Science behind Industry 4.0 - Array programming with NumPy

As part of predictive maintenance techniques, condition monitoring is used to detect anomalies and predict machinery’s health in real-time. Sensor data is used to verify whether a component failure is likely. Some failure occurs gradually and can be prevented by routine inspections and examinations. In contrast, other types of failures are more complicated to forecast. By using vast amounts of available data and extracting useful information, it is possible to lower costs, optimize capacity, and reduce downtime.

Real-time big data computation capabilities facilitate creating predictive analytics and monitoring to take preventive action in case of anomalies. Artificial intelligence (AI), especially machine learning (ML) techniques, helps identify certain behaviors that contribute to failure with high accuracy. The underlying machine learning frameworks suggest that any implementation is responsive to a formulation based on multi-dimensional arrays, which is the essence of array programming.

Array programming provides powerful solutions for applications to access, manipulate, and operate to an entire set of values at once. NumPy is a fundamental python library used for scientific computing and working with arrays. It plays a significant role in research analysis pipelines in various fields such as physics, chemistry, engineering, economics, and machine learning, to name a few.

What is NumPy?

“Num-pee”? “Num-pie”? Perhaps it does not matter how we pronounce it; NumPy stands for Numerical Python, and it is also used in basic linear algebra, Fourier transform, matrices, and basic statistical operations. It is the foundation of the scientific Python ecosystem and forms the basis for other scientific or numerical computation Python’s libraries, such as SciPy, Pandas, Scikit-Learn, and Matplotlib. NumPy is also the primary array programming library for the Python language.

Arrays are used to save multiple values in one single variable, and array programming refers to solutions that enable the operation on all the values of an array at once. Implementation wise, an array is a collection of items stored at series of memory locations, so the idea is to utilize the data’s properties where individual elements are similar or adjacent. The programmer can think and operate on complete aggregates of data without resorting to explicit loops of individual scalar operations. Programming languages such as MATLAB, Octave, and R support array programming.

Also, in data science, arrays are widely using, where speed and resources are crucial. There are lists in Python that serve the purpose of arrays, but lists are slow to process. The NumPy array, however, is up to 50x faster than traditional Python lists. The image shows the performance of taking two random arrays and adding them together. We can see that this operation in NumPy is practically the same for 10,000,000 elements, while the Python array grows faster.

Source: https://github.com/Pballer/dc-ds-071519/blob/master/blogs/array_vs_list/numpy_array_vs_py_list.ipynb

What is NumPy array?

A NumPy array is a data structure that efficiently stores and accesses multidimensional arrays . The array object in NumPy is called ndarray. The main reason why ndarrays are faster than Python lists is that NumPy arrays use the locality of reference principle, which means they are stored in one contiguous memory region so that processes can access and manipulate them very efficiently.

There are other differences between NumPy arrays and the standard Python lists. For instance, unlike Python lists, NumPy arrays have a fixed size at creation. Moreover, the elements in a NumPy array must be of the same data type and will be the same size in memory.

The fundamental attributes used to define NumPy arrays are shape, data-type, and strides. The shape of a ndarray defines the number of dimensions and items as a collection of N non-negative integers. The data-type specifies the type of elements stored in an array, such as real and complex numbers, strings, timestamps, and pointers to objects. The strides are the number of bytes to move forward in the memory to reach the next element. The strides tell us how many bytes we must skip in memory to move to the next position along a certain axis. Also, indexing is used to access subarrays, single elements, or elements that meet a specific condition. Arrays can be indexed with masks, scalar coordinates, or other arrays.

How NumPy does the operations faster?

We can take advantage of vectorization and broadcasting, so that you can use NumPy to its full capacity. Broadcasting is a more advanced concept in NumPy. It describes how it treats arrays with different shapes during arithmetic operations, leading to certain constraints, the smaller array is “broadcast” across the larger array to have compatible shapes. It provides a means of vectorizing array operations, which is a powerful ability within NumPy to express functions on entire arrays rather than their elements.

There is a lot of overhead involved in Python looping over an array or any data structure. However, vectorized operations in NumPy hand over the looping internally to highly optimized C and Fortran functions, offering faster and cleaner Python code. Machine learning is an area that can regularly utilize vectorization and broadcasting to speed up the implementation of the algorithms. Element-by-element reductions aggregates results across one axis, multiple axes, or all axes of a single array. Array-aware functions, such as sum, mean and maximum, perform reduction.

The image below shows how these fundamental array concepts are incorporated in NumPy.

Source: https://www.nature.com/articles/s41586-020-2649-2/figures/1

How does NumPy relate to the scientific Python ecosystem?

While Python as an open source interpreted programming language is an excellent tool for general-purpose programming with a highly readable syntax, rich data types, and comprehensive standard library, it was not explicitly designed for mathematical and scientific computing. In other words, neither Python itself nor its libraries have efficient facilities for the representation of multidimensional datasets, matrix manipulations, tools for linear algebra and any data visualization. Libraries in the scientific Python ecosystem provide fast implementations of the most important algorithms.

NumPy plays a leading part in interactive scientific computation, in which SciPy and Matplotlib are tightly coupled with NumPy. Combining these three libraries provides a solid foundation for array programming. The scientific Python ecosystem builds on top of this foundation to provide several widely used technique-specific libraries such as Pandas and Scikit-Learn, which underline various domain-specific projects such as NLTK and Biopython for Linguistics and Biology purposes, respectively.

For more information about this topic, read the paper “Array programming with NumPy”, by Charles R. Harris, K. Jarrod Millman, Stefan J. Van der Walt et al, by clicking here.

About The Author

Ali Aghelmaleki is a data engineer/scientist and an expert in the area of data science, Machine Learning, and Deep Learning for industrial processes and social science. He completed his MSc Web & Data Science from the Koblenz University, Germany, in 2018

Originally published at https://vikinganalytics.se.

AI-based predictive maintenance applications for industrial assets.