Instrumentation

# How do you handle non-linearities in your instrumentation measurements?

• Non-linearity in the context of instrumentation refers to the deviation from a linear relationship between a measuring instrument’s input and output.
• A change in the input would result in a proportionate change in the output in an ideal linear system.
• However, many real-world instruments exhibit non-linear behavior, which means that the relationship between input and output is not strictly proportional.
• Non-linearity is the maximum deviation from a straight line that connects the zero point of a measuring range with the endpoint/ full scale.
• The position or length traversed and the output signal has a linear relationship.
• The greatest possible deviation from a straight line on an output versus input graph is commonly referred to as nonlinearity.
• When dealing with non-linearities, it’s important to thoroughly understand the characteristics of the instrumentation system and the nature of the non-linearities involved.
• Additionally, regular calibration and validation checks are essential to ensure the ongoing accuracy of measurements, as factors such as sensor aging or environmental changes can impact the system over time.
• Handling non-linearities in instrumentation measurements is essential to obtain accurate and reliable data.
• Non-linearities arise from various sources, including sensor characteristics, signal conditioning, and data acquisition systems.
• The choice of technique depends on the specific problem at hand and the nature of the non-linear behavior being addressed.
• Often, a combination of these methods is used for a comprehensive understanding and analysis of nonlinear      systems.
• Here are some common techniques to address non-linearities in instrumentation measurements:
• Split the non-linear range into smaller segments and apply linear calibration to each segment and linear approximation is applied within each segment, and the outputs from these segments are then combined to provide an overall correction.
• This linearization method is most effective when the nonlinearity      is not severe.
• Polynomial functions are used to model and correct non-linearities, & to approximate the non-linear relationship.
• The order of the polynomial is determined by the complexity of the non-linearity.
• Higher-order polynomials are best suited for complex non-linearities, but we must be careful of over-fitting.
• Be cautious not to overfit the data, as this might result in inaccuracies for inputs outside the calibration range.
• For complex non-linearities, especially those that are difficult to model analytically, look-up tables can be used.
• Create a table to represent a map of input values to corresponding calibrated output values.
• This approach is useful when the relationship is well-defined but complex.
• These tables store precomputed output values corresponding to specific input conditions.
• During measurement, the instrument references the table to obtain the corrected output.
• Some sensors have built-in linearization circuits to compensate for their inherent non-linearities.
• These circuits can be part of the sensor design or added externally to the instrumentation system.
• Calibration is the process of determining and correcting errors in the measurement system.
• Calibration involves comparing measurements against known standards and adjusting the instrument settings accordingly.
• This involves measuring known inputs and comparing them to the instrument’s output.
• The non-linear relationship can then be modeled, and correction factors applied.
• A calibration curve is also known as a standard curve to measure some parameters of an instrument indirectly. That      gives desired values for the quantity as a function of values of sensor output.
• Calibration Curves relate the true physical quantity to the sensor’s output.
• These calibration curves can be derived experimentally through calibration procedures.
• Non-linearities can be mitigated by creating a calibration curve.
• Regular calibration is essential to correct for any deviations from linearity.
• The selection of sensors inherently exhibits linear behavior over the range of interest.
• This may involve selecting sensors with higher precision or using sensors specifically designed for the application.
• Some sensors come with compensation techniques designed to minimize non-linearities.
• These can include temperature compensation or correction algorithms.
• These signal-processing techniques are specifically designed for non-linear systems, such as filtering or digital compensation algorithms.
• These methods may include Fourier analysis, wavelet transforms, or other mathematical techniques depending on the nature of the signals.
• Employ signal processing techniques such as digital filtering or curve fitting algorithms to remove or reduce non-linear effects.

Averaging multiple measurements can help reduce random errors and improve the overall accuracy of the measurement, especially when dealing with non-linearities caused by noise.

• Implement feedback control mechanisms to continuously adjust the instrument based on the measured output.
• This can be particularly effective in real-time applications where dynamic adjustments are necessary.
• Implement adaptive control strategies that continuously adjust the calibration parameters based on real-time measurements.
• This approach is useful when non-linearities are subject to change due to factors like temperature variations.
• Adaptive techniques can help account for changing environmental conditions or sensor characteristics.
• Use advanced modeling techniques, such as neural networks or machine learning algorithms, to capture and correct for non-linearities.
• These techniques can learn complex relationships from data and provide accurate corrections.
• Apply post-processing algorithms to correct non-linearities after data acquisition.
• These algorithms can be mathematical transformations designed to linearize the data.
• Non-linearities in sensors are often influenced by changes in temperature.
• Implement temperature compensation techniques to minimize the impact of temperature on measurement accuracy.
• Adjust the gain of the signal conditioning circuit to account for non-linearities.
• This may involve using variable gain amplifiers or automatic gain control.

Use regression analysis techniques to model and correct non-linear relationships between variables.

In some cases, especially with highly complex non-linearities, artificial neural networks can be trained to map input data to corrected output values.

• Use digital signal processing techniques to apply correction algorithms to the measured data.
• This can involve using filters, algorithms, or mathematical operations to compensate for non-linearities.
• Use of Non-linear Components: Choose components and circuits that inherently compensate for non-linearities.
• For example, using diodes with logarithmic characteristics for certain measurements.
• Describing the relationship between variables using non-linear equations is a fundamental approach.
• These equations can take various forms, such as polynomial, exponential, logarithmic, or transcendental functions.
• Iterative Methods:  Solving nonlinear      equations iteratively using methods like Newton’s method or the bisection method.
• Finite Difference Methods: Approximating derivatives using finite differences is particularly useful when dealing with non-linear partial differential equations.
• Polynomial Approximation: Representing non-linear functions using polynomials through techniques like Taylor series expansion or interpolation methods.
• Piecewise Linearization: Approximating a nonlinear      function by breaking it into smaller linear segments within specific intervals.
• Gradient Descent: Iteratively updating parameters in the direction of the steepest ascent (or descent) to find the minimum (or maximum) of a function.
• Genetic Algorithms: Optimization algorithms are inspired by the process of natural selection, which can be used for global optimization of nonlinear      functions.
• Neural Networks: Deep learning models, particularly neural networks, are powerful tools for capturing complex non-linear relationships in data.
• Support Vector Machines (SVM):  SVMs can be adapted to handle non-linear relationships using non-linear kernels.
• Decision Trees and Random Forests:  These models can capture non-linear relationships through a series of hierarchical, non-linear decisions.
• Experimental Data Analysis: Using data from experiments to identify the non-linear behavior of a system through techniques like system identification or curve fitting.
• Control Systems: Implementing Nonlinear      control strategies specifically designed for non-linear systems, such as sliding mode control or adaptive control.
• Chaotic Systems Analysis: Techniques from chaos theory may be applied to study and understand non-linear, deterministic systems that exhibit chaotic behavior.
• Statistical Methods: Using models that do not assume a specific functional form, such as kernel regression or spline regression.
• Simulation and Computational Methods: Employing random sampling methods to simulate the behavior of nonlinear      systems.

Polynomial Regression is the only method to handle non-linearity by including polynomial terms.

Measurement of the nonlinearity of a process is based on two broad approaches.

1. Input & output relationship of the system or the model.

2. Output time series of the process.

Examples of nonlinear instruments include

1. Expanded scale electrical meters.
2. square root characterizers.
3. Position characterized control valves.

A nonlinear scale is one in which equal changes in the value of the physical quantity being measured are indicated by unequal distances on the scale of the measuring instrument.

Linearity in instrumentation is termed as the consistency of measurement over its entire range.

Non-linearity of a transducer is the measurement of the difference in Y offset of two lines of equal slope one going through the minimum points and the other one going through the maximum points of the output curve

### Sundareswaran Iyalunaidu

With over 24 years of dedicated experience, I am a seasoned professional specializing in the commissioning, maintenance, and installation of Electrical, Instrumentation and Control systems. My expertise extends across a spectrum of industries, including Power stations, Oil and Gas, Aluminium, Utilities, Steel and Continuous process industries. Tweet me @sundareshinfohe