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

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

An uncertainty measurement method for circuit board V-I curve based on multi-objective optimization interval

Technical field

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.

Background technique

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.

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.

Contents of the invention

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.

The technical problems to be solved by the present invention are achieved by adopting the following technical solutions:

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:

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;

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;

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;

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.

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;

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.

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.

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).

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:

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.

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:

Define the amount of data captured in the interval to be c:

The prediction interval coverage and average width are defined as follows:

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,

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:

where σ is the sigmoid function and s ₁ is the softened hyperparameter.

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:

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:

where s ₂ is a hyperparameter. PISD is defined as follows:

In the above method, the neural network training in step (5) includes the following steps:

(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) 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) 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;

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) 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.

In the above method, the specific method of generating the upper and lower bounds of the final interval in step (6) is as follows:

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,

in, and/> represents the upper and lower bounds of the final prediction interval, and m represents the number of repetitions.

The beneficial effects of the present invention are:

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. 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. 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. 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.

Description of the drawings

Figure 1 is a schematic diagram of the V-I curve uncertainty quantification process in the embodiment of the present invention;

Figure 2 is a data sampling circuit board in an embodiment of the present invention;

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.

Figure 4 is a diagram showing different examples of V-I curve data point distribution in the embodiment of the present invention;

Figure 5 is a structural diagram of a deep neural network in an embodiment of the present invention;

Figure 6 is an example of the prediction interval of V-I curve data in the embodiment of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and examples.

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.

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;

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) 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) 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) 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) 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) 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) 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.

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:

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.

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,

The Sigmoid function formula is as follows,

Define the amount of data captured in the interval to be c,

The prediction interval coverage and average width are defined as follows,

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,

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,

where σ is the sigmoid function and s ₁ is the softened hyperparameter.

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,

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,

where s ₂ is a hyperparameter. PISD is defined as follows,

The neural network calculation in step (5) of this embodiment includes the following steps:

(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) 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) 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;

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) 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.

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,

in, and/> represents the upper and lower bounds of the final prediction interval, and m=20 represents the number of repetitions.

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.