Basic Procedures and Methodological Support of the “Object-Based Environment for Engineering Calculation in the MATLAB System” Course

This paper looks at methodological aspects of the «Objectbased environment for engineering calculation in the MATLAB system» course offered to the second year students of Bauman Moscow State Technical University for mastering tools in the MATLAB environment, learning MATLAB language and object-oriented technology of working with classes and applications, designed for engineering calculations of ammunition characteristics. The paper presents the technology of organization of practical studies using resources of MATLAB Grader.


Introduction
Training of the new generation of research engineers ready to become leaders in high technology industrial sectors requires an innovative approach to organization of learning environment. Starting from the early noughties scientists of the «High-precision aircraft» division actively study and develop two types of information technologies for development of ammunition and means of destruction: using numerical modelling packages for detailed study of physical processes (for example, ANSYS AUTODYN or LS-DYNA) [1][2][3][4][5] and software packages for mathematical modelling which systemically link the entire learning process (for example, MATLAB) [6][7][8][9][10]16]. The «Object-based environment for engineering calculation in the MATLAB system» course was developed by SM4 «Highprecision aircraft» division in accordance with Self-imposed BMSTU educational standard, the basic professional educational program for students majoring in «Ammunition and fuses». The aim of studying the discipline is to master tools in the MATLAB environment, learn MATLAB language and object-oriented technology of working with classes and applications, designed for engineering calculations of ammunition characteristics [10][11][12][13][14]. Later on these skills and knowledge are used in the following courses: «Information technologies in design engineering», «Computer-aided engineering systems of means of destruction», «Munitions effectiveness», «Object based methods of evaluation of munitions effectiveness», «High-precision munitions guidance and control systems».

Main Text
Educational learning material for the «Object-based environment for engineering calculation in the MATLAB system» course include: ─ lectures and additional self-instructional material (electronic versions are distributed among students at the start of the semester); ─ tasks for practicals (handed out in electronic form ahead of each session; also developed are online versions of certain tasks using resources of MATLAB Grader); ─ homework (handed out to students in the middle of the semester); ─ developed software.  ─ presented mathematical models describing dynamics of warfare; ─ introduced mathematical models for targeting aerial vehicles; ─ special attention paid to optimization method including genetic algorithms; ─ object-oriented technologies also viewed in the context of engineering research. Additional materials for unsupervised activities (customized course of lectures «The theory of probability») look at object-oriented technology of probability calculation for solving different tasks of operations research tied with accidental events' analysis, algebra of random variables and functional relationships between them, systems of random vectors [15]. The materials cover the following problems: ─ probabilities of complex events; ─ Bayes' formula; ─ Bernoulli distribution; ─ discrete random variables; ─ base class of continuous random variables; ─ exponent rule and distribution classes tied with it; ─ normal law of distribution; ─ class of two-dimensional normally distributed vectors; ─ functions of random variable; ─ multiplicative functions of random variable; ─ additive functions of random variable. Software for individual use by students is published at the GitHub website (https://github.com/ETMC-Exponenta/ProbabilityAnalysis-M4/) and compiled into separate binary package. This library uses electronic formula technology [16]. Those formulas are syntactically built in the MATLAB work area as function calls having substantive interpretation in the theory of probability context. They perform actions depending on the combination of arguments. For example, if X is a random variable with a known law of distribution, G is a geometric shape or an array of non overlapping shapes, then the electronic formula [P, p] = Ver(X, G) computes probability P of the random variable X assuming a value within an interval G. Object X is created by a constructor of one of the random variable classes with the corresponding parameters, for example, X = Norm_2([1; 2], [3,2], 0.5) is a normal distribution on the plane object with mathematical expectations along coordinates equal to 1 and 2, mean-square deviation of 3 and 2, correlation coefficient between coordinates of 0.5. G object can be created by a constructor of circles with a given radius, centered in a certain point, G = Circ(2, [0;2]), rectangles G = Rect( [5,3]) or other shapes, may be also with the result of joining of overlapping of shapes ( Fig. 1 Results of computing electronic formula Ver depends on the structure of the object G. If G is an array of shapes, P is a probability of hitting at least one of them, p is an array of probabilities of hitting individual shapes. So, computing of the probability of hitting, for example, an ellipsoid using the universal electronic formula Ver is easier than using the special formula FLaplas based on tables of Laplace Transforms: >> k=[0.5; 1; 2; 3; 4]; X=CHI2(3); p=Ver(X, k.^2); >> g=2*FLaplas(k)-sqrt(2/pi).*k.*exp(-k.^2/2); >> p=p', g=g' p = 0.030857 0.19873 0.73851 0.9707 0.99887 g = 0.030857 0.19873 0.73851 0.9707 0.99887 Practical sessions are based on creative study of examples from electronic lectures and suggest using math modelling software package MATLAB (it is possible to use both a local version and an online version available at https://matlab.mathworks.com/ (Fig. 2)). Practical sessions suggest acquiring and consolidating of the following skills: ─ working with matrices and vectors in MATLAB; ─ building two-dimensional, three-dimensional and special graphs of functions; ─ programming in MATLAB environment; ─ solving systems of algebraic and differential equations; ─ solving optimization problems in MATLAB; ─ studying classes Point, Shape, Rect, Cir. Studying classes of threedimensional geometric objects. Studying methods of intersection of flat shapes. Solving flat shapes intersection problems using geometric object class methods in MATLAB environment; ─ studying methods of two-dimensional normally distributed random vectors class, computing probability of random points to assume positions inside flat shapes using methods of class Norm_2; ─ studying statistical methods for evaluation of frequency of values assuming positions inside flat shapes. Determining of possibilities for random points assuming positions inside areas of random configuration. Solving problems of statistical modelling using classes of geometric objects and random normally distributed vectors inside MATLAB environment.
Practical sessions based on additional materials offer self-instructional interactive learning to use online (or offline) version of MATLAB or the developed software. Adapted lecture course «The theory of probability» contains verified examples of problem-solving which can be copied into the MATLAB environment (the developed software). The solution can be obtained, text or graphic results visually compared with those in the lectures (Fig. 3) and, using the acquired skills, you can try to solve test problems from the educational materials. Some test problems are published in the online MATLAB Grader environment and are available to authorized students in certain time intervals during the course study (Fig. 4).
The homework is aimed at acquiring object-oriented technology skills for dealing with classes and creating a class for storing information about geometric (mathematical) objects in the MATLAB environment.
Preparing versions of practical problems in the MATLAB Grader environment is performed interactively in several steps (Fig. 5): ─ problem stating (it is possible to visually represent mathematical dependencies inside the text of the problem using LaTeX language); ─ creating model solution in MATLAB language, hidden from the student; ─ creating a template for the student in MATLAB language (when creating the template, the aim is also to link the developed library with functions which can be used for solving the problem); ─ determining solution verification criteria: using keywords and comparing the results obtained with benchmark values; ─ testing of the solution (it is possible to output graphic materials). Authorized access to online problems is performed by sending invitations through email. The course administrator totally controls the process of solving and correctness of the results obtained during manual and automatic analysis of CSV and Microsoft Excel pivot tables or text M-files (Fig. 6). It seems, the most optimal way of creating such problems is a preliminary preparation of materials in a text file because all tasks use textual notation of MATLAB language.

Conclusion
Using online technology for organizing practical sessions offers students additional tools for self-assessment, acquiring practical skills, preparing to classroom activities, reviewing of previously studied material. Perhaps, the so-called «inclusive technology» is the only possible way of getting information for people with limited access to real educational institutions. Unlike widely used «multiple choice tests» which are basically primitive tests with lists of different answers, using MATLAB Grader technology allows to perform a «creative» knowledge test. Well-considered use of object-oriented technology offers possibility to expand organization of practical sessions in the MATLAB Grader environment to wide variety of courses including humanities. All online tasks have a fundamental drawback which is impossible to rectify in modern conditions. It is impossible to perform a certified remote knowledge assessment of students. Possible solution for this problem is envisaged in a distant future.