Figure 1 shows 24 hours of current consumption for a nominal experiment. The thermostat is set at position 1. The refrigerator is empty and at the set-point temperature at the beginning of the experiment. The raw signal from which figure 1 is constructed contains values. During this one day experiment, the thermostat switches the compressor on and off 68 times. The mean time for the compressor being on is 194.8 s with a standard deviation of 11.1 s. The mean off-time of the compressor is 1064.3 s with a standard deviation of 25.7 s. The duty-cycle of the refrigerator for this experiment is 15.5%.
Refrigerators exhibit oscillatory behavior: there is the main compressor on/off cycle and the electrical circuit is powered by a 60 Hz AC. Figure 2 shows a frequency plot of the signal shown in figure 1. The plot shows amplitudes in the frequency range 0-0.025 Hz. The largest non-DC amplitude is at Hz. This frequency corresponds to a period of 1269.5 s which is within 99.1% of the mean duration of the compressor on/off cycle.
Figure 3 gives us a closer look on the current signal during one compressor-on cycle. The compressor is switched-on for 172 s. In the beginning the PTC thermistor is at room temperature and has low resistance. A few seconds after that the PTC thermistor heats-up due to the current flowing through it, its resistance increases and the current that flows through the start-winding of the compressor decreases. After the start-winding of the motor is switched-off the current signal becomes a simple sinusoid of 60 Hz and constant amplitude.
If we zoom-in the current plot even further we can see the start-up of the motor as shown in figure 4. It illustrates the start-up of the compressor by running current through a special start-up winding. This particular type of refrigerator uses a Resistance Start, Induction Run (RSIR) motor. The RSIR design uses a PTC thermistor as a time delay mechanism for spinning the single-phase AC motor.
Figure 4 is important in modeling the dynamics of the PTC. The PTC is a resistor whose resistance is heavily dependent on the temperature. To emphasize the fact that it behaves similar to an ordinary (mostly linear) resistor we show the compressor voltage during the start-up of a cycle. This is done in figure 5.
The sampling of the voltage and the current is synchronized by a common clock in the power logger that we have designed and use. To verify the correct working of this power logger we compute the product of the voltage and the current signals which is the power. The resulting compressor start-up power is consistent with how this type of AC electrical motors and PTC work and is shown in figure 6.
Figure 7 shows an FFT plot of the start-up current. The 60 Hz AC mains frequency is the dominant frequency which is no surprise. The Nyquist frequency of our power logger is 250 Hz and the shape of the AC sine is well-visible. There are aliased frequencies of small amplitude at 120 Hz and 180 Hz. There are several FFT components at 80 Hz and 200 Hz which are due to the choice of the ADC (they also appear in the voltage frequency plot).
Figure 8 shows an FFT plot of the start-up voltage. The voltage is almost perfectly sinusoidal which is consistent with the working of the AC motor. In our instrumentation design we use two simultaneously clocked ADCs of the same type (LTC2440). There are small frequency components (that we can digitally filter) which are due to the ADCs. The amplitudes of these frequencies (80 Hz and 200 Hz), however, are so small that there is no need of filtering for successful diagnostic analysis. These frequencies will be filtered by the diagnostic algorithm capabilities to deal with noise and error.
We have discussed in previous posts how to take a refrigerator and add actuators and sensors so the refrigerator becomes a diagnostic test-bed. Today we can start running diagnostic experiments and develop diagnostic algorithms and methods. An ultimate goal of ours is to build end-to-end diagnostic solutions in the context of repair, maintenance, or decision making.
Another goal is to create a diagnostic benchmark for continuous thermodynamic refrigeration systems. Of course in the process of experimentation we shall calibrate and validate our platform (convert sensors readings to Si units, inspect signal ranges, etc.). We want to have experimental controls, to be able to reproduce experiments, and to construct representative and validbenchmark. The approach of achieving this is by careful manual validation of the intermediate results.
Let us first define a diagnostic scenario. A diagnostic scenario is a set of time-series that contain information about:
all sensor data
the fault injection and the positions of all actuators
the conditions in the environment (these are preset constant values such as the thermostat position or the mains voltage)
A diagnostic benchmark contains many diagnostic scenarios. The length of most of our diagnostic scenarios will be 24 hours. The reason for that is there is a natural 24 hour cycle in the environmental temperature and that the slowest process of interest in our refrigerator (warming-up to ambient temperature) is several hours in duration.
Before anything else we collect data about the nominal working of the refrigerator. We will use this data for building nominal models, calibration, and validation. This is how the refrigerator temperature looks for one nominal scenario:
The plot above shows the readings from three DS18B20 temperature sensors and the thermostat position for the duration of one nominal experiment. The temperature in the freezer and in the refrigerator is oscillating around the set temperature as prescribed. The room temperature depends on the office HVAC and the outside temperature. There is a small bump in the room temperature probably due to closing the door for a noisy conversation.
The next plot zooms in the time and shows all temperature sensors and the thermostat position:
The plot above shows half an hour of the temperature and thermostat signals during the day. We can see that due to the fluid dynamics of the air in the refrigerator (the fridge is mostly empty except for the pipes that hold the sensors) some of the temperatures fluctuate more than others. The effect is pronounced for temperature sensors close to the evaporator.
More than 7% of the energy of a refrigerator is spent in cooling-down after opening the door. The door is an important refrigerator component and analyzing fault modes or fault regimes of the door (or the user that operates the door) is important for diagnosing the device.
To be able to open and close the door in a deterministic way, we have designed and installed a door opener. The door opener consists of a linear actuator, a motor controller and a 12V DC power supply. The video below shows opening and closing of the refrigerator door.
The linear actuator is a DC motor that drives a threaded rod. There are two switches that stop the motor when the rod is fully extended or fully retracted. The actuator can lift up to 200 pounds and is typically used in opening and closing truck doors. The threaded rod extends 12 inches (30.48 cm).
The motor controller is from model cars and can deliver of up to 2A of current at ±12V. It is very important that the controller uses a transistor-based H-bridge for reversing the polarity of the voltage so the door can be moved in both direction. The motor is controlled in an open-loop manner with the motor kept on for a predetermined amount of time (it takes approx. 18 s to open or close the door). The Arduino MEGA digital outputs connect directly to the motor-controller inputs and can use PWM to regulate the output voltage (and motor speed). We do not use PWM as it is not necessary to limit the speed of the linear actuator.
It is easy to get the "Hello, World!" of software radio to work with the USRP X310. Installing the hardware is straightforward, except it took some effort to discover the IP address of the 10Gb NIC which was not documented (I can imagine 10Gb interfaces are not common due to the still high price).
Compiling and running the software is also easy. Next is to learn it by copying the lab example of decoding and listening to an FM radio station (hopefully even after everybody moves to digital radio, they still keep some FM for testing.
This is how the GNU Radio implementation of an FM receiver looks like:
It turns out the strongest FM signal that I can receive in my office (our office in Palo Alto is very well shielded) is the KPFA public radio which transmits from Berkeley, California. The transmission antenna is 51.8 km away and there should be direct visibility.
It is always useful to see the spectrum of the raw signal. This is how KPFA looked like:
Finally, this is what I heard via the sound card (noise is not filtered and the SNR is relatively low):