The value of frequency response testing in nuclear systems has been appreciated for a number of years. Tests have been run to check stability margins and theoretical dynamics models. All of the early tests used sinu­soidal reactivity perturbations to excite the system. This approach was a direct implementation of the basic definition of the frequency response, but the equipment was expensive and not very durable (particularly in the hostile environment in the more advanced reactors). Nevertheless, a number of excellent tests were performed on reactor systems.

In the early 1960s, alternate testing procedures involving periodic binary (two-level) input signals were first used on reactors for frequency response measurements and for impulse response measurements (see Section 3.1). The work of Balcomb et al. (1) was the key contribution in the development of these procedures. The pseudo-random binary sequence was used in most of the measurements during this period. Tests using the pseudo-random binary sequence have two features that make them superior to oscillator tests for power reactor measurements:

1. The two-level inputs can be introduced by standard hardware, such as control rods, in many reactors.

2. The signal contains many harmonics, permitting the determination of the frequency response at a number of frequencies in a single test.

After the introduction and use of the pseudo-random binary sequence, other binary and ternary (three-level) signals with advantages over the pseudo-random binary sequence were developed. The needs for the improve­ments achievable with the newer signals and the manner in which the improvements were made are discussed in Chapter 3.

Frequency response measurements may also be made using nonperiodic inputs such as reactivity pulses or steps. These also allow the determination of the frequency response at a number of frequencies in a single test and have simple hardware requirements. The problem with this type of signal is that it may be difficult to achieve a high enough signal-to-noise ratio to achieve good accuracy.

Information on system dynamics can also be obtained by analyzing the inherent statistical fluctuations (noise) in the system output. If the frequency dependence of the statistical driving function is known, the shape of the amplitude of the system frequency response can be determined. If the fre­quency dependence of the driving function is not known, less quantitative information can be obtained, but the results can still be used for a diagnostic to indicate changing conditions. Noise analysis is very well documented (2-4) and will not be included in this book.

Other developments besides the improvements in testing procedures have occurred that further increase the practicality of frequency response testing. The first development has to do with data analysis. Particularly significant is the fast Fourier transform technique, which allows digital computer analysis of test data for a small fraction of the cost and time previously required. The data analysis problem has also benefited from the availability of new digital computers, particularly the small minicomputers that can be taken to the test site and can provide at least a first look at the results in seconds or minutes. The other major development has to do with data inter­pretation. A new technology called system identification has evolved to aid in extracting useful information from test results. Examples of the informa­tion that may be obtained are specific system coefficients such as temperature coefficients of reactivity or heat-transfer coefficients. This technology is still growing rapidly, but already it has been applied successfully and profitably on several nuclear reactor tests.