The superheterodyne receiver is a typical device widely used in electronics and information systems. Thus effective performance assessment and prediction for superheterodyne receiver are necessary for its preventative maintenance. A scheme of performance assessment and prediction based on Mahalanobis distance and time sequence analysis is proposed in this paper. First, a state observer based on radial basis function (RBF) neural network is designed to monitor the superheterodyne receiver and generate the estimated output. The residual error can be calculated by the actual and estimated output. Second, time-domain features of the residual error are then extracted; after that, the Mahalanobis distance measurement is utilized to obtain the health confidence value which represents the performance assessment result of the most recent state. Furthermore, an Elman neural network based time sequence analysis approach is adopted to forecast the future performance of the superheterodyne receiver system. The results of simulation experiments demonstrate the robustness and effectiveness of the proposed performance assessment and prediction method.
The superheterodyne receiver is one of the most successful forms of radio used in electronics and information systems. With good sensitivity, frequency stability, and selectivity, superheterodyne receivers can translate high-frequency signals to lower frequency signals to make high-quality voice and signals [
Although superheterodyne receivers are widely used, studies on their performance assessment and prediction have been rarely exploited. Only a few studies for some specific receivers have been investigated in the field of fault diagnosis and prognostics. Middleton proposed canonical non-Gaussian noise models for measurement and prediction of receiver performance in real interference environments [
In order to evaluate the performance degradation degree of the superheterodyne receiver system, at the first step, a state observer is usually established to estimate the system output [
As for the constantly updated performance prediction, many time-series analysis methods such as ARMA model and the Kalman filter are widely used for prediction of complicated system [
To solve the aforementioned problems, a method that combines Mahalanobis distance and Elman neural network is proposed in this study in order to realize the accurate performance assessment and prediction, which is beneficial in terms of improving the system’s operation reliability. Our original contributions are summarized as follows.
Firstly, a performance feature extraction method based on RBF observer is proposed for superheterodyne receiver system. Based on the extracted features, the health confidence value which reflects the performance of the system is then calculated by the Mahalanobis space.
Secondly, a prediction model based on Elman neural network is adopted to forecast the health state of superheterodyne receiver system. The time sequence analysis method is utilized with the Elman network model to make an effective
Besides, sufficient experiments are conducted based on a simulated superheterodyne receiver model with typical faults injection. The feasibility and effectiveness of our proposed model matching the receiver system are verified.
The paper is organized as follows: in Section
Figure
The block diagram of a superheterodyne receiver system model.
The faults of superheterodyne receiver have a great influence on the reliability and robustness of the system operation. According to statistical maintenance data, main faults of superheterodyne receivers include amplifier faults, local oscillator faults, and filter faults. In our study, intermediate frequency (IF) amplifier faults and local oscillator faults are selected to simulate the system degradation states, which are marked with red points in Figure
In the receiver system, the radio signal is firstly collected by the suitable antenna and then processed and transmitted to the mixer with random noise interference, which is an equivalent of a range of uncertainties. A local oscillator provides the mixing frequency, which is variable for tuning the receiver to different stations. The frequency mixer does the actual heterodyning which changes the incoming frequency signal to a fixed IF radio frequency. The IF bandpass filter and the amplifier supply most of the narrowband filtering and the gain for the signal. The demodulator extracts the audio or other modulation from the IF radio frequency, and then the extracted signal is amplified by the audio amplifier. The simulation model is established in MATLAB/Simulink environment, based on the principle of the superheterodyne receiver. The details of the simulation model are as follows: The signal source has a wave carrier with a frequency of 1000 kHz. The modulated baseband signal can be changed as required. And the signal module is packaged into a subsystem. The parameter of the attenuator module is 0.1, simulating the attenuation caused by the transmission distance from the transmitter to the receiver. In order to simulate the interference of electromagnetic environment, the AWGN channel is employed to add random white noise with a mean of 0 and a variance of 0.01 into the input radio signal, before the signal is transmitted to the receiver. The local oscillator (LO) is designed to generate local oscillator signal, which is used to mix with the input signal by changing the LO frequency. And the frequency is set to 465 kHz lower than the input radio frequency based on The mixer, shown in Figure The IF signal obtained from the mixer is then fed into the IF filter, a bandpass filter centered at 465 kHz with a bandwidth of 12 kHz. The IF amplifier can change the frequency levels in circuits that are too selective, difficult to tune. The gain for signal output is 20. Another IF filter is modeled to further eliminate the band noise with the same parameters of the former filter. The envelope detector is then designed to demodulate the signal from the filter and provide an output which is the envelope of the input IF signal. The upper and lower limits are set to inf and 0, respectively. The low-pass filter finally processes the signal obtained from the detector and send it to the audio amplifier. The passband edge frequency of the low-pass filter is 6 kHz.
Mixer of superheterodyne receiver.
This paper provides performance assessment and prediction for superheterodyne receivers, and the schematic diagram is shown in Figure
Performance assessment and prediction for a superheterodyne receiver.
The system health monitoring can be divided into two processes, that is, the assessment process and the prediction process. Both the performance assessment and prediction are based on the residual error of fault observer established upon a radial basis function (RBF) neural network.
Performance assessment hinges on the Mahalanobis space constructed by the features extracted from the residual error under normal operation condition. Then the similarity for features of monitoring data under different faults is calculated using the Mahalanobis distance in the Mahalanobis space. Finally, assessment for superheterodyne receiver is accomplished by normalizing the distance. The result of performance assessment is quantitatively indicated by a confidence value (CV). CV ranges from 0 to 1, indicating unacceptable and normal performance, and it usually decreases over time [
The assessment process and the prediction process are two respective steps. The prediction process needs to be carried out based on the result of the performance assessment. Both of them are updated over time with the time-invariant receiver system input and output.
A superheterodyne receiver is a nonlinear system in which the values of the parameters of the inner parts are inconvenient to obtain; hence the state observer is established with the system input and output signals. In the proposed performance assessment method, the previous-moment output amplitude in the normal state and time is utilized as input for the RBF neural network, whereas the output signal amplitude is used as target values for network training. After training, the created observer can generate the expected values of normal output signals. In this way, the residual error of the test data is obtained by calculating the difference values between the actual output signals and the estimated output signals. The residual error contains a large amount of state information of the system, which can be used to extract features for performance assessment of the system.
Suppose that the superheterodyne receiver system can be described as
The system state observer can be defined as
Then the state error is defined as
If
Since it is difficult to deduce the mathematic transfer function of the receiver system, RBF neural network is applied as the system observer considering its nonlinear fitting capability. As shown in Figure
Observer based on RBF neural network.
Here, a Gaussian function is employed as the radial basis function:
In (
In this study, the training parameters for the system observer are as follows: training error goal is
The residual error is calculated as follows:
When the superheterodyne receiver system works normally, the system operation station is similar to the normal state; thus the residual error is close to zero. The residual error in this situation is
The residual error can reflect the running state of the superheterodyne receiver system. Hence, time-domain analysis is applied to extract features from the residual error datasets. Here, the time-domain analysis refers to signal amplitude processing. The time-domain parameters of the signal include the mean value, the maximum value, the minimum value, and the root mean square value (RMS). In this study, we choose the RMS value, the mean value, and the peak value.
If The RMS value: The mean value: The peak value:
Then the feature vectors of superheterodyne receivers can be expressed as
The Mahalanobis distance is a measure of the distance between a point
If the feature vectors of the residual error are extracted, the Mahalanobis distances can be calculated as follows: Calculate the mean value of each feature vector: Calculate the standard mutation of each feature vector: Orthogonalize each feature vector and obtain its orthogonal matrix and transpose matrix: Calculate the correlation matrix of the orthogonal data: Then, the Mahalanobis distances are calculated using
The residual error obtained under normal condition of the superheterodyne receiver is used to extract the feature vectors, which can be denoted as
When the superheterodyne system operates in the condition of performance degradation, the feature vectors extracted from the residual error can be represented by
Finally, the calculated Mahalanobis distances are normalized to CVs as follows:
In (
According to the definition of the Mahalanobis distance, the feature vector obtained in the case of better performance has the nearer distance from the Markov space, and thus the CVs are higher accordingly [
The Elman neural network, as shown in Figure
Structure of Elman neural network.
The characteristic of the Elman neutral network is that it can maintain a sort of state since the output of hidden layer connects with its input by acceptor layer. This kind of self-connection makes the network sensitive to its historical state values, which increases the ability of dynamic information processing [
Mathematical model of the Elman neural network can be defined as follows:
As shown in Figure
Inputs and outputs of performance prediction.
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Manner of the prediction process.
In our study, several typical faults are injected into the simulation model to demonstrate effectiveness of the proposed method. In this simulation experiment, the input signal is a sine signal. The amplitude of system input is 1; the frequency of system input is 100 Hz. In the simulation, the sampling rate is 120 kHz, while the simulation duration is set 0.05 s. Thus 6000 data points of input and 6000 data points of output are collected in each case.
According to statistical maintenance data, main faults of superheterodyne receivers include amplifier faults, local oscillator faults, and filter faults. In this study, IF amplifier fault and local oscillator fault were introduced into the simulation model by changing some specific parameters of the fault components, and they represented the gradual degradation fault and the abrupt degradation fault. The details are listed in Table
Fault injection details.
Test number | Fault mode | Changed parameters for fault injection | Parameter (normal) | Parameter (fault) |
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1 | Normal | — | — | — |
2 | Amplifier fault | Gain | 20 |
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3 | Local oscillator fault | LO frequency (kHz) | 465 |
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The RBF neural network was firstly trained using the normal dataset, including the input/output data under normal working condition. Then it was applied to get the estimated output under these faults by inputting each fault dataset into the RBF neural network observer. By comparing the estimated output and the actual output, 6000 discrete residual errors were calculated in each case as shown in Figures
Residual error of amplifier fault state.
Residual error of oscillator fault state.
To assess the performance of the superheterodyne receiver system, one feature vector including 3 features was extracted from each 120 samples of the residual error. And the starting point of feature extraction slided every 10 points, which could be listed as
Feature vectors of superheterodyne receivers.
The three-dimensional feature vectors of normal state could construct the Mahalanobis space. Then the Mahalanobis distances of the two fault states were calculated and normalized to CVs. To demonstrate the proposed approach presented in the study, three tests were conducted and the results of the Mahalanobis distances and CVs were shown in Figures
Performance assessment of amplifier fault state.
Performance assessment of oscillator fault state.
In test 1, the superheterodyne receiver worked normally; thus the residual error kept a regular range and the values of Mahalanobis distance were close to zero, while its CVs were close to 1.
In test 2, an IF amplifier gradual fault was injected into the system at
In test 3, a local oscillator fault was introduced into the superheterodyne system, and then, as shown in Figure
According to the simulation results, the performance assessment for the superheterodyne system under noise was effective with injected faults of different degrees. The CVs obtained by this approach can quantitate the performance degradation of the system.
Performance assessment results of the IF amplifier gradual fault were used to validate the performance prediction. In order to know the performance degradation trend of the superheterodyne receiver after performance assessment, the Elman neural network was employed to predict the performance.
Let variable
The prediction results were shown in Figures
Performance prediction under amplifier gradual fault at
Performance prediction under amplifier gradual fault at
Performance prediction under amplifier gradual fault at
Performance prediction under amplifier gradual fault at
The advantage of the proposed method lies in the efficient synergy between RBF neural network observer and Mahalanobis distance measurement, which can make good use of the extracted feature vectors. On the other hand, there are some disadvantages in the study. The CVs, though useful in describing the performance of superheterodyne receivers quantitatively, need to be carefully investigated in their physical meaning.
Furthermore, there are several important open challenges as follows, which need to be further considered: The variables in the assembly process, which have an impact on the system performance, can be taken into account to fulfill a more integrated assessment [ The reliability and robustness of the system model should be analyzed properly, based on the main sources of uncertainty and disturbance affecting the considered system [ The effectiveness of the proposed algorithms should be validated and improved by data sampled from the actual superheterodyne receivers.
This work presents a method for performance assessment and prediction of superheterodyne receivers based on Mahalanobis distance measurement and time sequence analysis. The residual error is obtained by using a RBF observer and utilized to calculate Mahalanobis distance to measure the distance indicating the performance state of the superheterodyne receiver. Finally, an Elman neural network is used to predict the degradation trend of the superheterodyne receiver, which is critical to preventative maintenance. The simulation results showed that the proposed method can effectively assess and predict the performance of superheterodyne receivers.
The authors declare that there are not any potential conflicts of interest in the research.
This study was supported by the State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, China, and the Fundamental Research Funds for the Central Universities (Grant no. YWF-17-BJ-J-42), as well as the National Natural Science Foundation of China (Grant nos. 51575021 and 51605014).