An airborne filter circuit fault diagnosis method based on convolution feature fusion
By constructing a one-dimensional convolutional neural network to fuse voltage and current signal features, the problems of limited measurement points and incomplete single signal features in airborne circuit fault diagnosis are solved, and high-accuracy fault identification is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2025-09-22
- Publication Date
- 2026-06-26
AI Technical Summary
In airborne circuit fault diagnosis, due to the limited number of test points and the inability of the characteristic signals obtained from a single signal type to contain all the information of the entire circuit, misjudgments are made in the diagnostic results, and existing technologies are unable to accurately identify circuit faults.
A one-dimensional convolutional neural network is constructed using a convolutional feature fusion method to extract fault features from voltage and current signals respectively. More comprehensive feature information is obtained through adaptive weighted fusion, and fault classification is performed using the softmax function.
It improves the accuracy of airborne circuit fault diagnosis, overcomes the problems of limited measurement points and incomplete single signal characteristics, and achieves efficient fault identification.
Smart Images
Figure CN121114738B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of analog circuit fault diagnosis technology, specifically relating to a fault diagnosis method for airborne filter circuits based on convolution feature fusion. Background Technology
[0002] Avionics systems are the core systems of aircraft, playing a crucial role in navigation, flight control, and communication during various flight missions. Onboard circuits, the hardware foundation of avionics systems, are vital to the aircraft's operational status. The high-altitude, high-load, and high-vibration environments in which aircraft operate make their onboard circuits susceptible to various failures. Such failures can pose significant threats to social stability, the aviation economy, and even public safety. Therefore, research into fault diagnosis techniques for onboard circuits is essential to reduce aircraft safety risks and prevent dangerous situations caused by systemic failures.
[0003] In electronic devices, analog circuits account for the vast majority of faults. When an analog circuit fails, its electrical signals undergo significant changes. Therefore, the fault state is typically determined using current and voltage signals originating from the circuit itself. Traditional fault diagnosis often employs a fault comparison method, such as the fault dictionary method. This method involves creating a fault dictionary containing all possible faults and their characteristics, comparing the measured circuit signal characteristics with those in the dictionary to determine the circuit's health status and identify the type and location of the fault. While this method is widely applicable, the comparison process usually requires substantial experimental data and is time-consuming and labor-intensive. Therefore, its application is challenging in diagnosing many complex analog circuit faults.
[0004] In recent years, with the continuous development of machine learning technology, its application in the field of fault diagnosis has become increasingly widespread. Among them, deep learning, with its powerful feature extraction capabilities, can automatically extract internal features of circuit signals and classify faults based on the extracted features. Deep learning can solve complex classification problems through its efficient feature extraction capabilities, but it has certain shortcomings in the fault diagnosis of airborne circuits: First, due to the limited number of test points in airborne circuits, it is difficult to obtain circuit signal features at various locations in the circuit; second, the feature signals obtained from a single signal type cannot contain all the information of the entire circuit, which can easily lead to misjudgments in the diagnostic results.
[0005] Therefore, circuit fault diagnosis techniques that use a single type of electrical signal for diagnosis cannot cover all the fault characteristic information of the target circuit, which has a certain impact on the accuracy of the diagnosis results. Summary of the Invention
[0006] To overcome the aforementioned problems, this invention proposes a fault diagnosis method for airborne filter circuits based on convolutional feature fusion, belonging to the field of analog circuit fault diagnosis. First, voltage and current datasets for the circuit's health state and various fault states are obtained. The collected datasets are normalized and divided into training and test sets. Second, a one-dimensional convolutional neural network with two branches is constructed. The first branch extracts fault features from the voltage signal, and the second branch extracts fault features from the current signal. Then, the fault features extracted by the two branches are adaptively weighted and fused, and input into a fully connected layer. Finally, the one-dimensional convolutional neural network is trained on the training set, and its effectiveness is verified on the test set. This invention uses feature fusion to obtain more comprehensive feature information about circuit faults, overcoming the limitations of limited measurement points in airborne circuits, the weakness of circuit faults, and the incompleteness of single-signal fault features, thus improving the accuracy of the diagnostic results.
[0007] A fault diagnosis method for airborne filter circuits based on convolutional feature fusion, such as Figure 1 As shown, the specific technical solution includes the following steps:
[0008] Step 1, Obtain voltage and current datasets: Collect voltage and current data under the health status and various fault states of the airborne filter circuit, and normalize the collected voltage and current data to obtain voltage and current datasets.
[0009] Both the voltage dataset and the current dataset are divided into training set and test set, respectively.
[0010] Step 2: Construct a CNN feature fusion model;
[0011] The CNN feature fusion model includes a current feature acquisition module, a voltage feature acquisition module, a weighted fusion module, and a fully connected layer; the current feature acquisition module and the voltage feature acquisition module are both one-dimensional convolutional neural networks; the weighted fusion module is a multilayer perceptron.
[0012] Step 2.1: The current feature acquisition module extracts the fault features of the current signal to obtain the current fault features; the voltage feature acquisition module extracts the fault features of the voltage signal to obtain the voltage fault features.
[0013] Step 2.2: After pooling the voltage fault features and current fault features respectively, the fault features are concatenated to obtain the expanded vector of fault features;
[0014] Step 2.3: Fuse the expanded vectors of the fault features to obtain the fused feature vector;
[0015] Step 2.4: Input the fused feature vector into the weighted fusion module, calculate the weights of the weighted fusion, and perform adaptive weighted fusion to obtain multi-source fused weighted features.
[0016] Step 2.5: Input the multi-source fusion weighted features into the fully connected layer and use the softmax function for fault classification;
[0017] Step 3: Use the training set samples to train the CNN feature fusion model to obtain the trained CNN feature fusion model;
[0018] Step 4: Use test set samples to perform fault diagnosis on the trained CNN feature fusion model, identify fault states and compare them with the actual fault states of the circuit to verify the effectiveness of the model.
[0019] Furthermore, in step 1, the process of obtaining the voltage dataset and the current dataset is as follows:
[0020] Step 1.1: Use voltage and current sensors to collect voltage and current data of the airborne filter circuit under healthy and individual component failure conditions, respectively; the components include resistors, capacitors, and operational amplifiers.
[0021] Both voltage and current data are collected from n samples, and the sampling time for each sample is... for:
[0022] (1);
[0023] Where, n i is the length of the i-th sample; f is the sampling frequency when collecting samples;
[0024] Step 1.2: Normalize the voltage data collected in Step 1.1 and store it in the voltage dataset as a one-dimensional time-domain sample. The normalization equation for the voltage data is:
[0025] (2);
[0026] in, This is the normalized voltage value. This is the voltage signal value. This represents the minimum value of the voltage range, and this represents the maximum value of the voltage range.
[0027] Similarly, the normalization process for current data is the same as that for voltage data, and it is stored in the current dataset as a one-dimensional time-domain sample.
[0028] Step 1.3: Divide both the voltage dataset and the current dataset into training set and test set, and add labels for circuit fault states to the sample data in the training set.
[0029] Furthermore, in step 2, such as Figure 2 As shown: The one-dimensional convolutional neural network includes three convolutional layers, each followed by a max pooling layer. The first convolutional layer is followed by the first max pooling layer, the second convolutional layer by the second max pooling layer, and the third convolutional layer by the third max pooling layer. Each of the first and second max pooling layers is followed by an additional global average pooling branch, namely the first global average pooling branch and the second global average pooling branch. The first and second global average pooling branches perform global average pooling on the fault features pooled by the first and second max pooling layers, respectively, before connecting them to the feature concatenation layer. The third max pooling layer is followed by the feature concatenation layer.
[0030] The kernel sizes of the three convolutional layers are 7×1, 5×1 and 3×1, respectively; the number of filters are 32, 64 and 128, respectively; and the padding is 3, 2 and 1, respectively.
[0031] The activation function is ReLU, and the sizes of the three max pooling layers are 4, 3, and 2, respectively.
[0032] Furthermore, the feature concatenation layer concatenates the fault features to obtain an expanded vector of fault features:
[0033] Vector after voltage fault feature expansion :
[0034] (3);
[0035] in, This represents the vector input to the feature concatenation layer after global average pooling in the voltage feature acquisition module via the first global average pooling branch. This represents the vector input to the feature concatenation layer after the voltage feature acquisition module has undergone global average pooling through the second global average pooling branch. This represents the expanded vector output from the third maximum pooling layer of the voltage feature acquisition module.
[0036] Vector after expansion of current fault features :
[0037] (4);
[0038] in, This represents the vector input to the feature concatenation layer after global average pooling in the current feature acquisition module via the first global average pooling branch. This represents the vector input to the feature concatenation layer after the current feature acquisition module has undergone global average pooling through the second global average pooling branch. This represents the expanded vector output from the third maximum pooling layer of the current feature acquisition module.
[0039] Furthermore, in step 2, such as Figure 3 As shown, the adaptive weighted fusion process performed by the weighted fusion module is as follows:
[0040] Step 2.3.1, expand the vector of voltage fault features. Vector after expansion of current fault characteristics The fusion is performed to obtain the fused feature vector. :
[0041] (5);
[0042] Step 2.3.2, fuse the feature vectors The input is fed into the weighted fusion module to obtain multi-source weighted fusion features. ;
[0043] (6);
[0044] The weighted fusion module is a multilayer perceptron (MLP), which includes two fully connected layers; the first fully connected layer receives the fused feature vector. The data is then compressed; the second fully connected layer acquires the weights of the voltage fault characteristics. Weights of current fault characteristics The number of filters in the two fully connected layers are 128 and 2, respectively.
[0045] The technical effects of this invention are as follows:
[0046] This invention uses a feature fusion method to obtain more comprehensive feature information of circuit faults, overcoming the impact of limited measurement points in airborne circuits, the weakness of circuit faults, and the incomplete features of single signal faults on circuit fault diagnosis, thereby improving the accuracy of diagnostic results. Attached Figure Description
[0047] Figure 1 This is an overall flowchart of the present invention;
[0048] Figure 2 This is a structural diagram of the CNN feature fusion model of the present invention;
[0049] Figure 3 This is a structural diagram of the weighted fusion module of the present invention. Detailed Implementation
[0050] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments:
[0051] A fault diagnosis method for airborne filter circuits based on convolutional feature fusion, such as Figure 1 As shown, the specific technical solution includes the following steps:
[0052] Step 1, Obtain voltage and current datasets: Collect voltage and current data under the health status and various fault states of the airborne filter circuit, and normalize the collected voltage and current data to obtain voltage and current datasets.
[0053] The voltage dataset and the current dataset are divided into training set and test set, respectively.
[0054] Step 2: Construct a CNN feature fusion model;
[0055] The CNN feature fusion model includes a current feature acquisition module, a voltage feature acquisition module, a weighted fusion module, and a fully connected layer; the current feature acquisition module and the voltage feature acquisition module are both one-dimensional convolutional neural networks; the weighted fusion module is a multilayer perceptron.
[0056] Step 2.1: The current feature acquisition module extracts the fault features of the current signal to obtain the current fault features; the voltage feature acquisition module extracts the fault features of the voltage signal to obtain the voltage fault features.
[0057] Step 2.2: After pooling the voltage fault features and current fault features respectively, the fault features are concatenated to obtain the expanded vector of fault features;
[0058] Step 2.3: Fuse the expanded vectors of the fault features to obtain the fused feature vector;
[0059] Step 2.4: Input the fused feature vector into the weighted fusion module, calculate the weights of the weighted fusion, and perform adaptive weighted fusion to obtain multi-source fused weighted features.
[0060] Step 2.5: Input the multi-source fusion weighted features into the fully connected layer and use the softmax function for fault classification;
[0061] Step 3: Use the training set samples to train the CNN feature fusion model to obtain the trained CNN feature fusion model;
[0062] Step 4: Use test set samples to perform fault diagnosis on the trained CNN feature fusion model, identify fault states and compare them with the actual fault states of the circuit to verify the effectiveness of the model.
[0063] In step 1, the process of obtaining the voltage dataset and the current dataset is as follows:
[0064] Step 1.1: Use voltage and current sensors to collect voltage and current data of the airborne filter circuit under healthy and individual component failure conditions, respectively; the components include resistors, capacitors, and operational amplifiers.
[0065] Both voltage and current data are collected from n samples, and the sampling time for each sample is... for:
[0066] (1);
[0067] Where, n i is the length of the i-th sample; f is the sampling frequency when collecting samples;
[0068] Step 1.2: Normalize the voltage and current data collected in Step 1.1, and store them as one-dimensional time-domain samples in the voltage dataset and current dataset respectively. The normalization equation for the voltage data is:
[0069] (2);
[0070] in, This is the normalized voltage value. This is the voltage signal value. This represents the minimum value of the voltage range, and this represents the maximum value of the voltage range.
[0071] Similarly, the normalization process for voltage data is the same as that for current data;
[0072] Step 1.3: Divide both the voltage dataset and the current dataset into training set and test set, and add labels for circuit fault states to the sample data in the training set.
[0073] In step 2, such as Figure 2 As shown: The one-dimensional convolutional neural network includes three convolutional layers, each followed by a max pooling layer. The first convolutional layer is followed by the first max pooling layer, the second convolutional layer by the second max pooling layer, and the third convolutional layer by the third max pooling layer. Each of the first and second max pooling layers is followed by an additional global average pooling branch, namely the first global average pooling branch and the second global average pooling branch. The first and second global average pooling branches perform global average pooling on the fault features pooled by the first and second max pooling layers, respectively, before connecting them to the feature concatenation layer. The third max pooling layer is followed by the feature concatenation layer.
[0074] The kernel sizes of the three convolutional layers are 7×1, 5×1 and 3×1, respectively; the number of filters are 32, 64 and 128, respectively; and the padding is 3, 2 and 1, respectively.
[0075] The activation function is ReLU, and the sizes of the three max pooling layers are 4, 3, and 2, respectively.
[0076] The feature concatenation layer concatenates the fault features to obtain an expanded vector of fault features:
[0077] Vector after voltage fault feature expansion :
[0078] (3);
[0079] in, This represents the vector input to the feature concatenation layer after global average pooling in the voltage feature acquisition module via the first global average pooling branch. This represents the vector input to the feature concatenation layer after the voltage feature acquisition module has undergone global average pooling through the second global average pooling branch. This represents the expanded vector output from the third maximum pooling layer of the voltage feature acquisition module.
[0080] Current fault characteristics after expansion :
[0081] (4);
[0082] in, This represents the vector input to the feature concatenation layer after global average pooling in the current feature acquisition module via the first global average pooling branch. This represents the vector input to the feature concatenation layer after the current feature acquisition module has undergone global average pooling through the second global average pooling branch. This represents the expanded vector output from the third maximum pooling layer of the current feature acquisition module.
[0083] In step 2, such as Figure 3 As shown, the adaptive weighted fusion process performed by the weighted fusion module is as follows:
[0084] Step 2.3.1, expand the vector of voltage fault features. Vector after expansion of current fault characteristics The fusion is performed to obtain the fused feature vector. :
[0085] (5);
[0086] Step 2.3.2, fuse the feature vectors The input is fed into the weighted fusion module to obtain multi-source weighted fusion features. ;
[0087] (6);
[0088] The weighted fusion module is a multilayer perceptron (MLP), which includes two fully connected layers; the first fully connected layer receives the fused feature vector. The data is then compressed; the second fully connected layer acquires the weights of the voltage fault characteristics. Weights of current fault characteristics The number of filters in the two fully connected layers are 128 and 2, respectively.
[0089] The collected circuit fault states include three main categories: resistance changes and open circuits of individual resistors, capacitance changes and open circuits of individual capacitors, and operational amplifier voltage drops and open circuits. The offset for component parameter changes is 10% for resistors and 15% for capacitors. The first category includes two resistors connected to the non-inverting input of the operational amplifier in each of the two circuit stages; a rise or fall in resistance value and an open circuit at that point are each considered a fault state. The second category includes capacitors selected from each of the two circuit stages for filtering; a rise or fall in capacitance value and an open circuit at that point are each considered a fault state. The third category includes a drop in the operational amplifier's operating voltage and an open circuit in the operational amplifier. An additional normal circuit operation state is also included, totaling 17 circuit fault states. Voltage and current signals under these fault states are collected and reconstructed into a two-dimensional matrix for storage. The selected fault states and the number of samples for each fault state are shown in Table 1.
[0090] Table 1. Fault states and their sample sizes
[0091] Faulty components Fault codes Fault status Sample size / F0 / 400 R1 F1 R1 ↑ 400 R1 F2 R1 ↓ 400 R1 F3 R1 open 400 R6 F4 R6 ↑ 400 R6 F5 R6 ↓ 400 R6 F6 R6 open 400 C5 F7 C5 ↑ 400 C5 F8 C5 ↓ 400 C5 F9 C5 open 400 C8 F10 C8 ↑ 400 C8 F11 C8 ↓ 400 C8 F12 C8 open 400 V1 F13 V1 ↓ 400 V1 F14 U1 open 400 V2 F15 V2 ↓ 400 V2 F16 U2 open 400
[0092] Fault diagnosis experiments were conducted using voltage and current signal data collected under all fault types in Table 1, as well as voltage and current signal data collected under healthy conditions. All voltage and current signal data were input into a CNN feature fusion model for training. The final CNN feature fusion model was obtained after all samples had been trained.
[0093] Next, samples of all fault types and healthy states were recollected. The recollected sample data was then input into the trained CNN feature fusion model to obtain fault diagnosis results. The diagnosis results were compared with the true categories of the samples to verify the effectiveness of the model. The hyperparameters set during network training are shown in Table 2.
[0094] Table 2 Model Training Hyperparameters
[0095] hyperparameters Parameter value Batch Size 64 Learning rate 0.001 Number of iterations 50
[0096] The test set samples were used for fault diagnosis to obtain the final diagnostic results. Five experiments were conducted, and the average accuracy was calculated. The results showed that the average diagnostic accuracy of the present invention for unlabeled test set samples reached 99.5%, demonstrating high accuracy and verifying the effectiveness and feasibility of the method used in the field of circuit fault diagnosis. In addition to the method of the present invention, two other different methods were selected to diagnose faults on the same dataset. The first comparative method used only the voltage signal at the circuit input terminal for fault diagnosis of the test set samples, achieving an average accuracy of 92.5%. The second comparative method used only the voltage signals from two different sampling points in the circuit signal for fault diagnosis, achieving an average accuracy of 97.9%. The diagnostic accuracy and diagnostic reports of the three methods are compared in Table 3.
[0097] Table 3 Comparison of diagnostic results from different methods.
[0098] Diagnostic methods accuracy Recall rate F1 score Single voltage signal 0.93 0.93 0.90 Dual voltage signal fusion 0.98 0.99 0.98 Method of the present invention 0.99 0.99 0.99
[0099] By comparing the final method of this invention with the single-voltage signal method and the dual-voltage signal feature fusion method, it is shown that the method of this invention effectively overcomes the influence of limited measurement points of airborne circuits, weak circuit faults, and incomplete fault features of single signals on circuit fault diagnosis, and improves the accuracy of fault diagnosis.
Claims
1. A fault diagnosis method for airborne filter circuits based on convolutional feature fusion, characterized in that, The specific technical solution includes the following steps: Step 1, Obtain voltage and current datasets: Collect voltage and current data under the health status and various fault conditions of the airborne filter circuit, and normalize the collected voltage and current data to obtain voltage and current datasets. The voltage dataset is divided into a training set and a test set, and the current dataset is also divided into a training set and a test set. Step 2: Construct a CNN feature fusion model; The CNN feature fusion model includes a current feature acquisition module, a voltage feature acquisition module, a weighted fusion module, and a fully connected layer. Both the current and voltage feature acquisition modules are one-dimensional convolutional neural networks, comprising a feature concatenation layer and three convolutional layers. Each convolutional layer is followed by a max-pooling layer: the first convolutional layer is followed by a first max-pooling layer, the second convolutional layer by a second max-pooling layer, and the third convolutional layer by a third max-pooling layer. Each of the first and second max-pooling layers is followed by an additional global average pooling branch, namely the first global average pooling branch and the second global average pooling branch. The first and second global average pooling branches perform global average pooling on the fault features pooled by the first and second max-pooling layers, respectively, before connecting them to the feature concatenation layer. The third max-pooling layer is followed by the feature concatenation layer. The weighted fusion module is a multilayer perceptron. Step 2.1: The current feature acquisition module extracts the fault features of the current signal to obtain the current fault features; the voltage feature acquisition module extracts the fault features of the voltage signal to obtain the voltage fault features. Step 2.2 involves pooling the voltage fault features and current fault features separately, then concatenating the fault features to obtain the expanded fault feature vector. The specific steps are as follows: Vector after voltage fault feature expansion : （1）； in, This represents the vector input to the feature concatenation layer after global average pooling in the voltage feature acquisition module via the first global average pooling branch. This represents the vector input to the feature concatenation layer after the voltage feature acquisition module has undergone global average pooling through the second global average pooling branch. This represents the expanded vector output from the third maximum pooling layer of the voltage feature acquisition module. Vector after expansion of current fault features : （2）； in, This represents the vector input to the feature concatenation layer after global average pooling in the current feature acquisition module via the first global average pooling branch. This represents the vector input to the feature concatenation layer after the current feature acquisition module has undergone global average pooling through the second global average pooling branch. This represents the expanded vector output from the third max-pooling layer of the current feature acquisition module. Step 2.3: Fuse the expanded vectors of the fault features to obtain the fused feature vector; Step 2.4: Input the fused feature vector into the weighted fusion module, calculate the weights of the weighted fusion, and perform adaptive weighted fusion to obtain multi-source fused weighted features. Step 2.5: Input the multi-source fusion weighted features into the fully connected layer and use the softmax function for fault classification; Step 3: Use the training set samples to train the CNN feature fusion model to obtain the trained CNN feature fusion model; Step 4: Use test set samples to perform fault diagnosis on the trained CNN feature fusion model, identify fault states and compare them with the actual fault states of the circuit to verify the effectiveness of the model.
2. The airborne filter circuit fault diagnosis method based on convolutional feature fusion according to claim 1, characterized in that, In step 1, the process of obtaining the voltage dataset and the current dataset is as follows: Step 1.1: Use voltage and current sensors to collect voltage and current data of the airborne filter circuit under healthy and individual component failure conditions, respectively; the components include resistors, capacitors, and operational amplifiers. Both voltage and current data are collected from n samples, and the sampling time for each sample is... for: （3）； Where, n i is the length of the i-th sample; f is the sampling frequency when collecting samples; Step 1.2: Normalize the voltage data collected in Step 1.1 and store it in the voltage dataset as a one-dimensional time-domain sample. The normalization equation for the voltage data is: （4）； in, This is the normalized voltage value. This is the voltage signal value. This is the minimum value in the voltage range. This represents the maximum value within the voltage range. Similarly, the normalization process for current data is the same as that for voltage data, and it is stored in the current dataset as a one-dimensional time-domain sample. Step 1.3: Divide the voltage dataset into a training set and a test set, and divide the current dataset into a training set and a test set; and add labels for circuit fault states to the sample data in the training set.
3. The airborne filter circuit fault diagnosis method based on convolutional feature fusion according to claim 1, characterized in that, In step 2, the kernel sizes of the three convolutional layers of the one-dimensional convolutional neural network are 7×1, 5×1 and 3×1, respectively; the number of filters are 32, 64 and 128, respectively; and the padding is 3, 2 and 1, respectively. The activation function is ReLU, and the sizes of the three max pooling layers are 4, 3 and 2, respectively.
4. The airborne filter circuit fault diagnosis method based on convolutional feature fusion according to claim 1, characterized in that, In step 2, the adaptive weighted fusion process performed by the weighted fusion module is as follows: Step 2.3.1, expand the vector of voltage fault features. Vector after expansion of current fault characteristics The fusion is performed to obtain the fused feature vector. : （5）； Step 2.3.2, fuse the feature vectors The input is fed into the weighted fusion module to obtain multi-source weighted fusion features. ; （6）； The weighted fusion module is a multilayer perceptron, which includes two fully connected layers; the first fully connected layer receives the fused feature vector. And compress it; The second fully connected layer acquires the weights of voltage fault characteristics. Weights of current fault characteristics The number of filters in the two fully connected layers are 128 and 2, respectively.
5. An electronic device, characterized in that, include: One or more processors; Memory; One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs being configured to perform the method as described in any one of claims 1 to 4.
6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores program code that can be invoked by a processor to execute the method as described in any one of claims 1 to 4.