncertainty measurement method is used to obtain high coverage, narrow Width and small deviation multi-objective V-I intervals.

背景技术Background technique

V-I曲线测试是一种不加电的电路板故障诊断技术,适用于对任何器件的比较测试。由于器件故障通常伴随着管脚之间阻抗特性的变化,通过直接观察或比较正常电路板和故障电路板相同结点之间的V-I曲线,可以找到阻抗特性变化的结点,从而确定故障器件。V-I curve test is a power-free circuit board fault diagnosis technology, suitable for comparative testing of any device. Since device failure is usually accompanied by changes in impedance characteristics between pins, by directly observing or comparing the V-I curves between the same nodes on a normal circuit board and a faulty circuit board, the node where the impedance characteristics change can be found, thereby determining the faulty device.

V-I曲线测试中的不确定性会导致测量值与真实值之间存在偏差,影响正常电路板测量数据的准确性和V-I曲线性能的准确评估。例如测量环境的变化,测量设备的精度和准确性,校准的不准确或仪器偏移,元件的品质和特性存在批次差异等因素导致测量值产生波动或偏移。区间预测是统计学中一种考虑不确定性的方法,能够提供V-I曲线每个电压下对应电流的上界和下界,具有一定概率包含电流的真实值。常见的区间预测方法有Delta方法、贝叶斯方法、均值方差估计方法、Bootstrap方法和LUBE方法(见HadjicharalambousM,Polycarpou M M,Panayiotou C G.Neural network-based construction of onlineprediction intervals[J].Neural Computing and Applications,2020)。其中,Delta方法需要大量计算,在实践中难以有效应用。贝叶斯方法计算预测区间的准确性较低,因为每个参数都需要预先指定一个分布,这要求大量计算。均值方差估计方法产生的预测区间覆盖率较小,可能导致区间过于狭窄,不足以涵盖真实值。Bootstrap方法重复抽样过程可能需要大量计算资源对计算设备要求较高,且耗时较长。上述方法都假设数据遵循某种先验分布,然后在给定概率水平上计算数据可能落入的区间的上界和下界。LUBE(Lower-UpperBoundEstimation)方法是一种基于神经网络的区间预测方法,在任何数据分布的情况下,直接输出高覆盖率和较窄平均宽度的区间。然而,LUBE方法损失函数是不可微的,在训练时,只能使用非梯度算法,而梯度下降是训练神经网络的标准方法。此外,LUBE方法仅考虑了预测区间的宽度和覆盖率指标,忽略了预测区间的偏差,即预测值与真实值之间的平均误差。在实际应用中,即使区间具有较高的覆盖率和较窄的宽度,如果其偏差较大,那么在多次预测中,预测值很可能与真实值相差较远。这样的预测区间在实际决策和预测中可能并不可靠。Uncertainty in V-I curve testing will lead to deviations between measured values and true values, affecting the accuracy of normal circuit board measurement data and the accurate assessment of V-I curve performance. Factors such as changes in the measurement environment, the precision and accuracy of the measurement equipment, inaccuracies in calibration or instrument drift, batch differences in the quality and characteristics of components, and other factors cause fluctuations or shifts in the measured values. Interval prediction is a method in statistics that considers uncertainty. It can provide the upper and lower bounds of the corresponding current at each voltage of the V-I curve, and has a certain probability of containing the true value of the current. Common interval prediction methods include Delta method, Bayesian method, mean variance estimation method, Bootstrap method and LUBE method (see HadjicharalambousM, Polycarpou M M, Panayiotou C G. Neural network-based construction of online prediction intervals[J]. Neural Computing and Applications, 2020). Among them, the Delta method requires a lot of calculations and is difficult to apply effectively in practice. Bayesian methods are less accurate in calculating prediction intervals because each parameter needs to be pre-specified with a distribution, which requires extensive calculations. Mean-variance estimation methods produce prediction intervals with smaller coverage, which may result in intervals that are too narrow to cover the true values. The repeated sampling process of the Bootstrap method may require a large amount of computing resources, require high computing equipment, and take a long time. The above methods all assume that the data follows a certain prior distribution, and then calculate the upper and lower bounds of the interval that the data may fall into at a given probability level. The LUBE (Lower-UpperBoundEstimation) method is an interval prediction method based on neural networks, which directly outputs intervals with high coverage and narrow average width under any data distribution. However, the LUBE method loss function is non-differentiable, and only non-gradient algorithms can be used during training, and gradient descent is the standard method for training neural networks. In addition, the LUBE method only considers the width and coverage indicators of the prediction interval and ignores the deviation of the prediction interval, that is, the average error between the predicted value and the true value. In practical applications, even if the interval has high coverage and narrow width, if its deviation is large, the predicted value is likely to be far from the true value in multiple predictions. Such prediction intervals may not be reliable in actual decision-making and forecasting.

发明内容Contents of the invention

针对电路板V-I曲线数据不确定性,本发明提供一种基于多目标优化区间的电路板V-I曲线不确定度量方法。该方法可针对V-I曲线数据存在偏移和低密度情况,进行V-I曲线不确定的度量,实现V-I曲线区间上界和下界的确定。通过构造新的可微损失函数,在考虑高覆盖、窄宽度和小偏差三个方面,采用梯度下降训练神经网络的方式实现区间上界和下界的确定。Aiming at the uncertainty of circuit board V-I curve data, the present invention provides a circuit board V-I curve uncertainty measurement method based on multi-objective optimization intervals. This method can measure the uncertainty of the V-I curve and determine the upper and lower bounds of the V-I curve interval in view of the offset and low density of the V-I curve data. By constructing a new differentiable loss function and considering three aspects: high coverage, narrow width and small deviation, gradient descent is used to train the neural network to determine the upper and lower bounds of the interval.

本发明所要解决的技术问题采用以下技术方案来实现:The technical problems to be solved by the present invention are achieved by adopting the following technical solutions:

一种基于多目标优化区间的电路板V-I曲线不确定度量方法,所述的多目标优化区间是通过覆盖率、区间宽度和偏差三个指标获得优化的区间,包括以下步骤:An uncertainty measurement method for circuit board V-I curves based on a multi-objective optimization interval. The multi-objective optimization interval is an optimized interval obtained through three indicators: coverage, interval width and deviation, and includes the following steps:

步骤(1)、采集同一功能不同批次电路板V-I曲线,获取多个正常电路板多个测量节点的V-I曲线数据;Step (1): Collect V-I curves of different batches of circuit boards with the same function, and obtain V-I curve data of multiple measurement nodes of multiple normal circuit boards;

步骤(2)、判断V-I曲线数据类型,类型包含近似单值函数和多值函数两种类型,将多值函数类型按照电压上升段和电压下降段截断为两个近似单值函数类型;Step (2): Determine the V-I curve data type. The type includes two types: approximate single-valued function and multi-valued function. The multi-valued function type is truncated into two approximate single-valued function types according to the voltage rising section and the voltage falling section;

步骤(3)、为了解决数据采集设备可能存在的过度补偿问题而导致数据存在上下偏移问题,对步骤(2)得到的近似单值函数类型数据进行归一化处理来消除数据偏移问题。将预处理后的近似单值函数类型数据按照7:3划分为训练集和测试集,得到训练集S={(v1,i1),...,(vp,ip)}和测试集T={(vp+1,ip+1),...,(vn,in)},v表示电压,i表示电流,n表示数据点的总数;Step (3): In order to solve the possible over-compensation problem of the data acquisition equipment, which causes the data to have an upper and lower offset problem, the approximate single-valued function type data obtained in step (2) is normalized to eliminate the data offset problem. The preprocessed approximate single-valued function type data is divided into a training set and a test set according to 7:3, and the training set S={(v 1 ,i 1 ),...,(v p ,i p )} and Test set T={(v p+1 , ip+1 ),...,(v n ,i n )}, v represents voltage, i represents current, and n represents the total number of data points;

步骤(4)、在损失函数中引入预测区间偏差信息的优化目标,构建深度神经网络模型进行V-I曲线区间上界和下界的确定,能够自动获取具有高覆盖、窄宽度、小偏差特性的V-I曲线区间;所述的深度神经网络模型由一个输入层、多个隐藏层和一个输出层组成。Step (4): Introduce the optimization goal of prediction interval deviation information into the loss function, build a deep neural network model to determine the upper and lower bounds of the V-I curve interval, and automatically obtain a V-I curve with high coverage, narrow width, and small deviation characteristics interval; the deep neural network model consists of an input layer, multiple hidden layers and an output layer.

步骤(5)、将步骤(3)中训练数据输入深度神经网络模型中进行训练优化网络参数,然后将测试数据输入训练好的深度神经网络模型得到V-I曲线的预测区间;Step (5), input the training data in step (3) into the deep neural network model for training and optimize the network parameters, and then input the test data into the trained deep neural network model to obtain the prediction interval of the V-I curve;

步骤(6)、为了获取区间的可靠性,对数据进行多次仿真分析,采用结果的平均值作为最终区间。Step (6): In order to obtain the reliability of the interval, conduct multiple simulation analyzes on the data, and use the average of the results as the final interval.

上述方法中,步骤(2)中对于多值函数类型将V-I曲线的电压上升段和电压下降段进行分割,生成两个近似单值函数类型数据单独进行训练和预测。In the above method, in step (2), for the multi-valued function type, the voltage rising section and the voltage falling section of the V-I curve are divided, and two approximate single-valued function type data are generated for separate training and prediction.

上述方法中,步骤(3)中使用最大最小归一化方法,将V-I曲线中的电压和电流值归一化到区间(0,1)内。In the above method, the maximum and minimum normalization method is used in step (3) to normalize the voltage and current values in the V-I curve to the interval (0,1).

上述方法中,步骤(4)中神经网络的损失函数是包含了覆盖率、区间宽度和数据偏差信息的多目标损失函数构建过程如下:In the above method, the loss function of the neural network in step (4) is a multi-objective loss function that includes coverage, interval width and data deviation information. The construction process is as follows:

预测区间上下界分别为和/>区间应该具备理想的观测比例(1-α),常见的α选择为0.01或者0.05,The upper and lower bounds of the prediction interval are respectively and/> The interval should have an ideal observation ratio (1-α). The common α selection is 0.01 or 0.05.

长度为n的向量k表示每个数据点是否被所估计的区间覆盖,每一个元素ki∈{0,1}由以下公式决定:The vector k of length n indicates whether each data point is covered by the estimated interval. Each element k i ∈ {0,1} is determined by the following formula:

定义区间捕获的数据量为c:Define the amount of data captured in the interval to be c:

预测区间覆盖率和平均宽度定义如下:The prediction interval coverage and average width are defined as follows:

预测区间应该在满足覆盖率PICP≥(1-α)的前提下尽可能的减少平均宽度MPIW,因此仅需要考虑被覆盖数据点区域的MPIW,被定义为,The prediction interval should reduce the average width MPIW as much as possible under the premise of satisfying the coverage rate PICP≥(1-α), so only the MPIW of the covered data point area needs to be considered, which is defined as,

原始的PICP计算方式存在布尔变量ki,其构成的损失函数会导致在梯度下降过程中不可微,因此采用sigmoid函数进行软化,使其可微,计算公式如下:The original PICP calculation method has a Boolean variable k i , and the loss function formed by it will cause it to be non-differentiable during the gradient descent process. Therefore, the sigmoid function is used to soften it and make it differentiable. The calculation formula is as follows:

其中σ为sigmoid函数,s1为软化的超参数。where σ is the sigmoid function and s 1 is the softened hyperparameter.

在满足覆盖率的基础上,实现窄宽度、小偏差。高质量优化原则充分考虑了数据点与预测区间上下界的偏差关系,在损失函数中加入PISD优化目标,为了量化不确定性并提供基于高质量优化原则的最佳PI,定义损失函数如下:On the basis of satisfying coverage, narrow width and small deviation are achieved. The high-quality optimization principle fully considers the deviation relationship between the data point and the upper and lower bounds of the prediction interval, and adds the PISD optimization goal to the loss function. In order to quantify uncertainty and provide the best PI based on the high-quality optimization principle, the loss function is defined as follows:

其中,λ1和λ2为覆盖率和数据与区间偏差优化目标的平衡参数,PISD表示标准化的数据点与预测区间的偏差和,每一个数据点的PISD定义如下:Among them, λ 1 and λ 2 are the balance parameters of coverage and data and interval deviation optimization goals. PISD represents the sum of deviations between standardized data points and prediction intervals. The PISD of each data point is defined as follows:

其中s2为超参数。PISD定义如下:where s 2 is a hyperparameter. PISD is defined as follows:

上述方法中,步骤(5)中神经网络训练包括以下步骤:In the above method, the neural network training in step (5) includes the following steps:

(5.1)针对相应测量节点的V-I数据,使用步骤(4)的深度神经网络构建电压与上下界之间的非线性映射关系,每一层使用前一层的输出作为自己的输入,输出层两个输出单元为区间上界和下界;(5.1) For the V-I data of the corresponding measurement node, use the deep neural network in step (4) to construct a nonlinear mapping relationship between voltage and upper and lower bounds. Each layer uses the output of the previous layer as its own input, and the output layer has two The output units are the upper and lower bounds of the interval;

(5.2)选取V-I曲线训练数据进行神经网络训练,其中包含信号的正向传播和误差的反向传播两个过程;(5.2) Select V-I curve training data for neural network training, which includes two processes: forward propagation of signals and back propagation of errors;

(5.3)正向传播时,输入信号通过隐藏层作用于输出节点,经过非线性变换,产生输出信号,若实际输出与期望输出不相符,则转入误差的反向传播过程;(5.3) During forward propagation, the input signal acts on the output node through the hidden layer and undergoes nonlinear transformation to generate an output signal. If the actual output does not match the expected output, it will enter the back propagation process of the error;

误差反传时将输出误差通过隐藏层向输入层逐层反传,并将误差分摊给各层所有单元,以从各层获得的误差信号作为调整各单元权值的依据;During error backpropagation, the output error is backpropagated layer by layer through the hidden layer to the input layer, and the error is distributed to all units in each layer, and the error signal obtained from each layer is used as the basis for adjusting the weight of each unit;

(5.4)通过调整输入节点与隐层节点的联接强度和隐层节点与输出节点的联接强度以及阈值,使误差沿梯度方向下降,经过反复学习训练,确定与最小误差相对应的权值和阈值,训练停止。(5.4) By adjusting the connection strength between the input node and the hidden layer node and the connection strength between the hidden layer node and the output node, as well as the threshold, the error decreases along the gradient direction. After repeated learning and training, the weight and threshold corresponding to the minimum error are determined. , training stops.

上述方法中,步骤(6)中生成最终区间上界和下界具体方法如下:In the above method, the specific method of generating the upper and lower bounds of the final interval in step (6) is as follows:

进行多次仿真分析,所述的仿真分析即步骤(5)中的实验过程,然后分别对预测区间的上界和下界取平均值用于表示最终的预测区间。计算过程如下,Carry out multiple simulation analyses, which is the experimental process in step (5), and then average the upper and lower bounds of the prediction interval to represent the final prediction interval. The calculation process is as follows,

其中,和/>表示最终预测区间的上界和下界,m表示重复次数。in, and/> represents the upper and lower bounds of the final prediction interval, and m represents the number of repetitions.

本发明的有益效果是:The beneficial effects of the present invention are:

1、通过在损失函数中引入预测区间偏差信息的优化目标,建立了改进的预测区间优化框架,为预测区间优化提供了一种新的思路。考虑了数据点与区间上下界之间的偏差关系,生成的预测区间可以更加全面的捕获指定部分数据,降低了预测风险。1. By introducing the optimization goal of prediction interval deviation information into the loss function, an improved prediction interval optimization framework is established, which provides a new idea for prediction interval optimization. Taking into account the deviation relationship between the data points and the upper and lower bounds of the interval, the generated prediction interval can more comprehensively capture the specified part of the data and reduce the prediction risk.

2、将最优预测区间的构造与不确定性估计联系起来。利用该损失函数训练深度神经网络可以获得较好的预测精度和不确定性估计。2. Link the construction of the optimal prediction interval with uncertainty estimation. Using this loss function to train a deep neural network can achieve better prediction accuracy and uncertainty estimation.

3、使用最大最小归一化方法解决了V-I曲线中的上下偏移问题,将区间预测技术与深度学习模型强大的学习能力相结合并引入到电路板V-I曲线检测,构建优质的预测区间来量化V-I曲线的不确定性。提出了一个新的V-I曲线预测框架,提供了更多关于V-I曲线不确定性的信息。丰富了V-I曲线预测的研究内容,预测区间可以为决策者提供更全面的信息。3. Use the maximum and minimum normalization method to solve the upper and lower offset problem in the V-I curve. Combine the interval prediction technology with the powerful learning ability of the deep learning model and introduce it to the circuit board V-I curve detection to build a high-quality prediction interval for quantification. Uncertainty in the V-I curve. A new V-I curve prediction framework is proposed, which provides more information about V-I curve uncertainty. It enriches the research content of V-I curve prediction, and the prediction interval can provide decision makers with more comprehensive information.

4、预测区间量化测点处采集的V-I曲线具有的不确定性,辅助判断测试电路板上该测点是否发生故障,减少了原始V-I曲线对比检测带来的风险性。4. The prediction interval quantifies the uncertainty of the V-I curve collected at the measuring point, assists in determining whether the measuring point on the test circuit board has failed, and reduces the risk caused by the original V-I curve comparison test.

附图说明Description of the drawings

图1是本发明实施例中V-I曲线不确定性量化过程示意简图;Figure 1 is a schematic diagram of the V-I curve uncertainty quantification process in the embodiment of the present invention;

图2是本发明实施例中数据采样电路板;Figure 2 is a data sampling circuit board in an embodiment of the present invention;

图3是本发明实施例中V-I曲线原始数据上下偏移样例图。Figure 3 is a sample diagram of the upper and lower offset of the original data of the V-I curve in the embodiment of the present invention.

图4是本发明实施例中V-I曲线数据点分布不同样例图;Figure 4 is a diagram showing different examples of V-I curve data point distribution in the embodiment of the present invention;

图5是本发明实施例中深度神经网络结构图;Figure 5 is a structural diagram of a deep neural network in an embodiment of the present invention;

图6是本发明实施例中V-I曲线数据的预测区间样例。Figure 6 is an example of the prediction interval of V-I curve data in the embodiment of the present invention.

具体实施方式Detailed ways

下面结合附图和实施例对本发明进一步说明。The present invention will be further described below in conjunction with the accompanying drawings and examples.

为了使本领域的技术人员更好的理解本发明的技术方案,下面将结合实施例中的附图,对本发明进行更清楚、更完整的阐述,当然所描述的实施例只是本发明的一部分而非全部,基于本实施例,本领域技术人员在不付出创造性劳动性的前提下所获得的其他的实施例,均在本发明的保护范围内。In order to enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be described more clearly and more completely below in conjunction with the drawings in the embodiments. Of course, the described embodiments are only a part of the present invention. Not all, based on this embodiment, other embodiments obtained by those skilled in the art without exerting creative labor are within the protection scope of the present invention.

本实施例是一种基于多目标优化区间的电路板V-I曲线不确定度量方法,采集正常电路板测点的V-I曲线,进行数据预处理,并将V-I曲线数据分为训练集和测试集,深度神经网络的优化目标是由覆盖率、区间宽度、数据点与区间边界偏差构成的多目标损失函数,使用训练数据训练神经网络,使神经网络具备通过预测区间量化V-I曲线不确定性的能力,测试数据用于测试神经网络进行区间预测的能力。量化由于元器件特性或者环境变化导致的V-I曲线不确定性,提高基于V-I曲线的故障检测方法的可靠性。图2是本发明实施例中数据采样电路板;This embodiment is a circuit board V-I curve uncertainty measurement method based on multi-objective optimization intervals. It collects the V-I curves of normal circuit board measurement points, performs data preprocessing, and divides the V-I curve data into a training set and a test set. The depth The optimization goal of the neural network is a multi-objective loss function composed of coverage, interval width, data point and interval boundary deviation. The neural network is trained using training data, so that the neural network has the ability to quantify the uncertainty of the V-I curve through the prediction interval. Test The data are used to test the neural network's ability to make interval predictions. Quantify the uncertainty of the V-I curve caused by component characteristics or environmental changes, and improve the reliability of the fault detection method based on the V-I curve. Figure 2 is a data sampling circuit board in an embodiment of the present invention;

如图1所示,基于多目标优化区间的电路板V-I曲线不确定度量方法,该方法包括以下步骤:As shown in Figure 1, the uncertainty measurement method of circuit board V-I curve based on multi-objective optimization interval includes the following steps:

(1)对同一原理不同批次的正常电路板输入一个周期的正弦电压激励进行测量,获取批量的电路板V-I曲线数据,每一条V-I曲线为100个由电压-电流构成的数据点组成,针对多块电路板中的同一个测点共采集500条V-I曲线。(1) Input a period of sinusoidal voltage excitation to normal circuit boards of different batches with the same principle to measure, and obtain the V-I curve data of the batch of circuit boards. Each V-I curve is composed of 100 data points composed of voltage-current. For A total of 500 V-I curves were collected from the same measuring point on multiple circuit boards.

(2)判断电路板V-I曲线类型,由于测点并联多个元器件,所以其形状会呈现出多种多样的情况,但从实际应用角度考虑,类型归结为近似单值函数和多值函数两种类型,近似单值函数表示的是X对应的Y值之间不会存在很大的空白区域,此处的X和Y分别对应V-I曲线中的电压和电流,V-I曲线近似单值函数。多值函数类型表示X对应的Y值分为两个区域,并且两个区域之间存在空白区域。为了避免空白区域对检测的影响,将多值函数类型按照电压的上升阶段和电压的下降阶段截断生成两个单值函数类型数据;(2) Determine the V-I curve type of the circuit board. Since the measuring point is connected with multiple components in parallel, its shape will show a variety of situations. However, from the perspective of practical application, the type boils down to two approximate single-valued functions and multi-valued functions. A type, the approximate single-valued function means that there will not be a large blank area between the Y values corresponding to X. The X and Y here correspond to the voltage and current in the V-I curve respectively, and the V-I curve is an approximate single-valued function. The multi-valued function type indicates that the Y value corresponding to X is divided into two areas, and there is a blank area between the two areas. In order to avoid the impact of blank areas on detection, the multi-valued function type is truncated according to the voltage rising stage and voltage falling stage to generate two single-valued function type data;

(3)采集设备可能存在过度补偿而导致数据存在上下偏移问题,如图3所示。针对上下偏移问题进行最大最小归一化处理,将步骤(2)得到的近似单值函数类型数据中的电压和电流值归一化到(0,1)内,解决上下偏移问题并加快神经网络计算,将预处理后的近似单值函数类型数据按照7:3划分为训练集和测试集,得到训练集S={(v1,i1),...,(vp,ip)}和测试集T={(vp+1,ip+1),...,(vn,in)},其中p的值为0.7*n,训练集用于训练当前网络模型,向着损失函数变小的方向优化神经网络模型参数,测试集用于测试由训练集训练得到的最优模型的性能;图4是本发明实施例中V-I曲线数据点分布不同样例图;(3) The acquisition equipment may be over-compensated, causing data to shift up and down, as shown in Figure 3. Perform maximum and minimum normalization processing for the upper and lower offset problem, and normalize the voltage and current values in the approximate single-valued function type data obtained in step (2) to within (0,1) to solve the upper and lower offset problem and speed up For neural network calculation, the preprocessed approximate single-valued function type data is divided into a training set and a test set according to 7:3, and the training set S={(v 1 ,i 1 ),...,(v p ,i p )} and test set T = {(v p+1 ,i p+1 ),...,(v n ,in )}, where the value of p is 0.7* n , and the training set is used to train the current network model, optimizing the neural network model parameters in the direction of smaller loss functions, and the test set is used to test the performance of the optimal model trained by the training set; Figure 4 is a diagram of different sample distributions of VI curve data points in the embodiment of the present invention;

(4)在损失函数中引入预测区间偏差信息的优化目标,基于深度神经网络构建区间预测优化算法,基于“高覆盖、窄宽度、小偏差”的原则优化预测区间,优化V-I曲线数据低密度区域覆盖情况。网络结构如图5所示,深度神经网络模型由一个输入层、多个隐藏层、一个输出层组成,其中隐藏层中包含多层的中间层,每层中间层包含大量神经元用于计算。神经网络配置参数如表1所示,其中优化器使用adam,学习率采用0.03,学习率衰减速度为0.95,激活函数采用relu,隐藏层深度为6层,并且训练方式采用批训练,每一批数据量大小为100,迭代次数采用50。(4) Introduce the optimization goal of prediction interval deviation information into the loss function, build an interval prediction optimization algorithm based on deep neural network, optimize the prediction interval based on the principle of "high coverage, narrow width, small deviation", and optimize the low-density area of V-I curve data coverage. The network structure is shown in Figure 5. The deep neural network model consists of an input layer, multiple hidden layers, and an output layer. The hidden layer contains multiple intermediate layers, and each intermediate layer contains a large number of neurons for calculation. The neural network configuration parameters are shown in Table 1. The optimizer uses adam, the learning rate is 0.03, the learning rate decay speed is 0.95, the activation function is relu, the hidden layer depth is 6 layers, and the training method is batch training. Each batch The data size is 100, and the number of iterations is 50.

(5)将步骤(3)中训练数据输入神经网络中进行训练优化神经网络中神经元参数,然后将测试数据输入神经网络自动得到V-I曲线的预测区间。(5) Input the training data in step (3) into the neural network for training and optimize the neuron parameters in the neural network, and then input the test data into the neural network to automatically obtain the prediction interval of the V-I curve.

(6)为了获取区间的可靠性,对数据进行5次以上重复仿真分析,本实施例采用20次重复仿真分析,对20次获得的预测区间加权平均作为最终区间。本发明提出方法和已有方法应用在V-I曲线实验结果对比示例如附图6所示,其中黑色“星“形线为本发明提出方法实现效果,灰色普通线为已有方法实现效果,从图中可以明显的观察到黑色“星“形线上界和下界覆盖低密度数据区域的情况明显优于灰色普通线上界和下界,表明本发明提出方法可以有效的解决数据低密度问题,生成的预测区间可以实现高覆盖、窄宽度、小偏差,优于已有方法。(6) In order to obtain the reliability of the interval, the data is repeatedly simulated and analyzed more than 5 times. In this embodiment, 20 repeated simulation analyzes are used, and the weighted average of the prediction intervals obtained 20 times is used as the final interval. A comparative example of the V-I curve experimental results between the method proposed by the present invention and the existing method is shown in Figure 6, in which the black "star"-shaped line is the effect achieved by the method proposed by the present invention, and the gray ordinary line is the effect achieved by the existing method. From the figure It can be clearly observed that the upper and lower bounds of the black "star" shaped line covering the low-density data area are significantly better than the upper and lower bounds of the gray ordinary lines, indicating that the method proposed by the present invention can effectively solve the problem of low data density, and the generated The prediction interval can achieve high coverage, narrow width, and small deviation, which is better than existing methods.

本实施例步骤(4)中优化算法为构建由覆盖率、区间宽度、数据点与预测区间偏差关系的损失函数 构建步骤如下:The optimization algorithm in step (4) of this embodiment is to construct a loss function composed of coverage, interval width, data points and prediction interval deviation. The building steps are as follows:

预测区间上下界为和/>区间应该具备理想的观测比例(1-α),常见的α选择为0.01或者0.05,The upper and lower bounds of the prediction interval are and/> The interval should have an ideal observation ratio (1-α). The common α selection is 0.01 or 0.05.

长度为n的向量k表示每个点是否被所估计的区间覆盖,每一个元素ki∈{0,1}由下面公式决定,The vector k of length n indicates whether each point is covered by the estimated interval. Each element k i ∈ {0,1} is determined by the following formula,

Sigmoid函数公式如下,The Sigmoid function formula is as follows,

定义区间捕获的数据量为c,Define the amount of data captured in the interval to be c,

预测区间覆盖率和平均宽度定义如下,The prediction interval coverage and average width are defined as follows,

预测区间应该在满足PICP≥(1-α)的前提下尽可能的减少MPIW,于是仅需要考虑被覆盖点区域的MPIW,被定义为,The prediction interval should reduce MPIW as much as possible under the premise of satisfying PICP≥(1-α), so only the MPIW of the covered point area needs to be considered, which is defined as,

原始的PICP计算方式存在布尔变量ki,其构成的损失函数会导致在梯度下降过程中不可微,于是采用sigmoid函数进行软化,使其可微,计算公式如下,The original PICP calculation method has a Boolean variable k i , and the loss function formed by it will cause it to be non-differentiable during the gradient descent process, so the sigmoid function is used to soften it and make it differentiable. The calculation formula is as follows,

其中σ为sigmoid函数,s1为软化的超参数。where σ is the sigmoid function and s 1 is the softened hyperparameter.

定义高质量优化原则为,在满足覆盖率的基础上,实现窄宽度、小偏差。高质量优化原则充分考虑了数据点与预测区间上下界的偏差关系,在损失函数中加入PISD优化目标,为了量化不确定性并提供基于高质量优化原则的最佳PI,重新定义损失函数如下,The principle of high-quality optimization is defined as achieving narrow width and small deviation on the basis of satisfying coverage. The high-quality optimization principle fully considers the deviation relationship between the data point and the upper and lower bounds of the prediction interval, and adds the PISD optimization goal to the loss function. In order to quantify uncertainty and provide the best PI based on the high-quality optimization principle, the loss function is redefined as follows,

其中,λ1和λ2作为覆盖率和数据与区间偏差优化目标的平衡参数,PISD表示标准化的数据点与预测区间的偏差和,每一个点的PISD定义如下,Among them, λ 1 and λ 2 are used as the balance parameters of coverage and data and interval deviation optimization goals. PISD represents the sum of deviations between standardized data points and prediction intervals. The PISD of each point is defined as follows,

其中s2为超参数。PISD定义如下,where s 2 is a hyperparameter. PISD is defined as follows,

本实施例步骤(5)中神经网络计算包括以下步骤:The neural network calculation in step (5) of this embodiment includes the following steps:

(5.1)针对相应测点的V-I数据,使用步骤(4)的深度神经网络构建电压与上下界之间的非线性映射关系,每一层使用前一层的输出作为自己的输入,输入层的输入为电压数据,输出层两个输出单元为区间上界和下界;(5.1) For the V-I data of the corresponding measuring point, use the deep neural network in step (4) to construct a nonlinear mapping relationship between voltage and upper and lower bounds. Each layer uses the output of the previous layer as its own input. The input layer The input is voltage data, and the two output units of the output layer are the upper and lower bounds of the interval;

(5.2)选取V-I曲线训练数据进行神经网络训练,其中包含信号的正向传播和误差的反向传播两个过程;(5.2) Select V-I curve training data for neural network training, which includes two processes: forward propagation of signals and back propagation of errors;

(5.3)正向传播时,输入信号通过隐藏层作用于输出节点,经过非线性变换,产生输出信号,若实际输出与期望输出不相符,则转入误差的反向传播过程;(5.3) During forward propagation, the input signal acts on the output node through the hidden layer and undergoes nonlinear transformation to generate an output signal. If the actual output does not match the expected output, it will enter the back propagation process of the error;

误差反传时将输出误差通过隐藏层向输入层逐层反传,并将误差分摊给各层所有单元,以从各层获得的误差信号作为调整各单元权值的依据;During error backpropagation, the output error is backpropagated layer by layer through the hidden layer to the input layer, and the error is distributed to all units in each layer, and the error signal obtained from each layer is used as the basis for adjusting the weight of each unit;

(5.4)通过调整输入节点与隐层节点的联接强度和隐层节点与输出节点的联接强度以及阈值,使误差沿梯度方向下降,经过反复学习训练,确定与最小误差相对应的权值和阈值,训练停止。(5.4) By adjusting the connection strength between the input node and the hidden layer node and the connection strength between the hidden layer node and the output node, as well as the threshold, the error decreases along the gradient direction. After repeated learning and training, the weight and threshold corresponding to the minimum error are determined. , training stops.

本实施例中步骤(6)中生成最终区间过程。为了减少模型预测的随机性和学习模型的不确定性,重复仿真实验20次,然后对20次的预测区间取平均值用于表示最终的预测区间,计算过程如下,In this embodiment, the final interval process is generated in step (6). In order to reduce the randomness of model predictions and the uncertainty of the learning model, the simulation experiment was repeated 20 times, and then the average of the 20 prediction intervals was used to represent the final prediction interval. The calculation process is as follows,

其中,和/>表示最终预测区间的上界和下界,m=20表示重复次数。in, and/> represents the upper and lower bounds of the final prediction interval, and m=20 represents the number of repetitions.

以上显示和描述了本发明的基本原理、主要特征和本发明的优点。本行业的技术人员应该了解,本发明不受上述实施例的限制,上述实施例和说明书中描述的只是本发明的原理,在不脱离本发明精神和范围的前提下,本发明还会有各种变化和改进,这些变化和改进都落入要求保护的本发明内。本发明要求保护范围由所附的权利要求书及其等效物界定。The basic principles, main features and advantages of the present invention have been shown and described above. Those skilled in the industry should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and descriptions is only the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have various modifications. changes and improvements, which fall within the claimed invention. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims (6)

1. The circuit board V-I curve uncertainty measurement method based on the multi-objective optimization interval is characterized by comprising the following steps of:
step (1), collecting V-I curves of circuit boards with the same function and different batches, and obtaining V-I curve data of a plurality of measuring nodes of a plurality of normal circuit boards;
judging the type of the V-I curve data, wherein the type comprises two types of approximate single-value functions and multiple-value functions, and cutting off the multiple-value function type into two approximate single-value function types according to a voltage rising section and a voltage falling section;
step (3), in order to solve the problem of up-down offset of data caused by possible overcompensation of the data acquisition equipment, normalizing the approximate single-valued function type data obtained in the step (2) to eliminate the problem of data offset; dividing the preprocessed approximate single-value function type data into a training set and a testing set according to a ratio of 7:3 to obtain a training set S= { (v) 1 ,i 1 ),...,(v p ,i p ) Sum test set t= { (v) p+1 ,i p+1 ),...,(v n ,i n ) V represents voltage, i represents current, n represents the total number of data points;
step (4), introducing an optimization target of prediction interval deviation information into a loss function, constructing a deep neural network model to determine the upper boundary and the lower boundary of a V-I curve interval, and automatically acquiring the V-I curve interval with high coverage, narrow width and small deviation characteristics; the deep neural network model consists of an input layer, a plurality of hidden layers and an output layer;
step (5), inputting the training data in the step (3) into a deep neural network model for training and optimizing network parameters, and then inputting the test data into the trained deep neural network model to obtain a prediction interval of a V-I curve;
and (6) performing multiple simulation analysis on the data in order to acquire the reliability of the interval, and taking the average value of the results as a final interval.
2. The method for measuring uncertainty of a circuit board V-I curve based on a multi-objective optimization interval according to claim 1, wherein in the step (2), a voltage rising section and a voltage falling section of the V-I curve are divided for a multi-valued function type, and two approximate single-valued function type data are generated for training and prediction independently.
3. The method of claim 1, wherein the voltage and current values in the V-I curve are normalized to within the interval (0, 1) using a maximum and minimum normalization method in step (3).
4. The method for uncertainty measurement of a circuit board V-I curve based on a multi-objective optimization interval according to claim 1, wherein the loss function of the neural network in the step (4) is a multi-objective loss function including coverage, interval width and data deviation information, and the construction process is as follows:
the upper and lower boundaries of the prediction interval are respectivelyAnd->The interval should have an ideal observation ratio (1- α):
length ofThe vector k of n indicates whether each data point is covered by the estimated interval, each element k i E {0,1} is determined by the following formula:
defining the data volume captured by the interval as c:
the prediction interval coverage and average width are defined as follows:
the prediction interval should be reduced as much as possible by the average width MPIW, on the premise of satisfying the coverage PICP ∈ (1-a), so that only the MPIW of the covered data point area needs to be considered, defined as,
boolean variable k exists in original PICP calculation mode i The loss function formed by the method can not be micro in the gradient descending process, so that the sigmoid function is adopted for softening, the loss function can be micro, and the calculation formula is as follows:
wherein σ is a sigmoid function, s 1 Is a super parameter of softening;
on the basis of meeting the coverage rate, realizing narrow width and small deviation; the high-quality optimization principle fully considers the deviation relation between data points and the upper and lower boundaries of a prediction interval, a PISD optimization target is added into a loss function, and in order to quantify uncertainty and provide the optimal PI based on the high-quality optimization principle, the loss function is defined as follows:
wherein lambda is 1 And lambda (lambda) 2 For coverage and data to interval deviation optimization objective balance parameters, PISD represents the sum of deviation of normalized data points from predicted interval, PISD for each data point is defined as follows:
wherein s is 2 Is a super parameter; PISD is defined as follows:
5. the method for uncertainty measurement of a V-I curve of a circuit board based on a multi-objective optimization interval according to claim 1 or 4, wherein the training of the neural network in the step (5) comprises the following steps:
(5.1) aiming at V-I data of corresponding measuring nodes, constructing a nonlinear mapping relation between voltage and upper and lower bounds by using the deep neural network in the step (4), wherein each layer uses the output of the previous layer as the input of the device, and two output units of the output layer are an upper bound and a lower bound of a section;
(5.2) selecting V-I curve training data to perform neural network training, wherein the training data comprises two processes of forward propagation of signals and backward propagation of errors;
(5.3) in forward propagation, the input signal acts on the output node through the hidden layer, and the output signal is generated through nonlinear transformation, if the actual output does not accord with the expected output, the reverse propagation process of the error is shifted;
during error back transmission, the output errors are back transmitted layer by layer to the input layers through the hidden layers, the errors are distributed to all units of each layer, and error signals obtained from each layer are used as the basis for adjusting the weight of each unit;
and (5.4) reducing the error along the gradient direction by adjusting the connection strength of the input node and the hidden layer node and the connection strength of the hidden layer node and the output node as well as the threshold value, and determining the weight and the threshold value corresponding to the minimum error through repeated learning and training, and stopping training.
6. The method for uncertainty measurement of a circuit board V-I curve based on a multi-objective optimization interval according to claim 5, wherein the specific method for generating the upper bound and the lower bound of the final interval in the step (6) is as follows:
performing multiple simulation analysis, namely, the experimental process in the step (5), and then respectively taking average values of an upper bound and a lower bound of a prediction interval to represent a final prediction interval; the calculation process is as follows,
wherein,and->The upper and lower bounds of the final prediction interval are represented, and m represents the number of repetitions.
CN202311045960.5A 2023-08-18 2023-08-18 Circuit board V-I curve uncertainty measurement method based on multi-objective optimization interval Pending CN117074913A (en)

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