3.3.1. Ultrasonic Testing Experiment and Metallographic Observation Experiment
TC25 titanium alloy has good high-temperature strength and thermal stability, which makes it an ideal material for aero-engines.
Figure 2 is the process diagram of the entire ultrasonic testing test and metallographic observation experiment. The samples in this experiment are titanium alloy ring forgings produced by different process standards. The ring forgings were cut into 168 samples. Metallographic observation samples were prepared, and MR5000 inverted metallographic microscope was used for metallographic observation. More than 20 metallographic images were randomly selected on each sample. Typical metallographic images were shown in
Figure 3. All metallographic images of each sample were measured by a digital image processing software, Image J, to obtain the equivalent diameter, area ratio, and grain length/minor axis ratio of all intact primary α phases within the field of view.
For ultrasonic testing, the test surface of each sample is evenly divided into 6 sampling areas of 5 mm × 5 mm, and the ultrasonic testing of the sample is carried out by the contact longitudinal wave echo method. The instruments and equipment used are an Olympus 5077PR pulse generator, a 10 MHz Olympus single crystal straight probe V112-RM, and a Pico Scope 3000 series acquisition card. The size of the probe wafer is larger than the sampling area, which ensures the full coverage of the sample. The nonlinear component of the ultrasonic signals produced by the specimens was acquired using the P-wave collinear harmonic method and a RAM-5000-SNAP (RITEC Inc., Milwaukee, WI, USA) non-linear measurement system. The central frequencies of the transmitting and receiving transducers were 2.5 MHz and 5 MHz, respectively.
TC25 experimental material contains 168 effective samples, and each sample contains five ultrasonic characteristic values (mean sound velocity, mean attenuation, primary offset, secondary offset, and nonlinear coefficient) and one primary α phase grain size value. For the 168 effective samples, the K-fold cross-validation method is used to test the model accuracy, in which K is 3, i.e., 118 effective samples are randomly selected as the training set and the remaining 50 effective samples are used as the test set.
3.3.2. Constructing the Ultrasound Evaluation Model of the Grain Size of Primary α Phase
Each valid sample contains five ultrasonic characteristic values (mean sound velocity
, mean attenuation
, primary offset
, secondary offset
, and nonlinear coefficient
) and the grain size value
of one primary α phase.
Table 1 shows the partial original data of TC25 materials.
The set composed of five ultrasonic eigenvalues is taken as the input of real samples and expressed in the form of matrix , where , . Here, represents the number of samples , denotes the dimension of a single sample, and here.
The grain size value of one primary α phase is taken as the output of the real samples and expressed as the matrix . The two together construct a real sample set of TC25 titanium alloy. Because the magnitude of each ultrasonic eigenvalue in the real sample set is different, they are normalized to a unified interval.
The construction of the model is divided into the virtual sample generation process, the virtual sample validity analysis and screening process, and the modeling process. The detailed description is as follows.
- (1)
Virtual sample generation process.
The TC25 real training sample set is preprocessed and normalized to the [0, 100] interval to ensure the coding accuracy
. The coding length
is then obtained. A black-and-white image with a scale of
can be obtained by binary encoding of a valid sample. The image is shown in
(
Figure 4), which is the real image data after binary encoding. After preprocessing,
black-and-white image sets
can be obtained. Here,
is the sample set size of the real training sample set
.
The virtual sample image set
is generated by the GAN, where
is the number of a group of virtual sample image sets. The generated virtual sample image set is decoded and restored to a virtual sample set.
Figure 4 demonstrates the specific GAN framework, where
is an output image of generator G.
- (2)
Virtual sample validity analysis and screening process.
The optimal virtual sample set is generated by the algorithm, i.e., .
- (3)
Modeling process.
The real training sample set and the optimal virtual sample set are combined to form a new reconstructed sample set , where . Using , the support vector regression method was adopted to build the ultrasound evaluation model of the primary α phase grain size.
To verify the prediction model, the prediction accuracy of the real test samples in the model is set, i.e., the test accuracy value
is the indicator to test the quality of the model. The closer the value is to 1, the better the model. The formula is
where
is the number of real test samples,
is the value of the real test samples,
is the average value of the real test samples, and
is the predicted value of the real test samples.
The value and value of the model are calculated, and the three processes are repeated M times. The average values of the and are calculated.