Electric Vehicle Sales Catastrophe Averted (?)

The literature indicates catastrophic potential for electric vehicles around the year 2019. Amidst the predicted time, this research revisits the prequel analysis with state-of-the-art deterministic artificial intelligence methodologies to posit the potential for catastrophe in the upcoming year. The methodology has proven effective with motion mechanics, electrodynamics, and even financial analysis of sales date in the prequels, since the model commences with simple regression for mathematical model formulation asserting the certainty equivalence principle, followed by derivative modeling and eventually catastrophe analysis of the derivative models. The prequel analysis paradigms are retained in this sequel utilizing both monthly and cumulative sales data in simple least squares algorithms for predictive curve fitting to establish context and help correctly model the mathematical degree of the data. Extrapolation by forward time-propagation established predictions for models of various mathematical degrees (again merely for context). Next, catastrophe analysis (of the derivative form) revealed stable and unstable equilibrium points and then parametric variation was induced to evaluate the resulting behavior of the derivative models, highlighting the importance of the coefficient of the second order term (the acceleration or change of rate of sales as a forcing function). While the forcing function typically embodies both gasoline prices and vehicle charging proliferation, the relative stability of gas prices together with factors such as vehicle-to-grid elevate charging-station proliferation as the primary forcing function of slow-dynamics in catastrophe analysis. This brief manuscript revisits the prequel research to test the validity of those conclusions and with the benefit of the passage of time, reveal how well the mathematical modeling predicted real behavior. The main finding is the predicted potential catastrophe is less likely to occur and recommendations are made to insure catastrophe is averted.


Introduce the Problem
Recent literature  revealed the distinct possibility of an unexpected catastrophic crash in sales of electric vehicles in 2019.

Why is This Problem Important?
How does the study relate to previous work in the area? Subsequent to that prequel research, the rapid rise of non-stochastic artificial intelligence methodologies (Baker, 2018), (Sands, InTech, 2019), (Lobo, 2018) stemming from combinations of physics-based controls (Sands, Lorenz, 2009), (Sands, 2012), (Sands, 2015) and mathematical system identification from data (Sands, Comp., 2017), (Sands, J.Space Exp., 2017), (Sands, Kenny, 2017), (Sands, Phys J., 2017), (Sands, J.Space Exp., 2017), (Sands, Armani, 2018) together with adaptive systems methods (Nakatani, 2014), (Nakatani, 2016), (Sands, Aero, 2019), (Cooper, 2017), (Smeresky, 2018), (Sands, Algor., 2019), (Sands, Bollino, 2018) has been adopted and incorporated into new educational schemes driven by military operational imperatives (Kuklinski, et al., 2019), (Sands, Mihalik, 2016), (Bittick, et al., 2019), (Sands, "satellite", 2009), (Sands, Intl. J. Electro., 2018) with accompanying educational imperatives , . How does this manuscript differ from, and build on, the earlier report? These methods have been successfully applied to quite disparate disciplines piecemeal as the techniques have been developed, bestowing the ability for data-informed decision-making, e.g. should a military plan to invest heavily in electric vehicles with a realistic anticipation of a robust commercial industrial base. In this manuscript, state-of-the-art deterministic artificial intelligent methodologies (Smeresky, et al., 2020) are applied to first utilize optimal system-identification (simple regression) to provide deterministic models. By invoking the certainty-equivalence principle, those deterministic models are parameterized to establish decision-making and process control motivations by establishing the deterministic self-awareness statement. The math models are differentiated to yield differential models that are used in catastrophe analysis to predict a potential shock event in vehicle sales. Shock events inherent in some classes of differential equations embody rapid, unexpected dramatic changes in data, and they are also referred to as "jump discontinuities".

How do the Hypotheses and Research Design Relate to One Another?
Utilizing such methods previously used on (non-electric) military systems increase the likelihood of adoption, since the methods are well known and trusted.
1.1.4 What are the Theoretical and Practical Implications of the Study?
The main aim of this work is to ascertain whether the potential catastrophe has been averted, and use this information to make recommendations for the future. Catastrophe is driven by a slow-moving dynamic driven by a forcing function, predominantly gasoline prices and also electric-vehicle charging proliferation which is amplified by vehicle to grid (V2G) technology. (Vehicle to grid, 2018)

Materials and Methods
Materials and methods normally comprised of three sections: definitions, data, and methods to include details on the new additional data since the 2015 data used in the prequel . Here the definitions (Gohlke, 2018) and data (Light Duty, 2018), (Monthly Plug-in, 2018), (Plug-in, 2018), Cobb, 2018) are placed in the appendix at the end of the manuscript; while a brief contextual introduction to the methods (taken from deterministic artificial intelligence) utilized to produce the results in section 3 are included immediately in section 2.2 with background materials on electric vehicles in section 2.1

Methods
Using the new data articulated and explained in sections 2.1-2.3 along with, analysis methods taken from deterministic artificial intelligence are applied to the exact dataset used for the prequel, where the data has merely been appended with the new data bestowing results in the following section of this manuscript mas.ccsenet.org Modern Applied Science Vol. 14, No. 3;2020 3 comparable to the prequel. Definition of equations for the system that are optimal commence the effort such that sales data is reflected by the modeling. A brief divergence is taken (simple time-extrapolation) to establish the paradigm of the dynamics and grant a remedial expectation of the results. Next, the impact of slow-moving dynamics on the fast-moving (dominant) dynamic is investigated using differential forms of the optimal system equations. Such dual dynamic (slow and fast-moving) is the hallmark of Catastrophe theory, where often confounding nonlinear affects are seen. Decisions are often made using systems assumed to be linear, while otherwise unstable linear system models (those not settling at zero steady-state) can be slowly changing such that they can rapidly become stable (i.e. catastrophically settle at zero monthly sales). Equilibrium points are revealed by equating the differential forms (the principle re-parameterization) of the system equations to zero. Stability or instability is determined at each equilibrium. Slow modification of the differential equations illuminates "jump discontinuities" associated with potential catastrophe. Sales undesirably go to zero at a stable equilibrium point with a jump discontinuity.
The modification of system equations is driven by a forcing function predominantly comprised of gasoline prices and charging station proliferation, while gas prices are presumably not the dominant factor due to relative stability; and thus, EV charging station adoption amplified by V2G enhancements predominantly establish the forcing function.

Results
The following results follow the general process-flow of deterministic artificial intelligence: 1) perform optimal system identification, and then 2) reparametrize the optimal system dynamics to bestow predictive decision making. In this research, an intermediate step is inserted to establish the paradigm of the system dynamics and provide some measure of anticipation of expected results. Figure 1a shows the least squares analysis based on monthly and total sales of vehicles. The significant fact that actual cumulative sales data does not require a third-order (or higher) mathematical model to optimally fit the data, implying the existance of catastrophe of cumulative sales data (precititous, unexpected plummeting) is unlikely. The variance proportion of the dependent variable predictable by the independent variable is the coefficient of determination R in equation (1), while the correlation coefficient r, indicates the strength between variables and relationships, and may be calculated enroute to the coefficient of determination in equation (2). The basic equation of least squares is purposefully ommitted to preclude the accidental implication that system identificaion must be done with least squares, while other algorithms (e.g. extended least squares, posterior residuals, exponential forgetting, etc.) would also suffice (Sands, Computation 2017), (Sands, J.Space Exp. 2017).

System Identification: Optimally Fitting Data to Assumed Models
= , = 219.7 , = 0.4348 + 189.34 , = 0.0658 − 7.5938 + 409.7 , = 0.0019 − 0.2661 + 9.7575 + 145.14 , = −3 × 10 + 0.0074 − 0.6855 + 22.547 + 19.788 , Notice the proportion is not increased by increasing the order of the mathematical model, and thus a third-order system (and accompanying risk of catastrophe) is unnecessary. These facts fit intuition, since the cumulative total has built over years, and it is difficult to fathom a non-theoretical occurrence that would cause the cumulative total to go to zero (implying rapid depletion of the cumulative total via removal of hundreds of thousands of cars from the streets). This initial analysis is provided as an intermediate check of theory. Next, we commence the catastrophe analysis by switching to analysis of monthly sales data derivatives (as opposed to cumulative sales data) where equations (3)-(7) are the optimal system models established in the generic procedure of deterministic artificial intelligence, whose subsequent step is to parameterize to establish decision-making and process control motivations. The re-parameterization utilizes differential forms, but first we take a short informative digression to use extrapolation via forward time progression to bestow an initial instinct and establish an expected-result from the subsequent catastrophe analysis using differential forms.
It is also noteworthy to compare the prequel research results which concluded a potential catastrophe in 2019. mas.ccsenet   (3)-(7)

Discuss
The result amplified dynamics to very re indicating to the preq military u contempla celebrated t.org declining sales, 6, whose differ el representing prices) and ontrol variable ore, iteration o by modifying he prequel res due to its seco y of charging s e, etc.  Vol. 14, No. 3; users. Adoption by military units should be pursued, since such would establish a (non-fickle) client base, as such units tend to react relatively slowly to negative forcing functions.

Future Research
Periodic re-evaluation with updates sales data should be considered, especially in instances when driving functions change, especially gasoline prices).