Развитие теории оптимальных динамических измерений

Автор: Бычков Евгений Викторович, Загребина Софья Александровна, Замышляева Алена Александровна, Келлер Алевтина Викторовна, Манакова Наталья Александровна, Сагадеева Минзиля Алмасовна, Свиридюк Георгий Анатольевич

Журнал: Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование @vestnik-susu-mmp

Рубрика: Обзорные статьи

Статья в выпуске: 3 т.15, 2022 года.

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В работе представлен обзор результатов как аналитического исследования задач оптимального динамического измерения, так и результатов в области разработки алгоритмов численных методов для решения задач теории оптимальных динамических измерений. Основным положением теории оптимальных динамических измерений является моделирование искомого входящего сигнала как решения задачи оптимального управления с минимизацией функционал штрафа, в котором оценивается расхождение выходящих моделируемого и наблюдаемого сигналов. Данная теория появилась как новый подход для восстановления динамически искаженных сигналов. Математическая модель сложного измерительного устройства построена как система леонтьевского типа, начальное состояние которой отражает условие Шоуолтера - Сидорова. Первоначально математическая модель учитывала только инерционность устройства измерения, позже математическая модель стала учитывать возникающие в измерительном устройстве резонансы и деградацию устройства с течением времени. Последние результаты учитывают случайные помехи, и уже здесь сложилось несколько подходов: первый подход основан на производной Нельсона - Гликлиха, второй - на очищении наблюдаемого сигнала по методу Пытьева - Чуличкова, третий - на очищении наблюдаемого сигнала с использованием цифровых фильтров, например, Савицкого - Голея или одномерного фильтра Калмана.

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Математическая модель измерительного устройства, система леонтьевского типа, условия шоуолтера - сидорова, производная нельсона - гликлиха, винеровский процесс, оптимальное динамическое измерение, наблюдение, метод пытьева - чуличкова

Короткий адрес: https://sciup.org/147238553

IDR: 147238553 | DOI: 10.14529/mmp220302

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