Sensitivity Operator Framework for Analyzing Heterogeneous Air Quality Monitoring Systems

Air quality monitoring systems differ in composition and accuracy of observations and their temporal and spatial coverage. A monitoring system’s performance can be assessed by evaluating the accuracy of the emission sources identified by its data. In the considered inverse modeling approach, a source identification problem is transformed to a quasi-linear operator equation with the sensitivity operator. The sensitivity operator is composed of the sensitivity functions evaluated on the adjoint ensemble members. The members correspond to the measurement data element aggregates. Such ensemble construction allows working in a unified way with heterogeneous measurement data in a single-operator equation. The quasi-linear structure of the resulting operator equation allows both solving and predicting solutions of the inverse problem. Numerical experiments for the Baikal region scenario were carried out to compare different types of inverse problem solution accuracy estimates. In the considered scenario, the projection to the orthogonal complement of the sensitivity operator’s kernel allowed predicting the source identification results with the best accuracy compared to the other estimate types. Our contribution is the development and testing of a sensitivity-operator-based set of tools for analyzing heterogeneous air quality monitoring systems. We propose them for assessing and optimizing observational systems and experiments.

EPS System of Tractor Automatic Driving: An Improved LMI with Mixed Sensitivity Control Method

Electric power steering (EPS) is widely used in tractor automatic driving because of its good operation stability. However, there is a lack of research about solving robust problems and response ability simultaneously when the tractor encounters emergency steering in harsh fields. The traditional robust controller has poor tracking performance and antidisturbance ability when encountering emergency steering. This paper proposes to add the corresponding mixed sensitivity operator to the corresponding performance index in the controller. By adjusting the amplitude of the mixed sensitivity operator, the tracking performance and the speed of disturbance attenuation can be both adjusted for the tractor EPS system. Simulation and hardware in the loop experiments verify the antidisturbance ability of the controller and the torque tracking performance. The results show that the control method has strong robustness and robust stability, which can meet the practical requirements. Also, the power steering characteristic of the H∞ controller with hybrid sensitivity design method is better than that of an unoptimized one, and its robustness is better, and under external pavement interference, the following ability is stronger for the ideal hand torque and the steering is more stable.

NUMERICAL ANALYSIS OF THE OBSERVABILITY OF THE CITY ROAD NETWORK EMISSION SOURCES USING THE SENSITIVITY OPERATOR OF THE ATMOSPHERIC CHEMISTRY TRANSPORT AND TRANSFORMATION MODEL

Within the scenario approach, the observability of traffic emission sources is estimated from indirect monitoring data. What is new is that an approach based on sensitivity operators is used to estimate observability, which allows us to obtain a family of quasilinear operator equations for the source identification problem. This allows both solving and analyzing its properties. For the city of Novosibirsk, realistic weather scenarios, a scenario for the distribution of traffic emission sources and the location of monitoring sites are considered. In numerical experiments, the road network is identified smoothed over space. Concentration fields are restored with greater accuracy. Evaluation of the information about the sources contained in the data based on the analysis of the sensitivity operator allows one to get an express estimate of the inverse problem solution.

Sensitivity Operator Inverse Modeling Framework for Advection-Diffusion-Reaction Models with Heterogeneous Measurement Data

<p>Air quality monitoring systems vary in temporal and spatial coverage, the composition of the observed chemicals, and the data's accuracy. The developed inverse modeling approach [1] is based on sensitivity operators and ensembles of adjoint equations solutions. An inverse problem is transformed to a quasi-linear operator equation with the sensitivity operator. The sensitivity operator is composed of the sensitivity functions, which are evaluated on the adjoint ensemble members. The members correspond to the measurement data elements. </p><p>This ensemble construction allows working in a unified way with heterogeneous measurement data in a single operator equation. The quasi-linear structure of the resulting operator equation allows both solving and analyzing the inverse problem. More specifically, by analyzing the sensitivity operator's singular structure, we can estimate the informational content in the measurement data with respect to the considered process model. This type of analysis can estimate the inverse problem solution before its actual solution and evaluate the monitoring system efficiency with respect to the considered inverse modeling task [1,2]. </p><p>Numerical experiments with the emission source identification problem for air pollution transport and transformation model were carried out to illustrate the developed framework. In the numerical experiments, we considered in-situ, image-type, and integral-type measurement data.</p><p>The work was supported by the grant №075-15-2020-787 in the form of a subsidy for a Major scientific project from Ministry of Science and Higher Education of Russia (project "Fundamentals, methods and technologies for digital monitoring and forecasting of the environmental situation on the Baikal natural territory").</p><p><strong>References</strong></p><p>[1] Penenko, A. Convergence analysis of the adjoint ensemble method in inverse source problems for advection-diffusion-reaction models with image-type measurements // Inverse Problems & Imaging, American Institute of Mathematical Sciences (AIMS), 2020, 14, 757-782 doi: 10.3934/ipi.2020035</p><p>[2] Penenko, A.; Gochakov, A. & Penenko, V. Algorithms based on sensitivity operators for analyzing and solving inverse modeling problems of transport and transformation of atmospheric pollutants // IOP Conference Series: Earth and Environmental Science, IOP Publishing, 2020, 611, 012032 doi: 10.1088/1755-1315/611/1/012032</p>

Numerical algorithm for morphogen synthesis region identification with indirect image-type measurement data

Diffusion–reaction models are used to describe development processes in the framework of morphogen theory. The images of the concentration fields for the subset of the interacting morphogens are available. In order to interpret this data in terms of the model parameters, the inverse source problem is stated. The sensitivity operator, composed of the independent adjoint problem solutions ensemble, allows transforming the inverse problem to the family of nonlinear ill-posed operator equations. The equations are solved with the Newton–Kantorovich-type algorithm. The approach is applied to the morphogen synthesis region identification problem for the model of regulation of the renewing zone size in biological tissue.

Numerical Algorithms for Diffusion Coefficient Identification in Problems of Tissue Engineering

Identification algorithms of diffusion coefficients in a specimen with tomographic images of the solution penetration dynamics are considered. With the sensitivity operator, built on the basis of adjoint equations for diffusion process model, the corresponding coefficient inverse problem is reduced to the quasilinear operator equation which is then solved by the Newton-type method with successive evaluation of r-pseudo inverse operators of increasing dimensionality. The efficiency of the constructed algorithm is tested in numerical experiments. For comparison, a gradient-based algorithm for the inverse problem solution is considered.

Second-order sensitivity of parallel shear flows and optimal spanwise-periodic flow modifications

The question of optimal spanwise-periodic modification for the stabilisation of spanwise-invariant flows is addressed. A second-order sensitivity analysis is conducted for the linear temporal stability of parallel flows $U_{0}$ subject to small-amplitude spanwise-periodic modification ${\it\epsilon}U_{1},{\it\epsilon}\ll 1$. It is known that spanwise-periodic flow modifications have a quadratic effect on stability properties, i.e. the first-order eigenvalue variation is zero, hence the need for a second-order analysis. A second-order sensitivity operator is computed from a one-dimensional calculation, which allows one to predict how eigenvalues are affected by any flow modification $U_{1}$, without actually solving for modified eigenvalues and eigenmodes. Comparisons with full two-dimensional stability calculations in a plane channel flow and in a mixing layer show excellent agreement. Next, optimisation is performed on the second-order sensitivity operator: for each eigenmode streamwise wavenumber ${\it\alpha}_{0}$ and base flow modification spanwise wavenumber ${\it\beta}$, the most stabilising/destabilising profiles $U_{1}$ are computed, together with lower/upper bounds for the variation in leading eigenvalue. These bounds increase like ${\it\beta}^{-2}$ as ${\it\beta}$ goes to zero, thus yielding a large stabilising potential. However, three-dimensional modes with wavenumbers ${\it\beta}_{0}=\pm {\it\beta}$, $\pm {\it\beta}/2$ are destabilised, and therefore larger control wavenumbers should be preferred. The most stabilising $U_{1}$ optimised for the most unstable streamwise wavenumber ${\it\alpha}_{0,max}$ has a stabilising effect on modes with other ${\it\alpha}_{0}$ values too. Finally, the potential of transient growth to amplify perturbations and stabilise the flow is assessed with a combined optimisation. Assuming a separation of time scales between the fast unstable mode and the slow transient evolution of the optimal perturbations, combined optimal perturbations that achieve the best balance between transient linear amplification and stabilisation of the nominal shear flow are determined. In the mixing layer with ${\it\beta}\leqslant 1.5$, these combined optimal perturbations appear similar to transient growth-only optimal perturbations, and achieve a more efficient overall stabilisation than optimal spanwise-periodic and spanwise-invariant modifications computed for stabilisation only. These results are consistent with the efficiency of streak-based control strategies.